BER expression for maximum ratio combining in imperfect channel estimation environment

Abstract

This paper presents the performance of the Maximum Ratio Combining (MRC) technique for the downlink BPSK system. Generalized analytical Bit Error Rate (BER) is derived in closed form for imperfect channel estimators in complex flat fading environment. Analytical results show that BER depends on the cosine of estimated phase errors. Further, analytical and simulation results show that channel estimators are not required in real fading coefficients case, which is equivalent to perfect estimation case. In general, BER is defined in the range [0.5,1], but in this work complete range of BER i.e. [0,1] is related with estimated channel coefficients. However, the performance of two and more receiving antenna system slightly degrades as compared to the perfect channel estimator in real fading coefficients environment. Also, it has been shown that estimated amplitude coefficients have no effect on BER performance in a single antenna system, it’s only the estimated phase that matters; whereas for higher number of antennas, estimated amplitude as well as phase coefficients affect the BER performances.