noise reduction in fast fading channel using ofdm/tdm
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8/4/2019 Noise Reduction in Fast Fading Channel Using OFDM/TDM
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NOISE REDUCTION IN FAST FADING CHANNEL USING OFDM/TDM
Mr.A.Sagaya Selvaraj, Asst.Professor & Head Dr.R.S.D.Wahidabanu, Professor &Head
Department of Electronics and Communication Engg . Department of Electronics and Communication Engg
IFET College of Engineering, Villupuram -108 Govt.College of Engg. Salem-11
Research Scholar, Anna University, Chennai, India Anna University, Coimbatore, India
E-mail: [email protected] E-mail: [email protected]
ABSTRACT
Orthogonal Frequency Division Multiplex (OFDM)
modulation is being used more and more in telecommunication,
wired and wireless.. OFDM can be implemented easily, it is
spectrally efficient and can provide high data rates with
sufficient robustness to channel imperfections. MMSE-FDE can
improve the transmission performance of OFDM combination
with time division multiplexing (OFDM/TDM).
To improve the tracking ability against fast fading robustpilot-assisted channel estimation is done that uses time-domain
filtering on a slot-by-slot basis and frequency-domain
interpolation. The mean square error (MSE) of the channel
estimator is obtained and then a tradeoff between improving the
tracking ability against fading and the noise reduction is done.
BER is calculated by mat lab simulator and compared with
conventional OFDM. It is proved that the OFDM/TDM using
MMSE-FDE achieves a lower BER and provides better tracking
ability against fast fading.
Keywords: Orthoganal Frequency Division
Multiplexing(OFDM), BER (Bit Error Rate), MMSE (Minimum
Mean Square Error), Feedback Decision Equalization, …
1. INTRODUCTION:
In this paper, we focused on designing the mat lab
code for particular channel conditions that affects the BER
performance for Orthogonal Frequency Division
Multiplexing (OFDM) [1]. The channel used is RaleighChannel BPSK modulation has been used in this paper. We
derive the mean square error and using MMSE-FDE, we
again prove that the BER is reduced [4] [8] [9]. The main
objectives of my paper is to design and evaluate Orthogonal
Frequency Division Multiplexing (OFDM) in a Multipath
Fading Channel using computer simulation (MATLAB).To
obtain and compare between the theoretical and simulation
result for Orthogonal Division Multiplexing (OFDM) in
Raleigh channel. To obtain and compare the Bit Error Rate
(BER) Performance of OFDM.
2. OFDM/TDM TRANSMITTER RECEIVER MODEL
2.1 FDM TRANSMITTER CONFIGURATION
The following figure shows the configuration of an
OFDM transmitter[1][2]. In the transmitter, the transmitted
high speed data is first converted into parallel data of N sub
channels. Then, the transmitted data of each parallel sub
channel is modulated by BPSK based modulation.
fig 2.1. OFDM Transmitter
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2.1.1OFDM TRANSMITTER STRUCTURE
fig 2.2 OFDM Frame Structure
The OFDM/TDM transmission system model is
shown in the above Fig.2.1 Tc-spaced discrete time
representation is used, where Tc represents the fast Fourier
transform (FFT) sampling period. To reduce the PAPR, the
inverse FFT (IFFT) time window for the conventional
OFDM is divided into K slots (which constitute the
OFDM/TDM frame) shown in Fig 2.1. An OFDM signal
with reduced number of sub carriers ( Nm= Nc / K )is
transmitted during each time slot without inserting guard
interval (GI) between consecutive OFDM signals, where Nc
is the number of sub carriers in the conventional OFDM[1].
Hence, the transmission data rate is kept the same as
conventional OFDM, while the number of sub carriers is
reduced by a factor of K , thus reducing the PAPR[6].
3.1 TRANSMIT SIGNAL
A sequence of Nc data-modulated symbols
{d (i);i=0~ Nc-1} is transmitted during one OFDM/TDM
frame(equal to the IFFT block size of the conventional
OFDM). The data-modulated symbol sequence {d (i)} of Nc
symbols is divided into K blocks of Nm= Nc / K symbols each.
