Interference bounds for DS-CDMA systems based on chaotic piecewise-affine Markov maps

The performance of chaos-based asynchronous direct sequence-code division multiple access (DS-CDMA) systems are analyzed in the additive white Gaussian noise (AWGN) channel case. Previous upper bounds on the expected cochannel interference are improved and complemented with lower bounds accounting for maximum achievable performance. The bases for this investigation are mathematical tools from the statistical theory of dynamical systems and in particular some spectral properties of finite-dimensional restrictions of the Perron-Frobenius operator. A general lower bound is provided along with stricter upper and lower bounds in the particular case of piecewise-affine Markov (PWAM) maps used as spreading sequence generators. Detailed numerical examples of bound applicability are also provided.