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Theory and simulation of a wireless communication system based on orthogonal frequencydivision multiplexing : the limitations of OFDM in comparison with a single-carrier system

Haubrich, I.F.C.

Award date:2000

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Eindhoven Universi ty of Technology

Department of Electrical Engineering

Telecommunication Technology and Electromagnetics

Theory and simulation of a wireless

communication system based on Orthogonal

Frequency Division Multiplexing.

The limitations of OFDM in comparison with a single­

carrier system.

By l.F.C. Haubrich

Graduation report

January 1999-January 2000

Professor Prof.dr.ir. G. Brussaard

The Eindhoven University of Technology disclaims all responsibility for the contents of training and

graduation reports.

Summary

This report describes a modelled and simulated wireless communication system based on orthogonal

frequency division multiplexing (OFDM).

OFDM is a bandwidth-efficient multiple access scheme for digital communications. Optimum spectral

efficiency is achieved since the spectra of individual carriers mutually overlap, unlike the spectrum of

carriers in a conventional frequency-division multiplexing system. Nevertheless, carrier orthogonality

is maintained as long as the carriers are spaced in frequency at exactly the reciprocal of the symbol

interval.

The effects that may influence the performance of the system are considered and simulated with

Matlab. These influences can be divided into two main categories: channel influences and

transmitterlreceiver influences. The last category consists of errors due to power clipping, symbol

synchronisation, sampling frequency synchronisation and oscillator-related errors (carrier frequency

errors and carrier phase noise).

It was found that channel and synchronisation limitations have little effect on an OFDM system when

compared with the single-carrier system. On the other hand, a single-carrier system is more resistant to

oscillator-related errors. A final decision on whether to choose OFDM over a single-carrier system,

will therefore depend primarily on the quality of error correcting methods that can be used in each

system.

3

Contents

1 Introduction 9

2 Modulation schemes for high bit rate data transmission 11

2.1 Passband modulation schemes 12

2.1.1 Single-carrier passband modulation 13

2.1.1.1 (Differential) Phase Shift Keying (DPSK) 13

2.1.1.2 Quadrature Amplitude Modulation (QAM) 14

2.1.2 Multicarrier modulation 14

2.1.3 Concluding comparison between the presented modulation schemes 17

2.2 Orthogonal Frequency Division Multiplexing (OFDM) 17

2.2.1 The OFDM signal. 18

2.2.2 Introduction of a cyclic prefix (guard interval) 21

3 Limitations on a wireless communication system 23

3.1 Limitations of the wireless channel 23

3.1.1 Discrete channel model 24

3.1.2 Sources of Noise 26

3.1.3 Fading Channels 27

3.1.4 The 60 GHz wireless channel. 27

3.2 Limitations caused by the transmitter and receiver.. 28

3.2.1 Amplifier related error 28

3.2.2 Oscillator-related errors 28

3.2.2.1 Carrier frequency errors 28

3.2.2.2 Carrier phase noise 29

3.2.3 Symbol synchronisation errors 30

3.2.4 Sampling-frequency synchronisation errors 30

4 Error correction techniques 31

4.1 Equalisation of the channel 31

4.1.1 Linear equalisation 32

4.1.2 Decision feedback equalisation (DFE) 33

4.2 Amplifier error correction 33

4.3 Frequency estimators to cope with oscillator errors 33

4.4 Symbol synchronisation 34

4.5 Sampling-frequency synchronisation 35

5

5 Implementation of an OFDM communication system 37

5.1 General overview 37

5.2 The transmitter 38

5.2.1 Modulation 38

5.2.2 Serial to parallel conversion 38

5.2.3 Inverse discrete Fourier transform (IDFT) 38

5.2.4 Adding the cyclic prefix 38

5.2.5 Parallel to serial conversion 38

5.3 The channel 39

5.3.1 The transmit and receive filters 39

5.3.2 Physical channel 39

5.4 The receiver 40

5.5 Implementation of distorting effects 40

5.5.1 Implementation of a carrier frequency offset and phase noise .40

5.5.2 Implementation of synchronisation errors 41

5.5.3 Amplifier effect 41

5.6 Practical simulations remarks 41

5.6.1 Maintaining a constant bit energy 42

5.6.2 Channel rate versus timing errors 42

5.6.3 Simulate 42

6 Simulation Results 43

6.1 Influence of Gaussian noise on different subcarrier modulation schemes 43

6.2 Influence of multipath delay spread 45

6.2.1 Cyclic prefix 46

6.3 Effect of peak power clipping for OFDM 47

6.4 Influences of oscillator imperfections 47

6.4.1 Frequency errors 48

6.4.2 Carrier phase noise 49

6.5 Timing Requirements 51

6.5.1 Symbol synchronisation errors 51

6.5.2 Sampling-frequency synchronisation errors 52

7 Conclusions and Recommendations 53

7.1 Conclusions 53

7.2 Recommendations 54

8 References 55

6

Appendix A Constellations of modulation schemes S9

Appendix B Models of the 60 GHz indoor radio channel 60

Appendix C Structure of Simulate and Matlab code 62

7

Chapter 1

1 Introduction

The aim ofthis report is twofold. The first aim is to describe a wireless communication system based

on Orthogonal Frequency Division Multiplexing (OFDM), with its possibilities and limitations in

comparison with a single-carrier system. The second aim is to provide a Matlab model to simulate

both systems under various conditions.

At the Radiocommunications Group of the Telecommunication Technology and Electromagnetics

Division of the Eindhoven University of Technology, research is done in the field of wireless indoor

radio communication. The research has been carried out within the European program ACTS

(Advanced Communications Technologies and Services). Within this program the MEDIAN (Wireless

Broadband Customer Premises Network/Local Area Network for Professional and Residential

Multimedia Applications) consortium has started a project to evaluate the performance of a high-speed

wireless LAN that is able to support multimedia services. One of the contributions of the

Radiocommunications Group is to investigate possibilities to realise reliable data rates of 150 Mbits/s

over 60 GHz indoor radio channels. OFDM is considered as one of the options to achieve this goal.

Therefore, investigation of the potential and limitations of OFDM transmission by means of modelling

and simulation is necessary.

This report is organised as follows: In Chapter 2 an overview of modulation schemes for high bit rates

is given, including an OFDM system. Distorting influences on the wireless communication system,

caused by both the wireless channel and the system itself, are described in Chapter 3. Possible

solutions to deal with these distortions are briefly described in Chapter 4. The implementation of an

OFDM communication system in Matlab is presented in Chapter 5, followed by simulation results in

Chapter 6. In Chapter 7 this thesis ends with conclusions based on both theory and the results acquired

by simulations and is completed with recommendations concerning further research and extension of

the Matlab implementation.

9

Chapter 2

2 Modulation sche mes for high bit rate data transmission

For the choice of the modulation scheme in high bit rate data transmission there exist three main

possibilities with each one again splitting up into different sub-types and implementation approaches.

The first main division is into passband and baseband modulation where the passband scheme can be

subdivided into single-carrier and multicarrier modulation as is shown in Figure 2.1. The main

difference between passband and baseband modulation is the fact that in case of baseband modulation

the information stream is coded and spectrally shaped, but the position of its spectrum is not changed.

In case of passband modulation on the other hand the information is modulated onto a carrier that is

not constrained in its frequency, meaning that the transmission spectrum in this case can be transferred

to every desired frequency. Therefore the main practical difference is the position of the frequency

band used. While baseband modulation has a lowpass characteristic, beginning at or near zero,

passband modulation has a bandpass characteristic with the used band situated somewhere in the

frequency domain as can also be seen in Figure 2.1. In case of passband modulation one or more

carriers may be used for the transmission. In case of multicarrier modulation several carriers of

different frequencies are used to subdivide the frequency band into a bank of subchannels with each

subchannel virtually being an independent passband system. Together these subchannels compose a

continuous spectrum very similar to the one of single-carrier passband modulation.

High bit rate modulation

PSD

Baseband

f

PSD

Passband

f

Single-carrier Multicarrier

PSD

f

PSD

f

Figure 2-1 Basic structure ofmodulation schemes

11

(2.1a)

As the Radiocommunications Group is to investigate possibilities to realise reliable data rates of 150

Mbits/s over 60 GHz indoor radio channels, passband modulations schemes will be investigated more

closely.

2.1 Passband modulation schemes

The group of possible modulation schemes for wireless communications is composed of passband

modulation approaches, which can be subdivided into single-carrier and multicarrier schemes. The

main advantage of passband modulation is the possibility to transfer the transmit frequency band to

every desired point on the frequency axis and that there is no limitation to the use of the low frequency

portion, as in the case of baseband modulation. If this additional flexibility finally turns out to be an

advantage or a disadvantage depends very much on the system environment, noise environment and

other specific design issues. Moreover, as there are considerable differences in behaviour between

single-carrier and multicarrier systems, it is somehow difficult to define basic characteristics that apply

to all passband modulation schemes. However, some basic characteristics will be mentioned in the

following and then in the next sections deeper descriptions for two main passband modulation

techniques will be given separately.

For analytic evaluation of passband systems the so-called baseband equivalent model is typically used.

This means that the responses of the (baseband) transmit and receive filters can be used directly, while

the channel transfer function is transposed to baseband using Equation 2.1a and Equation 2.1 b for time

and frequency domain, respectively [1]. Knowledge of the exact passband modulation scheme is not

required for this kind of analytic treatment. Only the carrier frequencies (centre frequencies) of the

passband signal and the shaping effects of the transmitter and the receiver, seen as an overall system,

have to be known. The baseband equivalent of the channel impulse response is complex due to the

transfer in frequency. The same transpose has to be applied to the noise sequence, therefore leading to

complex noise samples.

hpassband (t) = Relh baseband (t) *ej•2

*"*fcarri

,,*t J

hpassband: Impulse response of the passband channel

hbaseband: Impulse response of the baseband equivalent model

fcarrier: Carrier frequency of the passband transmission system

H (f) = H baseband (f - fcanier) + H~aseband (-f - fcanier)passband 2

Hpassband: Frequency transfer function of the passband channel

Hbaseband: Frequency transfer function of the baseband equivalent model

12

(2.1b)

2.1.1 Single-carrier passband modulation

Single-carrier modulation schemes use only one carrier to transmit the whole datastream with a single

signal, occupying the whole available bandwidth. If no shaping filters are used, the transmit spectrum

of a single-carrier signal is approximately white in the centre region and has some rolloff characteristic

towards the band-edges, combined with a certain amount of excess bandwidth, as can be seen

schematically depicted in Figure 2.1. The use of shaping is to adapt the transmit spectrum optimally to

the channel transfer characteristics and noise environments, therefore achieving a gain in performance.

In the following sections two important single-carrier modulation schemes are briefly presented and

described.

2.1.1.1 (Differential) Phase Shift Keying (DPSK)

In phase shift keying (PSK) the transmitted data is encoded in the phase of the carrier. This means the

phase of the carrier waveform is shifted a certain amount of degrees depending on the size of the used

constellation and the transmitted symbol. For example in binary PSK the phase of the carrier is shifted

0° if a '0' is to be transmitted or 180° for a 'I'. By increasing the constellation size the number of

different phase shifts increases also, which means that the number of bits per symbol and thus the

capacity increases with the constellation size. In appendix A, the constellation of QPSK and 16-PSK is

shown. The increase of the constellation size is limited by the environment in which PSK is used. For

example quaternary PSK (QPSK) requires a SNR per bit of 9 dB for a probability of a symbol error of

10-6 while l6-PSK requires of SNR per bit of 15 dB to get the same probability [2, Chapter 5]. This

means a trade off between capacity and error rate has to be made.

Differential encoding is often used in conjunction with PSK. Differential encoding means that not the

actual phase of the symbol is transmitted but the difference in phase to the previous transmitted

symbol. The phase of the first symbol is determined by its difference to a chosen phase reference. The

main advantage of this technique is that the receiver does not have to determine the phase of each

symbol but only the difference to the previous symbol, resulting in a lower receiver complexity. The

differential encoding of the transmitted signal makes it also more resistant to phase shift by the

channel, since all the information is encoded in the phase difference, so a phase shift of all the symbols

has little effect. The performance ofDPSK in a noise environment is worse than that ofPSK, because

if a symbol is corrupted by the noise the following symbol will also be misinterpreted. Its resistance to

the phase rotation of the channel compensates this disadvantage of DPSK. If the channel however has

fast time varying phase shifts compared to the symbol rate, the phase of different symbols will be

differently corrupted and the advantage ofDPSK is gone.

13

2.1.1.2 Quadrature Amplitude Modulation (QAM)

QAM uses the effect that two signals, using the same carrier frequency, but being modulated onto a

sine and a cosine carrier, do not influence each other in an ideal environment. Basically QAM can be

understood as two-dimensional PAM with each of the two carriers (having 90° phase-offset) being

used with one-dimensional PAM. The total QAM symbol can be understood as a two-dimensional

constellation of signal points where the extension in each dimension depends on the number of

signalling levels of the one-dimensional PAM. In Appendix A, a 16-point rectangular QAM

constellation is depicted, which allows transmitting 4 bits per symbol equal to 2 bits per dimension.

An increase in the size of the signal constellation has the same effects as an increase of the number of

signalling levels in a one-dimensional PAM-system. Therefore a careful trade-off between used

bandwidth and necessary signal to noise ratio, in order to reliably transmit the chosen constellation,

has to be done. If rectangular constellations are used, 16-QAM requires a SNR of about 15 dB while

64-QAM requires about 21 dB for a symbol error rate (SER) of 10-6• This difference also shows the

cost of about 3 dB for the transmission of an additional bit per symbol (therefore 6 dB for additional

two bits) [2, Chapter 5]. The size of the signal constellation has little impact on the computational

complexity of the system, while considerable simplification is achievable by choosing the carrier

frequency to be an integer multiple of the symbol rate. It is interesting to compare the performance of

QAM with that of PSK for any given constellation size M, since both types of constellation are tow­

dimensioned. In [2] it is shown that QAM yields a better performance than M-PSK when M>4. For

example, 32 QAM has a 7 dB SNR advantage over 32-PSK.

2.1.2 Multicarrier modulation

Multicarrier modulation for transmission of digital data has been known already for almost 40 years,

but until very recently never played a major role in practical implementations, mainly due to its

considerably higher complexity in comparison with baseband and single-carrier modulation schemes

[3]. In recent years several advances have been made, reducing the complexity of multicarrier

modulation systems. The rapid advance in VLSI-technology, on the other hand, has somewhat relaxed

the requirements on complexity. By now multicarrier modulation is known under many different

names: discrete multitone (DMT), mainly used for wired systems with adaptive bit power allocation;

orthogonally multiplexed QAM (OQAM); discrete wavelet multitone (DWMT); orthogonal frequency

division multiplexing (OFDM); multicarrier modulation (MCM). Throughout this section the name

multicarrier modulation (MCM) will be used as a general term, not specifying forms and details of

implementation. The basic principle of MCM is to partition the frequency band into many parallel

subchannels, over which the data is transmitted (see Figure 2.1). The basic idea is to get narrowband

channels with almost flat amplitude transfer function and white noise, being uncorrelated between the

14

subchannels. The higher the number of subchannels and therefore the smaller the bandwidth of each

subchannel, the more the subchannels will approach these ideal characteristics. This results in much

simpler equalisation, as the partitioning itself already does a great part of it.

While the performance improves with an increasing number of subchannels, delay and complexity are

also increased. For MCM systems there exist different forms of separation between the subchannels:

• Per channel filtering in combination with a guard band between the subchannels

• Pulses with rectangular shape and sine-spectrum, with separation by baseband processing

In the first case only relatively low bandwidth efficiency can be achieved due to the limits of realistic

filters. Therefore the necessary excess bandwidth is relatively high and the guard bands have to be

relatively wide. Even to achieve only medium bandwidth efficiency the complexity due to the filter

banks becomes already prohibitively high.

In the second case the subchannels are simply modulated by rectangular-pulses, therefore leading to a

sine-form of the spectrum of each subchannel. These spectra theoretically have a infinite extension but

separation of the subchannels can be achieved by baseband processing such as discrete Fourier

transform or discrete wavelet transform. In this case there is no necessity for a guard band between the

subchannels.

The main task in MCM systems is to combat intersymbol and interchannel interference (lSI and ICI).

On a flat channel all the subchannels maintain complete orthogonality, therefore not interfering with

each other. lSI is no problem either on an ideal channel. The real channel, however, is severely

distorted and therefore orthogonality is getting lost, giving rise to lSI and ICI. Therefore a certain

amount of equalisation remains necessary also in the MCM system. The main influence of the channel

is to change amplitudes and phases for the different subchannels differently. Correction for this can be

done by complex-valued one-tap-per-channel equalisers, multiplying the received symbol with a

complex number that has to be learned during a start-up routine. lSI and ICI are caused mainly by two

different imperfections of the channel [3]. While lSI is due to the channel impulse response, ICI is

caused by asymmetries in the channel, especially toward the band-edges of the MCM signal. There

exist different methods to combat lSI and ICI that may be used exclusively or in combination:

• Guard period between the symbols

• Linear passband equalisation

• Baseband equalisation

• Vector coding/Structured channel signalling

15

Inclusion of a guard period of the length of the channel impulse response efficiently combats lSI, but

has the disadvantage of considerably reducing the achievable throughput as the impulse responses

have a considerable length.

Linear passband equalisation can be concatenated with MCM without the usual performance penalty

due to noise enhancement, as the bit allocation is done according to the SNR of the respective

subchannel. Linear passband equalisation, done by a short tapped delay line (TDL) can be combined

very well with a short guard period. In this case the task of the TDL is only to shorten the channel

impulse response to a length shorter than the guard period. The shorter the block length, the longer the

equaliser has to be in order to maintain the same relative rate loss. Here again a trade-off is necessary

between delay, rate loss and complexity.

Baseband equalisation is not a good candidate for MCM systems as a very complex cross-structure

would be needed in order to cope with ICI as each subchannel spreads into many of its neighbours.

Therefore an N*N matrix (with N being the number of subchannels) would be needed in order to deal

only with ICI. This matrix moreover would have to be 3-dimensional if lSI were also to be dealt with

by the same equaliser. The complexity of such a structure would be prohibitive.

