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The performance analysis of space-time trellis codes over rapid nonselective Rayleigh fading channels with imperfect channel state information is considered. A pilot-symbol-assisted-modulation scheme is used for channel estimation. The parameters used in this scheme, i.e., pilot spacing and Wiener filter length are chosen in a tradeoff between estimation accuracy, transmission rate/pilot overhead, and receiver complexity. A simple maximum likelihood receiver for M-ary phase shift keying modulation is derived. An exact closed-form pairwise error probability (PEP) expression and explicit PEP bounds are presented. It is shown that the performance loss caused by channel estimation errors increases mainly with the channel fade rate.