On distributions of correlation values of 3-phase spreading sequences of Markov chains

There has 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 of SSMA communication systems. Note that correlation values of L-phase sequences generally take complex values. In previous note, 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. We evaluate the variances of the real part of their correlation values, and discuss bit error probabilities of spread spectrum multiple access (SSMA) systems based on 3-phase spreading sequences of Markov chains.