1

CHAPTER-1

INTRODUCTION

Wireless technologies have evolved remarkably since Guglielmo

Marconi first demonstrated radio's ability to provide continuous contact with

ships sailing in the English Channel in 1897. New theories and applications of

wireless technologies have been developed by hundreds and thousands of

scientists and engineers through the world ever since. Wireless

communications can be regarded as the most important development that has

an extremely wide range of applications from TV remote control and cordless

phones to cellular phones and satellite-based TV systems. It changed people's

life style in every aspect. Especially during the last decade, the mobile radio

communications industry has grown by an exponentially increasing rate,

fueled by the digital and RF (radio frequency) circuits design, fabrication and

integration techniques and more computing power in chips. This trend will

continue with an even greater pace in the near future.

1.1. WIRELESS COMMUNICATION SYSTEMS:

A wide variety of different wireless data technologies now exist, some

in direct competition with one another, others designed to be optimal for

specific applications. Wireless technologies can be evaluated by a variety of

different metrics. Of the standards evaluated, these can be grouped as

1.Wireless Personnel Area Network (WPAN) systems 2.Wireless Local Area

Network (WLAN) systems 3.Wireless Metropolitan Area Networks (WMAN).

1.2. OFDM SYSTEMS:

Orthogonal Frequency Division Multiplexing (OFDM) has grown to be

the most popular communications systems in high speed communications.

OFDM technology is the future of wireless communications. OFDM is a

2

multicarrier transmission technique, which divides the bandwidth into many

carriers each one is modulated by a low rate data stream. In term of multiple

access technique, OFDM is similar to FDMA in that the multiple user access is

achieved by subdividing the available bandwidth into multiple channels that

are then allocated to users. However, OFDM uses the spectrum much more

efficiently by spacing the channels much closer together. This is achieved by

making all the carriers orthogonal to one another, preventing interference

between the closely spaced carriers. The difference between FDM and OFDM

is as shown in the figure 1.1.

Figure 1.1 Frequency spectrum of FDM signal and OFDM signal

OFDM is simply defined as a form of multi-carrier modulation where

the carrier spacing is carefully selected so that each sub carrier is orthogonal to

the other sub carriers. Two signals are orthogonal if their dot product is zero.

That is, if you take two signals multiply them together and if their integral over

an interval is zero, then two signals are orthogonal in that interval.

Orthogonality can be achieved by carefully selecting carrier spacing, such as

letting the carrier spacing be equal to the reciprocal of the useful symbol

3

period. As the sub carriers are orthogonal, the spectrum of each carrier has a

null at the centre frequency of each of the other carriers in the system. This

results in no interference between the carriers, allowing them to be spaced as

close as theoretically possible. Mathematically, suppose we have a set of

signals x p(t)∧xq (t) then,

∫a

a+T

x p ( t ) xq¿ (t )={K , p=q

1 , p ≠ q (1.1)

The signals are orthogonal if the integral value is zero over the interval

[a a+T], where T is the symbol period. Since the carriers are orthogonal to

each other the nulls of one carrier coincides with the peak of another sub

carrier. As a result it is possible to extract the sub carrier of interest.

Figure 1.2 Time and Frequency domain view of OFDM signal

1.2.1. OFDM Generation and Reception

Figure 1.3 shows the block diagram of a typical OFDM transceiver.

The transmitter section converts digital data to be transmitted, into a mapping

of subcarrier amplitude and phase. It then transforms this spectral

representation of the data into the time domain using an Inverse Discrete

Fourier Transform (IDFT). The Inverse Fast Fourier Transform (IFFT)

4

performs the same operations as an IDFT, except that it is much more

computationally efficiency, and so is used in all practical systems. In order to

transmit the OFDM signal the calculated time domain signal is then mixed up

to the required frequency. The receiver performs the reverse operation of the

transmitter, mixing the RF signal to base band for processing, then using a Fast

Fourier Transform (FFT) to analyze the signal in the frequency domain. The

amplitude and phase of the subcarriers is then picked out and converted back

to digital data. The IFFT and the FFT are complementary function and the

most appropriate term depends on whether the signal is being received or

generated. In cases where the signal is independent of this distinction then the

term FFT and IFFT is used interchange

.

