Semi-Blind Joint Channel and Symbol Estimation for Beyond Diagonal Reconfigurable Surfaces

Abstract

The beyond-diagonal reconfigurable intelligent surface (BD-RIS) is a recent architecture in which scattering elements are interconnected to enhance the degrees of freedom for wave control, yielding performance gains over traditional single-connected RISs. For BD-RIS, channel estimation, which is well studied for conventional RIS, becomes more challenging due to complex connections and a larger number of coefficients. Previous works relied on pilot-assisted estimation followed by data decoding. This paper introduces a semi-blind tensor-based approach to joint channel and symbol estimation that eliminates the need for training sequences by directly leveraging data symbols. A practical scenario with time-varying user terminal-RIS channels under mobility is considered. By reformulating the received signal from a tensor-decomposition perspective, we develop two semi-blind receivers: a two-stage method that transforms the fourth-order PARATUCK model into a third-order PARAFAC model, and a single-stage iterative process based on the fourth-order TUCKER decomposition. Identifiability conditions for reliable joint recovery are derived, and numerical results demonstrate the performance advantages and trade-offs of the proposed schemes over existing solutions.

Figures (14)

• Figure 1: Uplink BD-RIS assisted MIMO system
• Figure 2: Transmission protocol time structure: The channel estimation slot is divided into $I$ frames, each frame composed of $K$ blocks.
• Figure 3: Flowchart summarizing the proposed receivers.
• Figure 4: Third-order PARAFAC tensor model: The received signal at $(14)$ fits a fourth-order PARATUCK tensor model. From the third mode unfolding of the tensor $\boldsymbol{\mathcal{Y}}_{i,k}$, we derive a third-order PARAFAC model, with $\boldsymbol{\Omega}$, $\boldsymbol{\Psi}$ and $\overline{\boldsymbol{G}}$ as factor matrices.
• Figure 5: TUCKER tensor model: In this scenario, the tensor from the $i$-th frame, $\boldsymbol{\mathcal{Y}}_i$ in $(18)$, is rearranged to derive a fourth-order TUCKER model for the received signal tensor.