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This paper contains the performance analysis of a Bit Interleaved Coded Modulation (BICM) based multiple relay cooperative network. The relays are fixed and operating in a amplify-and-forward (AF) mode. The asymptotic bit error rate (BER) bounds of the cooperative system with the serial concatenated BICM using the M-ary Phase Shift Keying (M-PSK) modulation scheme over Additive White Gaussian Noise (AWGN) channels and Rayleigh fading channels are obtained. For the numerical results of union bound on BER, moment generating function (MGF) based approach is used. Maximal ratio combining (MRC) is used at the destination to obtain the advantage of spatial diversity. The analytical results are verified by comparing the results with those obtained from simulations.