Channel Orthogonalization with Reconfigurable Surfaces: General Models, Theoretical Limits, and Effective Configuration

TL;DR

This work studies channel orthogonalization in MU-MIMO using passive reconfigurable surfaces to enable orthogonal space-division multiplexing (OSDM). It derives formal restrictions and closed-form reflection-matrix configurations for FRIS, BD-RIS, and ARIS to realize arbitrary orthogonal channels, and proposes channel-selection and channel-estimation procedures with overhead bounds. A practical RS-configuration pipeline and an iterative channel-selection algorithm are developed to maximize channel gain while satisfying passive constraints, with extensive numerical validation under IID and Rician fading and imperfect CSI. The results indicate that BD-RIS offers a compelling balance of performance and complexity for achieving near-ideal orthogonality with passive elements, advancing the feasibility of OSDM in next-generation networks.

Abstract

We envision a future in which multi-antenna technology effectively exploits the spatial domain as a set of non-interfering orthogonal resources, allowing for flexible resource allocation and efficient modulation/demodulation. We may refer to this paradigm as orthogonal space-division multiplexing (OSDM). On the other hand, reconfigurable intelligent surface (RIS) has emerged as a promising technology which allows shaping the propagation environment for improved performance. This paper studies the ability of three extended types of reconfigurable surface (RS), including the recently proposed beyond diagonal RIS (BD-RIS), to achieve perfectly orthogonal channels in a general multi-user multiple-input multiple-output (MU-MIMO) scenario. We consider practical implementations for the three types of RS consisting of passive components, and obtain the corresponding restrictions on their reconfigurability. We then use these restrictions to derive closed-form conditions and explicit expressions for achieving arbitrary (orthogonal) channels. We also study the problem of exploiting the degrees of freedom (DoFs) from the channel orthogonality constraint to maximize the channel gain while maintaining the passive RS constraints, and we propose some initial methods with satisfying performance. Finally, we provide some channel estimation and RS configuration techniques within this framework, where the computations are assumed to be performed at the BS, and we derive some limits on the amount of overhead required to achieve channel orthogonalization with RSs. The numerical results confirm the theoretical findings, showing that channel orthogonality with passive RSs can be effectively achieved in practical environments as long as the direct channel is not significant with respect to the RS cascaded channel. We thus take some important steps towards realizing OSDM.

Figures (6)

• Figure 1: RS models considered in this work.
• Figure 2: Average channel gain versus direct channel power for IID Rayleigh fading scenario with $M=8$ and $K=4$.
• Figure 3: Orthogonalization failure probability versus direct channel power for IID Rayleigh fading scenario with $M=8$ and $K=4$.
• Figure 4: Condition number under imperfect-CSI in MU-MIMO with $M=8$ and $K=4$. Dashed lines indicate random orthogonal channel selection, while solid lines indicate orthogonal channel selection through Algorithm \ref{['alg:ch_sel']}.
• Figure 5: Rician scenario.

Theorems & Definitions (7)

• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Proposition 1
• Theorem 1
• Proposition 2