Joint Beamforming and Power Control in Coordinated Multicell: Max-Min Duality, Effective Network and Large System Transition

Abstract

Abstract-This paper studies joint beamforming and power control in a coordinated multicell downlink system that serves multiple users per cell to maximize the minimum weighted signal-to-interference-plus-noise ratio. The optimal solution and distributed algorithm with geometrically fast convergence rate are derived by employing the nonlinear Perron-Frobenius theory and the multicell network duality. The iterative algorithm, though operating in a distributed manner, still requires instantaneous power update within the coordinated cluster through the backhaul. The backhaul information exchange and message passing may become prohibitive with increasing number of transmit antennas and increasing number of users. In order to derive asymptotically optimal solution, random matrix theory is leveraged to design a distributed algorithm that only requires statistical information. The advantage of our approach is that there is no instantaneous power update through backhaul. Moreover, by using nonlinear Perron-Frobenius theory and random matrix theory, an effective primal network and an effective dual network are proposed to characterize and interpret the asymptotic solution.Index Terms-Power control, coordinated beamforming, maxmin duality, effective network, large system analysis, multicell network, nonlinear Perron-Frobenius theory, random matrix theory.

Survey of Large-Scale MIMO Systems

“…By contrast, in the BF associated with the nested structure, the optimal strategy can be found recursively, where the BF weight optimization Objective Function (OF) may be based on the fairness in power usage subject to satisfying the target SINR constraints [108], [110]. Another nested structure, whose OF focuses on Maximizing the Minimum (MAX-MIN) weighted SINR among UEs was proposed in [109], [111]. Unlike the hierarchical structure of [107], the optimal precoder of the nested structure [108], [109] is found as the solution of a joint optimization problem, which aims for striking a trade-off between providing a high SINR for the intra-cell UEs and mitigating the ICI.…”

“…There are several kinds of objectives in terms of either efficiency or fairness when multi-cell scheduling is applied in LS-MIMO systems, e.g., a) Minimizing the Maximum (MIN-MAX) the fairness in power consumption subject to certain SINR constraints [108], [110]: It aims to maximize the overall EE as a high priority by adjusting its coordinated beamforming scheme. A efficient solution can be obtained through Lagrange duality and random matrix theory; b) MAX-MIN SINR subject to certain sum-rate constraints [109], [111]: It enforces the overall system fairness by guaranteeing each UE's promised SINR. In the case of non-convex optimization problems, the optimal scheme may be derived by using nonlinear Perron-Frobenius theory; c) Maximizing the weighted sum rate subject to some eNBs power consumption constraints: This objective can be viewed as a combination of MAX-MIN fairness and maximum sum-rate.…”

QoS-aware User Load Management with Beamforming for Energy Efficiency in Wireless Networks

“…A load balanced cell sectorization scheme was discussed in [8] through efficiently exploiting the spatial degrees of freedom (DOF) with the help of vertical beamforming techniques and user location determination. In [9], a downlink and uplink dichotomy for the multi-cell case was projected, in which the signal to interference and noise ratio (SINR) restraints for neighbor users are avoided by reducing the overall transmitted power around all base stations. Furthermore, the congestion and power control methods were improved with the user spectrum allocation, power management, scheduling, and cooperative optimum downlink beamforming in [10]- [12] for the multi-cell environment of wireless networking.…”

Coordinated beamforming design for multicell systems with transceiver impairments: from perspective of spectral efficiency to energy efficiency

“…Coordinated or cooperative beamforming, where multiantenna reprocessing at neighboring base stations (BSs) are designed cooperatively, has been extensively studied in the existing literatures such as [3][4][5][6][7][8][9] and thereof. To be more specific, the transmit power minimization problem subject to signal-to-interference-and-noise-ratio (SINR) constraints at the remote users was addressed based on *Correspondence: huangym@seu.edu.cn 1 School of Information Science and Engineering, Southeast University, Nanjing 210096, China Full list of author information is available at the end of the article the uplink-downlink duality theorem for multicell multiuser downlink systems [3].…”

“…Recently, taking the user fairness in account, a decentralized coordinated beamforming algorithm was proposed to achieve the Pareto boundary of user rate tuples [8]. Further considering a massive MIMO case, an efficient coordinated multicell beamforming scheme was developed by exploiting the asymptotic behavior of massive MIMO channels, which could asymptotically achieve the optimal performance with limited intercell coordination [9].…”