Energy-Efficient Coordinated Beamforming Under Minimal Data Rate Constraint of Each User

Abstract

Coordinated beamforming has been optimized to maximize the sum rate under the transmit power constraints or to minimize the transmit power under the data rate constraints. In this paper, we design a precoder that maximizes the energy efficiency (EE) of multicell multiantenna downlink network with coordination and, in the meantime, ensures the minimal data rate requirement of each user. To find a solution of such a nonconvex optimization problem, we construct a convex subset of the original constraint set and a quasi-concave lower bound of the EE. Then, we propose an iterative algorithm to maximize the lower bound of the EE within the convex subset, which is shown to rapidly converge to a local optimum of the original problem. We evaluate the EE of the proposed algorithm through simulations under different user locations, data rate requirements, and numbers of antennas. The results demonstrate that the proposed precoder performs closely to an upper bound derived from interference-free assumption. When the circuit power consumption is dominant, the proposed precoder is much more energy efficient than the transmit power minimization precoder, as well as a precoder, including an interference alignment (IA) beamformer and the optimized transmit power maximizing the EE. Index Terms-Coordinated beamforming, energy efficiency (EE), precoding design, quality of service (QoS).1 In this paper, coordinated beamforming is a general notion for precoding with coordination among multiple BSs. Therefore, optimizing precoding explicitly or implicitly includes optimizing beamforming and transmit power. 0018-9545

Joint Fronthaul Link Selection and Transmit Precoding for Energy Efficiency Maximization of Multiuser MIMO-Aided Distributed Antenna Systems

“…In the following, we prove that this solution satisfies the KKT condition of Problem (26). According to Theorem 2, the converged solution V ⋆ satisfies the KKT condition of Problem (29). The Lagrangian 5 It is emphasized here that since Problem (26) is a nonconvex optimization problem, the converged solution depends on the initialization point from Stage I.…”

“…Furthermore, even though naturally the power constraints and rate requirements are in conflict with each other, the feasibility issues were not analyzed in [28], rather it was always assumed that the original problem is feasible. Transmit precoder matrices were optimized for maximizing the EE of the family of MIMO interference channels in [29] under rate constraints, where an iterative algorithm was proposed for maximizing the lower bound of the EE. However, link selection did not have to be considered in [29], since each user is served by a dedicated transmitter.…”

“…Transmit precoder matrices were optimized for maximizing the EE of the family of MIMO interference channels in [29] under rate constraints, where an iterative algorithm was proposed for maximizing the lower bound of the EE. However, link selection did not have to be considered in [29], since each user is served by a dedicated transmitter. Furthermore, the power constraints at each transmitter were not considered.…”

“…Furthermore, the power constraints at each transmitter were not considered. To check the feasibility of the problem, a heuristic method based on the interference alignment technique was proposed in [29] under the assumption of having infinite transmit power, which is not realistic. References [30] and [31] adopted the interference alignment technique and the zero-forcing method to eliminate the multiuser interference, respectively.…”

“…For the third layer, since the numerator and the denominator of the OF of Problem (31) 2 are concave and convex functions, respectively, Dinkelbach's method is guaranteed to converge to the globally optimal solution [41]. According to Theorem 2, the second layer is guaranteed to converge to the KKT conditions of Problem (29). In the following theorem, we prove the convergence of the first layer's iterative process, hence equivalently the triple-layer iterative algorithm is guaranteed to converge.…”