Investigating the Convergence and Bit Error Rate of Adaptive Algorithms over Time Varying Rayleigh Fading Channel

Abstract

The fastest growing segment of the communication industry is the mobile wireless communication system. However, the systems faced a lot of challenges such as delay in the propagation of signals due to time-varying channel and effect of high speed transmission over Rayleigh fading which result into Inter-Symbol Interference (ISI) distortion. Least Mean Square (LMS) and Normalized Least Mean Square (NLMS) have been previously used to adapt the system using the step size, and Eigen value. In this paper, the adaptive Algorithms over a time-varying channel were compared using convergence level, Bit Error Rate (BER), and Mean Square Error (MSE).

The system model consists of bits to symbol converter, 16-QAM modulator and Raised Cosine transmit filter, all at the transmitter, time-varying Rayleigh fading with Additive White Gaussian Noise added, and at the receiver are Raised Cosine Receive filter, 16-QAM demodulator, then each of the Adaptive LMS and NLMS filters which received delay from the Random integer generator, and the integer/symbol to bit converter at the output. The system model was simulated using MATLAB/SIMULINK software package. The algorithms were evaluated using convergence MSE at SNR of 10, 20 and 30dB over different number of iterations to determine the convergence rate, constellation diagram and BER. The results obtained showed that the flat convergence level of LMS and NLMS at SNR of 10dB are obtained with 300 and 200 iterations respectively, while 200 and 150 iterations are obtained at SNR of 20 and at SNR 30, the convergence level are obtained at 150 and 100 iterations respectively. BER values of 0.1598 and 0.0858 are obtained for LMS and NLMS respectively. Therefore, LMS algorithm took more iterations than NLMS algorithm to achieve the same error, and also lower BER value of NLMS is also in agreement with the result.

Keywords: Convergence, MSE, LMS algorithm, NLMS algorithm, Intersymbol interference (ISI).