The k -th block symbol sequence is denoted by {dk (i);
i=0~ Nm-1},where dk (i)=d (kNm+i) for k =0~K -1. Nm-point
IFFT is applied to generate a sequence of K OFDM signals
with Nm subcarriers. The OFDM/TDM signal can be
expressed using the equivalent low pass representation as
S(t)=sk
(t-kNm)for t =0~ Nc-1,
where k =[t / Nm] with [ x] representing the largest integer
smaller than or equal to x and s k (t ) is the k -th OFDM signal
with Nm subcarriers, is given by
for t =0~ Nm-1, where Es and Tc represent the symbol energy
and the sampling period, respectively. Before transmission
the last Ng samples in the OFDM/TDM frame are inserted as
the GI at the beginning of the frame.
3.2 GUARD INTERVAL
One key principle of OFDM is that since low rate
modulation scheme, where the symbols are relatively long
compared to the channel time characteristics suffer less from
inter symbol interference caused by multi path. It is the
advantageous to transmit a number of low rate streams in
parallel instead of a single high rate stream. Since the
duration of each symbol is long, it can be affordable to insert
a guard interval between the OFDM symbols and thus the
inter symbol interference can be eliminated. The transmitter
sends s cyclic prefix during the guard interval. The guard
interval also reduces the sensitivity to time synchronization
problems[8].
The orthogonality of sub channels in OFDM can be
maintained and individual sub channels can be completely
separated by using an FFT circuit at the receiver when there
are no ISI and inter carrier interference (ICI) introduced by
transmission channel distortion. The spectra of OFDM signal
are not strictly band limited, the distortion due to multi pathfading causes each sub channel to spread the power into the
adjacent channel. Moreover, the delayed wave with the delay
time larger than 11 symbol time contaminates the next
symbol. In order to reduce this distortion, a simple solution is
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to increase the symbol duration or the number of carriers.
However, this method may be difficult to implement in terms
of carrier stability against Doppler frequency and FFT size.
Another way to eliminate ISI is to create a cyclically
extended guard interval, where each OFDM symbol is
preceded by a periodic extension of the signal itself.
The total symbol duration:
Ttotal = Tg + Tn
Where,
Tg = guard time interval
Each symbol is made of two parts. The whole signal
is contained in the active symbol, the last part of which is
also repeated at the start of the symbol and is called a guard
interval. When the guard interval is longer than the channelimpulse response or the multi path delay, the effect of ISI can
be eliminated.
However, the ICI or in band fading still exists. The
ratio of the guard interval to the useful symbol duration is
application dependent[9][11]. The insertion of guard interval
will reduce the data throughput; Tg is usually smaller than
Ts/4.
After the insertion of a guard interval, the OFDM signal is
given by
s’(t)=∑∑di (k)exp(j2πf i(t-kTtotal))f’(t-kTtotal)
where f’(t) is the modified pulse waveform of each symbol
defined as
The OFDM signal is transmitted to the receiver;
however, the transmitted data, s’(t) is contaminated by multi
path fading and AWGN. At the receiver, the received signal
is given by
r(t)=h(τ,t)s(t-τ)dτ+n(t)
Where h(τ,t) is the impulse response of the radio channe
at time t, and n(t) is the complex AWGN.
3.3 FREQUENCY DOMAIN EQUALISATION
The GI inserted OFDM/TDM signal is transmitted over a
wireless channel. We assume a Tc-spaced time-delay discrete
channel having L propagation paths with distinct time delays
{τl; l=0~ L-1}.
The discrete-time impulse response h(t ) of the
channel can be expressed as
3.4 OFDM RECEIVER CONFIGURATION
At the receiver, received signal r(t) is filtered by a
band pass filter, which is assumed to have sufficiently wide
pass band to introduce only negligible distortion in the signal
An orthogonal detector is then applied to the signal where the
signal is down converted to IF band. Then, an FFT circuit is
applied to the signal to obtain Fourier coefficients of the
signal in observation periods [iTTotal , iTTotal + Ts].
