This paper investigates the energy efficiency (EE) optimization in downlink multi-cell massive multiple-input multiple-output (MIMO). In our research, the statistical channel state information (CSI) is exploited to reduce the signaling overhead. To maximize the minimum EE among the neighbouring cells, we design the transmit covariance matrices for each base station (BS). Specifically, optimization schemes for this max-min EE problem are developed, in the centralized and distributed ways, respectively. To obtain the transmit covariance matrices, we first find out the closed-form optimal transmit eigenmatrices for the BS in each cell, and convert the original transmit covariance matrices designing problem into a power allocation one. Then, to lower the computational complexity, we utilize an asymptotic approximation expression for the problem objective. Moreover, for the power allocation design, we adopt the minorization maximization method to address the non-convexity of the ergodic rate, and use Dinkelbach’s transform to convert the max-min fractional problem into a series of convex optimization subproblems. To tackle the transformed subproblems, we propose a centralized iterative water-filling scheme. For reducing the backhaul burden, we further develop a distributed algorithm for the power allocation problem, which requires limited inter-cell information sharing. Finally, the performance of the proposed algorithms are demonstrated by extensive numerical results.

This paper considers the application of reconfigurable intelligent surfaces (RISs) (a.k.a. intelligent reflecting surfaces (IRSs)) to assist multiuser multiple-input multiple-output (MIMO) uplink transmission from several multi-antenna user terminals (UTs) to a multi-antenna base station (BS). For reducing the signaling overhead, only partial channel state information (CSI), including the instantaneous CSI between the RIS and the BS as well as the slowly varying statistical CSI between the UTs and the RIS, is exploited in our investigation. In particular, an optimization framework is proposed for jointly designing the transmit covariance matrices of the UTs and the RIS phase shift matrix to maximize the system global energy efficiency (GEE) with partial CSI. We first obtain closed-form solutions for the eigenvectors of the optimal transmit covariance matrices of the UTs. Then, to facilitate the design of the transmit power allocation matrices and the RIS phase shifts, we derive an asymptotically deterministic equivalent of the objective function with the aid of random matrix theory. We further propose a suboptimal algorithm to tackle the GEE maximization problem with guaranteed convergence, capitalizing on the approaches of alternating optimization, fractional programming, and sequential optimization. Numerical results substantiate the effectiveness of the proposed approach as well as the considerable GEE gains provided by the RIS-assisted transmission scheme over the traditional baselines.

This paper considers the application of reconfigurable intelligent surfaces (RISs) to assist multiuser multiple-input multiple-output multiple access channel (MIMO-MAC) systems. In contrast to most existing works on RIS-assisted systems assuming the availability of full channel state information (CSI), only partial CSI is required in our investigation, including the instantaneous CSI of the channel from a RIS to a base station and the statistical CSI of the channels from user terminals (UTs) to the RIS. We investigate the joint design of both the transmit covariance matrices of the UTs and the RIS phase shift matrix under the system global energy efficiency (GEE) maximization criterion. To maximize the GEE, we first obtain closed-form solutions for the eigenvectors of the optimal transmit covariance matrices of the UTs. Then, we derive an asymptotic expression of the objective function with the aid of random matrix theory to reduce the computational cost. We further propose a low-complexity algorithm to tackle the GEE maximization problem with guaranteed convergence, capitalizing on the approaches of alternating optimization, fractional programming, and sequential optimization. Numerical results substantiate the effectiveness of the proposed approach as well as the GEE performance gains provided by RIS-assisted MIMO-MAC systems.