Non-Diagonal Versus Diagonal RIS Architectures in Nakagami- <i>m</i> Fading Channels

Reconfigurable Intelligent Surfaces (RIS) have emerged as a key technology for enhancing spectral and energy efficiency in sixth-generation (6G) wireless networks, paving the way for sustainable and green communication. This paper presents a comprehensive performance analysis of non-diagonal RIS architectures, where the incident signal on one element can be reflected by another element after an appropriate phase shift adjustment, resulting in a non-diagonal phase shift matrix. We first derive new closed-form approximations for the cumulative distribution function (CDF), probability density function (PDF), and moment-generating function (MGF) of the optimal received signal-to-noise ratio (SNR) over Nakagami-<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> fading channels. Furthermore, we derive accurate closed-form expressions for the outage probability, achievable spectral efficiency, symbol error probability (SEP), and diversity order. A realistic power consumption model for non-diagonal RIS-based systems is developed to evaluate their energy efficiency performance. To facilitate performance evaluation and further analysis, we introduce a unified closed-form expressions for the performance metrics of both diagonal and non-diagonal RIS configurations. Simulation results are presented to assess the accuracy of the derived closed-form expressions. Using the theoretical results, we analyze and compare the non-diagonal RIS with its diagonal counterpart. The results reveal that non-diagonal RIS significantly enhances the spectral efficiency of Rayleigh fading systems compared to conventional diagonal RIS setups. However, this enhancement in spectral efficiency comes at the cost of reduced energy efficiency due to the introduction of switch array in the non-diagonal architecture. Our results provide insights on the spectral and energy efficiency behaviors of each configuration, serving as a design guide for selecting suitable architectures based on specific performance criteria.