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In this paper, we present a general analysis of the performance of selection combining (SC), switch-and-stay combining (SSC), and switch-and-examine combining (SEC) systems in Rayleigh fading channels with imperfect channel estimation (ICE). The complex channel estimate and the actual fading are modeled as jointly Gaussian random variables. For SC systems with channel estimation error, closed-form expressions are obtained for the error rates of Ms-ary pulse amplitude modulation (PAM) and rectangular-quadrature amplitude modulation (QAM), and simple single integral formulas with finite integration limits are derived for the symbol error probability of arbitrary two-dimensional (2-D) modulation formats. These error probability expressions are then applied to three types of channel estimation errors potentially encountered in practical systems to study their impact on the performance of selection diversity. Moreover, single integral formulas with finite integration limits are derived for the performance of SSC and SEC systems with minimum mean square error (MMSE) channel estimation. Optimum switching thresholds for 2-D modulation formats with MMSE based switched combining are acquired through numerical computation.