Probability of Error Derivatives for Binary and Chaos-Based CDMA Systems in Wide-Band Channels

This paper presents detailed mathematical models of DS-CDMA systems based on binary and chaotic spreading sequences. These systems have been well investigated in the case of flat fading and noise presence in the channel. However, a comprehensive analysis of the systems operating in a wide-band channel does not exist. Therefore, in this paper, the systems are analyzed in detail, and expressions for the probability of error are derived in closed form assuming a wide-band transmission channel. Using both the signal representation in pure discrete time domain and the theory of discrete time stochastic processes, which have not been practically used before, the probability of error expressions are derived in closed form for single- and multi-user binary and chaos based DS-CDMA systems. The improvements in the probability of bit error due to multipath channel nature are quantified in dependence of the random delay and the number of users in the system. The wide-band channel is based on the Saleh-Valenzuela model proposed for the modern wireless networks.