Noise Reduction in Fast Fading Channel Using OFDM/TDM

8/4/2019 Noise Reduction in Fast Fading Channel Using OFDM/TDM

http://slidepdf.com/reader/full/noise-reduction-in-fast-fading-channel-using-ofdmtdm 1/13

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

(IJCSIS) International Journal of Computer Science and Information Security,

Vol. 9, No. 8, August 2011

203 http://sites.google.com/site/ijcsis/ISSN 1947-5500



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



204 http://sites.google.com/site/ijcsis/

ISSN 1947-5500



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




ISSN 1947-5500



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




ISSN 1947-5500



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




ISSN 1947-5500



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:

.




ISSN 1947-5500



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




ISSN 1947-5500



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.




ISSN 1947-5500



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




ISSN 1947-5500



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




ISSN 1947-5500



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




ISSN 1947-5500



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




ISSN 1947-5500



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.

REFERENCES

[1] S. Hara and R. Prasad, Multicarrier Techniques for 4G

Mobile Communications, Artech House, June 2003.

[2] C. V. Sinn, J. Gotze and M. Haardt, ”Common

architectures for TDCDMA and OFDM based mobile radio

systems without the necessity of a cyclic prefix,” MS-SS

Workshop, DLR, Oberpfaffenhofen, Germany, Sept. 2001.

[3] H. Gacanin, S. Takaoka and F. Adachi,”Bit error rate

analysis of OFDM/TDM with frequency-domain

equalization,” IEICE Trans. Commun., Vol.E89-B, No.2,

pp.509-517, Feb. 2006.

[4] S. Coleri, M. Ergen, A. Puri, and A. Bahai, ”Channel

estimation techniques based on pilot arrangement in OFDM

systems,” IEEE Trans. Broad., Vol. 48, No. 3, pp. 362 -370,

Sept. 2002.

[5] M. Hsieh and C. Wei, ”Channel estimation for OFDM

systems based on comb-type pilot arrangement in frequency

selective fading channels,” IEEE Trans. Consumer Electron.

Vol. 44, No. 1, Feb. 1998.

[6] (R1) W. Zeng, X. Xia and P. C. Ching, ”Optimal training

and pilot pattern design for OFDM systems in Rayleigh

fading,” IEEE Trans. Comm., Vol. 52, No. 4, Dec. 2006.

[7] Y.-C. Choi, P. J. Voltz and F. A. Cassara, ”On channel

estimation and detection for multicarrier signals in fast and

selective rayleigh fading channels,” IEEE Trans. Comm.

Vol. 49, No. 8, pp. 1375-1387, Aug. 2001.

[8] D. Falconer, S.L. Ariyavisitakul, A. Benyamin-Seeyar

and B. Eidson, ”Frequency-domain equalization for single

carrier broadband wireless systems,” IEEE Commun. Mag.

Vol. 40, Issue 4, pp.58-66, April 2002.

[9] J. Coon, M. Sandell, M. Beach and J. McGeehan

”Channel and noise variance estimation and tracking

algorithms for unique-word based single-carrier systems,”

IEEE Trans. Wireless Comm., Vol. 5, No. 6, June 2006.

[10] L. Deneire, B. Gyselinckx, and M. Engels, ”Training

sequence versus cyclic prefixa new look on single carrier

communication,” IEEE Commun. Lett., vol. 5, no. 7, pp

292294, July 2001.

[11] O. Edfors, M. Sandell, J.-J. van de Beek, S. K. Wilson

and P. O. Borjesson, ”OFDM channel estimation by singular

value decomposition,” IEEE Tran. Commun., Vol. 46, No. 7

pp. 931-939, July 1998.

[12] S. Haykin, Adaptive Filter Theory, Prentice Hall, 1996.




Date post:	07-Apr-2018
Category:	Documents
Upload:	ijcsis
View:	228 times
Download:	1 times

Noise Reduction in Fast Fading Channel Using OFDM/TDM

Documents