On the ultimate limits of chaos-based asynchronous DS-CDMA - II: Analytical results and asymptotics

The ultimate limits of chaos-based asynchronous direct-sequence code-division multiple access systems are investigated using the concept of capacity taken from information theory. To this aim, we model the spreading at the transmitter and the sampling of the incoming signal at the receiver with a unique linear multi-input multi-output transfer function depending on spreading sequences and on the users relative delays and phases. The capacity can be computed using a known formula and is a random quantity depending on the process generating the spreading codes and on the delays and phases that are random in asynchronous environments. In the companion paper, we show that chaos-based spreading is able to outperform classical spreading in most cases. We delve here into analytical investigations aimed at clarifying such phenomena and show that chaos-based spreading is actually able to reach the absolute maximum performance in the classical two-user case as well as when the number of users and the spreading factor grow to infinity. Under suitable conditions, and in complete analogy with what happens for suboptimal receivers dominated by multiple-access interference, maximum capacity is attained by spreading sequences whose auto-correlation profile is well approximated by an exponential trend with rate r-=-2+√3.