Massive MIMO mmWave Channel Estimation Using Approximate Message Passing and Laplacian Prior

This paper tackles the problem of channel estimation in mmWave large-scale communication systems. To leverage the sparsity of mmWave MIMO channels in the beam domain, we use discrete Fourier transform (DFT) precoding and combining and recast the channel estimation problem as a compressed sensing (CS) problem. The generalized approximate message passing (GAMP) algorithm is then used to find the minimum mean square estimate (MMSE) of each entry of the unknown mmWave MIMO channel matrix. Unlike the existing works, this paper models the angular-domain channel coefficients by a Laplacian prior and accordingly establishes the closed-form expressions for all the statistical quantities that need to be updated iteratively by GAMP. Further, to render the proposed algorithm fully automated, we develop an expectation-maximization (EM)-based procedure which can be readily embedded within GAMP's iteration loop in order to learn the unknown scale parameter of the underlying Laplacian prior along with the noise variance. Numerical results indicate that the proposed EM-GAMP algorithm under a Laplacian prior yields substantial improvements both in terms of channel estimation accuracy and computational complexity as compared to the existing methods that advocate a Gaussian mixture (GM) prior.