VOL. 6, NO. 9, SEPTEMBER 0 ISSN 89-6608 006-0 Asian Researc Publising Network (ARPN). All rigts reserved. BIT ERROR RATE, PERFORMANCE ANALYSIS AND COMPARISION OF M x N EQUALIZER BASED MAXIMUM LIKELIHOOD AND MINIMUM MEAN SQUARE ERROR MIMO RECEIVER FOR WIRELESS CHANNEL N. Satis Kumar and K. R. Sankar Kumar Department of ECE, SriRamakrisna Engineering College, Coimbatore, Tamil Nadu, India E-Mail: nsk0000@gmail.com ABSTRACT Tis paper investigates on te performance comparison of m x n equalizer based maximum likeliood (ML) and minimum mean square error (MMSE) MIMO receiver for wireless cannel. Te effect of fading and interference effects can be combated wit equalizer. Tis paper also analyses te performance of MMSE equalizer based receiver for MIMO wireless cannel. Te bit error rate (BER) caracteristics for te various transmitting and receiveing antennna are simulated in Matlab tool box and many advantages and disadvantages of te system are described. Te simulation carried out in signal processing lab sow tat te MMSE equalizer based receiver is a good coice for removing some inter symbol interference (ISI) and minimizes te total noise power. However te simulation results sow ML equalizer performance better. Te simulation tool box used is Matlab V.7.0 and te results were obtained at RF signal processing lab. Te results sow tat te BER decreases as te m x n antenna configurations is increased for bot ML and MMSE equalizer based detector. ML equalizer based detector out performs te MMSE receiver in terms of BER caracteristics. Keywords: wireless cannel, MIMO, MMSE, ISI, bit error rate, signal to noise ratio.. INTRODUCTION Wireless communication tecnology as sown tat wen multiple antennas at bot transmitter and receiver are employed it provides te possibility of iger data rates compared to single antenna systems [, ]. Te system wit multiple antennas at te transmitter and receiver is commonly referred as multiple input multiple output (MIMO) systems. Te multiple antennas are tus used to increase data rates troug multiplexing or to improve performance troug diversity. Tis metod offers iger capacity to wireless systems and te capacity increases linearly wit te number of antennas and link range wit out additional bandwidt and power requirements. MIMO cannel model [4, 5] is depicted in Figure- wit M transmitter and N receiver antennas. It can be acieved by iger spectral efficiency and link reliability or diversity (reduced fading).. ML EQUALIZER BASED RECEIVER It is a preferred metod of parameter estimation in statistics. It is an important tool for many statistical non-linear modeling tecniques. MLE estimate is obtained by maximizing te log-likeliood function since because te functions are monotonically related to eac oter; ence MLE estimate is obtained by maximizing eiter one. For determining te maximum likeliood estimators of te log-normal distribution parameters µ and σ, can be determined as follows, () were, ƒ L denote te probability density function of te log-normal distribution and ƒ N is te normal distribution. Terefore, using te same indices to denote distributions, we can write te log-likeliood function as Figure-. MIMO model. = Constant + () Since te first term is constant wit regard to µ and σ, bot logaritmic likeliood functions, l L and l N, reac teir maximum wit te same µ and σ. Hence, using te formulas for te normal distribution maximum likeliood parameter estimators and te equality above, we deduce tat for te log-normal distribution as 9
