Min-max fair coordinated beamforming via large systems analysis

Abstract

This paper considers base station (BS) cooperation in the form of coordinated beamforming, focusing on min-max fairness in the power usage subject to target SINR constraints. We show that the optimal beamforming strategies have an interesting nested zero-forcing structure. In the asymptotic regime where the number of antennas at each BS and the number of users in each cell both grow large with their ratio tending to a finite constant, the dimensionality of the optimization is greatly reduced, and only knowledge of statistics is required to solve it. The optimal solution is characterized in general, and an algorithm is proposed that converges to the optimal transmit parameters, for feasible SINR targets. For the two cell case, a simple single parameter characterization is obtained. These asymptotic results provide insights into the average performance, as well as simple but efficient beamforming strategies for the finite system case. In particular, the optimal beamforming strategy from the large systems analysis only requires the base stations to have local instantaneous channel state information; the remaining parameters of the beamformer can be calculated using channel statistics which can easily be shared amongst the base stations.

Reduced-Dimension Design of MIMO Over-the-Air Computing for Data Aggregation in Clustered IoT Networks

“…The "phased-zero-forcing (ZF)" precoding scheme proposed in [25] achieves complexity reduction by combining ZF precoding in the baseband domain and phase control in the radio frequency (RF) domain. On the other hand, a hierarchical architecture for implementing multiuser ZF receiver based on user clustering is shown in [26], [27] to yield complexity reduction. Another popular approach for reduced-dimension MIMO is called hybrid beamforming that decompose a MIMO transceiver into two cascaded components for analog and digital implementation [28]- [30].…”

Survey of Large-Scale MIMO Systems

“…The main objective of applying coordinated beamforming in LS-MIMOs is to improve the overall system performance, while reducing the coordination overhead. There are two popular coordinated beamforming schemes, namely the hierarchical [107] and the nested structure [108], [109].…”

“…Moreover, only the knowledge of the channel's spatial correlation matrices is needed for the BF-weight optimization, which is insensitive to the backhaul latency. 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].…”

“…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. For instance, when this BF is applied in an LS-MIMO system, all the eNBs are divided into two groups, 1) Selfish eNBs, whose UE SINRs are relative low; and 2) altruistic eNBs, whose UEs SINRs are relative high.…”

“…Thus, it is crucial to choose an objective with an appropriate metric function for the multi-cell scheduling schemes. 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.…”