Low-Rank Tensor Decomposition-Aided Channel Estimation for Millimeter Wave MIMO-OFDM Systems

We consider the problem of downlink channel estimation for millimeter wave (mmWave) MIMO-OFDM systems, where both the base station (BS) and the mobile station (MS) employ large antenna arrays for directional precoding/beamforming. Hybrid analog and digital beamforming structures are employed in order to offer a compromise between hardware complexity and system performance. Different from most existing studies that are concerned with narrowband channels, we consider estimation of wideband mmWave channels with frequency selectivity, which is more appropriate for mmWave MIMO-OFDM systems. By exploiting the sparse scattering nature of mmWave channels, we propose a CANDECOMP/PARAFAC (CP) decomposition-based method for channel parameter estimation (including angles of arrival/departure, time delays, and fading coefficients). In our proposed method, the received signal at the BS is expressed as a third-order tensor. We show that the tensor has the form of a low-rank CP decomposition, and the channel parameters can be estimated from the associated factor matrices. Our analysis reveals that the uniqueness of the CP decomposition can be guaranteed even when the size of the tensor is small. Hence the proposed method has the potential to achieve substantial training overhead reduction. We also develop Cramer-Rao bound (CRB) results for channel parameters, and compare our proposed method with a compressed sensing-based method. Simulation results show that the proposed method attains mean square errors that are very close to their associated CRBs, and presents a clear advantage over the compressed sensing-based method in terms of both estimation accuracy and computational complexity.