Abstract
Applying the particle filter (PF) technique, this paper proposes a PF-based algorithm to blindly demodulate the chaotic direct sequence spread spectrum (CDS-SS) signals under the colored or non-Gaussian noises condition. To implement this algorithm, the PFs are modified by (i) the colored or non-Gaussian noises are formulated by autoregressive moving average (ARMA) models, and then the parameters that model the noises are included in the state vector; (ii) the range-differentiating factor is imported into the intruder’s chaotic system equation. Since the range-differentiating factor is able to make the inevitable chaos fitting error advantageous based on the chaos fitting method, thus the CDS-SS signals can be demodulated according to the range of the estimated message. Simulations show that the proposed PF-based algorithm can obtain a good bit-error rate performance when extracting the original binary message from the CDS-SS signals without any knowledge of the transmitter’s chaotic map, or initial value, even when colored or non-Gaussian noises exist.
Highlights
Chaotic signals exhibit several special characteristics such as extraordinary sensitivity to initial conditions, aperiodicity, broad Fourier transform spectra and high security, which coincide with the requirements for signals used in secure communication systems [1,2,3,4]
A large number of chaotic secure communication schemes have been advanced in the last decades, including chaotic masking [1], chaotic shift keying [2], chaotic modulation [3], and chaotic direct sequence spread spectrum (CDS-SS) [4]
It can be concluded that the bit-error rate (BER) performance of the proposed particle filter (PF)-based algorithm is better than the nonlinear RPROP neural network and the unscented Kalman filter (UKF)-based algorithm on the non-cooperative communication condition, and approaches the level the algorithm in [25] that is belong to the cooperative communication could achieve
Summary
Chaotic signals exhibit several special characteristics such as extraordinary sensitivity to initial conditions, aperiodicity, broad Fourier transform spectra and high security, which coincide with the requirements for signals used in secure communication systems [1,2,3,4]. Sameh et al [8] develop a particle filter (PF) algorithm to solve the problem of chaotic state and unknown additive input estimation even if Gaussian or non-Gaussian noises that are known exist in the chaotic maps. A nonlinear Resilient back PROpagation (RPROP) neural network was proposed to estimate the chaotic sequences without knowing the transmitter’s structure under the additive white Gaussian noise (AWGN) condition [16], but the RPROP neural network method requires a training sequence that passes through the CDS-SS communication system to identify the unknown transmitter’s system, which can be hardly implemented in practice. A novel PF-based algorithm is proposed to blindly demodulate the CDS-SS communication system without any knowledge of the transmitter’s chaotic map, parameters, or initial value, and even under colored or non-Gaussian noise conditions. The proposed algorithm is implemented to blindly demodulate the CDS-SS signals
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