In this paper, we study the effect of imperfect channel estimation (ICE) on the performance of M-level quadrature amplitude modulation (M-QAM) with generalized selection combining (GSC) diversity and pilot-symbol assisted modulation (PSAM) in several types of fading channels (including Rayleigh, Rician and Nakagami fading). 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 ratio (SNR), which allows us to derive the accurate BER results of square and rectangular M-QAM with GSC and channel estimation errors. Our new BER expressions are general and yet easy to evaluate, and simplify to a closed-form expression for the Rayleigh fading case. Using our new analytical result, we evaluate the performance of M-QAM with PSAM, and present some interesting findings.