Optimal chaotic spread spectrum sequences for uplink CDMA systems

This paper derives general results on the partial autocorrelation function of the optimal spreading sequences for asynchronous CDMA systems with respect to the minimization of the average error probability under the standard Gaussian approximation (SGA) condition without the assumption of “independence” and “stationarity” on the spreading sequences. A practical implementation of the optimal real-valued spreading sequence by using chaotic dynamical systems, particularly dynamical systems with Lebesgue spectrum, is provided. Based on the ergodic theory of dynamical systems, we construct a family of optimal chaotic Chebyshev spreading sequences and analyze their performance. An asynchronous CDMA system using the optimal spreading sequences allows 15% more users than when random white sequences are employed. Simulation results show that the system performance using this family of chaotic Chebyshev spreading sequences are superior compared to Gold codes when employed for an asynchronous CDMA system