Vector coding and structured channel signalling use much more complex carriers than the usual MCM

schemes. More about this technique can be found in [4] and [5].

The output signal of a PSKlQAM system with uncorrelated pseudorandom data as input has an

amplitude probability distribution that is very near to continuous Gaussian. The output of an MCM

system then is the sum of many signals with Gaussian amplitude distribution. This leads, firstly, to a

high peak-to-average ratio of the transmit signal (high dynamic range) and, secondly, to high

requirements for the D/A-converter in the transmitter, if the transmitter is (which is usually the case)

built up in digital fashion. The high peak-to-average ratio can give rise to non-linear distortion or

clipping. For further treatment see Chapter 3. The sensitivity ofMCM to timing and synchronisation

errors has been a major disadvantage.

As the modulator/demodulator pair dominates the complexity of an MCM system, the transceiver

complexity is not highly dependent on the grade of distortion on the channel. A single-carrier or

baseband system, on the other hand, has its complexity dominated by the equaliser. Therefore the

complexity of such a system increases strongly with increasing channel distortion for that the system

has to be designed. This results in the complexities of the two systems approaching each other with

increasing channel distortion.

16

2.1.3 Concluding comparison between the presented modulation schemes

The decision for a certain modulation scheme depends always on the specific requirements of the

service that is to be realised with this transmission system. In case of wireless communication the

decision is therefore especially difficult, as there are several different services to be transmitted over

one common transmission platform. In the first place the decision for a passband transmission scheme

is not so much dominated by performance issues but much more by practical matters of

implementation. The decision between single-carrier and multicarrier modulation is then more

dominated by performance considerations. However, since in the MC system transmission is parallel,

the effect of fading is spread over many bits, which leads to lower sensitivity of this technique to

distortion of the indoor channel (see Chapter 3). Besides the longer symbol duration due to parallel

transmission of the MC technique has the added advantage to work in impulsive noise environments.

The other advantage is the efficient implementation of the modulator and demodulator by the Fourier

Transform (FFT) algorithm.

As stated before, by using pulses with rectangular shape there is no necessity for a guard band between

the subchanne1s. This is the case when OFDM is used, where the spectra of subchanne1s overlap each

other while satisfying orthogonality, giving rise to optimum spectral efficiency.

If OFDM is chosen, a subcarrier modulation scheme has to be selected. There are two main options,

coherent (QAM/PSK) or differential modulation (DPSK). The key idea behind coherent detection

techniques as discussed in [21], is that they somehow estimate the channel to obtain an absolute

reference phase and amplitude for each subcarrier in each OFDM symbol. In contrast to this,

differential detection does not perform any channel estimation, thereby saving both complexity and

pilots but at the cost of a reduced SNR performance. In [21] it is shown that coherent demodulation

performs much better than differential detection in the frequency domain. For the same data rate and

error probability, coherent demodulation can tolerate about three times as much delay spread as

differential detection. The reason for the relatively poor performance of differential in frequency

detection is the significant phase fluctuation between subcarriers.

2.2 Orthogonal Frequency Division Multiplexing (OFDM)

As mentioned above, Orthogonal Frequency Division Multiplexing (OFDM) is a method that allows

transmitting high data rates over extremely hostile channels at a comparable low complexity. OFDM

has been chosen as the transmission method for the European radio (DAB) and TV (DVB-T) standard.

Due to its numerous advantages it is under discussion for future broadband application such as

wireless ATM as well.

17

The main idea behind OFDM is to split the data stream to be transmitted into N parallel streams of

reduced data rate and to transmit each of them on a separate subcarrier. These carriers are made

orthogonal by appropriately choosing the frequency spacing between them. Therefore, spectral

overlapping among subcarriers is allowed, since the orthogonality will ensure that the receiver can

separate the OFDM subcarriers, and a better spectral efficiency can be achieved than by using simple

frequency division multiplex (see Figure 2.4). Next, a mathematical description of the OFDM signal

will be given and a typical OFDM system is presented.

2.2.1 The OFDM signal

In its most general form, the lowpass equivalent OFDM signal can be written as a set of modulated

carriers transmitted in parallel, as follows [6]:

set) = n~<Xl(~~Cn'kgk (t - nTs )), (2.2)

witht E [O,TJotherwise

(2.3)

andk

fk =- ,k =0... N -1Ts

(2.4)

Cn,k: symbol transmitted on the kth subcarrier in the nth signalling interval, of duration Ts

N: number of OFDM subcarriers

k kth subcarrier frequency.

Define the nth OFDM frame as the transmitted signal for the nth signalling interval of duration equal to

one symbol period T" and denote it by F,,(t). By substituting Fit) in Equation (2.2) instead of the term

in parenthesis which corresponds to the nth OFDM frame, the relation can be rewritten as

<Xl

set) = L Fn(t)n=-co

(2.5)

and thus, Fit) corresponds to the set of symbols en,!o k=O...N-1, each transmitted on the corresponding

subcarriers fk. Demodulation is based on the orthogonality of the carriers gil), namely:

Igk(t)g;(t)dt= Ts ·8(k-l)9\

and therefore the demodulator will implement the relation:

(2.6)

1C =-.n,k T

s

(n+l)Ts

I s(t)g;(t)dt.nTs

(2.7)

The block diagram of an OFDM modulator is given in Figure 2.2, while the demodulator is shown in

Figure 2.3, where, for simplicity, we have ignored the filters inherent in all communication systems.

18

•S(t}

•

Cn,N-J

Figure 2-2 OFDM modulator

Ie.) Ts

~ clI,o

Ts

• •S(t}

• •

Ie.) Ts

~ Cn,N-JTs

Figure 2-3 OFDM Demodulator

In order to make an OFDM system practical, a more economical implementation of the modulator and

demodulator is required, since according to Figure 2.2 and Figure 2.3 a large number, equal to the

number of subcarriers, of identical modulator/demodulator blocks would be needed. This can be

accomplished through discrete time signal processing and by making use of the filtering properties of

the discrete Fourier transform (DFT). By sampling the low pass equivalent signal of (2.2) and (2.5) at

a rate N times higher than the subcarrier symbol rate liT" the OFDM frame can be expressed as:

,m = O."N -1, (2.8)

which yieldsN-J '21fk m

FJm}= LCn.k / N =N.IDFT{Cn,dm}}.k=O

(2.9)

CII,k (mJ: value of symbol transmitted on the ktll subcarrier in the nth signalling interval at sample

moment (n+m/N)Ts

N: number of OFDM subcarriers

19

Next, we point out the difference between OFDM and FDM (frequency division multiplex). Let us

consider the power spectrum density for the two systems with data on all carriers. Further, let the data

streams originate from one, rate R, stream through an appropriate serial to parallel (SIP) conversion.

Figure 2.4 illustrates the two spectra indicating the occupied bandwidth W as function of the number

of carriers N.

W=4R/3

f f-2R/3 -R/3 R/3 2R/3 -R -R/3 R/3 R

Figure 2-4 OFDM versus FDM power spectrum density for N=3

From this figure one can see that the OFDM signal requires less bandwidth as the number of carriers is

increased, and in the limit we have:

lim W=N-4OO

N+Ilim --·R= RN-4OO N

= (2.10)

This is possible since there is spectral overlapping, which is then resolved making use ofthe

orthogonality of the subcarriers, as stated in Equations (2.6) and (2.7). By performing the sampling as

indicated, the OFDM signal is subject to no loss. This is so, since, in view of relation (2.10), the two

Nsided bandwidth of the OFDM signal (neglecting sidelobes due to the outer subcarriers) is W = -.

Ts

Then, the sampling rate of NITs is exactly the corresponding Nyquist rate, and hence there will be no

frequency domain aliasing.

In conclusion, apart from a constant multiplying factor ofN, the sampled OFDM frame can be

generated using an inverse DFT (modulation function), and hence the transmitted data can be

recovered from the OFDM frame through DFT (demodulation function). A block diagram of the

digital OFDM system employing DFT is given at the end of the next section (Figure 2.6), after

discussing the need for a cyclic prefix.

20

2.2.2 Introduction of a cyclic p refix (guard interval)

When a signal s(t) which is passed through a channel with impulse response h(t), the received signal is

given by the convolution:

ret) =h(t) *set) , (2.11)

and if the channel is not ideal, there will be inter symbol interference (lSI). It is convenient to view the

OFDM signal in terms of data frames, so we can appreciate that the channel will produce lSI within

the frame, and will also produce inter frame interference (IFI) among adjacent frames. Considering the

discrete time equivalent signal and the channel h;, i=O...L, with L being the maximum delay spread of

the channel (channel impulse response length), relation (2.11) becomes:

L

rm = I. hi 'sm_i'i=O

(2.12)

Figure 2.5 shows this convolution sum for the particular case of L=2. In this figure S".O represents the

first sample of the nth frame. From this graphical representation it can be seen that the introduction of

a guard interval oflength equal to the delay spread L of the channel between two adjacent frames will

"absorb" the channel delay and hence remove IF!.

• •

• •

+

___......._S_"._I_I ••• I S".N-I I S,,+I,O [.

+

17 0 •

.J SIl-I.N-2 I Sll-I.N-I I S".O

171·

• •

he·

• •

.J r,,-I,N-2 I r,,-I,N-I I rn.o r",! I··· I rn,N-I I rn+l.o [ •

Figure 2-5 Inter Frame Interference in OFDM systems

This may be accomplished by inserting L leading zeros in each frame at the transmitter and removing

them at the receiver. However, in order to also eliminate Inter Carrier Interference (ICI) within the

frame, it is better to use a cyclic prefix instead of an all zero guard interval. In this case, after dumping

the prefix at the receiver, one would get the periodic (cyclic) convolution of the transmitted data frame

and the channel.

21

The cyclically extended frame can then be written as

,m=-L... -l

,m = O...N -1'(2.13)

where (2.14)

After discarding the prefix, the received frame becomes

A L-I

F,,(m)=l..F,,(m-i)N·h; ,m=O...N-l,;=0

(2.15)

where (m-i)N represents a modulo N subtraction. This mean that if (m-i) is smaller than zero that m

must be replaced by m+N. After DFT demodulation we get

(2.16)

where Hk is the channel's transfer function at the subcarrier frequency fk from relation (2.4). Therefore,

by using a cyclic prefix the effect of the channel is transformed into a complex multiplication of the

data symbols with the channel coefficients Hk, and all ICI and IF! is removed. In view of these, the

block diagram of a basic OFDM system is as shown in Figure 2.6 .

C".N-I

C'~n,G

C'~",I

C'~I1.N-1

... ... ..... ...Parallel to.. ... Add ...

• ...lOFT

... • ....• cyclic Serial

• • prefix • PIS...... ...

Transmitter: Tx ,Ir

Channel

Channel H(w)

Noise :4;Receiver: Rx

~ ... ...~ ....

Serial to... ... Remove ~.... ~ ...• DFT • cyclic • Parallel ~

• • prefix • SIP... ... ....... ~ ~

Figure 2-6 Basic OFDM communication system

22

Chapter 3

3 Limitations on a wireless communication system

3.1 Limitations of the wi reless channel

The channel is the physical medium through which the transmitted data propagates. For wireless

communication the channel consists of free space, and for applications connected by wires the channel

may be copper twisted-pair cabling or optical fibre. The majority of telecommunication channels can

be categorised into five groups: wireline; wireless; storage; acoustic (underwater or ultrasonic); and

optic (fibre and line of sight wireless) channels. Each category has unique characteristics and the

following will discuss more closely the wireless channels.

Wireless channels are becoming far more prevalent with the growing popularity of cellular phones.

The medium connecting the transmitter with the receiver is free space and communication occurs by

radiating electromagnetic waves from an antenna.

A common phenomenon for wireless communication channels is that of multipath fading.

Fading is used to describe the rapid fluctuations of the amplitude of a radio signal over a short period

of time or travel distance, so that large-scale path loss effects may be ignored. Multipath fading is

caused by interference between two or more versions of the transmitted signal which arrive at the

receiver at slightly different times. These waves, called multipath waves, combine at the receiver

antenna to give a resultant signal which can vary widely in amplitude and phase, depending on the

distribution of the intensity and relative propagation time of the waves and the bandwidth of the

transmitted signal.

Multipath in the radio channel creates small-scale fading effects [7]. The three most important effects

are:

• Rapid changes in signal strength over a small travel distance or time interval

• Random frequency modulation due to varying Doppler shifts on different multipath signals

• Time dispersion(echoes) caused by multipath propagation delays.

Even when a line-of-sight exists, multipath still occurs due to reflections from the ground and

surrounding structures. The incoming radio waves arrive from different directions with different

propagation delays. The signal received may consist of a large number of plane waves having

randomly distributed amplitudes, phases, and angles of arrival. The multipath components combine

vectorially at the receiver antenna, and can cause the signal received to distort or fade. Even when the

23

receiver is stationary, the received signal may fade due to movement of surrounding objects in the

radio channel.

The channel can be represented at the baseband rate (the rate of transmission) by an equivalent

discrete time model. This consists of a transversal filter whose coefficients are given by the channel's

impulse response. The derivation found in [2, Chapter 10] of such a system will be outlined.

3.1.1 Discrete channel model

The equivalent lowpass transmitted signal for several different types of digital modulation techniques

has the form

00

s(t)= Lcig(t-iT) ,i=O

(3.1)

where Ci is the transmitted sequence and g(t) is some impulse with a band-limited

frequency response (generally selected to minimise lSI and so that the transmitted sequence remains

within the allocated bandwidth of the radio spectrum). After s(t) passes through a linear channel with

impulse response h(t) and additive white Gaussian noise, 1](t), the signal at the receiver is:

00

r(t)= Lc;/(t-iT) +1](t);=0

where f(t) is the convolution given by

00

f(t)= fg(t)h(t-T)dT-00

(3.2)

(3.3)

All digital receivers will have an analogue receive filter, ideally with impulse responseI (-t) whereIrepresents the conjugate off, prior to sampling. Consequently, if the receiver samples at times t = kT +

To, where k = 0, 1, .... and To is a timing offset, then the received signal OJ and sampled received

symbol OJk are

00

OJ k ~OJ(kT+To)= Lcid(kT-iT+To)+u(kT+To);=0

00

= Lcidk - i + Uk

i=O

{vJ : a sampled noise term

{v} : the noise signal

{d}: the overall impulse response for the communication system

{dJ: the sampled impulse response.

24

(3.4)

(3.5)

For all practical purposes, it is reasonable to assume that lSI will only affect a finite number of

symbols, i.e. dj = 0 for Iii> L. The channel memory or length of the channel is denoted by L.

Consequently, dj has the (two sided) Z-transform representation:

L -1D(z) = "i,d;z

;=-L(3.6)

or equivalent, in vector notation as, D = [d_L, ... , d_h do, d i , ... , dJ.

The problem with the system presented thus far is that the noise sequence, Uk, is correlated with D.

This causes difficulty with the evaluation of performance for a communication system and limits a fair

comparison between various systems. The noise term, u(t), is equal to

00

u(nT + To) = Jry(t)/* (t - nT - To) dt-00

(3.7)

As it is more convenient to deal with additive white noise when calculating error rate performance, the

correlation needs to be removed which is done by whitening the sequence. The autocorrelation

function, D(z), has 2L roots with the following symmetry. If p is a root, so is 1//. Then, D(z) can be

decomposed into

D(z) =H(z)H* (Z-I). (3.8)

Where H(z) has the roots, pi, P2> ... , PL, and due to symmetry H*(Z-i) has the roots,

1/ p;, 1/ p;, ... , 1/ p~ . The appropriate noise whitening filter has the Z-transform lIH*(Z-i) where

the roots of H*(Z-i) are uniquely selected so that they are all inside the unit circle (this results in a

minimum phase filter). Consequently, after OJk is passed through the whitening filter the output

sequence can be written as

L

Yk =I Ck_,/ln + '1k .;=0

Alternatively Equation (3.9) can be stated in vector notation as

Yk =CkH'+l1k

where H = rho, hi, h2, ... , hJ, Ck = [c/o ck-i, ck-], ... , Ck-J and prime represents transposition.

Figure 3-1 The equivalent baseband communication channel (incorporating transmit,

receive and noise whitening filters) with impulse response H and additive white Gaussian

noise.

25

(3.9)

(3.10)

In summary, the cascade of the transmit filter, g(t), the channel, h(t), the receive filter,!(-t), the

sampler and the whitening filter can be represented as an equivalent discrete time transversal filter, see

Figure 3.1.

A considerable amount of research effort has concentrated on the measurement

and characterisation of actual channels. The power delay profile of a channel can be defined as the

sequence with the elements

(3.11)

where the channel coefficients are possibly complex valued. All channels can be characterised by

defining the pre-cursor, cursor, and post-cursor. The cursor is the point of maximum energy of the

impulse response, given by Pmax = IIHII", .The pre-cursor consists of all the elements prior to the

cursor and the post-cursor contains all the elements after the cursor.

It is important to consider typical power delay profiles - channels - so that suitable low complexity

equalisation techniques can be developed. Desirable channels have a minimum phase nature (that is,

the zeros in the z -domain are within the unit circle) and the impulse response falls of according to an

exponential-like function. Although the communications model was developed such that minimum

phase channels would result, in practice these desirable channels cannot be guaranteed. All-pass

filtering could be used to shift the zeros inside the unit circle, however, for long channels this

rootfinding exercise demands excessive complexity. Even if a minimum phase channel is obtained,

this does not necessarily guarantee that peak energy occurs at the start of the impulse response.

3.1.2 Sources of Noise

The source of the noise occurring in the channel is externally or internally generated. External noise is

generated by man made or natural electrical activity. Shot, thermal, flicker, and burst noise are all

created by electronic components, and will be referred to as internal noise. Although small in

magnitude noise can cause havoc with communication systems, as high amplification often used in the

receiver. In fact, thermal noise is ubiquitous in communication and is one of the major noise sources.

The effects of noise can be minimised by increasing power in the transmitter. However, practical

constraints limit the transmit power. In the previous paragraph the additive noise is assumed to be

Gaussian.