FIG 3.4. OFDM Receiver
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The output, di’(k), of the FFT circuit of the ith OFDM
subchannel is given by
di’(k) = 1/Ts r(t) exp (-j2ðfi(t-kTtotal))dt
If the characteristics of delayed wave, hi’(k) in a
multipath fading environment can be estimated, therefore the
received data also can be equalized as
follows:
di’’ (k) = (hi’ * (k)) / (hi’(k)hi’ * (k) )) (di’(k))
where * indicates the complex conjugate.
By comparing dk and di’’ (k), the BER performance can be
calculated. The BER depends on the level of the receiver’s
noise. In OFDM transmission, the orthogonal is preserved
and the BER performance depends on the modulation scheme
in each sub channel.
FIG 3.4.1. OFDM Receiver Structure
The received signal can be expressed as
for t =- Ng~ Nc-1, where η(t ) is the additive white Gaussian
noise (AWGN) process with zero mean and variance 2 N 0/ Tc
with N 0 being the single-sided power spectrum density. After
removing the GI, the received signal {r (t ); t=0~Nc-1} is
decomposed into Nc frequency components { R(n); n=0~ Nc
1}by applying Nc-point FFT as
R(n)=S(n)H(n)+∏(n)
where S(n), H (n) and Π(n) are the signal component, the
channel gain and the noise component at the nth frequency,
respectively, given by
One-tap FDE is applied as
Here w(n) is the equalization weight for the nth frequency
and Πˆ (n) is the noise component after equalization. We
consider MMSE-FDE.
4. DIGITAL MODULATION SCHEMES4.1 DIGITAL MODULATION
Nowadays, digital modulation is much popular
compared to analog modulation. The move to digita
modulation provides more information capacity
compatibility with digital data services, higher data security
better quality communications, and quicker system
availability. Developers of communications systems face
these constraints:
Available bandwidth
Permissible power
Inherent noise level of the system
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The RF spectrum must be shared, yet every day there
are more users for that spectrum as demand for
communications services increases. Digital modulation
schemes have greater capacity to convey large amounts of
information than analog modulation schemes.
4.2 PHASE SHIFT KEYING (PSK)
PSK is a modulation scheme that conveys data by
changing, or modulating, the phase of a reference signal (i.e.
the phase of the carrier wave is changed to represent the data
signal). A finite number of phases are used to represent
digital data. Each of these phases is assigned a unique pattern
of binary bits; usually each phase encodes an equal number
of bits. Each pattern of bits forms the symbol that isrepresented by the particular phase.
There are two fundamental ways of utilizing the phase of a
signal in this way:
(i) By viewing the phase itself as conveying the information,
in which case the demodulator must have a reference signal
to compare the received signal's phase against; (PSK) or
(ii) By viewing the change in the phase as conveying
information – differential schemes, some of which do not
need a reference carrier (to a certain extent) (DPSK).
A convenient way to represent PSK schemes is on a
constellation diagram. This shows the points in the Argand
plane where, in this context, the real and imaginary axes are
termed the in-phase and quadrature axes respectively due to
their 90° separation. Such a representation on perpendicular
axes lends itself to straightforward implementation. The
amplitude of each point along the in-phase axis is used to
modulate a cosine (or sine) wave and the amplitude along the
quadrature axis to modulate a sine (or cosine) wave.
fig 4.2. Constellation Diagram
In PSK, the constellation points chosen are usually
positioned with uniform angular spacing around a circle. This
gives maximum phase-separation between adjacent points
and thus the best immunity to corruption. They are positioned
on a circle so that they can all be transmitted with the same
energy. In this way, the moduli of the complex numbers they
represent will be the same and thus so will the amplitudes
needed for the cosine and sine waves. Two common
examples are binary phase-shift keying (BPSK) which uses
two phases, and quadrature phase shift keying (QPSK) which
uses four phases, although any number of phases may be
used. Since the data to be conveyed are usually binary, the
PSK scheme is usually designed with the number o
constellation points being a power of 2.
4.3 BIT RATE AND SYMBOL RATE
To understand and compare different PSK
modulation format efficiencies, it is important to first
understand the difference between bit rate and symbol rate
The signal bandwidth for the communications channe
needed depends on the symbol rate, not on the bit rate.
