Fundamental limit in DS/CDMA with Reed-Solomon coded orthogonal signaling

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/N₀ needed for error-free communication is eln2 (2.75 dB) with RTT, and 4.79 (6.8 dB) with hard decision. The optimum code rate that minimizes the required E¯_b/N₀ 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 M×M Hadamard matrix with a user-specific random sequence of length N. We derive the minimum E¯_b/N₀ for error-free communication as a function of the number of users, the optimum code rate that minimizes E¯_b/N₀, and the maximum limit on the total information transmission rate