Title: Channel Estimation for Beyond Diagonal RIS via Tensor Decomposition

Abstract: Beyond Diagonal (BD) RIS has recently been proposed and proven theoretically to enhance channel gain and coverage. The performance of BD-RIS architectures and modes depends heavily on the accuracy of the channel state information. However, the conventional least squares (LS) estimator requires significant training and disregards the built-in block Kronecker structure of the composite channel. In this talk, we link the channel estimation problem for BD-RIS to a tensor decomposition problem. Specifically, we demonstrate that the received pilot signals can be organized as a three-way (3D) array or a third-order tensor that follows a block Tucker decomposition model. First, we discuss how the specific BD-RIS architecture affects the resulting tensor decomposition structure. Next, we demonstrate how interpreting the received pilot signals as a three-way tensor allows us to reformulate the cascaded channel estimation problem as a block-Tucker tensor decomposition problem. This yields decoupled estimates for the involved channel matrices, substantially improving performance over the matrix-based LS method. We discuss two algorithms to solve this problem. The first is a closed-form solution that extracts channel estimates via block-Tucker Kronecker factorization (BTKF). This boils down to solving a set of parallel rank-one matrix approximation problems. The second algorithm is based on a block-Tucker alternating least squares (BTALS) method that directly estimates the channel matrices using an iterative procedure. We highlight the trade-offs of the BTKF and BTALS methods. BTKF offers fast, parallel extraction of channel estimates in closed form, while BTALS provides a more flexible training design that reduces training overhead significantly compared to state-of-the-art methods.

Title: Mutual Coupling in Reconfigurable Wave Systems

Abstract: Dynamic metasurface antennas (DMAs), reconfigurable intelligent surface (RISs), and wave-based physical neural network (PNNs) are prominent contemporary examples of reconfigurable wave systems. Due to mutual coupling, their transfer functions depend in general non-linearly on the configuration of their tunable elements. Mutual coupling is hence often mitigated to simplify the configuration optimization. However, this reasoning overlooks that mutual coupling boosts the strength of the transfer function dependence on the tunable elements' configurations. First, I will present theoretical, numerical, and experimental evidence to demonstrate that the control over a DMA's radiation pattern substantially increases with the mutual coupling strength. Second, to reap this benefit of mutual coupling, I will pave the way toward in-software model-based optimizations of reconfigurable wave systems. Specifically, I will discuss a universal model-based framework for wave control in reconfigurable wave systems and show its experimental application to RIS. Third, I will clarify how the framework can also be directly applied to beyond-diagonal RIS (BD-RIS) based on a physics-compliant diagonal representation of BD-RIS. Furthermore, I will present the first BD-RIS prototype and introduce the BD-DMA concept.