Partially Coherent Compressive Phase Retrieval for Millimeter-Wave Massive MIMO Channel Estimation

Channel estimation is challenging for millimeter-wave (mmWave) massive MIMO systems. Leveraging the spatial sparsity of mmWave channels, compressive sensing (CS) based channel estimation been extensively studied. However, the mmWave hardware imperfections may introduce random phase distortions to the received pilots, which makes the conventional CS methods fail to estimate the channel. The compressive phase retrieval (CPR) method can be employed to solve this challenging problem. In this paper, we exploit the partial coherence in hybrid mmWave systems, i.e., the pilots sent from different radio frequency (RF) chains share the same phase distortion in the same time frame, while the phase distortions are different across different time frames. Based on this property, we propose an on-grid partially coherent CPR (PC-CPR) algorithm for mmWave channel estimation in the presence of severe phase distortions. Unlike the existing coherent channel estimation schemes that require perfect phase information or the noncoherent channel estimation schemes that ignore the phases of measurements, the proposed on-grid PC-CPR algorithm exploits the partial coherence property to estimate the sparse angle-domain channel vector. Furthermore, to solve the resolution limitation of the on-grid PC-CPR algorithm, we propose an off-grid PC-CPR algorithm that directly estimates the parameters of channel paths. The proposed partially coherent channel estimation framework subsumes the existing coherent and noncoherent channel estimation methods as special cases. Simulation results show that under the presence of random phase distortions, the proposed PC-CPR algorithms outperform noncoherent channel estimation methods with higher reliability and lower pilot overhead by leveraging the partial coherence.