Reliable Multi Carrier Differential Chaos Shift Keying Receiver Based on Low Rank Approximation of Matrices Estimation

In Multi-Carrier Differential Chaos Shift Keying (MC-DCSK) systems, after transmitted over wireless channels, the transmission errors in the reference chaotic signal will degrade the detection performances of the information-bearing signals at the receiver. In order to address this issue, in this paper, a Low Rank Approximation of Matrices (LRAM) aided MC-DCSK receiver is proposed based on the low rank characteristics of the information-bearing chaotic modulated signals sharing the same reference chaotic signal, with the aim to enhance the reliability performances. In the design, the received signal matrix is evaluated by the sum of a rank one matrix and a Gaussian noise matrix, and then the LRAM method is applied to derive the estimates of received signals to attain the optimal estimate of the reference chaotic sequence, which is subsequently used to recover the user data, thereby improving the reliability performances of MC-DCSK systems. Subsequently, the proposed LRAM detection is proved that is equivalent to the maximum likelihood estimation detection, then the theoretical security performances in terms of the information leakage is analyzed. The analysis shows that the security performances of the proposed system keep the same as those of the benchmark MC-DCSK systems. Simulation results demonstrate the superior Bit Error Rate (BER) performances of the proposed LRAM aided MC-DCSK systems over Additive White Gaussian Noise (AWGN) and multipath fading channels.