26

3.1.3 Fading Channels

The channel description of Section 3.1.1 has assumed that the coefficients determined for the eIR are

time invariant. However, this may not be true. For example, if the transmitter, receiver or parts of the

communication channel are moving the coefficients of the eIR can vary, producing a fading channel.

~Tx path 1 Rx

Figure 3-2 Situation when a signal is transmitted/rom Tx

and traverses the two paths to the receiver Rx

Fading channels can also occur for stationary transmitters and receivers. In order to illustrate the

phenomenon, consider the simple two path fading channel of Figure 3.2, where Tx is the transmitter,

Rx is the receiver, and paths 1 and 2 are the line of sight (LOS) and reflected radio wave paths through

the channel respectively. The signal strength at Rx is given as the phasor sum of the signals from each

path, hence, if set) is the received signal then

r(t) =(a,e- j2rrd,A-' +a2e-j2mJ~A-' )·s(t) (3.12)

where Ais the wavelength (of the modulating frequency), ax and dxare the attenuation and distance

along path x respectively. If the LOS signal is taken as the reference, the received signal takes the

form

-j2mJ,r(t)=r'(t)a,e A

-j2rr(d,-d,)a -where r' (t ) =(1 + _2 e A ) . s( t ) .

a,(3.13)

This type of fading is referred to as frequency selective as the amplitude is not constant and phase not

linear for all frequencies. Other forms of fading can occur when the transmitter, receiver, or channel

(i.e, moving vehicles) are in relative motion. In addition to the changing channel, Doppler shifting can

also occur and must be taken into account. The rate of fading is critical. The fade rate indicates how

fast the channel changes with respect to the baud rate. A slow fading channel is one where only minor

changes occur to the channel, hence, it can be assumed stationary for a prescribed period. For a fast

fading channel this stationarity cannot be assumed and the channel may change significantly during a

single symbol period.

3.1.4 The 60 GHz wireless channel

The small-scale variations of a (mobile) radio signal can be directly related to the impulse response of

the (mobile) radio channel. The impulse response is a wideband channel characterisation and contains

all information necessary to simulate or analyse any type of radio transmission through the channel.

27

This stems from the fact that a mobile radio channel may be modelled as a linear filter with a time

varying impulse response, where the time variation is due to receiver motion in space. The filtering

nature of the channel is caused by the summation of amplitudes and delays of the multiple arriving

waves at any instant of time. The impulse response is a useful characterisation of the channel, since it

may be used to predict and compare the performance of many different communication systems and

transmission bandwidths for a particular channel condition.

At the Dresden University of Technology measurements ofmm-wave indoor radio channels were

accomplished for several configurations. For simulations they have modelled the 60 GHz channel by a

conventional FIR-filter structure which resulted in the impulses given in Appendix B.

3.2 Limitations caused by the transmitter and receiver

One of the arguments against OFDM is that it is highly sensitive to synchronisation errors, in

particular to frequency errors [8]. Here an overview is given of the oscillator (transmitterlreceiver)

related problems: carrier frequency synchronisation errors and carrier phase noise. Also the effects of

symbol synchronisation and sampling-frequency synchronisation are discussed. But first the

consequences of the high peak-to-average ratio of the OFDM signal is discussed.

3.2.1 Amplifier related error

As mentioned in Section 2.1.2, an OFDM signal has a high peak to average power ratio. This can

cause problems at the transmitters amplifier, because a amplifier has a limited linear range. If the input

voltage exceeds the linear range the output voltage will saturate at its maximum level, resulting in

clipping of the signal. So it is important to stay within the linear range of the amplifier. On the other

hand the amplification should be as high as possible to maximise the transmitted power. A single­

carrier system has a relative constant amplitude so it is rather easy to determine the maximum allowed

amplification. For the OFDM signal this is much harder because of its high peak to average ratio. So it

is well possible that the amplification is too high and clipping will occur.

3.2.2 Oscillator-related errors

Differences and imperfections in the oscillators from the transmitter and the receiver introduce carrier

frequency errors and carrier phase noise.

3.2.2.1 Carrier frequency errors

Frequency offsets are created by differences in oscillators in transmitter and receiver. There are two

destructive effects caused by a carrier frequency offset in OFDM systems. One is the reduction of

signal amplitude (the sinc functions are shifted and no longer sampled at the peak) and the other is the

introduction of ICI from the other carriers. leI is caused by the loss of orthogonality between the

28

subchannels. In [9,10] the degradation of the BER caused by the presence of carrier frequency offset

and carrier phase noise for an AWGN channel is evaluated analytically. The relative frequency offset,

nonnalised by the subcarrier spacing, can be written as iJf =~, where iJP is the frequency offset,WIN

W the bandwidth and the N the number of subcarriers. The degradation Din SNR (in dB) for OFDM

can then be approximated by

D(dB) ~ ~(JriJfi Es = ~(JrN'iJP)2 Es for OFDM3lnlO No 3lnlO W No

D (dB) ~ ~(JriJfi = ~(Jr iJP)2 for SC.3lnlO 3lnlO W

(3.14)

Note that the degradation (in dB) increases with the square of the number of subcarriers and with

E/No, if iJP and Ware fixed. For a single-carrier system the D is independent of the energy-per­

symbol to noise ratio, E/No, because this factor is dominated by inter carrier interference. In Figure

3.3 the degradation is plotted as a function of the nonnalised frequency offset iJf, i.e. relative to the

subcarrier spacing.

10' ,--------,----------,--------,-------,--------,

10'

<D~

cD

a;;;~

E10'1

/'/'

/'./

.//

/

10·20C-~--.L.......C0.0-,----0-'--02-----'------0.0'---3----0:-':-04-----=-"0.05

Relati'o'l3 frequency otlset

Figure 3-3 The degration D as function ofthe relative frequency offset

3.2.2.2 Carrier phase noise

Carrier phase noise is caused by imperfections in the transmitter and receiver oscillators. For a

frequency-selective channel, no distinction can be made between the phase rotation introduced by a

timing error and a carrier phase offset [9]. An analysis of the impact of carrier phase noise is done in

[10]. The carrier phase noise can be modelled with a Wiener process 8(t) with E{8(t)} = 0 and

29

D(dB) ~

E{8(to+t)- 8(tO))2} = 47t131 t I, where 13 (in Hz) denotes the one-sided 3 dB linewidth of the Lorentzian

power density spectrum of the free-running carrier generator. Phase noise basically has two effects.

First, it introduces a random phase variation common to all subcarriers. The second and more

disturbing effect of phase noise is that it introduces ICI, because the subcarriers are no longer spaced

at exactly liT in the frequency domain. In [10] these effects are translated into a degradation in SNR,

i.e. the increase in SNR needed to compensate for the error, which can be approximated by

11 ( 47rN ..tJ Es for OFDM6ln10 W No

D(dB) ~ 1 (4 f3 JE s

6ln10 7r W NoforSC (3.15)

where W is the bandwidth and E/No is the per-symbol SNR. Note that the degradation increases with

the number of subcarriers, and again with E/No• Due to rapid variations of the phase noise, it may

cause large problems.

3.2.3 Symbol synchronisation errors

A great deal of attention is given to symbol synchronisation in OFDM systems. However, by using a

cyclic prefix, the timing requirements are relaxed somewhat. The objective is to know when the

symbol starts. The impact of timing errors has been analysed in [11]. A timing offset results in a phase

rotation of the subcarriers. This phase rotation is largest on the edges of the frequency band. If a

timing error is small enough to keep the channel impulse response within the cyclic prefix, the

orthogonality is maintained. In this case a symbol timing delay can be viewed as a phase shift

introduced by the channel, and the phase rotations can be estimated by a channel estimator (see

Chapter 4). If a time shift is larger than the cyclic prefix, lSI will occur.

3.2.4 Sampling-frequency syn chronisation errors

The continuous-time signal is sampled at the receiver, where mismatches in the sampling frequency

may occur. The effect of a clock frequency offset is twofold: the useful signal component is rotated

and attenuated and, in addition, ICI is introduced. The degradation of the BER performance, given

certain BER, can be defined as the increase of SNR at the input of the decision device needed to

compensate for the impairment. In case of a sampling frequency error, the effect of this impairment

depends on the considered carrier. The degradation Diin dB) for the QAM signal modulating the

carrier at frequency niT, assuming an A WGN channel ~Hk 1= 1, Vk) and small LJ.f/fs can be expressed

as [12]: D ~101o [1+i~[7r.n'LJ.fJ2Jn g/o 3 N f

o s

30

(3.16)

Chapter 4

4 Error correction techniques

4.1 Equalisation of the ch annel

As it can already be seen from the previous information, equalisation is a very crucial point for the

transmission performance. In case of a single-carrier system, where the signal is not subdivided, as it

happens for example in the multicarrier passband modulation, equalisation has to be done over the

whole used frequency band in order to remove the effects of lSI. Another task of is the whitening of

the additive noise, as most coding schemes only work optimally in presence of white noise.

Equalisation can be done in the transmitter or in the receiver or even in a shared fashion at both ends

of the transmission system. It depends on the environmental conditions and additional design

constraints, which of the equalisation concepts is the most suitable for a certain implementation. A

main problem for the equalisation is that in general the impulse response will not be known

beforehand and therefore either channel detecting or iteratively adaptive methods will have to be used.

The channel detecting methods use a training sequence, normally spectrally white, in order to estimate

the channel transfer function, and calculate the necessary equaliser settings for this channel response.

The drawback of this method is its inability of coping with variations of the channel characteristics

after the initial setting. Therefore in many cases only an initial setting is done by use of a training

sequence and later continuous updating of the equaliser settings is done iteratively. This method bears

the advantage of relatively fast initial setting. Iteratively adaptive equalisers have the advantage that

they are able to cope with variations of the channel characteristics and therefore can be used with less

security margin than would be needed in pure start-up setting to cope with variations in the channel

characteristics. The disadvantages are in general longer adaptation times at the beginning and the risk

of instability [1]. In the most approaches an initial training sequence, known to the receiver, is used for

the initial iterative adaptation. In this case adaptation works in a decision directed manner. This means

that the receiver makes a decision on which symbol had been sent by the transmitter and then

compares this output with the symbol of the known training sequence. Updates of the equaliser

settings are then computed taking into account the difference between the transmitted and the received

signal. This method can usually be used in wireless systems as in each case there is one pair of

transmitter/receiver assigned to a specific channel. In some other applications, especially in point to

multipoint transmission (for example digital satellite broadcast) things are more difficult, because no

training sequence can be used for the initial equaliser setting, but it has to be done using noisy

31

estimates of the incoming data stream. In the following sections some of the most common equaliser

will be briefly presented, pointing out their major advantages and disadvantages.

4.1.1 Linear equalisation

The simplest forms of equalisers are the so-called linear equalisers or finite impulse response (FIR)

equalisers. Generally they are realised in form of a tapped delay line (TDL). The delay introduced to

the signal by the equaliser as a whole depends on the position of the reference tap. The reference tap is

typically the one with the highest tap gain and it corresponds to the desired lSI-free sample value. The

incoming signal is sampled and quantised at the receiver's front end and then passed through the

equaliser. If the input to the equaliser is sampled in time intervals equal to the symbol period, the

system is called a symbol spaced (SS) equaliser while if the sampling period is smaller than the

symbol period it is called a fractionally spaced (FS) equaliser. In digital implementations the rate of an

FS-sampler is typically an integer multiple of the symbol rate. At the output of the FS-equaliser only

one sample per symbol period is taken for further processing. The performance of FS- and SS­

equalisers would be equal for input spectra that are strictly bandlimited to half the symbol rate (f/2).

However, in practice the incoming signal spectra always have a certain excess bandwidth that lead to

spectral overlap, especially in the case of SS-equalisers as they do not leave any guard band towards

the next copy of the input spectrum in the folded output of the sampler. The overall performance ofa

SS-equalised system is in practice about I dB below a FS-equalised system with optimal sampler

phase timing. For the optimisation of the adaptation of the linear equaliser there exist two different

criteria. The first is the zero-forcing (ZF) criterion that tries to force the equalised channel impulse

response to be zeroing at all the sampling instants. If this criterion is fully satisfied, no lSI is impairing

the data transmission. However, as realisable equalisers have a finite length, the optimal performance

can only be approximated with performance increasing with increasing number of taps, as the time­

span in that the impulse response has zero-crossings at the sampling instants is equal to the time-span

of the equaliser. As the ZF-equaliser only forces the impulse response to have zero-crossings at the

sampling instants, but does not define what happens between them, already slight deviations in the

sampling phase or slight sampler phase jitter may lead to considerable losses in performance. Another

optimisation criterion uses the sum of squared error (LMS-criterion (least mean square)) at the output

of the equaliser. Error in this sense is the difference between the sent symbol and the equaliser output.

lSI and noise compose this error, therefore the signal to distortion plus noise ratio at the equaliser

output is maximised. However, both forms of the linear equaliser neglect the task of whitening the

channel noise. In case of the LMS-equaliser the total SNR is optimised, but there is no defined

treatment of the noise spectrum. As the linear LMS-equaliser is superior to the ZF-type, it is used

32

typically in cases where no higher equalisation schemes can be used or as parts of them. The LMS­

criterion itself also is applied in other, higher equalisation approaches.

4.1.2 Decision feedback equalisation (DFE)

The linear equaliser of the proceeding section was trying to force the channel impulse response to

satisfy the Nyquist criterion and to avoid lSI by this. That approach did not make any use of the

knowledge of previously decoded symbols. An equaliser that does use this knowledge is called a

decision feedback equaliser (DFE), as the decisions made on the previous symbols are fed back into a

transversal filter, similar to a linear equaliser.

However, this kind of operation also has a few disadvantages. The first is that zero-delay decisions are

needed for the feedback. The second one is that, if a wrong decision is fed back into the feedback filter

(FBF) the probability of error rises for the next few symbol periods, as the wrong feedback value

travels through the filter. This is the reason why errors in systems, using a DFE, normally occur in

short bursts. As the task of an equaliser is not only the treatment of lSI, there is also added a so-called

feedforward filter (FFF). The task of this filter, that is built up exactly as the linear equaliser of the

previous section, is to whiten the noise and to minimise the lSI. The whitening of noise is

accomplished independently of the used optimisation scheme (minimum mean square error (MMSE)

or zero forcing (ZF), applied to the DFE as a whole).

In case of frequency selective fading channels, i.e. channels with spectral notches, some form of

coding is necessary to achieve acceptable bit error rates at lower SNR's. In these cases COFDM must

be used [13].

4.2 Amplifier error correction

Different peak power reduction schemes for OFDM are described in literature [14,15]. These methods

are based on leaving out weak subcarriers. Here, the non-information carrying subcarriers are

modulated depending on a threshold decision, so the overlay of the resulting reducing function and the

information carrying signal significantly reduces the out-of-band radiation of OFDM signals.

4.3 Frequency estimators to cope with oscillator errors

As described in Section 3.2.2 carrier frequency offsets are created by difference in oscillators in

transmitter and receiver. Several carrier synchronisation schemes have been suggested in the literature.

They can be divided in two categories: based on pilots or on the cyclic prefix.

Pilot-aided algorithms have been addressed in [16]. In that work some subcarriers are used for the

transmission of pilots (usually a pseudo-noise (PN) sequence). Using these known symbols, the phase

33

rotations caused by the frequency offset can be estimated. Under the assumption that the frequency

offset is less than half the subcarrier spacing, this is a one-to-one correspondence between the phase

rotations and the frequency offset. To assure this, an acquisition algorithm must be applied.

A related technique is to use the cyclic prefix which, to some extent, can be viewed as pilots. The

redundancy of the cyclic prefix can be used in several ways: e.g., by creating a function that peaks at

zero offset and finding its maximising value [17] or by doing maximum likelihood estimations [18]. In

[18] it is assumed that the cyclic prefix has the same size as the OFDM symbol (i.e. the useful symbol

is transmitted twice). If the frequency error is slowly varying compared the OFDM symbol rate, a

phase-locked loop (PLL) [2] can be used to reduce the error further.

It is interesting to note the relationship between time and frequency synchronisation. If the frequency

synchronisation is a problem, it can be reduced by lowering the number of subcarriers which will

increase the subcarrier spacing. This will, however, increase the demands on the time synchronisation,

since the symbol length gets shorter, i.e. a larger relative timing error will occur, Thus, the

synchronisations in time and frequency are closely related to each other.

4.4 Symbol synchronisation

As with frequency synchronisation there are two main methods for timing synchronisation: based on

pilots or on the cyclic prefix. In [19] a scheme is used where the OFDM signal is transmitted by

frequency modulation (FM). The transmitter encodes a number of reserved subchannels with known

phases and amplitudes. The synchronisation technique, with modifications, is applicable to OFDM

signals transmitted by amplitude modulation. Their algorithm consists of 3 phases; power detection,

coarse synchronisation and fine synchronisation.

The first phase (power detection) detects whether or not an OFDM signal is present by measuring the

received power and compare it to a threshold. The second phase (coarse synchronisation) is used to

acquire synchronisation alignment to within ±O.5 samples. This performance in not acceptable, but this

phase serves to simplify the tracking algorithm (which can assume that the timing error is small). The

coarse synchronisation is done by correlating the receive signal to a copy of the transmitted

synchronisation signal. To find the peak of this correlation with enough accuracy, a digital filter is

used to provide interpolate data values at four times the original data rate. In the last phase (fine

synchronisation) of the synchronisation, the subchannels with pilots are equalised with the estimated

channel obtained from pilots. Since the coarse synchronisation guarantees that the timing error is less

than ±O.5, the channel impulse response is within the cyclic prefix. The remaining phase errors on the

pilot subchannels are due to timing error and can be estimated by linear regression.

34

There are also synchronisation algorithms based on the cyclic prefix. Here the difference between

received samples spaced N samples apart is formed, r(k) - r(k+N). When one of the samples belongs to

the cyclic prefix and the other one to the OFDM symbol from which it is copied, the difference should

be small. Otherwise the difference (between two uncorrelated random variables) will have twice the

power, and hence on average, will be larger. By windowing this difference with a rectangular window

of the same length as the cyclic prefix, the output signal has minimum when a new OFDM symbol

starts.