Figure 1.3 Block diagram of OFDM transmitter and receiver

The high data rate serial input bit stream is fed into serial to parallel

converter to get low data rate output parallel bit stream. Input bit stream is

taken as binary data. The low data rate parallel bit stream is modulated in

Signal mapper. Modulation can be BPSK, QPSK, and QAM etc. The

modulated data are served as input to inverse fast Fourier transform so that

each subcarrier is assigned with a specific frequency. The frequencies selected

are orthogonal frequencies. In this block, orthogonality in subcarriers is

BITS SOURCE

QPSK MAPP

INGS - P IFFT

CHA

NN

E L

Add CP P - S

REMOVAL CP

S - PFFTP - S

SYMBOL DET.

BITS

5

introduced. In IFFT, the frequency domain OFDM symbols are converted into

time domain OFDM symbols. Guard interval is introduced in each OFDM

symbol to eliminate inter symbol interference (ISI). All the OFDM symbols

are taken as input to parallel to serial data. These OFDM symbols constitute a

frame. A number of frames can be regarded as one OFDM signal. This OFDM

signal is allowed to pass through digital to analog converter (DAC). In DAC

the OFDM signal is fed to RF power amplifier for transmission. Then the

signal is allowed to pass through additive white Gaussian noise channel

(AWGN channel).

At the receiver part, the received OFDM signal is fed to analog to digital

converter (ADC) and is taken as input to serial to parallel converter. In these

parallel OFDM symbols, Guard interval is removed and it is allowed to pass

through Fast Fourier transform. Here the time domain OFDM symbols are

converted into frequency domain. After this it is fed into Signal demapper for

demodulation purpose. And finally the low data rate parallel bit stream is

converted into high data rate serial bit stream which is in form of binary.

1.2.2. OFDM SYSTEMS:

The following block diagram shows Orthogonal Frequency Division

Multiplexing (OFDM) system consists of various blocks as in figure 1.4.The

input data bits are mapped by the modulation QPSK where the bits are

grouped as symbols and Inverse Fast Fourier transform is taken. Now the

training sequences and cyclic prefix are inserted which is passed through the

AWGN and Fading channel. With the help of synchronization, the OFDM

symbols are mapped to the original position if any offset occurs due to the

channel behavior. After that removal of cyclic prefix, training sequences and

FFT is taken for the OFDM symbols. Now the symbols are decoded into bits.

6

Figure 1.4 Block diagram of OFDM System with Synchronization

1.3. ISSUES ASSOCIATED WITH THE RECEIVER SUB-SYSTEM:

OFDM systems are very sensitive to timing synchronization, frequency

offset synchronization and frequency-selective fading channels. Carrier

frequency offset (CFO) estimation and compensation are critical in OFDM

communications, since the orthogonality of subcarriers makes a simple OFDM

receiver feasible. However, CFO destroys the orthogonality between active

users, and causes inter-carrier interference (ICI) and multiple-access

interference (MAI). Time synchronization is another issue involves finding the

best possible time instant for the start of received OFDM frame. So it is

necessary to mitigate the above two issues associated with the receiver sub-

system.

DATA BITS

SYNCHRONIZATION

QPSK MAPPING

IFFT CYCLIC PREFIX

AWGN & FADING

CHANNEL

REMOVE CYCLIC

PREFIX,TRAINING SEQUENC

FFTEQUAILIZATION

SYMBOL DETECTI

ON

TRAINING SEQUENC

E

7

1.4. LITERATURE SURVEY:

In [1], the authors discussed about synchronization using training

sequences. Estimation of timing offset, frequency offset are done in this

report.

In [2], symbol detection using one training sequence for two symbols.

The algorithm use Cram´er–Rao lower bound for frequency offset .

In [3], describes about Maximum Likelihood Estimation (MLE) of

symbol and carrier frequency offset with the help of Cyclic prefix .

In [4], describes optimal ML estimator of time and frequency offset

using window. The correlation residing in cyclic prefix samples and

useful data samples.

1.5. SCOPE OF THE WORK:

It is aimed to study the receiver synchronization algorithm of OFDM

systems which is shown in figure 1.4 by simulating a transceiver. With the

help of design specification chosen, the algorithm in [1] was carried out with

the help of MATLAB simulation considering the effects of multipath channel

impairments, Carrier Frequency Offset (CFO) and synchronization of OFDM

symbol.

