Sparse Millimeter Wave Channel Estimation Under Partially Coherent Phase Noise

Abstract

Millimeter wave (mmWave) systems, currently employed in 5G and IEEE 802.11ad/ay devices, enable high data rates through wide bandwidths and directional communication. However, high carrier frequencies used in these systems result in a higher phase noise than lower frequency systems. This paper investigates the problem of spatial channel estimation in the presence of severe phase noise, which manifests as partially coherent phase perturbations in the observed channel measurements. In this model, phase noise remains relatively constant within a packet but varies substantially across packets. Under such partially coherent phase noise, we first develop two computationally efficient on-grid algorithms to estimate narrowband mmWave channels: Partially Coherent Matching Pursuit (PCMP) and Enhanced Partially Coherent Matching Pursuit (EPCMP), assuming a known channel sparsity. Both algorithms exploit the sparse structure in mmWave channels, enabling a significant reduction in training overhead while achieving good estimation performance. The main difference between PCMP and EPCMP is how the sparse channel support is identified. The EPCMP algorithm can achieve better estimation performance at the cost of increased computational complexity compared to the PCMP algorithm. We then relax the known-sparsity assumption, adapt the proposed algorithms accordingly, and further extend them to the wideband case for an unknown sparsity. Additionally, we derive sufficient conditions to recover a support element with proposed algorithms. Simulation results demonstrate the advantages of our methods over comparable channel estimation benchmarks.