4.5 Sampling-frequency synchronisation

There are two types of methods of dealing with the mismatch in sampling frequency. In synchronised­

sampling systems a timing algorithm controls a voltage controlled crystal oscillator in order to align

the receiver clock with the transmitter clock. The other method is non-synchronised sampling where

the sampling rate remains fixed, which requires post-processing in the digital domain.

Because of the frequency mismatch, the OFDM symbol duration at the receiver, N(fs+M), differs from

the one at the transmitter, N/fs. Hence symbol synchronisation must be performed by a timing

algorithm. The algorithm ensures that the block ofN samples is well aligned within the corresponding

symbol period. This requires that, at regular intervals, samples are robbed (if <'1f>0) or stuffed (<'1f<O).

35

Chapter 5

5 Implementation of an OFDM communication system

In Chapter 2 a baseband equivalent model for the wireless transmission is described. This model has

ignored synchronisation errors and bandwidth limitations as described in Chapter 3. To include the

simulation of synchronisation errors and the limited bandwidth, receive and transmit filters are

implemented and the higher channel sampling rate is simulated by applying an oversampling

procedure, which will be described in Section 5.3.1. The basic model used for the implementation is

shown in Figure 5.1. In Section 5.1 a general overview is presented, which will be described in more

detail in 5.2,5.3 and 5.4. The implementation of the distorting effects as described in Chapter 3, are

discussed in 5.5, and followed by some practical implementation remarks in 5.6.

5.1 General overview

Figure 5.1 shows that the OFDM model can be divided in three parts, the transmitter, the channel and

the receiver. The implementation/function of each of these parts is described in Section 5.2 through

Section 5.4. The system is implemented in Matlab. This is done in a structured way so that each part

an be changed separately. The Matlab files can be found in Appendix C, where also a schematic

overview of the entire program is given.

Transmitter

=: =: =:Baseband AddData ------. --. SIP · IDFT · cyclic · PIS -

Source modulator · • prefix ·• · ·~ f----. f----.

Physical Channel L.. : Transmit filter L..I'" I

Channel

~I AWGN ~I Receive filter II

:= I: :=Received Baseband

Remove

~ .- PIS • DFT • cyclic • SIP ~data demodulator • • ·• • prefix ·.- ~ ~

Receiver

Figure 5-1 Implemented OFDM communication model37

5.2 The transmitter

The task of the transmitter is to convert the input data into an OFDM waveform. The input of the

transmitter is a binary data source with data rate R, which is implemented as a global variable.

5.2.1 Modulation

Depending on the chosen modulation scheme the input data is translated into complex numbers

containing the data in their angle and/or amplitude. Appendix A shows the constellations of the

implemented modulations schemes (BPSK/DBPSK/QPSK/I6QAM). The symbol rate at the output of

the modulator is RIK, with K the number ofbits per symbol.

5.2.2 Serial to parallel conver sion

After the modulation a serial to parallel conversion has to be done to assign each symbol to a

frequency. The number of frequencies is equal to N, the number of subcarriers used. So the width of

the data words at the output of the serial to parallel converter has to be N. The conversion lowers the

symbol rate per carrier to RlKN.

5.2.3 Inverse discrete Fourier transform (IDFT)

The IDFT transforms the complex symbols into sinus-functions with a starting phase and amplitude

corresponding to the complex symbols and adds them. The data rate does not change in the IDFT.

5.2.4 Adding the cyclic prefix

To protect the OFDM wave from channel influences a cyclic prefix is inserted. The length of the

cyclic prefix is variable, but the ideal situation is when it has the same length as the channel's impulse

response (see 2.2.2). If the channel's impulse response has length L, to add the prefix, a copy of the

last L values of the time signal has to be inserted at the beginning of the time signal. In the

programmed OFDM model, the length of the cyclic prefix can not exceed the number of carriers. The

adding of the prefix increases the symbol rate to:

5.2.5 Parallel to serial convers ion

Here the data words are converted back into a serial data stream. It increases the symbol rate N times.

R(l +~JThe symbol rate at the output of the parallel to serial converter RT is: RT == N

K

38

where Rc is the channel sampling rate.

5.3 The channel

The channel block consists of four blocks. Section 5.3.1 will describe the transmit and receive filters.

Section 5.3.2 will discuss the channel modelling and the noise generation.

5.3.1 The transmit and receive filters

Before the data can be sent through the channel, the symbol rate at the output of the transmitter has to

be adjusted to the channel sampling rate, which is implemented as a global variable. This upsampling

procedure consists of two steps: zero-insertion and filtering. For the first step a number of zeros Z is

added between each value of the transmitter output. Z can be calculated using the following equation:

Z= R c

R T

After the insertion of the zeros a raised cosine filter is used to interpolate the data. The transfer

function, a typical raised cosine filter, is shown in Equation 5.3.

T if o< IfI< (l - r)2T

H(f)= [ [ l]jn-Ifl- - + r T 1 - r 1 + rl+cos 2T - if--<Ifl<-

2r 2 2T 2T

(5.1)

o if IfI> 1+ r2T

r: ro11off factor

T: symbol time = l/RT

To interpolate, a transmit filter with transfer function H(j) would be sufficient. But in order to

bandlimit the noise at the receiver, a receive filter is also necessary. In the implementation a matched

filter response is provided, where the transfer function of the transmit filter is equal to the transfer

function ofthe receive filter, both are ~H ( f ) .The output ofthe receive filter will be sampled at the

proper sampling moment, with rate Z. to restore the original data rate.

5.3.2 Physical channel

Two different channels have been used in the simulations. First an AWGN channel, this channel only

adds Gaussian noise with a power depending on the EblNo ratio. The second channel used is a channel

with multipath delay spread, resulting only in amplitude distortion. This is modelled using a tapped

39

delay line filter with filter weights equal to the strength of the reflections compared with the line-of­

sight component. The number of reflections simulated is 4. The filter weights ofthis channel are

[1,0.5,0.4,0.3,0.1] with delays of lIRT • The "1" represents the undistorted LOS-component, the

"OS' represents the distortion ofthe second arriving signal component, with half the power of the

LOS-component.

A typical 60 GHz channel can be found in Appendix B. This channel model has not been used for

simulation because, as can be seen in the appendix, its BER is too high with simple OFDM and is

therefore not suitable for the simulation of the influences on the communication channel.

5.4 The receiver

The task of the receiver is to recover the transmit data from the sampled output of the receive filter.

The processing of the receiver's input is equal to processing done at the transmitter only in reverse

order. Therefore only a short summary is given here. See Section 5.2 for more details.

First serial to parallel conversion is applied to the data at in the input of the receiver. Then the cyclic

prefix is removed, which means the first L values of each of the parallel words are cut off. After the

removal the DFT is applied to regain the transmitted complex symbols. Now the data can be

reconverted to a serial stream. Finally the complex symbols are demodulated into binary data.

5.5 Implementation of distorting effects

As mentioned in Chapter 3, there are several imperfections that influence the performance of the

communication system. Section 5.5.1 shows how a carrier frequency offset and phase noise is

implemented. The implementation of synchronisation errors is described in Section 5.5.2, followed by

the amplifier effect in 5.5.3.

5.5.1 Implementation of a car rier frequency offset and phase noise

The influence of a carrier frequency offset and carrier phase noise is implemented as described in

Chapter 3: x(t) = r( t) *emf)

where:

r(t) is the received signal without carrier frequency offset and/or carrier phase noise,

x(t) is the received signal with carrier frequency offset and/or carrier phase noise.

40

Both can be simulated before the sampling of the output of the receive filter.

The carrier frequency offset is implemented with ¢(t) = 27[LlFt + ¢o, where LlF is the carrier offset.

The carrier phase noise is implemented with ¢(t) a Wiener process with E[¢(t)] = 0 and

E[¢(t + to) - ¢(to/] = 47[f3lt I. Here 13 is the one-sided 3dB linewidth of the Lorentzian power density

spectrum of the free running carrier generator. This means ¢(t) is a sample, with a length equal to the

received signal length, of a random normal process with an average of 0 and a variance of 47[13It I. For

simulation the LlF or 13 will be normalised to the subcarrier spacing.

5.5.2 Implementation of synch ronisation errors

There are two kinds of synchronisation errors implemented: symbol synchronisation error and

sampling frequency error. Both errors affect the sampling of the output of the receive filter. The

symbol synchronisation error is implemented by changing the starting point of the sampling. For

simulation this starting point error can be given as a fraction of the channel sampling rate.

The sampling frequency error changes the frequency at which the output is sampled, which is called a

phase jitter in the sample frequency. This phase jitter is modelled by a Gaussian random process, with

mean zero. The variance of this process is the simulation parameter for this error. For simulation the

variance can be given as a fraction of the channel sampling rate.

5.5.3 Amplifier effect

If the input voltage exceeds the linear range of the amplifiers, the output voltage will saturate at its

maximum level, resulting in clipping. The amount of clipping, is a simulation parameter. Therefore a

value (in dB), that represents the ratio of the maximum value of the signal before clipping and the

maximum value of the signal after clipping, can be given.

The maximum value of the transmit filter output is determined. With the given ratio, the maximum

value after clipping can be determined. Where the signal exceeds this maximum value, clipping will

be applied by reducing the signal value in these cases to the determined maximum value.

5.6 Practical simulations remarks

Sections 5.2 through 5.5 described the model of the implemented OFDM system. There are some

details however which need special attention.

The performance of a digital communication system is usually described as the bit error rate (BER)

versus the EbINO• Therefore it's important to keep track of the energy in de various signals and

manipulations during the simulation. Section 5.6.1 will describe all the necessary energy

manipulations needed. To simulate timing errors, upsampling and downsampling is implemented.

Section 5.6.2 will briefly discuss the size of the channel rate in relation to these timing errors.

41

5.6.1 Maintaining a constant b it energy

Since the simulations use the Eb/No ratio, its important to keep the bit energy in the various data

signals constant at unity throughout the system. Therefore after each manipulation the energy has to be

normalised. After modulation the complex symbols have to be divided through their average

amplitude. After the IDFT the data is multiplied with the square root of the number of carriers to set

the output energy per bit to one. Finally the receive and transmit filter combination and the channel

filter have to be normalised to an amplification of one. All the normalisation has to be undone at the

receiver. If all the normalisation functions are carried out, the bit energy will remain unity throughout

the simulation. So the additive noise power can easily be chosen as No and thus independent of the

used numbers of carriers and/or modulation scheme.

5.6.2 Channel rate versus tim ing errors

Section 5.5.2 describes the implemented timing errors. But to be able to vary the sampling phase jitter

and the starting point of the sampling in very small steps, the channel rate has to be much larger than

the transmitted data rate (RT). The amount of data that is interpolated depends on the channel sampling

rate. By making sure it is high enough, a large amount of data is interpolated and thus a more realistic

behaviour can be simulated.

5.6.3 Simulate

To simulate the entire system, both OFDM and single-carrier, with some or all it's influences, a Matlab

file called Simulate has been WTitten. With this file the simulation parameters like modulation type,

frequency offset and Eb/No etc. can be varied. They will automatically be used in the other files to

simulate the whole system and finally results in a bit error or symbol error rate.

With Simulate it is also possible to plot different signals like sent and received signal and the received

constellation.

The code of this function as well as all the other functions is given in Appendix C.

42

Chapter 6

6 Simulation Results

An OFDM system was modelled using Matlab to allow various parameters of the system to be varied

and tested. The aim of doing the implementation and simulations was to measure the performance of

OFDM compared to a single-carrier system under different channel conditions, and to allow for

different OFDM configurations to be tested. Six main criteria were used to assess the performance of

the OFDM system, which were its tolerance to channel (Gaussian) noise, multipath delay spread, peak

power clipping, carrier frequency offset, carrier phase noise and synchronisation errors.

6.1 Influence of Gaussian noise on different subcarrier modulation schemes

As explained in 2.1.3 different modulation schemes can be used in the OFDM system. The following

figures give some simulation results where differential BPSK is compared with coherent BPSK and

used over an AWGN-channel with constant phase rotation (Figure 6.1) and an AWGN-channel

without constant phase rotations (Figure 6.2)

: :. : :: :: :: 1:- :: :: .: : : :': : :- :: :- :: J :. __ .: :. : I: :: :: :: :: :: .: ':: :: : :: : ::- - - - - - 1- - - - - - -I - - - - - ... - - - - - - t- - - - - - - 1- - - - - -

- - - - - - ,- - - - - - -, - - - - -.., - - - - - - r - - - - - - 1- - - - - -

10 __ : :: ': :: :: :: :: :: .:' ~ .: .: .: .: .: J .: .: - .: .: : ~ .: .: .: .: :: .: ': .: : _

: : .: .: .: .: :: .: :: .: .: :.. =':' .: .: : .: .: .: .:. :: r:: .: .: .: .: .: .: I: .: .: .: .: .:-:: ~ ::: ::: :. ::: I: :. :. :. :: :. :'::: .:: .:: :. _ :. _ :. ::: - :. .:: .:: [ :. .:: .:: .:: : .:: ': .:: :. .:: :. :

_____ , ' ' l_~ __ , ' ______ , ' ' l ' _

1 ", I

: : : : : ': : : : : :': : : : : :'1 : : : : : ! : : : : : c : -= .: .: .: ': : .: : :----,------,-- --,- --r-----r-----,-----

---------------------------------------

, , ,10 ::::::::::::: I:: ::: ::: ::: ::: =1::: == ::: :: ::: ~ ::: ::: ::: ::: ::: i :; ::: ::: :::: :::: c ::: :::: :::: :0; :::: I;: :::: ::: :::: :::

-------------------------------~-------

10 1 ' ' __ ~ --~ ---- ----------

:: :: ===,= :: :: :: :: =, = :: = :: :: ~ ==:: : : i :: = : : : '= = : : : =': =: : :: : : : : ,: : : : : :,: : : -= : ::. : : : : : :; :: ::.: - : : : : ,: : : : :

10 :::::::::: ,= :: :: :: : :: ':: :: :: :: :: _ :: :: :: :: :: :! :: :: :: :: :: '= :::: :::: :::: =:::: ,= :::: :::: =::====:: '= =====': == : =~ ==_= : ~ =:: =: :: ~ :: :: :: :: :: ': : : : ::-----1------1----- I- I~ _- - - - -,- - - - - -, - - - - - -I - - - - T - - - ~ i - - - - - ,- - - - -

--~--,------,---- --- -,-- --,------,-----

Single Carner SystemAWGN channel

10' 1'"""',",",'-=,'-=,:0,::'," 00"'::=':',::",'-=o~o~o ~~:;.c,~=i'-::=i--,i;,~,,-=,~,~,,,"!Co0="':="0"='Ti,==-==;8~PS~K:: :: :: :: :: ': :: :: :: :: ::':: :: :: :: :: ~ :: :: :: :: :: ! :: :: :: :: :: ~ :: :: :: :: :: I -B- OBPSK

, ,.: .: ~ = = = = :: :: ~ :: :- :: = = ='= = = = = =:- : :! : : : : : : 1:: ':. ::- =- : : : ': : : : : :

10' ~ ~ ~ ~ ~ ~:~ ~ ~ :: ~ :: ~: ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ : ~ :::~ ~ ~ ~ ~ ~:: :. :: :: :: : ': :: :: :: :: _ -,:: :: :: :: :: : J :: :: : : : :: ::: :: : : : : : _ : :: :: : ::- - - - - - 1- - - - - - - - - - - - "1 - - - - - - .. - - - - - - 1- - - - -

Slng\a Callier System

lO'~~~_,,_=_=_,_,_,_A~",~"N~"h8:~n~!:,_p=~'7"R,~~,~~,~Ol,_80_"de:~,,~:_~_:_-=-_:_ ,,_,_-c=~=a:: .: =- :: .: :: I: :: .: .: .: .: :':: ::- .: : .: :: J :: .: .: .: .: .: r: :: : :: :: :: :: ': - BPSK: : : .:: :: .:: ': .:: :: :: :: :: :':: :: ::: :. :: :: J :: :: :: :: :: :: ~ :: ::: .:: ::: ::: ::: I::: -e- OBPSK

C~_-:-,_~__ ~::'--:--:~:::...;.-::~-~-- ": : : : : : : : : : : : ::: : : : : :

~ 1011

= = = = = =':: .: = = = = =' = = -: :: : : =- =- ': : : : : : :' =- : -

1 1 , , I-------------------------------" ,

oo'-----L----'-------'---<!l__--"c------L-----.J8 "

EblNo (dB)

10·S'--- -'-,---'--------:--~---'---------L--oo

EG'No (dB)

Figure 6-1 BPSK and DBPSK over channel with

constant phase rotation

Figure 6-2 BPSK and DBPSK over A WGN channel

As can be seen in Figure 6.1, DBPSK outperforms BPSK in the situation of constant phase rotation.

But as can be seen in Figure 6.2 and stated Section 2.1.3 BPSK has a better EblNo performance

compared with DBPSK. The simulation of different coherent modulation schemes can be seen in

Figure 6.3.

43

- - - - - -' - - - - - -,- - - - - .1 _

, ,------ ------------------ ----.------: : : : : :': _ - : : : L : : : : : :' : : : : : :_____ -, _ _ _ _ _ l- I _

- - - - - -, - - - - - - r - - 4 - - -I - - - - - -

- ·1 - - - - - - - - - - - -, - - - - - - r - - - - - ., - - - - - -______ ' L .1 _

-110

Single Carrier SystemAWGN Channel

100

t-=-:::::r::::::~E::::--=r::::::~E--=---=-_-=-_-=_-=_T'_CC_cc_=-_:-:-_-=--r--=---=-_-=-_-=_-=.T'.cc_cc_=-_=-=-_-=--F-=;======::::;l: : : : : :,: : : : : : : : : : : : :, : : : : :: : -+- BPSK

- --B-- OPSKl40AM: ~ 160AM

- - - - - -, - - - - - - l- - _ _ _ _ _ _ - - - - - -, - _ - _ _ _ _ I - - - - - - - - - - - -, - - - - - -

I I I I I I----------.--------- ------------- ----------- ---------- ..I I I I I

I I , I I I !-------------------.-. --- ----------------------_. ------------I I , I I I

cr: -2W 10C/J

______, _ _ L .' '- _ _ _ _ .1 L _

_____ .1 L .1 L. _ _ _ _ L I _

______, L ~ _, '- _ _ _ _ _ _ _ L I _ _ _

, , \ II! !

