Poster Paper Proc. of Int. Conf. on Advances in Computer Engineering 2011
Performance Evaluation of Coded and Adaptive Filter assisted MRC in Faded Wireless channels using Semi Analytic and Monte Carlo Approach Atlanta Choudhury Dept. of Electronics and Communication Engineering Tezpur University,Tezpur-784028, Assam, India. email@example.com
Kandarpa Kumar Sarma .Dept. of Electronics and Communication Technology Gauhati University, Guwahati-781014, Assam, India firstname.lastname@example.org Abstract- The work is related to performance evaluation of the use of error correction coding and adaptive equalization as an aid to Maximal Ratio Combining (MRC) in faded wireless channels using Semi Analytic and Monte Carlo approach. Modulation techniques used in this work are Bipolar Phase Shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK) and Differential Phase Shift Keying (DPSK) in Gaussian, multipath Rayleigh and Rician fading channels. The work considers the use of Least Mean Square (LMS), adaptive filter blocks as part of a MRC set-up and is tested under SNR variation between -10 to 10 dB . The results generated justify the use of the adaptive equalizer block as an aid to the MRC setup.
the best combination for the considered experimental framework. Though the work considers RLS filters also, for practical purposes the LMS - based adaptive filters are preferred due to their overall efficiency .The performance of these approaches are evaluated using Semi Analytic and Monte Carlo approach. II. WIRELESS CHANNELS AND BASIC CONSIDERATIONS OF MAXIMAL_RATIO COMBINING (MRC) T ECHNIQUE Wireless communication utilizes modulation of electromagnetic (radio) waves with a carrier frequency varying from a few hundred megahertz to several gigahertz depending on the system. Therefore, the behavior of the wireless channel is a function of the radio propagation effects of the environment. In such an environment the following may happen  : 1. Multiple delayed receptions of the transmitted signals due to the reflections of buildings, hills, cars and other Obstacles, etc. 2. Absence of a line-of-sight (LOS) path and prominence of non-LOS (NLOS) components. 3. Varying attenuation, time delay, phase shift etc in each path 4. Constructive and destructive addition of the constituent paths due to multiple phase shifts resulting in fluctuations in the signal strength. These factors act together to give rise to a phenomenon known as fading. The stochastic nature observed in wireless channels can be described by the Rayleigh and Rician fading which represent the absence and presence of a LOS component respectively. In such condition, the diversity techniques are used to improve reliability of reception. Out of several diversity techniques MRC is preferred due to the fact that it maximizes the correct reception and reduces intersymbol interference (ISI). In MRC, the signals from all of the M branches are weighted according to their signal voltage to noise power ratios and then summed. It uses linear coherent combining of branch signals so that output SNR is maximized  . The following section provides a brief outline of the theoretical basis of the MRC technique. The individual branch signals are:
Keywords: AWGN, Rayleigh, Rician, MRC, LMS, block code, Monte Carlo, Semi Analytic approach
I. INTRODUCTION Diversity combining is one of the most widely employed techniques in digital communications receivers for mitigating the effects of multipath fading. It contributes significantly towards improving the overall system performance. The most popular diversity techniques are equal-gain combining (EGC), maximal-ratio combining (MRC), selection combining (SC) and a combination of MRC and SC, called generalized selection combining (GSC)  . This work is related to the design of an MRC scheme assisted by coding and coding adaptive equalization block so as to investigate the performance of the combination in Gaussian and multipath slow fading channels. The work uses Bipolar Phase Shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK) and Differential Phase Shift Keying (DPSK) modulation in Gaussian, Rayleigh and Rician fading channels with SNR variation in the range -10 to 10 dB range. The objective is to determine the appropriate combination of MRC and adaptive filters such that better BER values are obtained for the given modulation techniques and the channel types. The work considers performance difference in terms of BER rate obtained using both using MRC, MRC - Equalizer and coding -MRC-Adaptive-Equalizer combination. Here Least Mean Square (LMS), N-LMS and Recursive Least Square (RLS) adaptive filters are taken as part of the set-up to determine ÂŠ 2011 ACEEE DOI: 02.ACE.2011.02.179
Poster Paper Proc. of Int. Conf. on Advances in Computer Engineering 2011 is the branch SNRs when all the branch noise powers are equal.