Symbol rate=bit rate \ the number of bits transmitted
with each symbol
Bit rate is the frequency of a system bit stream. Take
for example, a radio with an 8 bit sampler, sampling at 10
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kHz for voice. The bit rate, the basic bit stream rate in the
radio, would be eight bits multiplied by 10K samples per
second, or 80 Kbits per second. (For the moment we will
ignore the extra bits required for synchronization, error
correction, etc.).
4.4 BIT ERROR RATE FOR BPSK MODULATION
We will derive the theoretical equation for bit error
rate (BER) with Binary Phase Shift Keying (BPSK)
modulation scheme in Additive White Gaussian Noise
(AWGN) channel. With Binary Phase Shift Keying (BPSK),
the binary digits 1 and 0 maybe represented by the analog
levels and respectively. The system model
is as shown in the Figure below.
fig 4.4. Simplified Block Diagram with BPSK Transmitter-
Receiver
4.4.1 COMPUTING THE PROBABILITY OF ERROR
The received signal is,
when bit 1 is transmitted and
when bit 0 is transmitted.
The conditional probability distribution function (PDF) of
for the two cases are:
.
fig 4.4.1. conditional probability density function with bpsk
modulation
.If the received signal is greater than zero(y>0), then the
receiver assumes that binary “1” was transmitted. If the
received signal is less than zero(y<0),then the receiver
assumes that binary “0” was transmitted.
i.e., y>0, s1 is transmitted and
y<=0, s0 is transmitted
Probability of error given S1 was transmitted With this
threshold, the probability of error given S1 is transmitted is
p(e\s1)(the area in the blue region) Probability of error given
S0 was transmitted Similarly the probability of error given S
is transmitted is p(e\s2)(the area in the green region) Tota
probability of bit error:
.
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Given that we assumed that s1and s0are equally
probable i.e. p (s1)=p(s0)=1/2, the bit error probability is,
.
where,
The given function is the complementary error function
5.1 MULTIPATH
In wireless communications, multipath is the
propagation phenomenon that results on radio signals
reaching the receiving antenna by two or more paths. Causes
of multipath include atmospheric ducting, ionospheric
reflection and refraction and reflection from terrestrial object
such as mountains and buildings. The effects of multipath
include constructive and destructive interference and phase
shifting of the signal. This causes Rayleigh Fading named
after Lord Rayleigh. Rayleigh fading with a strong line of
sight is said to have a Rician distribution or tobe Rician
fading.
In digital radio communications such as GSM
Multipath can cause errors and affect the quality of
communications. The errors are due to Inter symbol
interference (ISI). Equalizers are often used to correct the ISI.
Alternatively, techniques such as orthogonal frequency
division modulation and Rake receivers may be used.
5.2 MULTIPATH FADING
Multipath Fading is simply a term used to describe
the multiple paths a radio wave may follow between
transmitter and receiver. Such propagation paths include the
ground wave, ionospheric refraction, re radiation by the
ionospheric layers, reflection from the earth’s surface or from
more than one ionospheric layer, and so on. Multipath fading
occurs when a transmitted signal divides and takes more than
one path to a receiver and some of the signals arrive out of
phase, resulting in a weak or fading signal. Some
transmission losses that effect radio wave propagation are
ionospheric absorption, ground reflection and free space
losses. Electromagnetic interference (EMI) both natural and
man made, interfere with radio communications.
The maximum useable frequency (MUF) is the
highest frequency that can be used for communications
between two locations at a given angle of incidence and time
of day. The lowest usable frequency (LUF) is the lowes
frequency that can be used for communications between twolocations.
5.3MULTIPATH CHANNEL CHARACTERISTICS
Because there are obstacles and reflectors in the
wireless propagation channel, the transmitted signal arrivals
at the receiver from various directions over a multiplicity o
paths. Such a phenomenon is called multipath. It is an
unpredictable set of reflections and/or direct waves each with
its own degree of attenuation and delay. Multipath is usually
described by: Line-of-sight (LOS): the direct connection
between the transmitter (TX) and the receiver (RX).
