Optimization of 3-phase spreading sequences of Markov chains

There has recently been intense interest in not only binary but also L-phase spreading sequences of Markov chains, where L=3,4, .... We need variances of correlation values of such sequences to evaluate bit error probabilities in asynchronous SSMA (spread spectrum multiple access) communication systems. Note that correlation values of L-phase sequences generally take complex values. In previous paper, we have considered 3-phase spreading sequences generated by general 3-state simple Markov chains, and have evaluated the variances of the absolute values of their correlation values in the complex plane. In this paper, we evaluate the variances of the real part of their correlation values, and give the optimum 3-phase spreading sequences of Markov chains in terms of bit error probabilities in asynchronous SSMA communication systems.