Performances of DS/SSMA communications with MPSK signaling and complex signature sequences

We study a direct-sequence spread-spectrum multiple-access (DS/SSMA) communication system with M-ary phase-shift-keyed (MPSK) signaling. Users in the system employ complex signature sequences, which are modeled as deterministic sequences. We present upper and lower bounds for the probability of bit error (p.b.e.) of a reference transmission. First, the conditional p.b.e., given the multiple-user interference (MUI), is obtained. Then, the conditioning is removed by averaging over the discretized probability density function (p.d.f.) of the MUI. The result is an upper (or lower) bound when the discretized p.d.f. is a shifted-high (or shifted-low) version of a sectioned p.d.f. This process requires the two-dimensional p.d.f. of the MUI, which is derived. Arbitrarily tight bounds can be obtained at the cost of increased computation. Numerical results are presented for complex FZC and near optimal 4-phase sequences, as well as real binary Gold sequences, for BPSK, 4-PSK, and 8-PSK. Gray code bit mapping is assumed, although the analysis can be applied to other bit mappings. Results show that complex sequences can yield better performance than binary sequences in MPSK signaling. Using complex sequences, the number of available signature sequences is greatly enlarged.<>