Performance Limits of Reed-Solomon Coded CDMA with Orthogonal Signaling in a Rayleigh Fading Channel

The asymptotic performance of Reed-Solomon coded M-ary orthogonal signaling with ratio-threshold test (RTT) type demodulation in a Rayleigh fading channel is considered. We show that the minimum E b =N 0 needed for error-free communication is e ln 2 (2.75 dB) with RTT, and 4.79 (6.8 dB) with hard decisions. The optimum code rate that minimizes the required E b =N 0 is e ?1 with RTT and 0.46 with hard decision, and the optimum ratio threshold approaches 1 for large M. Next, we investigate the fundamental limit in direct-sequence spread-spectrum multiple-access (DS/SSMA) system employing an M-ary orthogonal code of length N = Mm, which is obtained by spreading every row of an MxM Hadamard matrix with a user-speciic random sequence of length N. We derive the minimum E b =N 0 for error-free communication as a function of the number of users, the optimum code rate that minimizes E b =N 0 , and the maximum limit on the 1 total information transmission rate. Then, we consider a multi-rate DS/SSMA system, where a population of users simultaneously transmit at diierent power levels a variety of traac types of diierent information rates. We derive the minimum required E b =N 0 and the optimum code rate for each traac type.