X n Ag n n —————————————(1) where, A is complex envelope (amplitude), gn is channel gain; is additive white Gaussian noise (AWGN). The output of the combiner is
n 0 ———————————— ——(12)
X out Wn g n AWn g n Wn n ————(2) n 1
The branch gain is proportional to the channel gain and coherent combining. If A(t) is the original transmitted signal, the output signal after applying MRC is, L
MRC (t ) A(t )
L i 1
f i ni Lt
Where, fi (t) and ni(t) are fading envelope and additive noise of the ith path  . The received signal from the ith diversity path is, Fig.1: Maximal Ratio Combiner
The signal and the noise power at the outputs are:
If the additive noise is small enough to be neglected the received signal, ri(t) fi.A(t), Therefore, at high SNR when AWGN is small enough to be neglected. MRC yields the transmitted signal influenced by the type of fading. In the Mth branch diversity set up, the received signal can also be expressed as,
1 Ps | n g n A | | A |2 | n g n |2 -————(3) 2 n 2
PE | n n |2 | n | n 2 ————————(4) n
n 2 | n |2 —————————————(5) The phase Φi is uniformly distributed over the range [0; 2π]. f i is the fading observed and may be Rayleigh, Rician and Nakagami. In a mobile environment it is reasonable to assume that the received signal on the kth branch is superimposed by a large number of multipath signals. All component signals can be treated as m independent groups. In each groups, there are n j(j = 1; 2;….;m) irresolvable “sub-path“ signals which have almost identical amplitude and phase and the sum of sub-path signals in each group forms jth “resolve“ multipath component signal. The relevant signals becomes
is the branch noise power. The output SNR is,
P 1 S | n |2 PE 2
| n g n |2 n
|2 n 2
The above can be maximized using Schwartz inequality,
with the equality achieved when,
an * cbn —————————————— — (8) Assuming X k ( j ) and Yk ( j ) to be independent Gaussian
The result is, It is achieved when,
distributed, the amplitude of Rk ( j ) can be considered to be
max n ———————————— ——(9)
Rayleigh distributed. The received signal power on the kth
branch can be expressed as,
————————————— — (10) where, µk=(µk(1).µk(2)……….µk(m))T, <.> represents the norm operator.
A2 2 n
© 2011 ACEEE DOI: 02.ACE.2011.02.179
f k 2mk 2 178
Poster Paper Proc. of Int. Conf. on Advances in Computer Engineering 2011 mk being the fading parameter. Assuming flat fading and perfect knowledge of the channel, the weighting factor in an MRC combiner is,
Wk B.( f k . e j . Ak ) n
which at equalized state shall be maximum. A similar expression can be also developed for the coded signal as well which provides gain in combination of MRC and the equalizer.
Wk B ( f k . e jk ) Thus the instantaneous SNR combiner is given by  
at the output of the MRC
III. CODING AND BASIC CONSIDERATIONS EXPERIMENTAL DETAILS AND RESULTS
f k 2 k --------------------------------------(15)
The experimental work carried out can be summarized by the block diagram shown in Figure 1. Initially the data obtained in binary form are modulated using three different techniques namely QPSK, BPSK and DPSK. The aim is to use coherent and non-coherent modulation schemes so as to determine combinations to nullify the effects of stochastic nature of the wireless channel. The proposed system model is depicted in Figure 2. The signal at the receiver is captured by several diversity branches and passed on to the demodulation blocks. Before demodulation and reconstruction, there is an equalizer block which is combined with the MRC to make improvement in the SNR of the received signal. The equalizer is designed using the LMS algorithm and is provided a mean square error (MSE) convergence goal of 10"3. The equalizer takes around 150 iterations on an average to reach this goal for about 50 sets of data. Four path Rayleigh and Rician channels are generated using the considerations described in Section III. The set of characteristics for multipath fading generated using the parameters given in Table I by using Clarke- Gans Model. Similarly, the Rician channel generated using corresponding considerations.
Eb N 0 is the symbol energy to Gaussian Noise Spectral
Density ratio. The instantaneous input SNR per symbol for each branch is defined as,
Es ). f k 2 --------------------------------------------------(16) N0
The output of the MRC(Maximal Ratio Combiner) shall vary after the use of a post MRC LMS equalizer. Let be a vector applied to the equalizer. The equalizer with weight coefficients represented by W generated an output.
where, If signal
is the desired output (= a known signal
), the error
may be given as
ek d k dˆ k x k d k xˆ k y kt wk ---------------(18) The mean square error (MSE) |ek|2 at time instant k is obtained as,
E[ek* ek ] ----------------------------------------------------(19) The prediction error is dependent on tap gain vector WN which can be represented by a cost function J(WN) . The prediction error is dependent on tap gain vector WN which can be represented by a cost function J(WN). Minimization of MSE is related to J(WN) where P is a cross correlation vector between the desired response,
fig1: Block Diagram
and input signal given as
From the above equation,
To determine W, N training symbols are required. This is the LMS algorithm which required 2N+1 operations per iterations. With the equalizer placed after the MRC, The output SNR can be given as
Fig 2:Proposed system model of coding and adaptive equalization assisted
© 2011 ACEEE DOI: 02.ACE.2011.02. 179
Poster Paper Proc. of Int. Conf. on Advances in Computer Engineering 2011 After the channels are generated the modulated signals are convolved to provide the transmission effect. Additive Gaussian noise is mixed with values of -3, 1 and 3 dB for three separate channel sets each of size twenty. At the receiver end the MRC process is carried out with two and three branch configurations. The three branch configuration provides better results but at the cost of greater computational constraints. The updating process of the weights of the MRC system is linked to the equalizer in a way that the process continues adaptively till the SNR crosses the fixed threshold value. The use of the equalizer block with the MRC system is thus justified. The data before modulation is coded using linear block code (Hamming code) in (7, 4) format which help to improve the quality of the received signal in the figure 5. Experiments are carried out with and without the equalizer block. Results are derived from of the set-up for SNR ranges between -10 and 10 dB. The presence of the equalizer block improves the BER values as depicted by Figure 4.
