Channel Estimation and Passive Beamforming for Intelligent Reflecting Surface: Discrete Phase Shift and Progressive Refinement

Prior studies on intelligent reflecting surface (IRS) have mostly assumed perfect channel state information (CSI) available for designing the IRS passive beamforming as well as the continuously adjustable phase shift at each of its reflecting elements, which, however, have simplified two challenging issues for implementing IRS in practice, namely, its channel estimation and passive beamforming designs both under the constraint of discrete phase shifts. To address them, we consider in this paper an IRS-aided single-user communication system and design the IRS training reflection matrix for channel estimation as well as the passive beamforming for data transmission, both subject to the new constraint of discrete phase shifts. We show that the training reflection matrix design with discrete phase shifts greatly differs from that with continuous phase shifts, and the corresponding passive beamforming design should take into account the correlated IRS channel estimation errors due to discrete phase shifts. Moreover, a novel hierarchical training reflection design is proposed to progressively estimate IRS elements' channels over multiple time blocks by exploiting the IRS-elements grouping and partition. Based on the resolved IRS channels in each block, we further design the progressive passive beamforming at the IRS with discrete phase shifts to improve the achievable rate for data transmission over the blocks. Extensive numerical results are presented, which demonstrate the significant performance improvement of proposed channel estimation and passive beamforming designs as compared to various benchmark schemes.