VOL. 6, NO. 9, SEPTEMBER 0 ISSN 89-6608 006-0 Asian Researc Publising Network (ARPN). All rigts reserved. (3) Te Maximum Likeliood receiver tries to find, wic minimizes J (4) Since te modulation is BPSK, te possible values are + or -. To find te Maximum Likeliood solution, we need to find te minimum from te all four combinations of and (5) 3. MMSE EQUALIZER In MIMO wireless communication, an equalizer is employed wic is a network tat makes an attempt to recover a signal tat suffers wit an Inter symbol Interference (ISI) and improves te BER caracteristics and maintains a good SNR. A minimum mean square error (MMSE) estimator is a metod in wic it minimizes te mean square error (MSE), wic is a common measure of estimator quality. Minimum mean-square error equalizer, wic does not usually eliminate ISI completely but instead, minimizes te total power of te noise and ISI components in te output. A minimum mean square error (MMSE) estimator describes te approac wic minimizes te mean square error (MSE), wic is a common measure of estimator quality. Te main feature of MMSE equalizer is tat it does not eliminate ISI completely but, minimizes te total power of te noise and ISI components in te output. Let x be an unknown random variable, and let y be a known random variable. An estimator x^ (y) is any function of te measurement y, and its mean square error is given by MSE = E {(X^ -X )} (6) were te expectation is taken over bot x and y. Te MMSE estimator is ten defined as te estimator acieving minimal MSE. In many cases, it is not possible to determine a closed form for te MMSE estimator. In tese cases, one possibility is to seek te tecnique minimizing te MSE witin a particular class, suc as te class of linear estimators. Te linear MMSE estimator is te estimator acieving minimum MSE among all estimators of te form AY + b. If te measurement Y is a random vector, A is a matrix and b is a vector. Let us now try to understand te mat for extracting te two symbols wic interfered wit eac oter. In te first time slot, te received signal on te first receive antenna is, y = x +, x + n = [, ] x x + n (7) Te received signal on te second receive antenna is, y =, x +, x + n = [,, ] Were x x + n (8) y, y are te received symbol on te first and second respectively., is te cannel from st transmit antenna to st receive, is te cannel from nd transmit antenna to st receive, is te cannel from st transmit antenna to nd receive, is te cannel from nd transmit antenna to nd receive x, x are te transmitted symbols and n, n are te noise on st and nd receive antennas. Te equation can be represented in matrix notation as follows: y y Equivalently,, = + (9),, x x n n y = Hx + n (0) Te Minimum Mean Square Error (MMSE) approac tries to find a coefficient W wic minimizes te E {[W y-x ] [W y-x ] H } Criterion, Were W = Equalization Matrix H = Cannel Matrix and n = Cannel noise y = Received signal. 0
VOL. 6, NO. 9, SEPTEMBER 0 ISSN 89-6608 006-0 Asian Researc Publising Network (ARPN). All rigts reserved. To solve for x, we need to find a matrix W wic satisfies WH =I. Te Minimum Mean Square Error (MMSE) detector for meeting tis constraint is given by, W = [H H H+ N o I) - H H () Tis matrix is known as te pseudo inverse for a general m x n matrix Were, H H H = =,, + +,,,,,,,,, + +,,, () 4. SIMULATION RESULTS AND DISCUSSIONS Te simulations were carried out at RF Signal Processing Lab. Figure- and Table- sows tat as te number of receivers (n) is increased keeping te number of transmitters (m =, 3 and 4) as constant it is observed tat te (BER) decreases in ML equalizer. 0.3 0.5 0. 0.5 BER comparison of ML equalizer for xn MIMO receiver x x3 x4 x5 B it E rror R ate 0.5 0. 0.5 0. BER comparison of ML equalizer for 3xn MIMO receiver 3x 3x3 3x4 3x5 3x6 0. -0-8 -6-4 - 0 4 (a) -0-8 -6-4 - 0 4 (b) 0.5 0. 0.5 0. BER comparison of ML equalizer for 4xn MIMO receiver 4x 4x3 4x4 4x5 4x6-0 -8-6 -4-0 4 (c) (d) Figure-. Comparison of BER analysis for m x n antenna configurations of ML equalizer.