Following to this introduction, Chapter 2 describes various multipath

channels and provides introduction to synchronization. Chapter 3 explains the

techniques involved in synchronization of OFDM receiver over time, carrier

frequency and phase offsets. The simulation specifications and observed

results have been discussed in Chapter 4. Chapter 5 concludes the work carried

out in project work phase-I and ends with future work to be carried out in the

phase-II.

8

CHAPTER-2

MULTIPATH CHANNELS AND INTRODUCTION OF

SYNCHRONIZATION In this chapter we will first describe fading and multipath, the

performance-limiting phenomena that occur in wireless atmospheric radio

channels, and then turn our attention to modeling and simulation of these

channels. Fading and Multipath occur in many radio communication systems.

These effects were first observed and analyzed in troposcatter systems in the

1950s and early 1960s. In any wireless communication system there could be

more than one path over which the signal can travel between the transmitter

and receiver antennas. The presence of multiple paths is due to atmospheric

scattering and refraction, or reflections from buildings and other objects. In a

multipath situation, the signals arriving along different paths will have

different attenuations and delays and they might add at the receiving antenna

either constructively or destructively. If the path lengths and/or the geometry

change due to changes in the transmission medium or due to relative motion of

the antennas, as in the mobile case, the signal level might be subjected to wild

fluctuations. Multipath fading affects the signal in two ways: dispersion (time

spreading or frequency selectivity) and time-variant behavior.

Mobile communication is affected, in addition to multipath (or small-

scale fading), to another type of fading which is referred to as shadow or large-

scale fading. Shadow fading reveals itself as an attenuation of the average

signal power. Shadow fading is induced by prominent terrain contours (hills,

buildings, etc.) between transmitter and receiver. The receiver is said to be

shadowed by these objects.

9

2.1. WIRELESS CHANNELS:

Wireless channels operate through electromagnetic radiation from the

transmitter to the receiver. In principle, one could solve the electromagnetic

field equations, in conjunction with the transmitted signal, to find the

electromagnetic field impinging on the receiver antenna. This would have to

be done taking into account the obstructions caused by ground, buildings,

vehicles, etc. in the vicinity of this electromagnetic wave.

A good understanding of the wireless channel, its key physical

parameters and the modeling issues, lays the foundation for simulating a

wireless channel. The defining characteristic of the mobile wireless channel is

the variations of the channel strength over time and over frequency. The

variations can be roughly divided into two types

Large-scale fading, due to path loss of signal as a function of

distance and shadowing by large objects such as buildings and

hills. This occurs as the mobile moves through a distance of the

order of the cell size, and is typically frequency independent.

Small-scale fading, due to the constructive and destructive

interference of the multiple signal paths between the transmitter

and receiver. This occurs at the spatial scale of the order of the

carrier wavelength, and is frequency dependent.

2.1.1. Rayleigh channel:

Rayleigh channel is also a kind of slow fading channel. In a radio link,

the RF signal from the transmitter may be reflected from objects such as hills,

buildings, or vehicles. This gives rise to multiple transmission paths at the

receiver. The relative phase of multiple reflected signals can cause

constructive or destructive interference at the receiver. This is experience over

10

very short distances (typically at half wavelength distances), thus is given the

term fast fading. The Rayleigh distribution is commonly used to describe the

statistical time varying nature of the received signal power.

2.1.2. Discrete multipath channel model:

If a multipath channel is composed of a set of discrete resolvable

components that originate as reflections or scattering from smaller structures,

e.g., houses, small hills, etc., it is called a discrete multipath channel. The

model in its most general form has, in addition to variable tap gains, variable

delays and a variable number of taps. This model is applicable mostly to

rapidly changing environments. The low pass-equivalent impulse response of a

discrete multipath channel is given in the following equation 2.1,

c (τ ,t)=∑k=1

K( t )

ak ( τ k (t ) , t ) δ(τ−τ k ( t )) (2.1)

With the corresponding output is given by,

y (t )=∑k=1

K(t )

ak ( τk ,t ) s (t−τk (t )) (2.2)

For many channels it can be assumed as a reasonable approximation that

the number of discrete components is constant and the delay values vary very

slowly and can also be assumed constant. The model then simplify

y (t )=∑k=1

K(t )

ak ( t ) s (t−τ k ) (2.3)

This multipath channel model can be realized by means of multi tap FIR

filter, where the number of taps depends on number of reflected paths.