- - - - - -, - - - - - - I - - - - - -, - - - - - - t - - - - - -, - - - - - - I - - - - - -, - - - - -

, , " "- - - - - -, - - - - - - I" - - - - - -I - - - - - - I - - - - - -, - - - - - - - - - - - - -, - - - --

- - - - - ., - - - - -------------

- - - - - -' - - - - - -- - - - - -' - - - - - -

- - - - - -, - - - - - -

10"______1 -

- - - - - -, - - - - - -_ _ _ _ _ _I _ _ _ . __ !... I L ' _ _ _ _ _ _ _ ' 1 I _ _ _ _ _ _

, , I " I"-------------------------------------- -------------------------1 , , , 1 1 1 , 1

10-4 L-__-'-- -'--__-'-- -'--__-'-- -'---'-_-'-- -'----->_-'-- _

-4 -2 0 2 4 6 B 10 12 14 16Eb/No (dB)

Figure 6-3 Different modulation schemes over A WGN channel

The results show the typical trade off between capacity and symbol error rate (SER). The perfonnance

of the BPSK is the best but it has the lowest capacity, l6-QAM has the highest capacity but perfonns

the worst of the three schemes. It was also found that the SER perfonnance ofOFDM is similar to a

standard single-carrier digital transmission. This is to be expected, as the transmitted signal is similar

to a standard frequency division multiplexing system.

44

6.2 Influence of multipath delay spread

For simulation of the influence of multipath delay spread, a single-carrier system and the OFDM

system for a different number of carriers was tested with on multipath AWGN-channel, with a line-of­

sight component and four attenuated reflections, as described in Section 5.3.2.

Single Carrier and OFDM SystemChannel: AWGN + A. QPSK

I 'I I-----------------------------------~-~

" I!

