Robust and Energy Efficient Sparse-Coded OFDM-DCSK System via Matrix Recovery

In this paper, we devise a sparse-coded orthogonal frequency division multiplexing (OFDM) differential chaos shift keying (DCSK) communication system based on low-rank matrix recovery which can handle Gaussian background noise and outlier-contaminated symbols simultaneously. As the noise-free OFDM-DCSK symbol matrix has rank 1, we exploit the vector outer product for its modeling, while sparse coding is also applied to reduce the transmission energy. To demodulate information bits from the sparse-coded signal, we formulate an objective function which consists of a sum of Frobenius norm for rank-1 matrix recovery and $\ell _{0}$ -norm for identifying the possibly outlier-contaminated symbols, with a self-adaptive weight parameter. The resultant optimization problem is solved iteratively via block coordinate descent, and the Laplacian kernel with the Silverman’s rule is adopted for outlier detection. Theoretical analysis including convergence of the objective function, bit error rate (BER), energy efficiency and computational complexity, are provided. Simulation results show that the proposed system has comparable mean square error and BER performance with the $\ell _{p}$ -norm minimization based matrix recovery approach at $p=2$ in additive white Gaussian noise, and is superior to that of $p=1$ in Middleton class A noise, even when sparse coding is applied. Moreover, compared with other binary DCSK systems, our system achieves higher energy efficiency thanks to the sparse coding.

I. Introduction

A wireless communication system is easily attacked by malicious users for its inherent openness to natural environments and broadcast characteristics. To protect the system from being attacked, chaotic communication is a powerful encryption technique [1], thanks to the high-security properties of chaotic sequences [2] such as sensitivity of initial value, good auto-correlation, resistance to interference, pseudo randomness and ergodicity. Chaotic communication techniques are widely used in data transmission, including ultra-wide-band (UWB) [1], [3], power line communication (PLC) [4], and vehicle-to-vehicle (V2V) communication [5]. The chaotic sequences are used to modulate information bits, and this kind of techniques is referred to as chaotic modulation, which can be classified as coherent and non-coherent types. Their difference is that the former needs to regenerate the chaotic sequence at the receiver while this procedure is not required in the latter. Therefore, non-coherent modulation has less complexity than the coherent one, and has been widely discussed [6], [7].