VOL. 6, NO. 9, SEPTEMBER 0 ISSN 89-6608 006-0 Asian Researc Publising Network (ARPN). All rigts reserved. S. No. Table-. Bit error rate value for = -0dB m x n Value m x n Value m x n Value x 0.9 3x 0.47 4x 0.7 x3 0.633 3x3 0.833 4x3 0.89 3 x4 0.33 3x4 0.386 4x4 0.4 4 x5 0.096 3x5 0.003 4x5 0.3 5 - - 3x6 0.07089 4x6 0.074 Now let us consider te simulation analysis of MMSE equalizer for x n antenna configurations wic means keeping te transmitter antenna as two and vary te number of antennas in te receiver side. From te matlab figure window sown in Figure-, it s evident tat te BER decreases as te receiver antenna increases for te zero forcing equalizer. For a better clarity te data from te figure window is taken and plotted in te form of bar cart as sown in Figure-3. Figure-3 and Table- sows tat as te no. of receivers (n) is increased keeping te no. of transmitters (m =, 3 and 4) as constant it is evident tat te Bit Error Rate (BER) decreases in MMSE equalizer and also wen te number of transmitters is less tan te number of receivers BER decreases and vice versa. comparison of BER analysis of MMSE equalizer for various configurations of MIMO receiver comparison of BER analysis of MMSE equalizers for various configurations of MIMO receiver 0 - x x3 x4 x5 0-3x 3x3 3x4 3x5 3x6 0 - -0-9 -8-7 -6-5 -4-3 - - 0 3(a) 0 - -0-8 -6-4 - 0 4 3(b) comparison of BER analysis of MMSE equalizer for various configurations of MIMO receiver 0-4x 4x3 4x4 4x5 4x6 0 - -0-8 -6-4 - 0 4 3(c) Figure-3. Comparison of BER analysis for m x n antenna configurations of MMSE equalizer. 3(d)
VOL. 6, NO. 9, SEPTEMBER 0 ISSN 89-6608 006-0 Asian Researc Publising Network (ARPN). All rigts reserved. Table-. Bit error rate values for m x n antenna configurations of MMSE equalizer. S. No. Bit error rate value for E b /N o = -0dB m x n Value m x n Value m x n Value x 0.33 3x 0.633 4x 0.75 x3 0.77 3x3 0.883 4x3 0.93 3 x4 0.385 3x4 0.448 4x4 0.5 4 x5 0.099 3x5 0.077 4x5 0. 5 - - 3x6 0.079 4x6 0.087 CONCLUSIONS Tis paper is a simulation study on te performance comparison analysis of M x N Equalizer based ML and MMSE receiver for MIMO wireless receiver. Hence a more balanced linear equalizer is te Minimum mean square error equalizer, wic owever is not eliminate ISI completely but instead minimizes te total power of te noise and ISI components in te output. From te above te following observations are made.ml is low computational complexity. It minimizes te probability of a sequence error. Hence from te above graps it is evident tat te BER decreases as te number of receiving antenna increases wit respect to number of transmitting antenna in ML equalizer based MIMO receiver. Tis equalizer is used for mobile communication link. ML equalizer outperforms MMSE based equalizer for MIMO Wireless cannel. ACKNOWLEDGEMENT Te autors express teir sincere tanks to Te Management, Te Director Academics (SNR Caritable Trust), Te Principal, Sri Ramakrisna Engineering College, for teir constant support and encouragement given to us. Te Autors also extend teir eartfelt tanks to te DC members, Dr. R. Rangarajan, te Dean Dr. Maalingam engineering college and Dr. Sankar Narayanan te Dean EASA College of Engineering for teir tecnical support and guidance to complete tis researc work. [3] K. Co and D. Yoon. 00. On te general BER expression of one and two-dimensional amplitude modulations. IEEE Transactions on Communications. 50: 074-080. [4] D. Tse and P. Viswanat. 005. Fundamentals of Wireless Communications. Cambridge Press. [5] X. Zang and S. Kung. 003. Capacity analysis for parallel and sequential MIMO equalizers. IEEE Transactions on Signal Processing. 5: 989-3003. [6] B. Hassibi. 000. A fast square-root implementation for BLAST. 34 t Asilomar Conf. Signals, Systems and Computers. pp. 55-59. [7] N. Prasad and M. K. Varanasi. 004. Outage capacities of space-time arcitecture. Information Teory Worksop, San Antonio, Texas. pp. 4-9. [8] M. Varanasi. 995. Group detection for syncronous Gaussian code-division multiple-access cannels. IEEE Transactions on Information Teory. 4: 083-096. REFERENCES [] N. Satis Kumar and K.R. Sankar Kumar. 0. Performance Analysis of M X N Equalizer Based Minimum Mean Square Error (MMSE) Receiver for MIMO Wireless Cannel. International Journal of Computer Applications. 6(7): 47-50. doi: 0.50/0-76. [] H. Zang, H. Dai, Q. Zou and B. L. Huges. 006. On te diversity-multiplexing tradeo for ordered SIC receivers over MIMO cannels. IEEE International Conference on Communications (ICC), Istanbul, Turkey. 3