Multilinear Singular Value Decomposition for Millimeter Wave Channel Parameter Estimation

Fifth generation (5G) cellular standards are set to utilize millimeter wave (mmWave) frequencies, which enable data speeds greater than 10 Gbps and sub-centimeter localization accuracy. These capabilities rely on accurate estimates of the channel parameters, which we define as the angle of arrival, angle of departure, and path distance for each path between the transmitter and receiver. Estimating the channel parameters in a computationally efficient manner poses a challenge because it requires estimation of parameters from a high-dimensional measurement - particularly for multi-carrier systems since each subcarrier must be estimated separately. Additionally, channel parameter estimation must be able to handle hybrid beamforming, which uses a combination of digital and analog beamforming to reduce the number of required analog to digital converters. This paper introduces a channel parameter estimation technique based on the multilinear singular value decomposition (MSVD), a Tucker form tensor analog of the singular value decomposition, for massive multiple input multiple output (MIMO) multi-carrier systems with hybrid beamforming. The MSVD tensor estimation approach is more computationally efficient than methods such as the canonical polyadic decomposition (CPD) and the Tucker form of the MSVD enables paths to be extracted based on signal energy. The algorithms performance is compared to the CPD method and shown to closely match the Cramer-Rao bound (CRB) of channel parameter estimates through simulations. Additionally, limitations of channel parameter estimation and communication waveform effects are studied.