A tensor approach to higher order expectations of chaotic trajectories. II. Application to chaos-based DS-CDMA in multipath environments

For pt. I see ibid., vol. 47, no. 11, p. 1571-1583 (2000). Chaos-based DS-CDMA systems in presence of a dispersive channel are analyzed to obtain analytical expression for key quantities involved in performance evaluation. To do so a simple but realistic exponential model for dispersive channel characterization is adopted to derive an estimation of the magnitude of error causes in terms of second-, third- and fourth-order correlation properties of the spreading sequences. These properties are analytically computed by choosing a suitable set of chaotic-maps for sequences generation and using some tools from the general theory developed in the companion paper. Such a theory expresses higher order expectations as products between tensors made of the spreading symbols and tensors accounting for the mixed causal-stochastic nature of the chaotic generators. The factorization of these tensors naturally leads to a handy exponential form for correlations. With this a closed form is given for the variances of disturbing terms which, under the standard Gaussian assumption, determine the system performance. Such closed forms are finally exploited to optimize the performance of the system under different channel and load conditions, showing an improvement over what can be obtained by some classical spreading sequences.