In this paper, the bit error rate (BER) of 16 differential amplitude phase shift keying (16DAPSK) modems in future mobile communication system is derived analytically. The channel employed in this paper is the frequency-selective and fast Rayleigh fading channel, corrupted by cochannel interference (CCI) and additive white Gaussian noise (AWGN). Exact expressions for the probability distributions of the differential phase and amplitude ratio are derived for the BER calculation. The BER and optimum boundary are obtained for various channel conditions. In addition, the results for the BER in the presence of CCI are provided.