11

2.2. INTRODUCTION OF SYNCHRONIZATION:

Synchronization is the method which synchronizes the transmitter and

receiver of the OFDM symbols. There are two categories of synchronization

in general:

Data-Aided methods: A known data sequences is to be transmitted and

which has to be known to both transmitter and receiver. The drawback

of the data-aided scheme is the leakage of the bandwidth efficiency due

to redundancy overhead.

Two methods are used namely,

Pilot based Training sequence based

In pilot based, the data symbols is known to both transmitter and

receiver. The pilots are inserted in between of OFDM symbols. Generally it is

complex form and operated in the frequency domain.

In training based, a block of data symbols is known to both transmitter

and receiver. This block of data symbol is inserted either at the starting of

OFDM symbols or at the end of the OFDM symbols . Due to this information

rate is reduced.

Non-Data-Aided methods: Non-data-aided methods or called blind

relying on the cyclostationarity and virtual sub-carriers, etc. The blind

estimation requires a large amount of computational complexity.

12

Techniques in Synchronization:

Correlation based

In correlation based method, the main idea is to perform correlation

between the data symbols and to find which position is having correlation

peak.

Two approaches are used namely

Correlation is done between the received data and its delayed parts

Correlation is performed with the received data and with the local sequences.

The different types of synchronization errors are given by a tree diagram

shown in figure 2.1.

Figure 2.1 Types of synchronization error

Synchronization Errors

Timing Errors Frequency Errors

Sampling clock Symbol timing RF Oscillator Doppler effect

Timing Offset Frequency offset

13

We consider the effects of Symbol timing and RF mismatch oscillator which

leads to timing offset and frequency offset respectively are explained in the

future chapters

CHAPTER-3

OFDM RECEIVER DESIGN CONSIDERATIONSIn digital radio communication systems information symbols are

transmitted by means of suitably chosen waveforms that modulate a carrier

signal with a suitably chosen frequency. Due to the radio environment,

imperfections generate fluctuations in these waveforms actually are received.

Because of these fluctuations, the receiver's knowledge of the

transmitter’s carrier frequency and waveform constellation is not always

sufficient to assure reliable detection. In order to detect the information

symbols reliably, the receiver may need to counteract the channel

uncertainties.

The requirements on the synchronization depend, among other factors,

on the type of modulation. This chapter is concerned with how channel

uncertainties are estimated in orthogonal frequency-division multiplexing

(OFDM) transmission systems. It addresses the estimation of symbol time

offsets, carrier frequency offsets and phase offs

Before an OFDM receiver can demodulate the subcarriers, it has to

perform two synchronization tasks. First it has to find where the symbol

boundaries are and what the optimum timing instants are to minimize the

effect of inter carrier interference (ICI) and inter symbol interference (ISI).

Second it has to estimate and correct for the carrier frequency offset of the

received signal because any offset which introduces ICI. In this chapter we

14

discuss timing synchronization techniques, frequency offset estimation

techniques and phase offset estimation techniques in detail in order to nullify

the effects of ICI. The baseband modulated signal s(n) , after parallel to serial

conversion and IFFT is expressed as,

s (n )= 1N ∑

k=0

N−1

dk e( j 2 πk(n−L)

N ) (3.1)

The received complex signal that is transmitted over a multipath channel

with impulse response h(n,l), x(n) is the output signal which is expressed as

x(n)=∑l

h ( n ,l ) s (n , l) (3.2)

The received signal is corrupted by AWGN noise and fading by

channel. The offsets between the transmitter and receiver is modeled in

received signal with schematic shown in figure 3.1. The received is modeled

with equation (3.3).

r (n)=x (n−d)e j 2 П ∆ fn/N+ w(n) (3.3)

Where,

d -Unknown arrival time of the received symbol

∆ f - Frequency offset.

w ( n ) - AWGN channel

15

Figure 3.1 Block diagram of time, frequency, phase offset insertion in

transmitted signal with AWGN channel

The estimated offsets are used to correct the received signal before

passing the same to the detector. The process carrier out in the course is

depicted in figure 3.2.

Figure 3.2 Internal blocks of Synchronization

3.1. SYMBOL SYNCHRONIZATION OF OFDM SYSTEM:

OFDM is a well known multi-carrier modulation technique which can

provide significant robustness to channels with long delay spreads at the cost

of a loss in spectral efficiency. OFDM efficiently modulates N parallel sub-

carriers by performing an N-point inverse discrete Fourier transform (IDFT) on

N complex data symbols. The output of the IDFT consists of N samples which

are referred to as an OFDM symbol.

