In this paper we estimate the average bit-error probability of a direct-sequence spread-spectrum multiple-access (DS-SSMA) system using MPSK and a linear coherent detector on the satellite mobile channel (SMC). The formulas derived in this paper are suitable for various types of signature sequences and chip waveforms. The numerical results are presented for DS-SSMA using BPSK and QPSK with random signature sequences and three different chip waveforms: the rectangular, the cosine, and the root Nyquist filter (RNF) with rolloff rate, /spl beta/=0.4. The results show that the performance of a DS-SSMA system with complex random signature sequences is superior to a system using binary random signature sequences on Gaussian and Rician (K=10) channels, while on flat fading Rayleigh channels the performance for both systems is similar. In DS-SSMA, the RNF has the highest bandwidth efficiency of the three chip waveforms. The performance of DS-SSMA is also analyzed on the SMC using the Gaussian approximation (GA) method. Compared to the estimated results, GA gives a pessimistic approximation for binary random signature sequences on Gaussian and Rician channels.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>