BER analysis of arbitrary QAM for MRC diversity with imperfect channel estimation in generalized ricean fading channels

Imperfect channel estimation (ICE) can severely degrade the bit error rate (BER) of digital modulations with maximum ratio combining (MRC) diversity reception. The resulting performance analysis problem in its most general setting has not been addressed before. In this paper, the effect of ICE on the BER of an arbitrary square/rectangular Gray-coded quadratic amplitude modulation (QAM) in generalized Ricean fading channels when MRC reception is employed is analyzed. A general expression for the bit error probability of an arbitrary square/rectangular QAM scheme is first derived. This general formula requires a number of conditional probabilities, which is derived in closed form for independent and nonidentically distributed (i.n.d.) Rayleigh-fading channels with MRC and ICE. An efficient numerical method is also presented to compute the conditional probabilities for i.n.d. and correlated Ricean fading. In addition, extensive Monte Carlo simulations that agree excellently with the analytical results are presented.