Reliable Low-Rank Approximation of Matrices Detection Aided Multicarrier DCSK Receiver Design

Multicarrier differential chaos shift keying (MC-DCSK) systems transmit the reference chaotic signal for information recovery to remove the complex synchronization circuit. However, transmission errors in the reference chaotic signal would induce the error propagations when directly used for demodulations. In order to address this issue, we propose a low-rank approximation of matrices (LRAM) detection method to improve the reliability performances. In our design, we exploit the low-rank characteristic of MC-DCSK signals sharing the reference chaotic signal. Instead of directly using the received reference chaotic signal for correlated demodulation, we propose to apply the LRAM method to jointly estimate the reference signal and the information-bearing signal. We use the singular value decomposition and generalized LRAM methods to minimize the distances between the estimates and transmitted data. Thus, the signal-to-noise ratio (SNR) can be improved to achieve lower bit error rate (BER). Moreover, theoretical BER expression is derived and LRAM-aided system is proved to be capable of proving the maximum-likelihood detection for received signals. Simulation results demonstrate the BER performances of our design outperform counterparts over additive white Gaussian noise and fading channels.