Effect of Channel Estimation Errors on $M$ -QAM With MRC and EGC in Nakagami Fading Channels

We study the effect of imperfect channel estimation (ICE) on the error probability performance of $M$-level quadrature amplitude modulation ( $M$-QAM) with maximal-ratio combining and equal-gain combining diversity formats in Nakagami fading channels. We provide a novel formulation of the bit-error rate (BER) of $M$-QAM with ICE in terms of the signal constellation-dependent effective signal-to-noise ratios (SNRs) or amplitudes, which allows us to derive the general, accurate, and easy-to-evaluate BER formulas for square and rectangular diversity $M$ -QAM with channel estimation errors. Our result shows that the performance loss caused by ICE may be manifested by the signal decision space distortion and a scaling of the effective SNR. Using our analytical result, we evaluate the performance of $M$-QAM with pilot-symbol assisted modulation and present some insightful findings.