Use of Chebyshev Polynomial Kalman Filter for pseudo-blind demodulation of CD3S signals

Chaos based communication represents an attractive solution in order to design secure multiple access digital communication systems. In this paper we investigate the use of piecewise linear chaotic maps as chaotic generators combined, on the receiver side, with Chebyshev Polynomial Kalman Filters in a dual scheme configuration for demodulation purpose. Piecewise linear maps results into enhanced robustness properties of the spreading chaotic sequence, while approximation of nonlinear systems through Chebyshev polynomial series allows closed form estimation of mean and variance. Therefore, statistical moments can be computed by means of simple algebraic operations on matrices in compact form. In this work we extend these concepts to a dual Chebyshev Polynomial Kalman Filter scheme, suitable for signal recovery in chaos based spread spectrum systems. Numerical simulations show that the proposed method achieves lower error levels on a wide range of the bit-energy-tonoise- power-spectral-density ratio with respect to a state-of-the-art method based on unscented Kalman filters.