I I I , •----------.----------------------------

1 , 1 I I , I I----------------------------------------------~--

I , I I ! I I

~~~~-~-~-~-~-~-'-§i~~§j~~~~- -, - - - - - - c - - - - - -, - - - - - - ,- - - - - - , - - - - - - ,-

I I I I I I

- - - - -, - - - - - - 1- - - - - - -I - - - - ,- - - - - - -I - - - - - - 1- - - - - - ., - - - - - - ,- - -

I I I ! I I , I

- - - - - -, - - - - - - ,- - - - - - -, - - - - - - - - - - -, - - - - - - ,- - - - - - I - - - - - - ,- - -

.,10

a::wCD

- Single Carrier---+- BCarriers-- 32 Carriers--9- 64 Carriers--ilo- 128 Carriers

10 '4'--------:-O------",---------'--------:':,2,-----------"'6c:---,------2~O-------,l-24,------------:2':-8 ­

Eb/No (dB)

Figure 6-4 The effect ofmultipath 011 a SC alld the OFDM system

It can be seen in Figure 6.4 that with increasing the number of carriers the performance gets better.

This is because the fading of the channel is spread over an increasing number of bits with increasing

the number of carriers. However, for a large number of carriers the performance enhancement is not

large.

45

6.2.1 Cyclic prefix

The BER as a function ofthe cyclic prefix length, using the channel from the previous section, is

depicted in Figure 6.5.

OFDM SySlemChannel: AWGN+A, OPSK, 8 Carriers

___ L L L l L _

::::===:=c=~::::::::::~:::::::::::::::::::c:::::::::::::::::::~:::::::::::::::~:::::::::::::::::::::~::::::::::::::::::c:::::::::::::::::::::_____ '- '- I.. !.. !.. L L _

, I I I I I I-------------------------------------------------------I I , I I ,

______ L L L L L _

,

-2 I I10 - - - - - - - - - - - - - - - -

______ '- L _

a:wCD

I I I I I I-------------------- ---------------------------------" I I I I

I I I I I I I-------------------------------------------------------I I I I I I I

10.3

:::::.:::::: ~ :: :: :: :: :: :: ; :: :: :: :: :: :: ; :: :: :: - :: :: ; :: :: :: :: :: :: ; :: :: :: :: :: :: ; :: :: :: :: :: :: ; :: :: :: :: :: ::------------------------- -----------------------------____ ._'- '- '- L l '- L _

Figure 6-5 Pelformance ofan OFDM system versus the cyclic prefIX for different values ofthe EblNo ratio

From Figure 6.5 it is clear that increasing the cyclic prefix might improve the performance ofthe

system. The Eb1N0=35 dB-curve reaches a ver low BER (10-7) for a cyclic prefix equal and larger than

4 symbols. But with increasing the cyclic prefix has a negative effect on the bandwidth efficiency.

Therefore, there is an optimum cyclic prefix to minimise the bit error rate. This value is equal to the

channel delay spread, which is in case of the simulated channel equal to four, because there are four

attenuated reflections. It is shown, that for an EblNo less than 20 dB a cyclic prefix has no effect,

because the noise effect is dominant to the multipath effect.

46

6.3 Effect of peak power clipping for OFDM

As stated in Chapter 3 the peak power ratio tends to decrease the efficiency of the RF power amplifier.

One way of reducing the peak power ratio is to clip the signal, which results in a degradation of the

BER.

- ~ - - ,- - - - - - - - - ,- - - - - - - - - ,- - - - - - - - - I - - - - - - - - -, - - - -

- EblNo = 0 dB :::::: ,: : : : : : : : : ,: : : : : : : : :,: : : : : : : : :,: : : : : : : : :,: : : :~ Eb1No=4dB ::::: :':::::::: :':::::::: :':::::::: :':::::::: :'::::-f3- EblNo = B dB - '- - - _ . ' ' ' - - - -' - - - -~ Eb/No =10 dB ' I I I !~ Eb/No:::: 12 dB - - - - - - ,- - - - - - - - -,- - - - - - - - -,- - - - - - - - -,- - - - - - - - -1- - - -

10" ::::::::::::::::::::::::::::::.::: ': :::::::: :::: :: ::'::: :::::: - - - _I: ::::::.: :': :: :::::::: ::.: :': ::::::

10.2

- - - - - - - -

a:UJCD

·310

- - - - - - === === - - - - - == = == = == ===- ===========:' ====, ,- -------------------

12106 BPeak before to peak alter clipping ratio (dB)

10·s '----- -'-- -"-- -----'- '---- -'---- -'-_-.Jo

Figure 6-6 Effect ofpeak power clipping 011 all OFDM system for differellt values oftlte EblNo ratio

In Figure 6.6 the effect of peak power clipping on an AWGN-channel using QPSK is depicted.

As can be seen from the simulation results in Figure 6.6, the transmitted OFDM signal could be

heavily clipped with little effect on the received BER. In fact, the signal could be clipped up to 4 dB

without a significant increase in the BER. This means that the signal is highly resistant to clipping

distortions caused by the power amplifier used in transmitting the signal. It also means that the signal

can be purposely clipped so that the peak to average ratio can be reduced allowing an increased

transmitted power.

6.4 Influences of oscillato r imperfections

Differences and imperfections in the oscillators from the transmitter and the receiver introduce

frequency errors and carrier phase noise.

47

6.4.1 Frequency errors

There are two destructive effects caused by a carrier frequency offset (CFO) in OFDM systems. One is

the reduction of signal amplitude (the sine functions are shifted and no longer sampled at the peak)

and the other is the introduction of ICI from other carriers. In Figure 6.7 through Figure 6.10, the

effect of frequency errors is depicted. These simulations were performed on an AWGN-channel.

- - - .... - - - + - - - + - - - ... - - - ... - - - .. - - - ... - - - _i - - - -I - - -

~ ~ ~ ~ ~ ~ ~ : ~ ~ ~ : ~ ~ ~ : ~ ~ ~ = ~ ~ ~ = ~ ~ ~ =~ ~ ~ j~ ~~~: ~Od~B I

= = = = = = = ~ = = = = = = = :!: = = = = = = = = = = = =. = = = =. = = = =' = = =- - - ,. - - - r - - - r - - - T - - - , - - - , - - - , - - - , - - - -, - - --- - -- -- -- - -- - -- - - -- - - -- - -- - -- -- -- -- - --: : : [ : : : ! : : : ! : : : ! : : : J : : : J : : : J : : : :' : : : -': _____ .... ... ... .. ... --- ... -~_ ... - __ _i.

---,.---r---r---T---'---'---'---___ I- ... ... oj. -l ..J __

10-3 = = = ~ = = = ~ = = = = = = = == = = = = = = = = = = == = = == = =::::::!::::::::: r::::::!:::::!:::::: J.:::::: J.:::::::':::::::'::::::: : : [ : : : I : : : ! : : : I : : : ::! : : : J : : : :' : : : :' : : :

10 '----,-L-,-------,--,L-:----:-L,---,O-".004:-:--0:-:005L.:---,O.~006-,--------,O--'.OOc::7----:-0.008L,----,-,'-,-----,-J

Carriel Frequency Ollsel (dellaF)

10" __ ..J - - 4

:::c:::t:::t:-- _:::l:.:::J::::J:::.J::-- - - r - - - T : .:: __ : : : 1 : : =- J : : : J : : : J : : -: :' : .:: .:: :1 : : :

___ L 1 .I. .1 .J_--- - --- ---- - - -- -----

:: .: :: [ :: .: :: ! :: :: :: r :: :: .: ! :: :: :: J :: :: .: ::' :: :: :: J .:. _:::r::::!: __ !:::l:::J::::J::::::!:::___ L~_~1 1 .1 __- - - - - - -

:: :: :: r: :: :: :: ! :: :: :: 1. :: :: :: ! :: :: :: J: :: :: :: :J :: :: :: J :: :: :: :;I :: :: :: :1 :: :: ::__ :: [: .: :: .: I :: .: .: ! .: :: :: ! .: .: .: J :: .: :: J .: .: :: :' :: :: :: :' .: :: :: :' :: :: ::

=::r:::r:::!:::I:::::::c::::r:::r::::r:-

IO''---~--~--'---_----L__---'--__-L-__'--_~_,___-~-_

a 004 0.005 0.006 a 008Carrier Frequency Offset (dettaF)

OFDM System

lO'o-=~"",~~--.--~~-r-=~A~W7G-,N~Ch~'"7"'-,'·~Q,-PS7K'-,E~l>'N~o.,.'-,1O~d~B~r-=-~,....,..~~=~-=-""

10

Figure 6-7 The effect ofa CFO on an OFDM system at

EblNo = 1OdB, for 4 and 8 carriers

Figure 6-8 The effect ofa CFO on an OFDM system

at EblNo = 5 and 10 dB,for 4 carriersOFOM System

'"l ••• •••• ·•·• '-F"~"'''.'' .•••.•••.•...Single Camel Syslem

lO'r=~""~~__,__~~,--,~=-7-,AW,.:.G~N~Ch--,·r""~~c:Q~PS'--K,.__o~=_o~~_.,.__~_~_-'_C-=C_~_-'_~_~:: :: =- !:. : =- =- ! - =- - ! - :: :: ! - :: :: J :: :: :: J : : : :' : :: : ., :: : : :' =- - -

.:: .:: .:: [ ::: ::. :: ! ::. _ :: ! : :: : I : : ::: J ::: ::: : J : ::: : J ::: : : :::' : ::: : :' : : :::- - - -, - - - -, - - - -, - - - -, - --

___ L .L_._l.-------------:::!:::::::r::::r:::.:r:

..J j __ ~.J -' _----------,_ -,.4--,------- ----- ----

, , , , I , , , ,---------------------------------------- - .. - - - .. - - - .. - - - .., - - - ... - - - ... - - - .... - - - -I - - ­

~ - ,. - - - r - - - T - - - T - - - -, - - - , - - - , - - - , - - - -I - - ­

---1---_ ... _-_.1._-- >_

~ 10'"_ .L .L 1 J J .J -' I _

-- - -- - --- -- - - -- - _ .. - - - - - - -- - - -- ---- - - ,. - - .. ~ - - T - - - T - - - , - - - , - - - , - - - , - - - -, - - -- - ---- - - - -- - - - - -- - --- - - -- -- - -- -- -- -- ---_ 4 :: r:: : ::: ::: ! ::: ::: ::: ! ::: ::: ::: I : ::: ::: J ::: ::: ::: :' ::: : ::: :::' : ::: ::: :' ::: : ::: :::' : ::: :

- ... - - - ... - - - + - - - -+ - - - ... - - - ... - - - ... - - - ..... - - - -, - - -

I-BPSK\-a- QPSK

J-------=-=----=-=--------=-~~~~a 0 004 0 005 0.006 0.007 0.009 001Carrier Frequency Offsel (denaF)

105

~ :: :: - = : : : : : : :: = : : : -:. - - =- :: - _--=- - :: : =- ":! : : - _I __ _ _ t : : =- :l =- __ :J =- : : :J : : :: =' : : :: :1: =- :

.:: : : [ __ .:. I :: _ : I : : : 1 : : .:: J : : : J : : .:: J .:: : :: .::' .:: .:: .:: :' -: .:: .::---1----+---+----+--- ... --- ... --- ... --- -------

~ ~ ~ : = = = : = ~ ~ : ~ ~ ~ : = = = : = = ~ = = = = = = = = I-B- ~~~:~Od~B I·,,'---~----'---L---,-.L_,___-,,-L-___:_J._,_-----L_,___-,__L_:-:-__,__'c_:_--,-J

0.002 0.006 0.008 001 0.012Carner Frequency Ollsel (dellaF)

Figure 6-9 The effect ofa CFO on an OFDM

system at EblNo = 5dB,for QPSK and BPSK

Figure 6-10 The effect ofa CFO on a SC system at

EblNo = 5 and 10 dB

48

From Figures 6.7, 6.8, 6.9 and 6.10 we observe that OFDM is much more sensitive to frequency offset

than a single-carrier system. The higher sensitivity of OFDM as compared to single-carrier is caused

by the N times longer duration of an OFDM symbol and by intercarrier interference due to loss of

carrier orthogonality. We can also see that for low values of the CFO, the BER increases with Eb/No

as stated in Section 3.2.2.1. But the single-carrier system does not increase as much as the OFDM

system for increasing Eb/No, because here only noise interference plays a part, there is no inter carrier

interference. As to be expected from theory and shown in Figure 6.9, increasing the constellation size

increases the BER.

6.4.2 Carrier phase noise

A carrier phase noise (CPN) introduces a phase rotation, which can be modelled as a Wiener process,

as described in Section 5.5.1. In this case the variance of phase noise increases with time. The

simulation results, again using an AWGN-channel, can be found in Figures 6.11 to 6.14.

49

,"0

- 4 G.1mers, EbJNo = 10 dB-e- 4 Ca"iers, EbINo = 5 dB-'T- Single Gamel, EbINo .. 10 dB-b- Single Camer, EbINo = 5 dB

Single Carner and OFDM Sy&l&mAWGN CI1annel, QPS/(

===~===3===3===---.,---,---..,------------------

- - - -+- - - - .. - - - .. - - - "1 - - - "1 - - - .... - - - ... - - __ I _

- - - T - - - T - - - T - - - "'i - - - -, - - - -, ~ - - ~, - - -

- - - i" - - - 1 - - - I - - - I - - - -, - - - -, - - - -, - - - -, - - -

, , 1 , I , I ,--------------------- --------------===t ===1: ==='1 =:: := s :: :: :: s ===S ==:: 3 ====':: :: =: : : >: : : : :i : : : .:; : : : :l : : : :l : : : ::. : : : ::. : : : :,: : :

- - - -, - - -I I " I I I

:: :: = - :: :: :: = :: :: :: = ~ = = ~ ~ ~ ~ § ~ ~ ~ ~ ~ ~ § ~ ~ ~ ~ ~I ~ ~ ~_ : : [ : : : r : : : ! : : : I : : : ] : : : :J : : : :J : : : :J : : : :': : :

=== ~ === ~ === ~ ===2 === ~ === ~ ===:; =: : :; : : ==, ===1 I 1 I 1 I • , I---------------------------------------til I I I , , 1

.. ~--='o,:--,----='02=---:':----c:'c-----,o':-,,---=o':-,.----:'CO--:':---o='=,,----:Belo

..

..

..,~

...

,10

:::l:::J::::J:-_:::J:':'::J:--

:: :: = :: = = = ~ = = - - : :: :: ~ = = = =' :: = = =' = :: =

---'1-------T------ .... ---

:::r:::---1---

___ 1 1 .1_

- - ~ - - - - - ==:: i :: :: :: :J ::: :: :: :J ::: :: :: :J :: ::: ::: =- ::: : : :1: : :_ : : [ : : : I : : : I : : : 1 : : : ] : : : J : : : :' : : : :1 : : : :': : :

___ 1.. 1 -' -' _

------- ---------------

.. .:----::';-----:'0,:-'-----;:C;---o=",c--o=",-----,:':----:O':-.7----:'0,':-'----:'0,:-'__J

Belo

Single Carner and OFDM System

"'f'''T=--o"''=--OT_,,~o-Wi:NiC'i~''''''''-'oe~i-'QiPSKi,~EbINo~';'=O'iB,,:==--o,,,=':2~=='il:r::: ::::r:::J:::J:::1::: :::J::::J:::J::

---of---;---;--

Figure 6-11 The effect ofCPN on a SC and an OFD"'~

system at EblNo = 10 dB

Figure 6-12 The effect ofCPN on a SC and an OFDM

system at EblNo = 5 and 10 dB

OFDM Syslem, e CarriersEbiNo. 30 dB, Bet.1_ 0 0125

15r-----.------,-----r-----'---,----._----,--~

"

1 1 , , 1 , 1 I.------------------- -----------------, I I , 1 I

OFDM System

10.1r-_--,-_~---.__._--AWTG-N-Ch-."-".,'_Eb_"'o_._','B_---;:--_--,-_-===

= = = ~ = = = ~ = = = ~ ~ ==l = = = ~ = = = 3===~ ====: ===~~___ !.. !. ! 1 _ _ _' __' , , , _I I I I I I ,------------------- -- ---------------, ,

- - - r - - - T - - - T - - - T - - - - "1 - - - -, - - - -, - - - -, - •

1 I I , 1 , ,---------------------------- ----------I I I 1 I I 1

-, - - - -, - - - -, - - - -, - - -1 I " I I

--~------------------------------------

I I I , , I I I I

'. ,

10·30'---~-·--.iO,,--Oi,3--J---C0~,--~--COL7----,'0,--'_ __.i,--_Be~

.' .~L,-----,'---~.oc-,----"----"c",-----'----,"',---Re~1 HI1

Figure 6-13 The effect ofCPN on all OFDM system at

EblNo = 5 dB,for QPSK alld BPSK

Figure 6-14 The effect ofCPN on the received

constellation ofan OFDM system

From Figures 6.11, 6.12 and 6.13 we observe that OFDM is more sensitive to carrier phase noise than

the single-carrier system. The higher sensitivity of OFDM as compared to single-carrier is, just like

with the carrier frequency offset, caused by the N times longer duration of an OFDM symbol and by

intercarrier interference due to loss of carrier orthogonality. We can also see that the BER again

increases with EblNo as stated in 3.2.2.2. As with CFO, the BER increases with the constellation size.

The effect of carrier phase noise on the received constellation of an OFDM system is shown in Figure

6.14. The effect of the phase noise on the received constellation of an OFDM system is similar to that

of an OFDM signal corrupted by white noise.

50

6.5 Timing Requirement s

6.5.1 Symbol synchronisation errors

Starting to sample at the wrong moment, which resulted in Figure 6.15, simulates symbol

synchronisation errors (SSE).

Single Carrier and OFDM SystemAWGN Channel, QPSK, Eb/No ~ 10 dB

100

o-=_--=_c-=-_"",,_-=_--=_:r:-_"",,_-=_CC_C-=-_-=_--,:-=-=-_-=_--=_CC_::-::T_-=_--=_c-=-_"",,_-=_--=_:-C-"",,_-=_cc_=-=-_-=_-=_",_=-=-_-=_--=_cc_=-=-_T"":_CC_=-=-_-=_--=_cc_::r::-_-::_-=_cc_=-=-_-::_--,:-_=-=-_-::_--=_c-=-_"::1_-=_--=_c-=-_"""_-=_--=_:-:0

0.90,80,7

- - - r - - - - - -I - - - - - - r - - - - - -, - - - - - -- - -, - - - - - - ,... - - - - - -, - - - - . -

0.4 0.5 0.6Relative symbol synchronization error

, , , 1

- - - - ,- - - - - - - - - - - - - I" - - - - - -, - - - - - - - - - - - -, - - - - - -

1 , 1 1 , 1--------------------------------------------

0.3

_I: :: :: : : :: i: :: : : :: : :,:: : : : : :: [ : : : : : :, : :: : : :: : i: : :: :: :. : :, : : :. :. : :

'::1: ::: ::: ::: ::: ::: c : : ::: ::: ::: :::': : : : : : [ : : : : : :' : : : .:: : : c :: .=. .:: : ::: :' :: ::: ::: : ::: :- -I - - - - - - t- - - - - - -, - - - - - - .. - - - - - -, - - - - - - ... - - - - - -, - - - - - -- -, - - - - - - r - - - - - -, - - - - - - r - - - - - -, - - - - - - r - - - - - -, - - - - - -

- - - - -I - - - - - - ... - - - - -

- -, - - - - - - r - - - - - -

1 1 1 1 , , I--------------------------------- ----------------1 1 , 1 ,

- - - - - -, - - - - - - . - - - - - -~'- - -~-- -~.- - ~~~ - -~,- - -~-- -~.- : ~:: : :::==:::: : : : :

::: ::: ::: ::: ::: :::' ::: ::: ::: ::: ::: ::: c ::: ::: ::: ::: ::: :::'::: ::: ::: ::: ::: ::: c ::: ::: ::: ::: ::: :'::: ::: ::: ::: ::: ::: c ::: ::: ::: ::: ::: :::'::: ::: ::: ::: ::: :::

____, L ' L ' L ' _

---------------------------------------------.---______I ~ _ L I L. I '- • _

- ::: ::: ::: ::: ::: :'::: ::: ::: ::: ::: ::: i:. ::: ::: ::: ::: ::: :' ::: ::: ::: ::: ::: ::: L ::: ::: ::: ::: ::: :::' ::: ::: ::: ::: ::: ::: c ::: ::: ::: ::: ::: :' ::: ::: ::: ::: ::: :::

0.20,1

- Single Carrier--B- 8 Carriers--6- 32 Carriers--+- 128 Carriers

- - - - - -, - - - - -- - - - - -, - - - - -

::::::::.::,::------

------------

, ,

- - - - - _: - - - - ~:::: - ::: :::::~ ::::- _: - - - - :- ~ ::::::::::::- ~ :- :::::: ::::~.: : -=- ~ - :,: : : : - _ ~ : : : : : :, : :: -=- -=- : : c : : : : : :,: : : : : : <: : : : : : :, : : : : : : c : : : : :: :,:: =- : : : :

••••••~ ••••.• ' .•••••••••• ;•••..••••••.• ~ ••••. " •.. ;..... , .••••o

·s10

cr:well

: : : : : :' : : L • ' c : : : : : :1: : : : : : [ : : : : : :' : : : : : : c : : : : : :' : : : : : :

______I __ • L ' _ _ _ _ _ _ _ ' !... ' '_ ~ ' _

::: :. ::: ::: ::: :' ::: : : : : : [ : : : : : :,: : : : - -::::::,:::::: [ : : : : : :' : : : : : : i: : : : : : :': : : : : :

Figure 6-15 The effect ofSSE on a SC and an OFDM system

Figure 6.15 shows that there is no difference in sensitivity to symbol synchronisation between OFDM

and a single-carrier system. Next the influence of the length of the cyclic prefix on the sensitivity to

symbol synchronisation for EblNo = 10 dB and EblNo = 30 dB is shown in Figures 6.16 and 6.17.

_ J ..J , I _

---------------------: J :: :: :: :: :J : : :: _ :' :: :: :: : :' : : : ::

: J :: :: : :: :' :: :: :: :: :' :: : :: : ::':: :: :: ::- - .... - - - - .... - - - - -, - - - - -, - - - .

,====!:====~====~=::::::::r:::::r::::::.1::::::::::r:::::::r:::::r:

10~ ::::::::::::::::: ~ :: :: :: :: J :::::: -: :. :: :: :: = :: :. :: : ::' :: :: :: :. ::' : :: : ~:: :: :: :: r: :: :: :: :: r: :: :: : : : : :: J :: : :: :: ::J :: : :: =- :' :: :: :: :. :.': : ':' :: : :: : [ :: : :: : I : :: : :: :r :: :: ::: :: J ::: : : : :' : :: : : :' : ::: :. : :':: : :: ::

:::! :: : : : :J : : : : :' :: :: : : :': : : :

:r ::: :: : :: J : : :: :: J :: ::: : :: :' : :: : : :1:: :: ::: :::

___ .1 ..J ... , , _

----------------------------

_ _ _ _ _J ..J I ' _

-------------------------

: :: : I : : : : :J :: :: .: : =' : : : :: :' :. :: : : :':: : : :___ J: .:: :: :: : J : : : : :' :: : ::: ::: ::' : : : : :1: :: : :::

: : :: :: r: :: :: : :: t :::::: I :: : :: = ::J ==== ::J = : : = =' ==== =, ====:: :: :: :: [ :: ::: :::::: :::.:: I : ::: ::: :: J : : :: :: ] ::: : ::: ::: :' ::: : : : :': ::: : :::

OFOM SystemAWGN Chaf'lf'lel. QPSK, .32 Carner" EblNo '" 10 dB

"

,0'

- - - - r - - - - T - - - - T - - - - ., - - - - ., - - - - -, - - - - -, - - - -_ _ _ _ ... ... .1 -l ... -I \ _

