PCI-MF: Partial Canonical Identity and Matrix Factorization Framework for Channel Estimation in mmWave Massive MIMO Systems

Beamforming using massive number of antennas in millimeter wave (mmWave) communication is a promising solution for providing gigabits-per-second data rates in cellular networks. However, perfect channel state information (CSI) estimation is a key requirement, which is not practically feasible in massive multiple-input-multiple-output (MIMO) systems. Hence, compressive sensing (CS) and matrix completion methods have been proposed in the literature to reduce the channel estimation overhead. In this paper, a novel method utilizing partial canonical identity (PCI) based CS and matrix factorization (MF) framework, henceforth termed as PCI-MF, has been proposed to recover complete mmWave CSI by estimating only a few channel coefficients. Specifically, a few estimated noisy channel coefficients are represented as a combination of PCI and discrete Fourier transform (DFT) matrix in a CS framework to recover the sparsest solution of the channel matrix. This framework exploits the fact that both PCI and DFT matrices are highly incoherent. The sparse matrix determined above has been used to recover the rank of the channel matrix. The knowledge of the rank, along with the sparse coefficients recovered above, have been used jointly in a matrix factorization framework to recover the actual channel matrix. PCI-MF has been compared with the conventional and the state-of-the-art methods for two different datasets by varying parameters such as the number of transmitting and receiving antennas, antenna configuration, signal-to-noise ratio and measurement ratio. In order to validate the proposed method for realistic applications, one dataset is generated in a real-world setting in the New York City.