Tensor-Based Channel Estimation and Reflection Design for RIS-Aided Millimeter-Wave MIMO Communication Systems
Sepideh Gherekhloo, Khaled Ardah, André L. F. de Almeida, Martin Haardt
Abstract
In this work, we consider both channel estimation and reflection coefficient design problems in point-to-point reconfigurable intelligent surface (RIS)-aided millimeter-wave (mmWave) MIMO communication systems. First, we show that by exploiting the low-rank nature of mmWave MIMO channels, the received training signals can be written as a low-rank multi-way tensor admitting a canonical polyadic (CP) decomposition. Utilizing such a structure, a tensor-based RIS channel estimation method (termed TenRICE) is proposed, wherein the tensor factor matrices are estimated using an alternating least squares method. Using TenRICE, the transmitter-to-RIS and the RIS-to-receiver channels are efficiently and separately estimated, up to a trivial scaling factor. After that, we formulate the beamforming and RIS reflection coefficient design as a spectral efficiency maximization task. Due to its non-convexity, we propose a heuristic non-iterative two-step method, where the RIS reflection vector is obtained in a closed form using a Frobenius-norm maximization (FroMax) strategy. Our numerical results show that TenRICE has a superior performance, compared to benchmark methods, approaching the Cramér–Rao lower bound with a low training overhead. Moreover, we show that FroMax achieves a comparable performance to benchmark methods with a lower complexity.