- - - - r - - - - T - - - - - - - - ., - - - - ., - - - - -, - - - • -, - - - -____ l- J. • .1 .. ... ... , _

10..0'-----------,0~,------"0,:-------,0L.,3------,J-0 ..-----,-------,OL,S---0:L,.------,JO,"",----"0,8Relatllle 'yrrbol synchrol"lIzation error

1O..0L-------,0"',,------"0,:--------,0'-=-,---0:'-:,-----,-----:'O,""S----=o'-=-,.---0=",,:-----.J08Relallve syrrbol synchronization error

Figure 6-16 Resistance of OFDM with varying

cyclic prefIX to SSE at Eb/No = 10dB

Figure 6-17 Resistance ofOFDM with varying

cyclic prefIX to SSE at Eb/No = 30 dB

51

Figures 6.16 and 6.17 show that an increase in de length of the cyclic prefix decreases the sensitivity

to a symbol synchronisation error, because the symbol timing offset may vary over an interval equal to

the guard time without causing leI or IF!. The effect of a higher EbfNo is the same as explained in

Section 6.2.1, the noise plays less dominant role compared with the timing error.

6.5.2 Sampling-frequency syn chronisation errors

The effect of sampling phase jitter (SPJ) is simulated and the results are depicted Figures 6.18 and

6.19.

Single Camel and OFDM S)"slemAWGN Channel, QPSK, EblNo '" 30 de

- - - -; - - - -, - - - -, - - - -, - - - -, - - -

I I I I , I I- -----------------------------I I I I I I I

10 '------'---------:<'i:--'--------c-'----------,-'----------,-L-------,-=------,-'------L,--------,J002 003 0.04 0.05 0.06 0.07 008 009

Relative variance or s8fllJhng rrequency ;tler

Figuur 6-18 The effectofa SPJ on a Single

Carrier and an OFDM Sytem at EblNo = 30 dB

OFDM S't'!l.lem

I0' c-=-,.--"--,.--r-"--"--:-:-l~~AW,..,GN,,Ch_""---,M---," ',..,C.,,""---,"'-=""---,No-,,"30---,'---,"-'--:-""T'::"-=-::--::-::1==: : : : I- : : : : l.- : : : : .l. : : : : .J : : : : ..J : : : : :, : : =- =- -e- BPS:: :: :: :: L : :: :: :: I :: :: :: :: ::i :: :: :: :: J :: :: :: :: j :: :: :: :: ::' :: :: :::: - OP~

- - - - .. - - - - ... - - - - ... - - - - .... - - - - ... - - - - -I __ • _

I I , I P

- - I - - - - I - - - - ... - - - - "'i - - - - -, - - - - - - - -, - - -

I I I I I,--------------"----- ---------------- - - - t- - - - - .. - - - - .... - - - - -l - - - -1 - - - - -I - - - - -I - - --------------------- ---------------------------------- --------------- ---, , ,-------------------------------- -----

I I I ,-----------------------+" ,

10.J =-:::!::: ~ :. ! : : : : ! :: :: : _ J : :. :: : :J : : : : :' : : : : :': : :

:: : : : I: :: - : : I : : : :: I - :: : : J : : : : :' : :: :: : ::' :: : : : :': :: ::- - - .,. - - - - - - - - , - - - .... - - - - -, - - - + -, - - -

- - - -, - - - T -. - -, - - - - ""i - - - - -, - - - - -, - - - - -, - - •-- ----- ---------------------------

I I , I J

- - - - - T - - - - 1 - - - - l - - - - -, - - - - -, - - - - -, - - -

, t I , I----------.-------------------------_., I I I

10: O"=-,----:c"O,Oc:-3 -~"------:-'O0C:-5 -----:-'O,"'CC---:-'OOc:-,-----:-'0"'c:----:-'::-­Relative variance or tl1e 11lfllJ',ng frequency JItter

Figuur 6-19 The effect ofSPJfor two constellatio

sizes at EblNo = 30 dB and 8 carriers

In Figure 6.18 it can be seen that the BER due to a sampling phase jitter decreases with the number of

carriers. With increasing numbers of carriers the symbol duration increases over which the phase shift

(caused by the jitter) is equally distributed. Figure 6.19 shows that the sensitivity to SPJ increases with

the constellation size. This is because a smaller constellation tolerates a larger phase shift than a larger

constellation size.

52

Chapter 7

7 Conclusions and Recommendations

7.1 Conclusions

An OFDM communication system is modelled and implemented in Matlab.

The perfonnance of the OFDM system in tenns of the of bit error rate versus signal-to-noise ratio was

evaluated over an AWGN and a multipath channel. In a fixed bandwidth the effects of increasing the

number of carriers was investigated. It was shown that the perfonnance over a multipath channel

improves with increasing the number of carriers. However, the improvement of perfonnance for the

large number of carriers is not large. Application of a cyclic prefix in the OFDM transmission and its

effects on the perfonnance ofthe system was investigated. It was shown that this optimal value could

be reached with a cyclic prefix of a length equal to the channel delay spread.

Besides the channel characteristics, the transmitter and receiver characteristics playa role in the

perfonnance of the OFDM system. Four of these characteristics are simulated: peak power clipping,

oscillator-related errors, symbol synchronisation and sampling-frequency errors.

The peak power ratio limits the efficiency of the RF power. However, it was shown that it is possible

to reduce the peak power ratio of OFDM to quite acceptable levels with little impact on the bit error

ratio.

By viewing the simulation results concerning the oscillator-related errors (frequency offset and carrier

phase noise) it can be concluded that OFDM is orders of magnitude more sensitive to frequency offset

and phase noise than single carrier (SC) modulation. Sensitivity increases with the number of carriers

and with the constellation size. The higher sensitivity of OFDM as compared to SC modulation is

caused by the N times longer duration of an OFDM symbol and by the intercarrier interference due to

loss of the carrier orthogonality. Lowering the number of subcarriers, which will increase the

subcarrier spacing, can reduce the frequency synchronisation error. This will, however, increase the

demands on the time synchronisation, since the symbol length gets shorter, i.e. a larger relative timing

error will occur, thus, the synchronisation in time and frequency are closely related to each other.

53

With respect to timing offsets, OFDM is relatively more robust; in fact, the symbol timing offset may

vary over an interval equal to the guard time without causing ICI or IF!. The BER degradation due to a

sampling frequency offset depends on the square of the carrier index and the relative frequency offset.

With increasing number of carriers the OFDM system becomes more robust to a mismatch in the

sampling frequency.

The (negative) effects on an OFDM system were implemented, simulated and compared to a single­

carrier system. But to choose between a single-carrier system and OFDM for communication over a

wireless 60 GHz channel, the error correcting equalisation techniques, brief described in Chapter 4,

must be implemented and tested. Even without the limitations of the oscillators and the timing errors,

the 60 GHz channel needs some form of equalisation. Simple OFDM can not achieve acceptable bit

error rates as can be seen in Appendix B.

7.2 Recommendations

The Matlab implementation of the OFDM system is programmed in a structured way, so that

extensions like equalisers and channel coding techniques can be implemented easily.

After that, depending on the simplicity (and with that the costs) and effectiveness of the equalisation

techniques to deal with the effects as described in this report, a definite modulation scheme can be

chosen.

54

Chapter 8

8 References

[1] Qurechi, S.V.H.

ADAPTIVE EQUALISATION.

PROCEEDINGS OF THE IEEE,

Vol. 73 (1985), No.9, p.1349-1487.

[2] Proakis, J.G.

DIGITAL COMMUNICATIONS.

McGraw-Hill, third edition, 1995.

[3] Bingham, l.A.C.

MULTICARRIER MODULATION FOR DATA TRANSMISSION: AN IDEA WHOSE TIME HAS

COME.

In: IEEE Communications Magazine,

May 1990, p. 5-14.

[4] Kasturia, S., Aslanis, J.T. and Cioffi, J.M.

VECTOR CODING FOR PARTIAL RESPONSE CHANNELS.

IEEE TRANSACTIONS ON INFORMATION THEORY,

Vol. 36, No.4, July 1990, p. 741-762.

[5] Sistanizadeh, K.

BLOCK CODING CAPACITY OF HIGH BIT RATE DIGITAL SUBSCRIBER LINES BY THE

STRUCTURED CHANNEL SIGNALING TECHNIQUE.

IEEE TRANSACTIONS ON COMMUNICATIONS,

Vol. 39, No.6, June 1991, p. 866-876.

[6] Cvetkovic, Z.

MODULATING WAVEFORMS FOR OFDM.

In: PROCEEDINGS 1999 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH

AND SIGNAL PROCESSING,

Vol. 5, 1999, p. 2463 -2466.

55

[7J Rappaport, T.S.

WIRELESS COMMUNICATIONS.

Prentice Hall, 1996.

[8J Sari, H., Karam, G. and Jeanclaude, I.

TRANSMISSION TECHNIQUES FOR DIGITAL TERRESTRIAL TV BROADCASTING.

In: IEEE Communications Magazine,

February 1995, p. 100-109.

[9] Pollet, T and Moeneclaey, M.

SYNCHRONIZABILITY OF OFDM SIGNALS.

In: PROCEEDINGS GLOBECOM'95,

Singapore, Nov. 1995, vol. 3, p. 2054-2058.

[10J Pollet, T., Blade!, M. van and Moeneclaey, M.

BER SENSITIVITY OF OFDM SYSTEMS TO CARRIER FREQUENCY OFFSET AND WIENER

PHASE NOISE.

IEEE TRANSACTIONS ON COMMUNICATIONS,

Vol. 43,1995, No. 2/3/4, p. 191-193.

[IIJ Pollet, T., Moeneclaey, M.

THE EFFECT OF SYMBOL SYNCHRONISATION ON THE BER PERFORMANCE OF OFDM

SYSTEMS.

In: PROCEEDINGS OF THE FOURTH INTERNATIONAL WORKSHOP ON DIGITAL SIGNAL

PROCESSING TECHNIQUES APPLIED TO SPACE COMMUNICATION,

London, September 1994, p. 5.15-5.18.

[12J Pollet, T., Spruyt, P., Moeneclaey, M.

THE BER PERFORMANCE OF OFDM USING NON-SYNCHRONIZED SAMPLING.

In: PROCEEDINGS OF GLOBECOM '94,

Vol. 1, p. 253-257.

56

[13] Stott, lH.

EXPLAINING SOME OF THE MAGIC OF COFDM.

In: PROCEEDINGS OF 20TH INTERNATIONAL TELEVISION SYMPOSIUM 1997,

Montreux, June 13-17.

[14] Schmidt, H., Kammeyer, K.D.

REDUCING THE PEAK TO AVERAGE RATIO OF MULTICARRIER SIGNALS BY ADAPTIVE

SUBCARRIER SELECTION.

In: PROCEEDINGS OF ICUPC '98,

Vol 2, p. 933-937

[15] Muller, S.H., Huber, lB.

A COMPARISON OF PEAK POWER REDUCTION SCHEMES FOR OFDM.

In: PROCEEDINGS OF GLOBECOM '97,

Vol. 1, p. 1-5.

[16] Classen, F., Meyr, H.

FREQUENCY SYNCHRONISATION ALGORITHMS FOR OFDM SYSTEM SUITABLE FOR

COMMUNICATION OVER FREQUENCY-SELECTIVE FADING CHANNELS.

In: PROCEEDINGS OF IEEE VEHICULAR TECHNOLOGY CONFERENCE,

Stockholm, June 1994, vol. 3, p.1655-1659.

[17] Daffara, F., Adami, O.

A NEW FREQUENCY DETECTOR FOR ORTHOGONAL MULTICARRIER TRANSMISSION

TECHNIQUES.

In: PROCEEDINGS OF IEEE VEHICULAR TECHNOLOGY CONFERENCE,

Chicago, July 1995, vol. 2, p. 804-809.

[18] Moose, P.

A TECHNIQUE FOR ORTHOGONAL FREQUENCY-DIVISION MULTIPLEXING FREQUENCY

OFFSET CORRECTION.

IEEE TRANSACTIONS ON COMMUNICATIONS,

Vol. 42, number 10, p. 2908-2914.

57

[19] Warner, W.D., Leung, C.

OFDMIFM FRAME SYNCHRONISATION FOR MOBILE DATA COMMUNICATION.

IEEE Transactions on Vehicular Technology,

Vol. 42, number 3, p.302-313.

[20] Hiller, H., Zeisberg, S., Hosel, H., Kull, B.

RESEARCH RESULTS OF WIRELESS INDOOR COMMUNICATIONS SYSTEMS

COURSE 1: COURSES FOCUSING ON THE RESEARCH RESULTS OF WIRELESS INDOOR

COMMUNICATION SYSTEMS,

Chapter 3, p. 47

[21] Nee, R. van, Prasad, R.

OFDM FOR WIRELESS MULTIMEDIA COMMUNICATIONS,

Artech House Publishers, 2000.

58

Appendix A Constellations of modulation schemes

BPSK Constellation

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

-0.8

)-1 -0.5 0 0.5

QPSKJ4-QAM ConstellationX X

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

-0.8

-1 )(-1 -0.5 0 0.5 1

16-QAM Constellation3 X X X X

2

X X X X

0

-1 X X X X

-2 [

)~ )( )( )'(-3-3 -2 -1 0 1 2 3

59

Appendix B Models of the 60 GHz indoor radio channel

Numerical values (filter coefficients) of the generic impulse response samples representing a typical

line of sight (LOS) 62 GHz indoor channel with 200 MHz RF bandwidth and omnidirectional

antennas are shown in B-1.

The numerical values (filter coefficients) of the generic impulse response samples representing a

typical non line of sight (NLOS) 62 GHz indoor channel with 200 MHz RF bandwidth and

omnidirectional antennas are shown in B-2.[20]

The destructive effect on the performance of simple OFDM of these channels is shown on the next

page.

Table B-1 Model of60Ghz indoor LOS Channel

Number of Relative Real part Imag. part

filter delay time linear linear

coefficient in ns

0 0 0.45023402 0.86621991

1 5 0 0

2 10 0 0

3 15 -0.00118146 0.03175096

4 20 -0.11530161 -0.13648934

5 25 0 0

6 30 0 0

7 35 -0.0297353 -0.01119513

8 40 -0.01073347 0.02990505

9 45 0.10021063 0.00728164

10 50 0 0

11 55 -0.00792121 -0.01556035

12 60 0 0

13 65 0 0

14 70 0.02800481 -0.02856065

Table B-2 Model of60GHz indoor NLOS Channel

Number of Relative Real part Imag. part

filter delay time linear linear

coefficient in ns

0 0 0.194008 0.37325852

1 5 0 0

2 10 0 0

3 15 -0.00494651 0.13293465

4 20 -0.48274379 -0.57145242

5 25 0 0

6 30 0 0

7 35 -0.12449552 -0.04687168

8 40 -0.04493882 0.12520619

9 45 0.41956101 0.03048672

10 50 0 0

11 55 -0.03316445 -0.06514792

12 60 0 0

13 65 0 0

14 70 0.1172503 -0.11957749

60

OFDMSystem

10° .-----_-_T_- -_- -_---.-------,--6-0-G-H-Z-in-,d-O-O-'-L-O-S-c-h-a-n,ne-I----r-----~----,_-_,- - - - - - -I ~ _ ... ... I ... 1 , oj. _

- - -,- - - - - - - ., - - - - - - - r - - - - - - -, - - - - - - - T - - - - - - - ,- - - - - - - -, - - - - - - - T - - -

- - - - -,- - - - - - - I - - - - - - - - - - -

- r - - - - - - -, - - - - - - - T - - - - - - - ,- - - - - - - -, - - - - - - - T - - -

__ ' .J L ' .1 , , 1. _

, ,_______ I _ _ _ _ _ _.J L I .1 , _

-110

I I I I---------------------------------------------- _ -I ... _ _ _ _ _ _ h- I ... - 1 - - , oj. _

- - - : : :J : ::: ::: ::: ::: ::: _ - ::: ::: ::: ::: ::: ::: :::'::: ::: ::: ::: ::: ::: ::: 1 ::: ::: ::: ::: ::: ::: ::: ': ::: ::: ::: ::: ::: ::: :::1::: ::: ::: ::: ::: ::: ::: I ::: ::: :::- - - - - - -I ... ... j , I - __ - - - - .. - __

- - - - - ., - - - - - - - r-- - - - - - -I - • - - - - - - - - - - - - 1- - - - - - - -, - - - - - - - .. - - -

- - - - - - -I - - _ ... I- - - - __ -I - - - - - - - 'i' - - - - - - - 1- - - - - - - -I - - - - - - - .. - - -

I , 1 1 1 , 1 1------------------------ -----------------------------------, ,-------------

0:: -,w 10CD

,-:: : : : : : : I: : : : : : : J : : : : : : : c : : : : : : :1: : : : : - : :r : : : : : : : c : : : : : : :1: : : : : : - T - -- - - - - - -1- - - - - - - ., - - - - - - - r - - - - - - -\ - - - - - - - T - - - - - - - 1- - - - - - - -I - - - - - - - T - - ------------------------------------- ---------------------------_______ ' .J L I _ _ _ _ _ _ _ _ _ _ _ 1 ~ I J.. _

_ I .J .... I .J. 1_ _ _ _ I .J. _

_ _ _ _ _ _ _ 1 .J L I _

- - - -, - - - - - - - -I - - - - - - - 1- - - - - - - - - - - - - - "'j - - - - - - 1- - - - - - - -I - - - - - - - I - - -, , ,

- --- -- - -- --- -- - - -- - -----, , ,

-310 - - - -, - - - - - - - " - - - - - - - c - - - - - - -, - - - - - - - • - - - - - - - ,- - - - - - - - - - - - - - •-------------------------------------------------- - ----------______ I .J • "- I ... 1 • _I I _

- - - -, - - - - - - - "I - - - - - - - t - - - - - - -I - - - - - - - "'j - - - - - - - ,- - - - - - - -I - - - - - - 'I - - ------------------------------------------ --------

~ ~ g:~~::~~: ~~~~ ~ = = = = = = = := = = = = = = =: = = == = ==~ ======= := = = ==== =: = = =- === ~ =- -- - - - 1 - - - - - -., - - - - - - - r - - - - - - -I - - - - - - - T - - - - - - - 1- - - - - - - -I - - - - - - - T - - -

2824201612Eb/No (dB)

84o10-4"------'-------'--------'--------'---------'--------'------'--------"---

-4

OFDMSystem

10° .- -,- ---, ~-6-0-G-H-z-in-dTo-o-'-N-L-O-S-c-ha-nrn_e_I .- ,--- -.__-,I I I I I I I

------------------ ----------- --------- ---------

-, - - - - • - - -I - - • - - - - 1- - •• - - - - -1- - - - - - - "I: I - 8 Carriers, BPSK I- - - - - - ,- - I -e- 8 Carners, QPSK - - -

____ .J \ ' _ _ _ _ _ _1. '_ _ _ _ ' !. _

_ _ _ _ _ _ I _ _ _ J. '_

~:-:~'C,~__:__O_~~_~-=+__"__=__~~"'~..~ ~ , , _

0::wCD - - - - - - ., - - - - - - - r - - - - - - -I - - - - - - - "I - - - - - - - I~ - - - - - - -, - - - - -

-1- - - - - - - -I - - - - - - - ,- - - - - - - -I - - - - - - - "'j - - - - - - - 1- - - - - - - -I - - - - - - - 'I - - -

",L~ ~-------"------------l~-4 a 4 8 12 16 20 24 28

Eb/No (dB)

61

Appendix C Structure of Simulate and Matlab code

bit2symb~

simulate

~Gioballnit

~I I

TxRx BPSKDesignTxRxFilter

+I

TxRx DBPSK

IDesignChannelFilter ..

J I~

TxRx_QPSK

genRandSeq

I

TxRx 16QAM

I•transmitter t--- ... //.4,.

.......

+ 1r

genAWGN ~ channel ~ TxRx OFDM

~

~n

dispSignal +-- ....receIver-----.

62

function err=simulate(signaIMode,M,snr,clipping,intercept,errs,SyncError,SampError,CarrierOffset,Beta)

% function crrsimula[<:,(signal Modc,M,sn r,c Ii ppi ng,intcrccpt,crrs,SyneError.SampError,CarrierOffsct ,Beta)(~'O

% Simulation ofa digital transmission.I~/O

Resulting error rate.

% signuJMode(!_/()

{~/~

0''(I

0,,"

Signaling mode. Possible values:

BPSK OFDM-BPSKDBPSK ODFl'v1-DBPSKQPSK OFJ)l'.·1-QPSK16QMv1 OfDM-16QAM

Number or symbols to be transmitted (number of frames = \/I/CARRIERS).Bit SN R (ldB] units) in the channel.Amount of clippingldB) to apply to thc signal.amount of clipping (dB}20Iog lu(Peak of original signaliPeak of signal after cl ipping).Allows to intercept the different signals and to plot their \vaVefOI1l1:

%\:1Ole) snr% clipping~!J;l

%, intercept0''0

(~-~ intereept=O --> no graphic displayl'dintercept"·' I --.> transmitted analog signalintercept 2 --> eye diagramintereept=4 --> receivt'd analog signalinterceptS --> rl'ceived signal constellation

(bitl, J)

(bit::'. 1)(biL~= I)

(bit41)

';-n CITS

'% SyncCrror% SampError0''0

% CarrllTOfLei

n''0

close allclear global

Indicates which error rate is to be returned, as follows:

errs'''·O --> bit error"errs= I --> symbol errors

Sync nror, a fraction of the sample ratcSampling frequency phase jitter variance, a fraction of the sample rate

CUTier frequency offse1

The illll'··,ided 3d[3 linewidtlJ of the Lorent/ian power density 'pcctrumoft11c free-running oscillator.

if (intercept>15) I (intereept<O)errorCParamcter intercept out of range: "intercept":);return

end

% lnitiali/ation global vuriablesGloballnit;global CARRIERS ChRate BPS;

0,;, Lktermination 01' signaling modep=find(signalMode=='-');if -isempty(p)

mode=signaIMode(p+ I :length(signaIMode));clse

mode=signaIMode;CARRIERS=1;

end

63

M=M*CARRIERS;

if stremp(mode,'BPSK')BPS=l;

elseif stremp(mode,'DBPSK')BPS=l;M=M-l;

elseif stremp(mode,'QPSK')BPS=2;

elseif stremp(mode,' 16QAM')BPS=4;

0,0 Total number of symbols transmitted

% Number of bits per BPSK symbol.

% Number of bits per QPSK symbol.

% Number orbits pcr 16QAM symbol.

clse error('Jnvalid argument: "signaIModc".');return

end

% Design Tx, R'( and channel filters

DesignTxRxfilter(BPS,M);DesignChannelFilter;

