On the average codeword-capacity optimality of chaos-based asynchronous DS-CDMA

The ultimate limits of chaos-based asynchronous DS-CDMA communication is assessed in terms of Shannon capacity for two classes of maps yielding exponentially decaying autocorrelation of the spreading sequences. Detailed analytical computation performed in the classical two-users system show that, for any possible choice of the spreading factor, a suitable chaotic map exists which generates sequences maximizing capacity in terms of number of averaged codewords per pair of system use. Moreover, when the spreading factor grows to infinity, such an optimal map is characterized by an autocorrelation decay with rate r=-2+√3, similarly to what was found in the simple case of correlation receivers.