Non-line-of-sight (NLOS): the path arriving after reflection
from reflectors. The illustration of LOS and NLOS is shown
below.
fig 5.4. Effect Of Multipath On Mobile Station
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Characteristics of a Multipath Channel are
– this is the interval for which a symbol remains inside a
multipath channel
with one line of sight (LOS) path & several multipath, the
signals from the multipath being delayed and attenuated
version of the signal from the LOS path Multipath will cause
amplitude and phase fluctuations, and time delay in the
received signal.
6 COMMUNICATION CHANNEL
6.1 RAYLEIGH FADING CHANNEL
Rayleigh fading is a statistical model for the effect
of a propagation environment on a radio signal such as that
used by wireless devices. It assumes that the power of asignal that has passed through such a transmission medium
(also called a communications channels will vary randomly
or fade according to a Rayleigh distribution – the radial
component of the sum of two uncorrelated Gaussian random
variables. It is reasonable model for tropospheric and
ionospheric signal propagation as well as the effect of heavily
built up urban environment on radio signals. Rayleigh fading
is most applicable when there is no line of sight between the
transmitter and receiver.
Fig 6.2. Principle Of Multipath Channel
As shown in the model above, the path between base
station and mobile stations of terrestrial mobile
communications is characterized by various obstacles and
reflections. The radio wave transmitted from the base station
radiates in all directions.
These radio waves, including reflected waves that are
reflected off of various objects, diffracted waves, scattering
waves, and the direct wave from the base station to the
mobile station.
Therefore the path lengths of the direct, reflected
diffracted, and scattering waves are different, the time each
takes to reach the mobile station is different. The phase of the
incoming wave also varies because of the reflection.
As a result, the receiver receives a superpositionconsisting of several waves having different phase and time
of arrival. The generic name of a radio wave in which the
time of arrival is retarded in comparison with this direct wave
is called a delayed wave.
Then, the reception environment characterized by a
superposition of delayed waves is called multipath
propagation environment.
7. CHANNEL ESTIMATION TECHNIQUES FOR
PILOT
7.1 VARIOUS CHANNEL ESTIMATION TECHNIQUES
Channel estimation can be done in 3 ways. They are:
1. Channel estimation with TDM pilot.
2. Channel estimation with FDM pilot.
3. Channel estimation TDM pilot with first order
filtering.
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Fig 7.1. General Pilot Symbol Assisted OFDM
7.1.1 CHANNEL ESTIMATION WITH TDM-PILOT
For OFDM/TDM with pilot-assisted channel
estimation using TDM-pilot ,a pilot signal is transmitted
followed by Nd OFDM/TDM data frames is given below. Nc
subcarriers are used as pilots. First, by reverse modulation,
the instantaneous channel gain estimate Hg(n) at the nth
subcarrier is obtained .Then, Nc-point IFFT is applied to {
Hg(n); n=0∼ Nc−1 } to obtain the instantaneous channel
impulse response {h(τ ); τ =0∼ Nc−1 }. Assuming that the
actual channel impulse response is present only within the
GI, the estimated channel impulse response beyond the GI is
replaced with zeros to reduce the noise Finally, Nc-point FFT
is applied to obtain the improved channel gain estimates
{He,g(n); n=0∼ Nc−1 }.
