Inte rnatio nal Jo urnal o f Sc ie ntific & Eng inee ring Re se arc h Vo lume3, Issue 1, January 2012 1

ISS N 2229-5518

Channel Estimation in Multipath fading

Environment using Combined Equalizer and

Diversity Techniques

Deepmala Singh Parihar , Prof. Ravi Mohan

Abs tract - The channel estimation has become very vast f ield due to different types of interf erence present in w ireless channel and in equipments. In this thesis, estimation algorithms f or digital communications systems in the presence of Additive White Gaussi an noise and Mult ipath environment are explored and their perf ormance is investigated. In particular, least square Error and Zero f orcing equalizers are used to provide the optimum solution and compensate f or Inter -Symbol error. As the BER perf ormance of equalizers in variable in mult ipath f ading channel theref ore w e have combined Equa l Ga in comb ining and Maximal Rat io Comb ing Diversity techniques, and searched that Maximal Ratio combining techniques is able to f ight w ith Co-Channel interf erence and Inter-symbol interf erence problem.

Ke ywords : - OFDM, Equa lizer, Diversity, QAM

—————————— ——————————


Wireless communication [1] systems require signal processing techniques that improve the link performance in hostile mobile radio environments. Complex channel estimation i.e. estimation of channel gain, which includes phase and amplitude. Equalization, diversity and channel coding are three techniques which can be used independently or in tandem to improve received signal quality and link performance over small scale times and distances. In flat fading environment, estimation of the channel using trained sequence of the data has been studied and implemented in [2]. Then pilot data of some required percentage of data length is inserted into the source data. It is used to estimate the random phase shift of the fading channel and train the decision to adjust the received signal with phase recover. So, finally phase estimation using training symbol is implemented in flat fading environment. The radio channels in mobile radio systems are usually multipath fading channel, which are causing intersymbol interference (ISI) and intercarrier interference (ICI) in the received signal. To remove ISI and ICI from the signal many kind of equalizers and diversity algorithms can be used. Detection algorithms based on trellis search like Least square error (LSE) and Zero forcing (ZF) algorithms for equalization[3] and Maximal ratio combining (MRC) and Equal gain combining (EGC) for diversity techniques [4] offer a good receiver performance, but still often not much computation. Therefore, these algorithms are currently quite popular. Channel estimation in frequency selective has different approach then compared with flat fading environment.
Semi analytical method to evaluate BER of quadrature amplitude modulation (QAM) and additive noise where pilot assisted linear channel estimation and channel equalization. A novel channel estimation scheme for
OFDMA uplink packet transmissions over doubly selective channels was suggested in [5 ].


OFDM is a spectrally efficient modulation technique [6]. It is conveniently implemented using IFFT and FFT operation. There are very fast and efficient implementation of the FFT and IFFT, which is the big reason of the popularity of OFDM. It handles frequency selective channels well when combined with error correction coding. In other words OFDM is frequency division multiplexing of multicarriers which are orthogonal to each other i.e. they are placed exactly at the nulls in the modulation spectra of each other. In OFDM data is divided into several parallel data streams or sub-channels, one for each sub carrier which are orthogonal to each other although they overlap spectrally. Each subcarrier is modulated with a conventional modulation scheme (QAM or QPSK) at a low symbol rate, maintaining total data rates similar to conventional single carrier modulation schemes in the same bandwidth.
Figure 1 Subdivision of the channel bandwidth W into
narrowband sub channels of equal width ∆f
The advantages of OFDM include its robustness to narrowband cochannel interference. High spectral efficiency and its low sensitivity to time synchronization errors.

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Besides these advantages it has some disadvantages like its complexity and sensitive to Doppler shift and frequency synchronization problems. OFDM requires a more linear power amplifier.
Figure 2 Block diagram of OFDM transmitter and receiver FFT is written as ... (1)

3.1 Zero Forcing Algorithm s:

In a zero forcing equalizer, the equalizer coefficients Cn are chosen to force the samples of the combined channel and equalizer impulse response to zero at all. For a channel with frequency response F(f) the ZF equalizer . Thus the combination of channel and equalizer gives a flat frequency response and linear phase must satisfy Nyquists criterion.

.... (4)

Zero Forcing equalizer has the disadvantage that the inverse filter may excessively amplify noise at frequencies where the folded channel spectrum has h igh attenuation.

3.2 Least Mean Square Algorithms:

A more robust equalizer is the LMS equalizer where the criterion used is the minimization of the MSE between the desired equalizer output and the actual equalizer output. Define the input signal to the equalizer as a vector yk.
Mean Square Error is

WN be the complex-valued phase factor
Thus, X (k) becomes

Similarly IFFT is written as,


... (2)
… (3)

… (5)

Equalization can be used to any signal processing operation that minimizes intersymbol interference (ISI). Since the mobile fading channel is random and time varying, equalizer must track the time varying characteristics of the mobile channel and thus are called adaptive equalizer.


