A Low-Rank Sparse Tensor Recovery-Based Channel Estimation Scheme for RIS-Assisted mmWave OFDM Systems

This paper proposes a low-rank sparse tensor recovery-based channel estimation (LRSTR-CE) scheme for RIS-assisted mmWave MISO-OFDM systems. Specifically, the uplink cascaded channel of the system can be represented as a low-rank sparse channel tensor in the angle-delay domain due to the limited scattering paths. Leveraging such representation, the scheme contains two steps. First, the scheme designs the sensing matrices, i.e., the base station combining matrix and the RIS reflection matrix, to meet the proposed uniqueness condition that guarantees the one-to-one correspondence between the high-dimensional channel tensor and lower-dimensional channel observation. The sensing matrices design is formulated as a power/constant module-constrained matrix optimization problem. Second, the scheme reconstructs the channel tensor from the channel observation, which is formulated as a low-rank constrained tensor optimization problem. The above problems are solved using manifold optimization techniques, which convert the original problem with non-convex constraints into an unconstrained optimization problem on manifolds, eliminating the need for relaxation of the non-convex constraints and achieving higher accuracy. Simulation results demonstrate superior performance in terms of channel estimation accuracy.