Time-Varying Phase Noise Estimation, Channel Estimation, and Data Detection in RIS-Assisted MIMO Systems via Tensor Analysis
Jianhe Du, Yuan Cheng, Libiao Jin, Feifei Gao
Abstract
In this paper, we propose a nested tensor-based framework for the time-varying phase noise (PHN) estimation, channel estimation, and data detection in downlink reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output (MIMO) systems. Due to the structure of time-varying PHN and RIS phase shifts, we construct the received signal at the mobile station (MS) as a fourth-order tensor. By designing the multi-blocks time-domain transmission scheme, this fourth-order tensor can be converted into a third-order nested tensor model to facilitate the parallel factor (PARAFAC) decomposition. Based on the reconstructed nested PARAFAC model, we develop two algorithms to jointly estimate the time-varying PHN and channels. The first one achieves the minimum mean square error (MMSE) with iterative algorithm. The second one adopts certain approximation and could yield closed-form solutions by sacrificing a little bit performance. With the estimated time-varying PHN and channels, we further detect the data via the proposed vectorized Kronecker-based zero-forcing (VKBZF) approach. Moreover, to quantitatively evaluate the performance of the proposed algorithms, we derive the Cramér-Rao bound (CRB) as the benchmark. Simulation results demonstrate that the proposed algorithms provide superior estimation and detection performance compared with the existing state-of-the-art algorithm, and require less pilot overhead.