Fig 7.1.1. OFDM Pilot Block Insertion
7.1.2 CHANNEL ESTIMATION WITH TDM-PILOT
AND TDFF
Fig 7.1.2. Channel Estimation With TDFF
The pilot signal {p(i); i = 0 ∼ Nm−1 } is inserted into( K −
1)th slot (i.e., dK−1(i) = p(i) for i = 0 ∼ Nm −1)and into the
GI as a cyclic prefix .Since the same pilot is used for al
frames, the ( g − 1)th frame’s pilot slot acts as a cyclic prefix
for the gth frame’s GI. Thus, the channel estimation can be
performed using the gth frame’s Nm-sample GI. Similar
frame structure was presented for SC transmission. The
channel gain estimate and noise variance estimate to be used
for FDE are denoted by He,g(n)and 2σ2e,g respectively
Hg(n) and σ2
g are replaced by He,g(n) and σ2e,grespectively
The received pilot {rg(t ); t = − Nm ∼ −1 } in the GI is filtered
on a slot-by-slot basis by the time-domain first-order filtering
to increase the signal-to-noise power ratio (SNR) of the pilo
signal. The filtered pilot signal is obtained as
for t =− Nm∼ −1, where γ is the forgetting factor with the
initial condition r 0(t ) = r 0(t ). Then, Nm-point FFT is applied
to decompose {rg(t ); t = − Nm ∼ −1 } into Nm sub carrier
components {Rg(q); q=− Nm∼
−1 } as
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With q=n\k for n=0 and the initial condition
R0(q)= R0(q). The instantaneous channel gain estimate at the
qth subcarrier is obtained by removing the pilot modulation
as
where ,P(q) and P(q) denotes the qth
frequency component of {p(t ); t =0∼ Nm−1 }.Since
the channel estimates are obtained only at the
frequencies n=0, Nm, 2 Nm,. . ., ( Nc-1) . Hence, an
interpolation is necessary to obtain the channel gains for all
frequencies (i.e., n = 0 ∼ Nc −1). Frequency-domain
interpolation is applied. First, Nm-point IFFT is performed on
{ Hg(q); q = 0 ∼ Nm−1 } to obtain the instantaneous channel
impulse response {h(τ ); τ = 0 ∼ Nm−1 } as
Then, Nc-point FFT is applied to obtain the
interpolated channel gain estimates {He,g(n); n = 0 ∼ Nc −1 }
for all Nc frequencies as
7.1.3 CHANNEL ESTIMATION WITH FDM-PILOT
For pilot-aided channel estimation with FDM-pilot
using frequency-domain interpolation an Nm equally-spaced
pilot subcarriers among Nc subcarriers are used. First, by
reverse modulation, the instantaneous channel gain est imate {
Hg(q); q = nNm for n =0 ∼ Nc−1 } at the pilot subcarriers is
obtained. where Nm is the number of pilot subcarriers. Since
q = nNm , the channel estimates are obtained only at the
frequencies n=0, Nm, 2 Nm,. . ., ( Nc-1)Hence, the frequency-
domain interpolation is used to obtain the channel gains for
all frequencies (i.e., n=0∼ Nc−1). Nm-point IFFT is
performed on { Hg(q); q = 0 ∼ Nm −1 } to obtain the
instantaneous channel impulse response {h(τ ); τ =0∼ Nm−1 }
and then, Nc-point FFT is applied to obtain the interpolated
channel gain estimates {He,g(n); n=0∼ Nc−1 }.
7.2 PILOT SEQUENCE SELECTION
Fig 7.2. Pilot Amplitude
(a) constant amplitude in frequency-domain (FD),
(b) constant amplitude in time-domain (TD) and
(c) constant amplitude in both time- and frequency domains
(Chu).
A selection of pilot sequence is an important design
issue. If the amplitude of P(n) drops at some frequencies, the
noise component in the channel estimate will be enhanced and
thereby, the estimation accuracy will degrade leading to poor
performance. To avoid the noise enhancement, it is desirable
that P(n) has constant amplitude irrespective of n. On the
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contrary, if P(n) is constant for all n, a large amplitude
variation may appear in p(t ) and consequently, the pilot signal
may be distorted due to nonlinear power amplification. So chu
sequence is used as the pilot which makes amplitude constant
in both time and frequency domain.
7.3 NOISE POWER ESTIMATION
The noise component at the qth pilot subcarrier can
be estimated by subtracting the received pilot component
He,g(q) P(q) from Rg(q) as
for q=0 ∼ Nm−1.
The noise variance estimate can be obtained as
7.4 OFDM DEMODULATION
By applying Nc-point IFFT after FDE, we obtain the
time-domain OFDM/TDM signal r ̂(t ) , which can be
expressed as
for t =0~ Nc-1.
Then, the decision variable for the ith data symbol in the k th
slot can be obtained using Nm-point FFT as
for i=0~ Nm-1 and k =0~K -1.
8. SIMULATION RESULTS AND ANALYSIS
We assume BPSK data-modulation with Nc=256
and Nm=16. Chu sequence is used as the pilot given by
for t =0∼ Nm−1 .
