Message Passing-Based Sparse Spatial Channel Estimation Robust to Partially Coherent Phase Noise

Channel estimation can lead to a substantial training overhead in millimeter wave (mmWave) and terahertz (THz) systems employing large arrays. Prior work has leveraged channel sparsity at these frequencies to reduce this overhead. Most of the sparsity-aware algorithms, however, assume perfect phase coherence in the channel measurements, which is disrupted due to phase noise. Due to the errors induced by phase noise, standard sparse channel estimation algorithms assuming perfect phase coherence can fail. In this paper, we consider a frame structure in which the channel measurements are acquired over multiple packets. Our model assumes that the phase errors remain constant within a packet and vary considerably across different packets, leading to partially coherent channel measurements. We develop a message passing-based technique for sparse channel estimation under such partially coherent phase errors and show that our approach achieves a lower channel reconstruction error than comparable benchmarks.