Beyond Diagonal RIS-Aided Networks: Performance Analysis and Sectorization Tradeoff

Reconfigurable intelligent surfaces (RISs) have emerged as a spectrum- and energy-efficient technology to enhance the coverage of wireless communications within the upcoming 6G networks. Recently, novel extensions of this technology, referred to as multi-sector beyond diagonal RIS (BD-RIS), have been proposed, where the configurable elements are divided into <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> sectors (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> ≥ 2) and arranged as a polygon prism, with each sector covering 1/<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> space. This paper presents a performance analysis of a communication system that is assisted by a multi-sector BD-RIS operating in time-switching (TS) mode. Specifically, we derive closed-form expressions for the moment-generating function (MGF), probability density function (PDF), and cumulative density function (CDF) of the signal-to-noise ratio (SNR) per user. Furthermore, exact closed-form expressions for the outage probability, achievable spectral and energy efficiency, symbol error probability, and diversity order for the proposed system model are derived. To evaluate the performance of multi-sector BD-RISs, we compare them with the simultaneously transmitting and reflecting (STAR)-RISs, which can be viewed as a special case of multi-sector BD-RIS with only two sectors. Interestingly, our analysis reveals that, for a fixed number of configurable elements, increasing the number of sectors improves outage performance while reducing the diversity order compared to the STAR-RIS configuration. This trade-off is influenced by the Rician factors of the cascaded channel and the number of configurable elements per sector. However, this superiority in slope is observed at outage probability values below 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup>, which remains below practical operating ranges of communication systems. Additionally, simulation results are provided to validate the accuracy of our theoretical analyses. These results indicate that increasing the number of sectors in multi-sector BD-RIS-assisted systems significantly enhances performance, particularly in both spectral and energy efficiency gains. For instance, our numerical results show an average increase of 184% in spectral efficiency and 128% in maximum energy efficiency when transitioning from a 2-sector to a 6-sector configuration.