(R2-1)The propagation channel is an L=16-path block
Rayleigh fading channel having exponential power delay
profile with decay factor α as shown below. The zero-mean
independent complex path gains {hl; l=0∼ L−1 } remain
constant over one OFDM/TDM frame length and vary frame
by-frame. Without loss of generality, we assume τ 0 = 0 < τ 1
< · · · < τL−1 and that the lth path time delay is τl = lΔ
where Δ (≥ 1) denotes the time delay separation between
adjacent paths. The maximum time delay of the channel is
equal to the GI length (i.e., L= Ng).
Fig 8.1. Average BER Performance
We plot the average BER performance using the proposed
channel estimation as a function of Eb/N 0 for fDTs=0.0001
and α=0 dB. The optimum γ is used for each Eb/N 0 value. I
can be seen from the above figure that the OFDM/TDM with
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the proposed channel estimation achieves a much better BER
performance than OFDM; the required Eb/N 0 for BER=10−3
reduces by about 6.5 dB in comparison
with OFDM using TDM-pilot when fDTs=0.0001. The
Eb/N 0 degradation of OFDM/TDM in comparison to ideal
channel estimation is only about 0.6 dB.
Since γ is one of the key parameters in the estimator, the
robustness of the algorithm is discussed when γ is fixed.
Fig 8.1.1. BER In Raleigh Channel
The above figure illustrates the average bit error
rate (BER) performance with: (i) ideal CE, (ii) optimum γ
(i.e., γopt ) and (iii) fixed γ. BER performance is plotted as a
function of Eb/N 0 at fDTs=10−2. The figure shows that, for a
lower Eb/N 0 (i.e., Eb/N 0<15 dB), the BER with fixed γ=0.5
is almost the same as with γopt . As expected, γopt and fixed
γ=0.5 give the same BER at Eb/N 0=15 dB because γ=0.5 is
optimum value at Eb/N 0=15 dB and fDTs=10−2. However,
as Eb/N 0 increases (i.e., Eb/N 0>15 dB) the BER with fixed
γ=0.5 approaches a floor value of about BER=10−3, while
the performance with γopt consistently improves.
8.1 TRADE OFF BETWEEN THE NOISE REDUCTION
AND ROBUSTNESS AGAINST THE CHANNEL TIME
SELECTIVITY
The MSE equation is given by,
The MSE of channel estimator with time-domain
first-order filtering and frequency-domain interpolation is no
a function of the channel frequency-selectivity and it is only
a function of Es/N 0 and the channel time selectivity.
The first term of the above equation represents the influence
of AWGN, while the second term represents the influence of
the channel time-selectivity. Thus, a trade-off is present; as
the filter coefficient γ increases (decreases), the
channelestimator becomes more (less) robust against the
channel time selectivity while on the other hand, the
estimator ability to reduce the noise decreases (improves).
(R2-1) This trade-off property computed using the above
equation and is plotted as a graph .
0 5 10 15 20 2510
-5
10-4
10-3
10-2
10-1
Average Eb/No,dB
B i t E r r o r R a t e
BER for BPSK modulation with 2x2 MIMO and MMSE equalizer (Rayleigh channe
theory (nTx=2,nRx=2, ZF)
theory (nTx=1,nRx=2, MRC)
sim (nTx=2, nRx=2, MMSE)
Fig 8.1.2 . MMSE Equalization
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9 CONCLUSION
Thus the performance evaluation of OFDM/TDM
using MMSE-FDE with practical channel estimation in a fast
fading channel was presented. A tracking against fast fading
is improved by robust pilot-assisted channel estimation that
uses time-domain first-order filtering on a slot-by-slot basis
and frequency-domain interpolation. The MSE of the channel
estimator using time-domain first-order filtering and
frequency-domain interpolation was derived and then, a
tradeoff between improving the tracking ability against
fading and the noise reduction was discussed. It was shown
that the OFDM/TDM using MMSE-FDE provides a lower
BER and a very good tracking ability against fading in
comparison with conventional OFDM while keeping thesame data-rate transmission.
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