Fig 4: MRC plot with three branches and equalization
TABLE I PARAMETERS USED FOR SIMULATING CHANNEL USING CLARKE-GANS MODEL
Fig 5: BER calculation by using linear block (7,4) code
IV. SEMI ANALYTIC APPROACH AND MONTE CARLO SIMULATION FOR PERFORMANCE EVALUATION The semianalytic (SA) technique works well for certain types of communication systems, but not for others. The semi analytic technique is applicable if a system has all of the following characteristics: 1) Any effects of multipath fading, quantization, and amplifier Non linearity must precede the effects of noise in the actual channel being modeled. 2) The receiver is perfectly synchronized with the carrier, and timing jitter is negligible. 3) The noiseless simulation has no errors in the received signal constellation.
Fig 3: BER calculation by using coded adaptive equalizer and MRC
Fig 6: BER calculation by using Monte Carlo Approach
ÂŠ 2011 ACEEE DOI: 02.ACE.2011.02.179
Poster Paper Proc. of Int. Conf. on Advances in Computer Engineering 2011 The improvement is noticeable despite a SNR range of around -10 to 10dB. The system can be improved further if some error correcting codes can be incorporated during transmission. The work on an extended scale is applicable to mobile and wireless communication transmitting data through Gaussian and multipath fading channels. Here we have compared the bit error rate of various modulation schemes in a faded channel using Semi Analytic and Monte Carlo approach. REFERENCES  T. S. Rappaport: “Wireless Communications: Principles and Practice, Second Edition” Pearson Education, Seventh Indian Reprint, 2004.  J. G. Proakis: “Digital Communications, Fourth Edition” McGraw-Hill Publication, 2001  S. Haykins: Adaptive Filter Theory, 4th Ed., Pearson Education, New Delhi, 2002  A. B. Idris, R. F. b. Rahim and D. b. Mohd Ali: “ The Effect of Additive White Gaussian Noise and Multipath Rayleigh Fading On BER Statistic in Digital Cellular Network “ International COnference on RFand Microwave Conference, Malaysia, pp. 97 - 100, Sept 12 14, 2006.  W. Hamouda: “ Performance Analysis of Space Time MMSE Multiuser Detection for coded DS-CDMA systems in Multipath Fading Channels”, IEEE Transactions on Wireless Communications, Vol.5, No.4, pp: 829 -838, April, 2006.  A. Maaref and S. Aissa: “ Performance and analysis of Orthogonal Space Time Block Codes in spatially correlated MIMO Nakagami Fading Channels”, IEEE Transactions on Wireless Communications, Vol. 5 , No. 4, April, 2006.  R. Y. Yen: “ A General Moment Generating Function for MRC Diversity over Gaussian Gain Fading Channels”, Department of Electrical Engineering, Tamkang University, Tamsui, Taiwan, Tamkang Journal of Science and Engineering, vol. 9, No 4, pp: 353 356, 2006.  R. H. Ismail and M. M. Matalgah: “ BER analysis of BPSK modulation over the Weibell Fading Channel with CCI”, In Proceedings of IEEE 64th Vehicular Technology Conference (VTC-2006), pp. 1 - 5, 2006.  K. Teknomo: “ Monte Carlo Simulation Tutorial”, Available at www.people.revoledu.com kardi tutorial Simulation, downloaded on 9-02-2011
Fig 7: MCS of BER estimation of MRC in Rayleigh faded channel
Fig 8: MCS for BER estimate Vs symbol delay of MRC in Rayleigh faded Channel
Monte Carlo Simulation (MCS) is a class of numerical method for computer simulations or computer experiments to generate random sample data based on some known distribution for numerical experiments . The direct output of Monte Carlo simulation method is generation of random sampling. Other performance or statistical outputs are indirect method, which depend on the applications. Some of the results derived using SA and MCS.A plot of BER estimate in Rayleigh fading channel generated using coding and MRC. The phase error generated by this arrangement while the BER related to symbol delay is shown in Figure 8. The evaluation framework thus prepared clearly indicates the effectiveness of coding and adaptive equalization assisted MRC in tackling stochastic behavior of the wireless channels. V. CONCLUSION This work is an attempt to investigate the effect of combined use of coding, MRC and equalization in Gaussian and multipath fading channel with strong LOS and N-LOS components. At the receiver end, after the MRC stage, when an LMS equalizer is placed and linked to adaptively update the connecting weights of the MRC system, the BER improves considerably both in Gaussian and fading channels.
© 2011 ACEEE DOI: 02.ACE.2011.02. 179