Low-Complexity Channel Estimation Protocol for Non-Diagonal RIS-Assisted Communications

Non-diagonal reconfigurable intelligent surfaces (RIS) offer enhanced wireless signal manipulation over conventional RIS by enabling the incident signal on any of its $M$ elements to be reflected from another element via an $M \times M$ switch array. To fully exploit this flexible configuration, the acquisition of individual channel state information (CSI) is essential. However, due to the passive nature of the RIS, cascaded channel estimation is performed, as the RIS itself lacks signal processing capabilities. This entails estimating the CSI for all $M \times M$ switch array permutations, resulting in a total of $M!$ possible configurations, to identify the optimal one that maximizes the channel gain. This process leads to long uplink training intervals, which degrade spectral efficiency and increase uplink energy consumption. In this paper, we propose a low-complexity channel estimation protocol that substantially reduces the need for exhaustive $M!$ permutations by utilizing only three configurations to optimize the non-diagonal RIS switch array and beamforming for single-input single-output (SISO) and multiple-input single-output (MISO) systems. Specifically, our three-stage pilot-based protocol estimates scaled versions of the user-RIS and RIS-base-station (BS) channels in the first two stages using the least square (LS) estimator and the commonly used ON/OFF protocol from conventional RIS. In the third stage, the cascaded user-RIS-BS channels are estimated to enable efficient beamforming optimization. Complexity analysis shows that our proposed protocol significantly reduces the BS computational load from $\mathcal{O}(NM\times M!)$ to $\mathcal{O}(NM)$, where $N$ is the number of BS antennas. This complexity is similar to the conventional ON/OFF-based LS estimation for conventional diagonal RIS.

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 $L$ sectors $(L \geq 2)$ and arranged as a polygon prism, with each sector covering $1/L$ space. This paper presents a performance analysis of a multi-user communication system 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, 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. Moreover, a comparison is performed with the simultaneously transmitting and reflecting (STAR)-RISs, a special case of multi-sector BD-RIS with two sectors. Our analysis shows that for a fixed number of elements, increasing the sectors improves outage performance at the expense of reduced diversity order compared to STAR-RIS. 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 $10^{-5}$, which remains below practical operating ranges of communication systems. Additionally, simulations are provided to validate the accuracy of our theoretical analyses showing a notable $182\%$ increase in spectral efficiency and a $238\%$ increase in energy efficiency when transitioning from a 2-sector to a 6-sector configuration.