Beyond diagonal reconfigurable intelligent surfaces (BD-RIS) is a new advance in RIS techniques that introduces reconfigurable inter-element connections to generate scattering matrices not limited to being diagonal. BD-RIS has been recently proposed and proven to have benefits in enhancing channel gain and enlarging coverage in wireless communications. Uniquely, BD-RIS enables reciprocal and non-reciprocal architectures characterized by symmetric and non-symmetric scattering matrices. However, the performance benefits and new use cases enabled by non-reciprocal BD-RIS for wireless systems remain unexplored. This work takes a first step toward closing this knowledge gap and studies the non-reciprocal BD-RIS in full-duplex systems and its performance benefits over reciprocal counterparts. We start by deriving a general RIS aided full-duplex system model using a multiport circuit theory, followed by a simplified channel model based on physically consistent assumptions. With the considered channel model, we investigate the effect of BD-RIS non-reciprocity and identify the theoretical conditions for reciprocal and non-reciprocal BD-RISs to simultaneously achieve the maximum received power of the signal of interest in the uplink and the downlink. Simulation results validate the theories and highlight the significant benefits offered by non-reciprocal BD-RIS in full-duplex systems. The significant gains are achieved because of the non-reciprocity principle which implies that if a wave hits the non-reciprocal BD-RIS from one direction, the surface behaves differently than if it hits from the opposite direction. This enables an uplink user and a downlink user at different locations to optimally communicate with the same full-duplex base station via a non-reciprocal BD-RIS, which would not be possible with reciprocal surfaces.

翻译：超对角可重构智能表面（BD-RIS）是可重构智能表面技术的新进展，其通过引入可重构的单元间连接，能够生成不局限于对角形式的散射矩阵。BD-RIS 近期被提出，并已被证明在增强无线通信信道增益和扩大覆盖范围方面具有优势。独特的是，BD-RIS 可实现以对称和非对称散射矩阵为特征的互易与非互易架构。然而，非互易 BD-RIS 为无线系统带来的性能优势和新应用场景仍未得到探索。本研究迈出了填补这一知识空白的第一步，探讨了全双工系统中的非互易 BD-RIS 及其相对于互易架构的性能优势。我们首先基于多端口电路理论推导了一个通用的 RIS 辅助全双工系统模型，随后基于物理上一致的假设建立了一个简化的信道模型。利用所考虑的信道模型，我们研究了 BD-RIS 非互易性的影响，并确定了互易与非互易 BD-RIS 在上行链路和下行链路中同时实现目标信号最大接收功率的理论条件。仿真结果验证了理论分析，并突显了非互易 BD-RIS 在全双工系统中带来的显著优势。这些显著增益源于非互易性原理，该原理意味着：如果波从一个方向入射到非互易 BD-RIS，其表面行为与波从相反方向入射时不同。这使得位于不同位置的上行链路用户和下行链路用户能够通过一个非互易 BD-RIS 与同一个全双工基站进行最优通信，而这对于互易表面是无法实现的。