Private Communications with Chaotic Code Division Multiple Access: Performance Analysis and System Design

Abstract

In this dissertation we develop a class of pseudochaotic direct-sequence code division multiple access (DS/CDMA) systems that can provide private and reliable communication over wireless channels. These systems exploit the sensitive dependence of chaotic sequences on initial conditions together with the presence of channel noise to provide a substantial gap between the bit error probabilities achievable by intended and unintended receivers. We illustrate how a desired level of private communication can be achieved with a systematic selection of the system parameters. This type of privacy can be readily combined with traditional encryption methods to further ensure the protection of information against eavesdroppers.

The systems we propose employ linear modulation of each user's symbol stream on a spreading sequence generated by iterating a distinct initial condition through a pseudochaotic map. We evaluate and compare the uncoded probability of error (Pr(e)) achievable by intended receivers that know the initial condition used to generate the spreading sequence to the associated Pr(e) of unintended receivers that know the modulation scheme but not the initial condition. We identify the map attributes that affect privacy, and construct algorithmic design methods for generating pseudochaotic spreading sequences that successively and substantially degrade the unintended user performance, while yielding intended user performance similar to that of conventional DS/CDMA systems. We develop efficient metrics for quantifying the unintended receiver Pr(e) and prove that it decays at a constant rate of 1/sqrt(SNR) in AWGN and fading channels. In addition, we show that this decaying rate is independent of the available degrees of diversity in fading channels, showing in the process that only intended receivers can harvest the available diversity benefits. Moreover, we illustrate that the pseudochaotic DS/CDMA systems can provide reliable multiuser communication that is inherently resilient to eavesdropping, even in the worst-case scenarios where all receivers in a network except the intended one collude to better eavesdrop on the targeted transmission. We also develop optimized digital implementation methods for generating practical pseudochaotic spreading sequences that preserve the privacy characteristics associated with the underlying chaotic spreading sequences.