Blind equalization of single-input single-output fir channels for chaotic communication systems

Recently we have developed a simplified recursive adaptive blind channel equalization method for Single-Input Single-Output (SISO) chaotic communication systems. Even though the simplified recursive algorithm gives superior results compared to the state of the art chaotic blind channel equalization algorithms, it has a very important limitation: convergence of the adaptive algorithm is ensured for only Strictly Positive Real (SPR) channels. In this study, we propose a non-recursive chaotic blind channel equalization algorithm that works regardless of whether the channel is SPR or not. First, a statistically optimum fixed filter is designed assuming that the channel is known. Then, it is shown via computer simulations that its performance is very close to that of the statistically optimum fixed filter. Furthermore, it gives better results especially for non-SPR channels compared to the well-known minimum nonlinear prediction error method and the simplified recursive algorithm developed in our previous work. The method is computationally simple and does not impose any restrictions on the channel other than being a finite impulse response filter. Since the instantaneous gradient is used to derive the adaptive algorithm, the proposed method works for slowly and smoothly varying linear channels as well.