Delay

Frequenc

y and phas

e offse

t

AWGN &

Fading channel

noiseSignal

from transmitte

r

Signal to Receiver

16

Hence, OFDM needs to employ time and frequency synchronization.

Time synchronization is to decide for the symbol boundaries. Commonly, a

sequence of known symbols- preamble (training sequence) is used to detect the

symbol boundaries. It has less sensitivity to timing offset as compared with

single-carrier systems, since timing offset does not violate the orthogonality of

subcarriers in OFDM system, but causes ISI in single-carrier systems.

The OFDM symbol is added with training sequences and cyclically

extended and transmitted over the air. If the channel is static during the

duration of one OFDM symbol and if the receiver is perfectly synchronized,

the sub-carriers orthogonality is maintained at the receiver. Therefore, the data

transmitted on each sub-carrier can be recovered by means of a DFT.

However, the receiver has to be synchronized with the transmitter both in

frequency and time domain.

The method uses the training sequence to detect the beginning of the

OFDM symbol. The frame contains four OFDM symbols and 128 training

symbols are distributed as in the figure 3.3. The first subblock of training

sequence (Trn.seq) has 64 symbols is prefixed to the first OFDM symbol,

remaining 64 symbols are divided into four subblocks and appended at the end

of each OFDM symbols having 270 symbols.

Trn

.

Seq

CP+Data Tr.

Seq.

CP+Data Tr.

Seq.

CP+Data Tr.

Seq.

CP+Dat

a

Tr.

Seq.

Figure 3.3 Structure of OFDM symbols with training sequence

17

3.1.1. Synchronization using training sequence method:

In this work, the training sequence of 128 symbols is generated and

inserted at appropriate position as shown in figure 3.3. Instead of correlating

the cyclic prefix in the conventional method, the local copy of the training

sequence is correlated with the received signal to achieve timing

synchronization. In a buffer having a length of one subframe containing the

received signal, the samples over training sequences length are collected from

their reference locations in the transmitted sequence format and correlated with

the local copy of training sequence. The algorithm is described by equation

(3.4),

d ML=max {∑k=d

N t−1

rtr (k ) tr¿ ( k+ N )} (3.4)

Where,

dML =Estimated Timing point

Nt= Length of training sequence

tr(k) = reference training sequence

rtr(k) = training sequence from received signal r(k)

3.2. CARRIER FREQUENCY OFFSET:

One of the principal disadvantages of OFDM is sensitivity to frequency

offset in the channel. There are two deleterious effects caused by frequency

offset; one is the reduction of signal amplitude in the output of the filters

matched to each of the carriers and the second is introduction of ICI from the

other carriers which are now no longer orthogonal to the filter. Because, in

OFDM systems, the carriers are inherently closely spaced in frequency

domain.

18

3.2.1 Carrier frequency offset estimation and correction:

The received signal spectrum is shifted from its optimum location by the

offset between the local and transmitter carrier. The offset reflected in the

sampling leads to addition of interference from the symbols transmitted on

other subcarriers to the desired subcarrier. This interference is called

intercarrier interference (ICI). This is illustrated in figure 3.4.

A frequency offset estimate may be generated at the receiver with the

aid of known training sequences to the receiver. An algorithm based on

correlating the cyclic prefix is presented to estimate frequency offset from the

demodulated data signals in the receiver. The technique involves repetition of

a data symbol and comparison of the phases of each of the carriers between the

successive symbols. Since the modulation phase values are not changed, the

phase shift of each of the carriers between successive repeated symbols is due

to the frequency offset. The frequency offset is estimated using a maximum

likelihood estimate (MLE) algorithm as in equation (3.5).

Figure 3.4 Carrier Frequency Offset in OFDM spectrum

19

The procedure for obtaining frequency offset is obtained by leaving the

training sequences, considers only the OFDM symbols which include CP. The

correlation of cyclic prefix with the tail of the OFDM symbols yields the

estimated value of frequency offset, provided by equation (3.5) and this

method is called as maximum likelihood estimate (MLE) .

