Beamspace Channel Estimation via PARAFAC Decomposition for RIS Assisted Millimeter-Wave Multiuser MISO Communications

The reconfigurable intelligent surface (RIS) with massive low-cost passive reflecting elements integrated on a planar surface has the ability to favourably reconfigure the wireless propagation environment, thereby significantly improving the performance of wireless communication networks. In this work, we consider uplink (UL) channel estimation for the RIS assisted millimeter-wave multiuser multiple-input single-output beamspace system where the base station (BS) is equipped with lens antenna array. This channel state information (CSI) estimation task is extremely challenging for two reasons. First, the BS only has limited number of radio frequency chains but the size of beamspace channel is very large. Second, the number of passive components in the RIS is abundance but they lack signal processing capabilities. By exploiting the parallel factor (PARAFAC) decomposition of the received signals, we derive an iterative estimation algorithm, called unitary approximate message passing (UAMP), to accurately estimate the channels between the BS and the RIS as well as the channels between the RIS and the users. To guide the selection of the system parameters, we provide the uniqueness conditions for our PARAFAC decomposition based channel estimation. To theoretically verify the efficiency of our UAMP algorithm, the Cramér-Rao bound (CRB) of the estimation is also derived. Besides, we investigate the achievable downlink (DL) sum rate for the channel estimation obtained by the proposed algorithm by using the maximum power beam selection, the optimized phase shift matrix and the zero forcing precoding. Extensive simulation results demonstrate the excellent mean squared error (MSE) performance of our UAMP estimation algorithm. In particular, for sufficiently high UL signal-to-noise ratio, the MSE of our channel estimation reaches the CRB. Simulation results also show that the DL sum rate achieved by the estimated CSI is very close to that obtained by the perfect CSI. Theoretical analysis and simulation results thus validate the effectiveness and reliability of our beamspace channel estimation approach.