# Generalized Approximate Message Passing for Massive MIMO mmWave Channel Estimation with Laplacian Prior

## TL;DR

This paper introduces a novel Bayesian channel estimation method for massive MIMO mmWave systems using GAMP with a Laplacian prior, improving accuracy, speed, and complexity over existing approaches.

## Contribution

It develops a Laplacian prior-based GAMP algorithm with an EM procedure for automated parameter learning, enhancing mmWave MIMO channel estimation.

## Key findings

- Improved channel estimation accuracy and achievable rate.
- Faster convergence of GAMP with Laplacian prior.
- Reduced computational complexity compared to Gaussian prior methods.

## Abstract

This paper tackles the problem of millimeter-Wave (mmWave) channel estimation in massive MIMO communication systems. A new Bayes-optimal channel estimator is derived using recent advances in the approximate belief propagation (BP) Bayesian inference paradigm. By leveraging the inherent sparsity of the mmWave MIMO channel in the angular domain, we recast the underlying channel estimation problem into that of reconstructing a compressible signal from a set of noisy linear measurements. Then, the generalized approximate message passing (GAMP) algorithm is used to find the entries of the unknown mmWave MIMO channel matrix. Unlike all the existing works on the same topic, we model the angular-domain channel coefficients by Laplacian distributed random variables. Further, we establish the closed-form expressions for the various statistical quantities that need to be updated iteratively by GAMP. To render the proposed algorithm fully automated, we also develop an expectation-maximization (EM) based procedure that can be easily embedded within GAMP's iteration loop in order to learn all the unknown parameters of the underlying Bayesian inference problem. Computer simulations show that the proposed combined EM-GAMP algorithm under a Laplacian prior exhibits improvements both in terms of channel estimation accuracy, achievable rate, and computational complexity as compared to the Gaussian mixture prior that has been advocated in the recent literature. In addition, it is found that the Laplacian prior speeds up the convergence time of GAMP over the entire signal-to-noise ratio (SNR) range.