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Downlink reconfigurable intelligent surface (RIS)-assisted multi-input-multi-output (MIMO) systems are considered with far-field, near-field, and hybrid-far-near-field channels. According to the angular or distance information contained in the received signals, 1) a distance-based codebook is designed for near-field MIMO channels, based on which a hierarchical beam training scheme is proposed to reduce the training overhead; 2) a combined angular-distance codebook is designed for hybrid-far-near-field MIMO channels, based on which a two-stage beam training scheme is proposed to achieve alignment in the angular and distance domains separately. For maximizing the achievable rate while reducing the complexity, an alternating optimization algorithm is proposed to carry out the joint optimization iteratively. Specifically, the RIS coefficient matrix is optimized through the beam training process, the optimal combining matrix is obtained from the closed-form solution for the mean square error (MSE) minimization problem, and the active beamforming matrix is optimized by exploiting the relationship between the achievable rate and MSE. Numerical results reveal that: 1) the proposed beam training schemes achieve near-optimal performance with a significantly decreased training overhead; 2) compared to the angular-only far-field channel model, taking the additional distance information into consideration will effectively improve the achievable rate when carrying out beam design for near-field communications. 

This paper deals with the unavailability of full CSI in ultra-dense user-centric TDD C-RAN. To reduce the channel training overhead, we consider the incomplete CSI case, where only large-scale inter-cluster CSI is available. Channel estimation for intra-cluster CSI is also considered, where we formulate a joint pilot allocation and user equipment (UE) selection problem to maximize the number of admitted UEs with fixed number of pilots. A novel pilot allocation algorithm is proposed by considering the multi-UE pilot interference. Then, we consider robust beam-vector optimization problem subject to UEs' data rate requirements and fronthaul capacity constraints, where the channel estimation error and incomplete inter-cluster CSI are considered. Simulation results demonstrate its superiority over the existing algorithms.