In telecommunication, a diversity scheme refers to a method for improving the reliability of a message signal by using
Equalization is the process of adjusting the balance
between frequency components within an electronic signal.
The circuit or equipment used to achieve equalization is
called Equalizer [7]. Equalization compensates for ISI created by multipath within time dispersive channels. If the modulation bandwidth exceeds the coherence bandwidth of the radio channel, ISI occurs and modulation pulses are spread in time into adjacent symbols. An equalizer within a receiver compensates for the average range of expected channel amplitude and delay characteristics. Equalizers must be adaptive since the channel is generally known and time varying. So, an adaptive equalizer compensates for an unknown and time varying channel, it requires a specific algorithms to update equalizer coefficients and track the channel variations, we use zero forcing (ZF) algorithm and least square error (LSE) algorithm.
two or more communication channel with different characteristics. Diversity plays an important role in combating fading and co-channel interference and avoiding error bursts. It is based on the fact that individual channels experience different levels of fading and interference. Multiple version of the same signal may be transmitted and/or received and combined in the receiver. Diversity technique may exploit the multipath propagation, resulting in a diversity gain, often measured in decibels.
Diversity combining is the technique applied to combine the multiple received s ignals of a diversity reception device into a single improved signal. Various diversity combining techniques can be distinguished.

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4.1 Equal Gain Combining (EGC):

All the received signals are summed coherently. With two receive antennas, the BER with equal gain combining is

.... (6)

The effective with EGC is

4.2 Maximal Ratio Combining (MRC):

.... (7)

Figure 3 QAM modulator
For a 4-QAM signal, we have M = 4, so we have 4 symbols representing a two bit word. Therefore, for M = 16 and 64, we have 16 symbols representing a four bit word and 64
symbols representing a six bit word respectively.
It is often used in large phased array systems. The received signals are weighted with respect to their SNR and then summed. The resulting SNR yield where
is SNR of the received signal k.


The bit error probability e
expressed in equation is
M-ary QAM
for M-ary QAM is

Given that the effective bit energy to noise ratio with maximal ratio combining is , the total bit error rate is

pe  4(1 

1 ).T .


3 . E M  1 No

… (11)

the integral of the conditional BER integrated over all
possible values of.

. (8)


If we set the simulation environment for the OFDM based wireless modulation, then we get the variable performance for equalizers as well as for diversity techniques.
The effective with MRC is

5 Q AM

… (9)

The following results have been obtained with the considered combinations.
Figure 1, shows the effect of 256 OFDM subchannels, 4 QAM
with 1000 number of iterations.

BER with 'LS','MRC','ZF','EGC' and with 256 subchannels, 4 QAM and 1000 iterations



Quadrature amplitude amplitude (QAM) conveys two
digital bit streams by changing the amplitudes of two carrier 10-1
waves using amplitude shift keying. These two sinusoidal waves are out of phase with each other by 90 degrees.


The in-phase signal (the I-signal, e.g., cosine waveform) and a quadrature phase signal (the Q-signal, e.g., sine waveform) are amplitude modulated with a finite number of amplitudes and summed, resulting a combination of phase shift keying and amplitude shift keying.
The QAM equation is represented as follow in equation




0 3 6 9 12 15 18 21 24 27 30

SNR in dB

Figure 1.

s(t )  A

2 cos((t )) cos(2f t )  A

2 sin((t )) sin(2f t )

c T c c T c


Where …. (10)


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ISS N 2229-5518
















Figure 2, shows the effect of 1024 OFDM subchannels, 4
QAM with 1000 number of iterations.

BER with 'LS','MRC','ZF',EGC' and with 1024 subchannels, 4 QAM and 1000 iterations



Figure 4, shows the effect of 1024 OFDM subchannels, 32
QAM with 1000 number of iterations .



BER with 'LS','MRC','ZF',EGC' and with 1024 subchannels, 32 QAM and 1000 iterations










10 -0.08






0 3 6 9 12 15 18 21 24 27 30

SNR in dB

Figure 2







0 3 6 9 12 15 18 21 24 27 30

SNR in dB

Figure 4
Figure 3, shows the effect of 512 OFDM subchannels, 32
QAM with 1000 number of iterations.

BER with 'LS','MRC','ZF','EGC' and with 512 subchannels,32 QAM and 1000 iterations

















The wireless communication without the channel estimation results in high errors. Therefore channel estimation is most important to know the parameters of the channel and also to get the knowledge of affecting parameters.
If we look at the simulation result with 1024 sub channels and 1000 iterations, we find that the BER curve is becoming linear and therefore with high number of

0 3 6 9 12 15 18 21 24 27 30

SNR in dB

Figure 3
subcarriers and with 1000 iterations we get better results
compared to 256 and 512 sub channel conditions.
One thing is clear here that with lower order QAM modulation techniques results are not much comparative, but results in bunching like the optimum performers.
Only the change between performances can be seen with lower number of subcarriers and with 1000 iterations.

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ISS N 2229-5518

Therefore we conclude with this assumption that with 1000 iterations we have better performance of used algorithms and MRC is very much able to show expected results.


[1] THEODORE S. RAPPAPORT, “Wireless Communication, Principles and practice,” 2nd Edition.

[2] Zhifeng Chen, “Performance Analysis of Channel Estimationand adaptive

equalization inslow fading Channel”. University of Florida.

[3] Jan-Jaap van de Beek, Ove Edfors, magnus Sundell, Sarah Kate Wilson and

PerOla B. rjesson, “OnChannel estimation inOFDMsystems”.

[4] D.G.Brennan, “Linear diversity combining techniques”,

[5] P. Fertt and G.Matz, “Multi-user channel estimation in OFDMA uplink systems based on irregular sampling and reduced pilot overhead”, In Proceeding of IEEE ICASSP 2007.[

[6] Edfors,O. Sandell, M., Van de beek, J-J., Landsttrom, D, and sjoberg, F., An

introduction orthogonal frequency division multiplexing, Luled Sweden: Luled Tekniska universitet, 1996, pp. 1-58.


Deepmala SinghParihar


Shri Ram Institute of Technology, Jabalpur

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