Reconfigurable Intelligent Surface-Aided Single-Input Single-Output K-Complex Symbol Golden Codeword-Based Modulation

Abstract

Small reconfigurable intelligent surfaces (RISs) have greater potential for flexibility and ubiquity compared to large RISs. In the literature, the theoretical average bit error probability (ABEP) of a phase-adjustable element access-point-based RIS (AP-RIS) is derived by exploiting the central-limit theorem for large surface size. Hence, the analysis does not hold for small surface sizes. In this paper, we first formulate a simple closed-form expression for the ABEP of a phase-adjustable element AP-RIS with $M$ -ary quadrature amplitude modulation ( $M$ QAM). Compared to the results available in literature, this expression is valid even for small RISs. Second, we investigate AP-RIS-aided single-input single-output $K$ -complex symbol Golden codeword-based modulation, which encodes/transmits $K~M$ QAM symbols in each of $K$ consecutive independently faded time slots. The encoding ensures that each symbol experiences $K$ different fadings, hence resulting in a $K$ -fold increase in diversity order, while the AP-RIS maximizes the received signal-to-noise ratio (SNR) in each slot and yields significant SNR gains with increasing size. An increase in $K$ yields significant SNR gains for small RISs. A theoretical bound on the ABEP is formulated and validated by simulation. Finally, a detector based on sorted symbol set sphere decoding is devised.