Equalization in chaos-based communication systems using kernel adaptive filtering

Abstract

Chaos-based communication systems have attracted attention of researchers in academy and industry in the last decades. A particular family of such systems has as basic idea to use the transmitted message to modify a known nonlinear chaotic signal generator (CSG). In the receiver, the knowledge of the employed nonlinear CSG in conjunction with chaotic synchronization permits to recover the original message. These systems are an alternative for spread spectrum communication with a possible increase in the security in the physical layer, since it is necessary to perfectly know the CSG in the receiver to decode the message. However, the lack of robustness of chaotic synchronization in relation to channel noise and intersymbol interference still poses a barrier for their practical use. The problem of equalization for such systems have been tackled for a while, and algorithms based on the normalized least-mean squares have presented auspicious results for linear channels. For nonlinear channels, Kernel Adaptive Filters (KAFs) have been used since they are able to solve nonlinear problems implicitly projecting the input vector into a larger dimension space, where they can be linearly solved. Therefore, in this paper, we propose the use of KAFs with two purposes: to equalize linear and nonlinear channels and, at the same time, decode the message without knowledge of the CSG in the receiver. Simulation results show that the proposed solution is able to perform these tasks.