A Novel Prior-Based Channel Estimation and Activity Detection in Cell-Free mMTC Systems

Abstract

We consider the problem of joint channel estimation (CE) and device activity detection (DAD) in the uplink of a cell-free millimeter wave massive multiple-input multiple output (mMIMO) system for massive machine-type communication. We know that the mMIMO channel is spatially correlated, and is sparse in the angular domain. The correlation and sparsity are captured by tailoring a Gaussian prior. This prior is then used to design a centralized variational Bayesian learning (cVBL) algorithm for CE and DAD. The variational approximation in cVBL algorithm reduces its complexity from cubic to linear in terms of devices. We next propose an asynchronous decentralized VBL (adVBL) algorithm, wherein each AP locally estimates its channel from all the devices. The adVBL algorithm is robust to the AP failures, and its complexity is invariant of the number of APs. The adVBL algorithm is developed by reformulating cVBL updates as global optimization problems, and by deriving their local counterparts using the alternating direction method of multipliers. Through extensive numerical studies, we show that the proposed cVBL and adVBL algorithms i) outperform several existing algorithms; ii) require much less pilot overhead; and iii) estimate large-scale fading, unlike the existing ones.