∆ w=−( 1N )arg(r (k )r¿ (k+N )) (3.5)

3.3. PHASE OFFSET:

Frequency estimation alone could not complete the carrier

synchronization, additionally it requires estimating and correcting the phase

offset also. Let the CFO corrected signal is represented is d(k), then the

resultant frequency offset corrected signal r(k), which is represented as

r (k )=d (k )e jθ (3.6)

All the symbols are phase rotated by a constant ɵ. To estimate the

phase, received signal is r(k) is multiplied with conjugate of training sequence,

which is represented as

y (k )=E [r (k )∗( conj(training sequence))] (3.7)

The angle of y(k) provides the estimate of the phase. With this, the

phase corrected signal is obtained as z(k) given by,

z (k )=r (k )e− j< y(k) (3.8)

This z(k) is synchronized signal which is passed through a OFDM

demodulator for further processing to retrieve the information from the signal.

20

CHAPTER 4

OFDM RECEIVER SIMULATION

The block diagram of OFDM system shown in figure has been carried

out with the following design specifications with anomalies described in the

earlier chapters like Time offset, Carrier Frequency offset and phase offset.

4.1. DESIGN SPECIFICATIONS:

In this work, the simulation parameters have taken as stated in [1]. This

used 256 point fast Fourier transform (FFT) with 240 active subcarriers, 15

guard subcarriers, 14 cyclic prefix, sample frequency of 1.6MHz, subcarriers

spacing of 6.25kHz, number of OFDM symbols per time slot is 4, training

sequences of 128. These have been summarized in table 4.1(a), (b).

Table 4.1(a) Design specification (I)PARAMETERS VALUE

Nfft 256NUsed Carriers 240Number of lower frequency guard sub carriers 8Number of higher frequency guard sub carriers 7Cyclic prefix 14

Table 4.1 (b) Design specification (II)PARAMETERS VALUE

Sample frequency 1.6MHzSample time (Ts ) 625ns(1/1.6MHz)Number of OFDM symbols per Timeslot 4OFDM symbol interval 168.75µs( 270 * Ts)CP length 8.75µs ( 14*Ts )Sub carrier spacing 6.25KHz(1.6MHz/256)Number of training sequences 128 symbols

(64+16+16+16+16)Modulation QPSK

21

4.2. SIMULATION OF OFDM SYSTEM IN AWGN CHANNEL:

In the first step simulation was carried out to estimate the effect of

AWGN channel on bit error rate (BER) performance over signal power to

noise power ratio (SNR). The simulated result is plotted in figure 4.1,and it is

observed that OFDM system requires minimum of 11dB SNR to yield BER of

10-4.

Figure 4.1 SNR vs. BER curve for AWGN channel

4.3. SIMULATION OF OFDM SYSTEM IN RAYLEIGH CHANNEL:

The simulation of OFDM system is carried out with the help of

following design specification in Rayleigh multipath channel

Table 4.2 Design specification

Sampling Time 0.1nsPath delays in ns 0 781 156 2344Path gains in dB 0 -3 -6 -9Delay spread 2344nsDoppler shift 0Fading type Frequency selective & slow fading

22

4.4. SYMBOL SYNCHRONIZATION OF OFDM SYSTEM:

A well-known drawback of OFDM is that it requires accurate symbol

synchronization because the OFDM signal is demodulated based on symbol

structure and the arriving time of the received signal is unknown. Wrong

symbol synchronization would cause the inter-symbol interference (ISI), and

then bring up an increase of bit error rate (BER), so it is essential to achieve

accurate and fast symbol synchronization for OFDM system.

The following graph shows that when offset = 125 and estimated timing

is 1084, the OFDM system gets synchronized to the estimated timing.

Figure 4.2 Probability occurrence of estimated timing

4.4.1. Observations:

From the simulation it has been inferred that after an SNR value greater

than 0 dB OFDM system is properly synchronized.

For different value of offsets, simulation is confirms that the system gets

exactly synchronized for positive SNR.

23

4.5. CARRIER FREQUENCY OFFSET ESTIMATION:

As we saw in the earlier chapters CFO is due to the mismatch of the RF

oscillator in the transmitter and receiver side of the OFDM system.

In the figure 4.3 as SNR value increases, MSE of estimated CFO

decreases under Rayleigh channel.

Figure 4.3. SNR Vs MSE for ∆ω=0.0019

The following table gives estimated offset for SNR=20 dB.

