Pursleys aperiodic cross-correlation functions revisited

Pursleyʹs aperiodic cross-correlation function of one delay parameter, which plays an important role in the quasi-synchronous state, is revisited. Using sequences up-sampled by a factor of M, we generalize this function to the one with two discrete delay parameters which play an important role in asynchronous state. Furthermore, Markov spreading sequences are shown to be simply generated by a two-state Markov chain. Applying the central limit theorems, in particular, the Fortet-Kac theorem to the aperiodic cross-correlation function of spreading sequences with Markovity, we can get theoretical estimate of the variance of multiple-access interference.