Eigenvalues distribution and average Shannon capacity of asynchronous DS-CDMA systems with classical and chaos-based spreading

We aim at comparing classical and chaos-based spreading sequences considering the Shannon capacity of the resulting system. Due to asynchronism, capacity turns out to be a random variable whose average can be computed once that the pdf of the eigen-values of a random matrix is known. We estimate such a pdf by Monte Carlo computation and try to fit it with a simple model. It turns out that the straightforward application of asymptotic results that hold for synchronous systems with random spreading is ineffective. Yet, a slight generalization of the profiles indicated by that theory allows a fitting of the empirical data with a relative error below 0.8% in all tested cases. Finally, by observing both the raw numerical evidence and the approximation based on pdf fitting, we are able to show that chaos-based spreading is able to produce a capacity increase with respect to classical codes designed to mimic purely random sequences.