if (SyneError>ChRate) I (SyneError<O)errorCParameter SyneError exeeedes range: "SyncError".');

end

% Calculation of number' of bits 10 be transmitted

B=M*BPS;snr=snr+ IO*Jog IO(BPS);

Berrors=O;Serrors=O;

'''" (;enerate data to be transmitted

x = genRandSeq(B);

()'O Put data into transmitter

% Total number of bits,% Convert bit SNR to symbol SNR,

%, Bit error eoullt.% Symbol error count.

y=transmitter(x,signaIMode);

% Put data from tranSnlJ1tc'r into channel

y=eh annel(y,sn r, in tereept,e lipping);

'~,;, Put transmitted data illto receiver

y=reeeiver(y,signalMode,intereept,SyneError,SampError,CarrierOffset,Beta);

% Calculate number of bit errors and symbol errors

Berrors = Berrors+nnz(x-y);symbx = bit2symb(x, BPS);symby = bit2symb(y, BPS);Serrors=Serrors+nnz(symbx-symby);

'l,() Calculate bit error rate and symboll'rror rate

ber=Berrors/(B);

64

ser=Serrors/(B/BPS);

if errs==Oerr=ber;

eIsei f errs== 1err=ser;

end

clear global;

function symbol = bit2symb(datalN, BPS)

1)'0 function symbol = bit2symbldataIN, BPS)0''0

% Conv<?rts binary d'-lta into symbols'% symbol symbol output data

% datalN% BPS

binary input datanumber of bib per symbol

ifBPS==2datalN = reshape (datalN, 2, length(datalN)/2);datalN (2,:) = datalN(2,:) * 2;datalN = sum(dataIN);

elseif BPS ==4datalN = reshape (dataIN, 4, length(dataIN)/4);dataIN (2,:) = datalN(2,:) * 2;dataIN (3,:) = dataIN(3,:) * 4;dataIN (4,:) = dataIN(4,:) * 8;dataIN = sum(dataIN);

end

symbol = datalN;

function GlobalJnitO;

I>;, lniti:lli/ation l)f simulation paramders.

global CARRIERS SIM_TYPE;global MxChLength DataRate ChSplRate ;

CARRIERS=8 ;MxChLength=O;DataRate = 200e6;ChSplRate = 1600e6;

function out=genRandSeq(number)

out=randint( 1,number,2);function DesignTxRxFilter(BPS,M)

% 1 - Only add white noise, np channel, no Tx/Rx filter% :2 - Add whitc noise and simulate channel, no T,,/Rx filter'~.;, .3 - Add white noisc, simulate channel and usc T,,!Rx filter

% Number ofOFDM carriers.~.() Compensated channellcngth in symbols (cyclic prefi,,)% Data frequencyI~·O Channel Sampl ing Rate

global DataRate ChSplRate MxChLength;global ChRate SIM_TYPE CARRIERS;

if SIM TYPE == 3

65

ORate = OataRate * (I + MxChLength/CARRIERS)/BPS;SplRate = round (ChSplRate / ORate)

[numer,denom]= rcosfir(0.5, [-3 3], SplRate, I,'sqrt');%[numer, Genom] rcosiir (0.5, 3, SplRate. 1, (JJ) I,'sqn');

denom = I;Filtdelay = (length(numer)-I )/SplRate;

elsenumer = I;denom = I;SplRate = I;Filtdelay = 0;

endChRate = SplRate;

% if no tx/rx. filter is simulated

save 'C:\matlab files ofdm\TxRxFilter' numer denom SplRate Filtdelay;

function OesignChannelFilter 0

global ChRate SIM_TYPE;

if SlM TYPE ~= 1ifSJM TYPE == 3

numer = [I 0.50.4 0.30.1]; %Channel with nlultipathChdelay = 0;nullen = zeros(l ,ChRate-1 );dummy = numer( 1);for counter = 2:length(numer)

dummy = [dummy nullen numer(counter)] ;endnumer = dummy;denom = I;

else(',;, Usc l!lcorctical impulse rl'sponse withom upsamplillg (SIM-TYPE 2)numer = [1 0.50.4 0.30.1]; %Channel with nlultipathdenom = 1;

Chdelay = 0;end

else% Don't usc an impulse response tSJrv'_TYPE 1)

numer = I;denom = I;Chdelay = 0;

end"",To plot impulsl' rcsponsl':%llunll'rJllus = IO*log I0 (ahs( Ilumcr. "nul11cn.f3bs(numcr"collj(numer'»);%plot (nutlll'r_plus,'.');%numerplus

save 'C:\matlab files ofdm\ChanneIFilter' numer denom ChRate Chdelay;

function dataOUT=transmitter(dataIN ,mode)

66

% function dataOUT"transrnittend,HalN,mode):

% Digital transminel' emulator.(~,;, Filler data should be located in the file 'marlab n1cs ofdm\TxRxFiltcr.mat'.

% dataOUT0,d,'% datafN% mode

".'0

%, Initialize global variabks.

!\tlodulated output signal.

fnput binary data.Transmitter operation mode. Possible values:

BPSK . OFDM-BPSKDBPSK ,OFDM-DBPSKQPSK • OFD\:l-QPSK16QAlvl .OFDM-I 6QAM

global SIM_TYPE MxChLength; '!'{, hom Globallnitglobal SRCnumer SRCdenom Totalfilterdelay;global ChRate;

% Load TX.'Rx filter. norl11ali/C1tioll and Totalfilterdclay calculation

iflength(SRCnumer) == 0

load 'c:\matlab files ofdm\TxRxFilter';

ChRate=SpIRate;EqNoiseBW=numer*numer';SRCnumer=numerlsqrt(EqNoiseBW);

SRCdenom=denom;TotalfiIterdeIay=2 *1" iltdel ay;

end

% Implement transmitters.

p=find(mode=='-');if -isempty(p)

mode=mode(p+ I: length(mode));end

if strcmp(mode,'BPSK')data=TxRx_BPSK(datalN ,'tx ');

elseif strcmp(mode,'DBPSK');data=TxRx_DBPSK(dataIN ,'tx');

eiseif strcmp(mode,'QPSK')data=TxRx_QPSK(dataIN,'tx');

elseif strcmp(mode,' 16Q/\I\:I')data=TxRx_1 6QAM(dataIN,'tx');

else errorClnvalid argument: "mode".');end

{!'o Implement OFD\·1.

'\'u NonnaliN SRC filter.

",;, Ac,'ounts for the both Tx and Rx filter.

67

if -isempty(p)data=TxRx_OFDM(data,'tx');

end

if SIM TYPE == 3% Make data compatible with channel rateN=length(data);

dataOUT=zeros(l,ChRate*N);dataOUT( 1:ChRate: length(dataOUT))=data;

'% Power normalization for upsamplingdataOUT = dataOUT*sqrt(ChRate);

'% Add zeros to compensate tor filter delaysdataOUT = [dataOUT zeros(l, ChRate*Totalfilterdelay)];

"", Power normal i/atiol1 for the adding of the lerosdataOUT = dataOUT * sqrt((length(dataOUT)+ChRate*Totalfilterdelay)/length(dataOUT));

elsedataOUT = data;

end

68

function dataOUT=channeI(dataIN,snr,intercept,cIipping)

% function dataOUT=channl'l(dataJ1\,snr,intcrcepl,clJpping)

% Simulation ofa veetor channel with AWGN.I),~ Filler dala should be located in the file 'matlab files ofdm\ChannclFilter.mat'.

%dataOUT

%, dataIN°'0 snr%inlcrcept~/O

Reccived data stream.

Transmilted data stream.Symbol signal to noise ratio [siNo at the receiver ([dB] units).Allows to intercept the different signals and to plot their waveform:

inlwcept=O --> no graphic displayedinterct'pt= I --> transmilled analog signalintercept<! --> eye diagramintercept=4 --> received analog signalintercept"8 --> received signal constellation

(bitl=l)(bill I )(biI3= l)(bit41 )

%clipplng0''0

~/o

.:\mount of cl ipping(dB) to apply to the signal.amount of c\ ipping (d B)=2010g lC,( Peak of original signa\!Peak of signal after clipping).

global SRCnumer SRCdenom ChRate;global SIM_TYPE Totalfilterdelay;

if SIM TYPE -= 1load 'c:\matlab files ofdm\ChanneIFilter';

%Calculate equivaknt noise handwith.EqNoiseBW=numer*numer';

,~,;,power norrn::dintionCHnumer=numer/sqrt(EqNoiseBW);CHdenom=l;

% Pllt data through tml1smit filter.signal=filter(SRCnumer,SRCdenom,dataIN);

% Plot transmitted analog signal.if rem(fix(intercept),2)

dispSignal(signal,ChRate,'tx')end

% Remove Ix fiirer delay.if Totalfilterdelay

signal( I :ChRate*((Total filterdelay-4)/4))=[];end

if SIM TYPE==3% Apply peak power clippingsignaIRE=real(signal);maxampRE= I01\(-clipping/20)* max(signaIRE);signaIRE(find(signaIRE>maxampRE))=maxampRE;signalRE(fi nd(signal RE<-maxampRE))=-maxampRE;signaIIM=imag(signal);maxamplM= 101\(-clipping/20)*max(signaIIM);signaIIM(find(signaIIM>maxampIM))=maxampIM;signaIIM(find(signalIM<-maxampIM))=-maxampIM;signal=signaIRE+i*signalIM;

end

69

'~'o Put data through channel filter.signal=filter(CHnumer,CHdenom,signal);

% for power Iwrmalization of r('ceivc filter signalprefi Iter=(signal*signal')/length(signal);

0,(, Plit data through receive filter.signal=filter(SRCnumer,SRCdenom,signal);

%power normalizationpostfi Iter=(signal*signal ')/length(signal);signal=signallsqrt(postfilter/prefilter);

else

signal = dataIN;end

% Nonnaliz.iltion of power.snr= I O"(snr/lO);noisePW= IIsm;

% Converting [d8]s to Iin('ar scale.% Data and channel are nOj"ll1ali/ed.

% Generate c()mplex additive whit(' Gaussian noiscnoise=genAWGN(length(signal),noisePW);

ifSIM_TYPE == 3% Filtl'r th(' noisc.

noise=fiIter(SRCnumer,SRCdenom,noise);end

"'(' Add noise to signui.dataOUT=signal+noise;

'% Plot r('ceived analog signal.if rem(fix(intercept/4),2)

d ispSignal(dataO UT,ChRate,'rx ')end

0,;, Plot Ey'C diagwl11.if rem(fix(intercept/2),2)

d ispS ignal(dataOUT,ChRate,'eye')end

function noise=genAWGN(N,power)

% function noisegcnA WGN(N,power,cph:){;/~

",;, Zero mean AWGN low-pass l'quiva1cnt noisc generator.

'","Gencrutcd noise v('('tor.Required length for th(' noise vector.Power of the low-pass equivalent noise.

~() noisei!';)N°'0 powerif (power==O)

noise=O;return;

endnoise=randn( I ,N)+i*randn( I ,N);% Power C01Tcction f3ctor:% the powcr of the low-pass equivalent,~.;) is double of the in-pksc (quadraturc)°'0 component's power.

power = power/2;noise=noise*sqrt(power);

70

fun ction dataOUT=receiver(dataIN ,signal Mode, intercept,SyncError,SampError,CarrierOffset,Beta)

% function dataOUTrcceiven data IN,signal Mode, intercept,Sync Error,SampError,CarrierOffsct,Bcta):

1)'0 Multipurpose digital receiver emulator,

% dataOUT

%datalN% signalMode0''0

~/o

?/O°'00''0

0,,t>

'!';, intercept(~/~

OutPLlt daw in binary formal.

Received corrupkd data stTeam,Signaling mode. Possible values:

BPSK OFDM-BPSKDBPSK ODF!\'l-DBPSKQPSK OFDM-QPSK16QAM OFDM-16QAM

Allows to intercept the different signals and to plot their \vaveform:

intercept 0 --> no graphic displayedintercept= I --> tnUlsmitted analog signalintcrcep1'2 --> eye diagramintcreept4 --> received analog signa!intercept=S --> received signal constellation

(bitl=l)(bit21)(bit31 )(bit4= I)

% SyncError% SampError1.'/;)

"", CarricrOffset

% Beta

Sync crror, a fraction of the sample r:lteSampl ing jJ-eqllcncy phase jitter variancc, a fraction of the sample rat<~

Carrier t1'eqllcncy offset.

The one-sided 3dB lincwidth of the Lorentzian powcr density spectrLlfl101 the free-running oscillator

% Initialization of global variables.

global ChRate Totalfilterdelay ;global CARRIERS BPS DataRate MxChLength ChSplRate;global SIM_TYPE;

if SIM_TYPE ==3

% Starling ppint eJTol'start_error=round(SyneError*ChRate);

% Step errorstep_error = sqrt(SampError)*ChRate;

% Carrier ti'Cquellcy errordeltaF = ChSplRate * CarrierOffset;

",,, Nprma!ize to the SUbCJITicr spacingRs = CARRIERS*BPS*(l +MxChLength/CARRIERS)/DataRate;deltaf= deltaF * Rs;COFreq = exp(i * 2*pi * deltaf * I /Iength(dataIN) * (-Iength(dataIN)/2:1ength(dataIN)/2-1) );

if Beta -=°% Phase noiseBeta = ChSplRate * Beta;

PN = normrnd (0, sqrt(4*pi*Beta*Rs*lIIength(dataIN)*[-length(dataIN)/2:1ength(dataIN)/2-I));PN = exp(i*PN);

71

elsePN = I;

end

dataIN = dataIN .* COFreq.* PN;

%, Remove rx fille'r delaydataIN( 1:ChRate*((Total filterdelay+4)/4))=[];

'!'" Sample the received signalupperbound = (length(dataIN)- ChRate*(Totalfilterdelay/2)) + start_error;index = [1 +start_error:ChRate:upperbound];

if step_error-=OIi = length(index);index (I) = index(l) + round(abs(nonnrnd(O,step_error)));index (Ii) = index(li) - round(abs(nonnrnd(O,step_error)));index (2:li-l) = index(2:li-l) + round(nonnrnd(O,step_error,l,li-2));

enddataSPL = dataIN (index);

else

dataSPL = datalN;

end

% Implement OFDrv! prcrcceivcr.

p=find(signaIMode=='-');

if -isempty(p)mode=signaIMode(p+1:length(signaIMode));dataSPL=TxRx_OFDM(dataSPL,'rx');

elsemode=signaIMode;

end

if rem(fix(intereept/8),2)dispSignal(dataSPL,ChRate,'const')

end

t!/I) In1p!~lnCnl. rcccivcr~>

if stremp(mode,'BPSK')dataOUT=TxRx_BPSK(dataSPL,'rx');

elseif stremp(mode,'DBPSK')dataOUT=TxRx_DBPSK(dataSPL,'rx');

elseif stremp(mode,'QPSK')dataOUT=TxRx_QPSK(dataSPL,'rx');

elseifstremp(mode,'16QAM')dataOUT=TxRx_16QAM(dataSPL,'rx');

else error('Jnvalid argument: "mode".');end

72

function dispSignal (data, ChRate, type)

O,() function dispSignal (data, ('hRate, type)

% Displays a signal

0/0data% ChRate% type%(";'0

0''0

0,

'"~/I)

if stremp(type, 'tx')figure;subplot (2,1, I);plot (real(data));title CTransmitted analog signal');xlabelCReal part');subplot (2, I,2);plot (imag(data));xlabel Clmaginary part');

clseif strcmp (type,'rx')figure;subplot (2,1, I);plot (real(data));titleCReccived analog signal');xlabelCReal part');subplot (2, I,2);plot (imag(data));xlabel Clmaginary part');

elseif strcmp (type,'eyc')

signal data to be displayednumbcr of samples bctween symbolsType of signal to be displayedtx: transmittcd analog signalrx: rcceived analog signaleye: eye diagramconst: signal conslellation

Id = length(data);wid = floor(ld/(5*(ChRate)));len = floor(ldlwid);

data = data (l :wid*len);data = reshape (data,len,wid);

figure;subplot (2, 1,1);plot (real(data),'b');titleCEye diagram received signal')

xlabelCReal part');subplot (2, I,2)plot (imag(data),'b');xlabel Clmaginary part');

elseif strcmp (type,'const')figureplot (data,' :);titleCReceived signal constellation');

xlabelCRcal axis');ylabeICIll1aginaryaxis');

elsedisp Clnvallid type used in DispSignaL');

cnd

73

function dataOUT=TxRx_OFDM(dataIN,mode)

% function dataOUTTxRx~OFDM(dataIN,rnode)0/.,"% OFDM signal transmitter and receiver.1;'0"", "rrunsl11itler:

The input data must have a length multipleo t' "CARRI ERS", the number of OFDrVl curric'rs.

Transmit/Receive operation l11ode:

mode = 'tx' =

mode "." 'rx' .....

global CARRIERS MxChLength;

dataOUT=[];if isempty(dataIN)

retumend

if strcmp(mode,'tx')

if rem(length(dataIN),CARRIERS)errorCData sequence has incorrect length.');return

end

ld = length(dataIN);dataIN = reshape (dataIN, CARRIERS, Id/CARRIERS);dataOUT = ifft(dataIN);'~'(' Norrnalize output power to I.dataOUT=dataOUT*sqrt(CARRIERS);

transmitreceive

if MxChLength ~= 0 % Add cyclic prefixdataOUT = conj(dataOUT');dataOUT = [dataOUT(:,CARRIERS-MxChLength+ 1:CARRIERS) dataOUT];dataOUT = conj(dataOUT');

end

dataOUT = conj(dataOUT(:)');

elseif strcmp(mode,'rx')

Id = length(dataIN);dataIN = reshape (dataIN, CARRIERS+MxChLength, Id/(CARRIERS+MxChLength));

if MxChLength -= 0 °'0 Remove cyclic prefixdataIN (I:MxChLength,:) = [];

end

datalN=datalN/sqrt(CARRIERS); % Undo power normalization done at Tx.dataOUT = fft (datalN);dataOUT = conj(dataOUT(:)');

else errorCInval id operation mode.');end

74

function dataOUT=TxRx_QPSK(dataIN,mode)

% function dataOUT=T\R\QPSK(dataIN.mode)

(~,;, QPSK signal transmitter and receiver.

% Transmitter:Thc input data should be in binary unipolarformat and must have a length l11ultiple of 2.

0.;' Receiver:0''0

0''u

%, mode0/0;10,0

0,,,'(!I;)

if isempty(dataIN)dataOUT=[];return;

end

ExeessPower=2;

if stremp(mode,'tx')

Coherellt detection is assumed und symbol bysymbol hard decision is performed.Output is in binary unipolar format.

Transmit/receive operation mode:mode ."". 'tx'·· transmitmode = 'rx'= receive

n=length(dataIN);if rem(n,2)

dataOUT=[];errorCData sequence has incorrect lcngth.');

end;

y=dataIN( I :2:n);y=I-2*y;x=dataIN(2:2:n);x=I-2*x;dataOUT=x+i*y;dataOUT=dataOUT/sqrt(ExeessPower);

elseif stremp(mode,'rx')

dataIN=dataIN*sqrt(ExcessPower);y=imag(dataIN);y=(1-sign(y))/2;x=real(dataIN);x=(1-sign(x))/2;n=2*length(dataIN);dataOUT( I :2:n)=y;dataOUT(2:2:n)=x;

else errorClnvalid operation 1110de.');end

% Process quadrature component.(~.() Gray encoding (indirectly).(~'(' Process in-phase component.% Gray cnCl)(linl!- (indirectly).% Build complex QPSI( signal.% Normal i/.e average output power to 1.

% Undo power norrll:Jlization done at lx.'~,,! Process quadrature component.% Gray decoding (indirectly).% Process in-phase component.% Gray decoding (indirectly).'~'() Build detected daw vector.

75

function dataOUT=TxRx_16QAM(dataIN,mode)

% !'unction dataOUT=TxR x 16QA M(L!ataIN.!11odc)

%, 16-QAM sibnal lransmilter and receiver.();o

% Transmitter:The inpllt data should be in binary unipolarformat and must have a length multiple of4.

%, Receiver:

"'0 mode

Coherent detection is assumed and symbol bysymbol hard decision is performed.Output is in binary unipolar format.

Transmitlrecei ve operation mode:

if isempty(dataIN)dataOUT=[];return

end

ExcessPower= I0;

if stremp(mode,'tx')

mode = 'tx'mode ..... 'rx'

transmitreceive

n=length(dataIN);if rem(n,4)

dataOUT=[];errorCData sequence has incorrect length.');

end

dataIN = reshape (dataIN, 4, length(dataIN)/4);dataIN (2,:) = dataIN(2,:) * 2;dataIN (3,:) = dataIN(3,:) * 4;

dataIN (4,:) = dataIN(4,:) * 8;dataIN = sum(dataIN);dataOUT = dmodce (dataIN ,1 ,1, 'qask', 16);0,;, Normalize average output pO\\l'r to 1.dataOUT=dataOUT/sqrt(ExcessPower);

elseif strcmp(mode,'rx')

% Undo power normal il'ation done at Tx.dataIN=dataIN*sqrt(ExeessPower);

dataOUT = ddemodce (dataIN, I, I, 'qask' , 16);dataOUT = convbase (dataOUT, 4, I);

elsc errorClnvalid operation mode.');end

76

function dataOUT=TxRx_BPSK(dataIN,mode)

% !'unction dataOlrr"=T\RxBPSK(daiaIN,mode)

% BPSK signaltransmiiter and re('eiver.

% Transmitter:The input data should be in binary unipolarformaL

% Receiver:

% mode

Coherent detection is assumed and symbol bysymbol hard decision is performed.Output is in binary unipolar formal.

Transmit/receive operation mode:

if isempty(dataIN)dataOUT=[];return;

end

ExcessPower= I;

if strcmp(mode,'tx')

mode = 'tx'=mode ""c 'rx'c.c.

transmitreceive

dataOUT=sign(dataIN-.5);dataOUT=dataOUT/sqrt(ExcessPower);

clscif strcmp(mode,'rx')dataIN=dataIN*sqrt(ExcessPower);

dataOUT=sign(real(dataIN));nuliindex=find(dataOUT==-1 );if -isempty(nullindex)

dataOUT(nullindex)=zeros(size(nullindex));end;

else errorClnvalid operation mode.');end

% NorrnaliLc average output power to I.

% Undo powI?r l1orrnall/.ation donI? a1 Tx,

77

function dataOUT=TxRx_DBPSK(dataIN,mode)

(~o !'unction dataOUT=T\R\..... BPSK(dataIN,mode)0,,0

'!'D DBPSK signaltransmittcr and receiver.I)''0

0/0 Transmitter:The input data should be in binary tmipolarformat.

% Receiver:0''0 Symbol by symbol hard decision is performed.

Output is in binary unipolar format.

TralbmitireceiVl' operation mo<k:% modeI)/~

(}o0,/0

(~ll)

if isempty(dataIN)dataOUT=[];return

end

ExeessPower= I;

if stremp(mode,'tx ')

mode ."". 'tx' 'co

mode = 'rx' =transmitreceive

% Differential encodingdataOUT = zeros (1, length(dataIN)+ I);

dataOUT( I) = I;for eounter= I :length(dataIN)

dataOUT (eounter+ I) = -xor (dataIN(eounter),dataOUT(eounter));end

% BPSK mappin;sdataOUT=sign(dataOUT-.5);

dataOUT=dataOUT/sqrt(ExeessPower);

elseif stremp(mode,'rx')

dataIN=dataIN *sq rt(ExeessPower);

0,(. Differelltial dL'codingdataIN = abs(di ff(expO *angle(dataIN))));

'!") BPSK dL'-mappingoneindex = find (dataIN<=sqrt(2));nullindex = find (dataIN>sqrt(2));

dataOUT = zeros (1 ,length(dataIN));dataOUT(oneindex) = 1;dataOUT(nullindex) = 0;

else error('Invalid operation mode.');end

0," Normalize average output power to ].

% Undo power normalization done at Tx.

78