Phase-Shift-Free $M$-Phase Spreading Sequences of Markov Chains

We consider the optimum spreading sequences of Markov chains in terms of the mean value of the limit of variance of the normalized multiple-access interference for asynchronous spread-spectrum multiple access communication systems. We first define a novel class of spreading sequences, namely the phase-shift-free M(ges 3)-phase spreading sequences. Then we theoretically and experimentally show that the optimum phase-shift-free M-phase spreading sequences of Markov chains are superior to the optimum binary spreading sequences of Markov chains in terms of the bit-error probabilities based on the central limit theorem for periods N > 5.