A Maximum Distance Separable Code Based RIS-OFDM: Design and Optimization

In this paper, we propose a novel orthogonal frequency division multiplexing (OFDM) waveform framework by capitalizing on the benefits of maximum distance separable (MDS) code and the reconfigurable intelligent surface (RIS). The proposed scheme is referred to as MDS-OFDM-RIS. The proposed design scheme consists of (i) an MDS code based amplitude and phase modulation scheme for OFDM transmission, which helps increase the minimum Hamming distance among symbols and improve on the error detection capabilities, (ii) a RIS that is placed near the radio frequency (RF) source, (iii) as well as a reduced-complexity maximum likelihood (RC-ML) detection algorithm at the receiver by utilizing the error detection ability of the MDS codes. We derive an upper bound for the bit error rate (BER) and a closed-form expression of the mutual information. Using the obtained analytical expressions, we formulate two optimization problems and derive the corresponding optimal solutions for RIS phase shifts. It is found that the two optimization problems share the same optimal solution, which indicates that the obtained RIS phase shifts optimize the system BER and channel capacity simultaneously. Simulation results show that compared with conventional OFDM systems, the proposed system can better combat multipath fading and provide higher channel capacity, especially when the RIS phase shifts are optimal. Moreover, the accuracy and low complexity of the proposed RC-ML detection scheme are demonstrated by numerical results.