Table 4.3. Estimated Frequency offset for Rayleigh channel (SNR = 20dB)

Frequency offset Estimated offset(AWGN channel)

Estimated offset (Rayleigh channel)

0.0019 0.0019 0.00140.0029 0.0029 0.00270.0039 0.0039 0.00400.0049 0.0049 0.00470.0059 0.0049 0.00550.0069 0.0069 0.00670.0079 0.0079 0.00830.0089 0.0089 0.0084

24

It is observed that the offset is possible to estimate exactly while the

channel is AWGN. If the noise increases or channel becomes highly

faded, the error in the estimate becomes larger beyond the values shown

in the table 4.3.

4.5. PHASE OFFSET ESTIMATION

In figure 4.4 as SNR increases, MSE of Phase offset estimation (in

radian) decreases.

Figure 4.4 SNR Vs MSE of phase offset(0.5235 in radian)

25

The following table shows estimation of phase for different values of

offset shown in Table 4.4

Table 4.4 Phase estimation in AWGN, Rayleigh

channel(SNR=20dB)

As in the case of frequency estimation, the phase estimate also works

well in the higher SNR and deviates from the expected while the noise

increases as well as fading increases.

Phase offset(in radian)

Estimated offset(AWGN

channel)

Estimated offset(Rayleigh

channel)0.5236 0.5241 0.53960.6109 0.6107 0.61700.6989 0.6990 0.69530.7854 0.7850 0.79160.8727 0.8730 0.88540.9599 0.9596 0.96581.0472 1.0468 1.03401.1345 1.1348 1.15031.2217 1.2218 1.29731.3090 1.3090 1.4966

26

CHAPTER- 5

CONCLUSION AND FUTURE WORK

5.1. CONCLUSION:

Thus in this project OFDM system is simulated based on the selected

specifications and receiver algorithm was verified with the help of MATLAB

by considering the receiver design anomalies like timing offset, Carrier

Frequency Offset, phase offset. Timing synchronization is done with the help

of training sequences inserted between the OFDM symbols. Carrier frequency

offset is cancelled by means Maximum Likelihood Estimate (MLE) and Phase

offset is estimated and corrected with the help of training sequence

The insertion of training sequence aids the synchronization with

minimum estimation error.

Introduction of training sequence reduces the information rate.

It is observed that OFDM system requires minimum of 11dB SNR to

yield BER of 10-4 in the case of AWGN channel which is required to

be yielded by the optimum estimator.

It has been inferred that for SNR value of greater than 0dB, the

OFDM system is properly synchronized with the aid of training

sequence.

In CFO and Phase estimation, it is observed that for SNR value

greater than 10dB, MSE values reduces and errors are obtained in

10−7.

27

5.2. FUTURE WORK:

In this project phase-I, the synchronization with the aid of training

sequence has been studied. In the next phase of this project work, it is

intended to study another synchronization scheme proposed in [6], which is a

pilot based joint estimate technique. The outcome of the simulation is to be

compared with the present work for the selected specifications.

28

REFERENCES

[1]. Zhang Rong-tao Xie Xian-zhong Wang Xi(2006)’ Synchronization

Algorithm for OFDM based on Training Cyclic Prefix’- International

Conference on Communication Technology ICCT, pp.1 - 4

[2]. Schmidl T M, Cox D C. (1997)’ Robust frequency and timing

synchronization for OFDM.’ - IEEE Transactions on Communications,

Volume 45 No.12 pp.1613 - 1621

[3]. Van de Beek J J, Sandell M, Boriesson P (1997)’ ML estimation of time

and frequency offset in OFDM Systems’ - IEEE Transaction on Signal

Processing, volume 45 No.7 pp.1800 - 1805

[4]. Lee. J, Lou, H and Toumpakaris, D. (Oct. 2004)’Maximum likelihood

estimation of time and frequency offset for OFDM systems ’- Electronics

Letters. Volume 40, Issue 22, 28 Page(s):1428 - 1429

[5]. Michele Morelli, Member IEEE, C.-C. Jay Kuo, Fellow IEEE, and

Man-On Pun, Member IEEE – ‘Synchronization Techniques for Orthogonal

Frequency Division Multiple Access (OFDMA) ‘: A Tutorial Review

[6]. Hung Nguyen-Le and Tho Le-Ngoc (2010)’ Pilot-Aided Joint CFO and

Doubly-Selective Channel Estimation for OFDM Transmissions ‘IEEE

transactions on broadcasting, vol. 56, no. 4 Page No: 345-362