text: This paper examines a CoMP system where multiple base-stations (BS) employ coordinated beamforming to serve multiple mobile-stations (MS). Under the dynamic point selection mode, each MS can be assigned to only one BS at any time. This work then presents a solution framework to optimize the BS associations and coordinated beamformers for all MSs. With target signal-to-interference-plus-noise ratios at the MSs, the design objective is to minimize either the weighted sum transmit power or the per-BS transmit power margin. Since the original optimization problems contain binary variables indicating the BS associations, finding their optimal solutions is a challenging task. To circumvent this difficulty, we first relax the original problems into new optimization problems by expanding their constraint sets. Based on the nonconvex quadratic constrained quadratic programming framework, we show that these relaxed problems can be solved optimally. Interestingly, with the first design objective, the obtained solution from the relaxed problem is also optimal to the original problem. With the second design objective, a suboptimal solution to the original problem is then proposed, based on the obtained solution from the relaxed problem. Simulation results show that the resulting jointly optimal BS association and beamforming design significantly outperforms fixed BS association schemes.
  @cite_30: This paper studies distributed optimization schemes for multicell joint beamforming and power allocation in time-division-duplex (TDD) multicell downlink systems where only limited-capacity intercell information exchange is permitted. With an aim to maximize the worst-user signal-to-interference-and-noise ratio (SINR), we devise a hierarchical iterative algorithm to optimize downlink beamforming and intercell power allocation jointly in a distributed manner. The proposed scheme is proved to converge to the global optimum. For fast convergence and to reduce the burden of intercell parameter exchange, we further propose to exploit previous iterations adaptively. Results illustrate that the proposed scheme can achieve near-optimal performance even with a few iterations, hence providing a good tradeoff between performance and backhaul consumption. The performance under quantized parameter exchange is also examined.
  @cite_33: In this paper, we address the problem of the coordinated beamforming design for multi-cell multiple input single output (MISO) downlink system subject to per-BS power constraints. The objective is taken as the maximization of the minimum signal-to-interference plus noise ratio (SINR), while a complete analysis of the duality between the multi-cell downlink and the virtual uplink optimization problems is provided. A hierarchical iterative scheme is proposed to solve the virtual uplink optimization problem, whose solution is then converted to derive the one of the multi-cell downlink beamforming problem. The proposed algorithm is proved to converge to a stable point. Additional, the complexity of the proposed algorithm is analyzed. Simulation results show that, in contrast to existing multi-cell beamforming schemes, the proposed algorithm achieves better performance in terms of both rate per energy (RPE) and the worst-user rate.
  @cite_36: 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.
  @cite_23: 
  @cite_15: This paper considers maximizing the network-wide minimum supported rate in the downlink of a two-cell system, where each base station (BS) is endowed with multiple antennas. This is done for different levels of cell cooperation. At one extreme, we consider single cell processing where the BS is oblivious to the interference it is creating at the other cell. At the other extreme, we consider full cooperative macroscopic beamforming. In between, we consider coordinated beamforming, which takes account of inter-cell interference, but does not require full cooperation between the BSs. We combine elements of Lagrangian duality and large system analysis to obtain limiting SINRs and bit-rates, allowing comparison between the considered schemes. The main contributions of the paper are theorems which provide concise formulas for optimal transmit power, beamforming vectors, and achieved signal to interference and noise ratio (SINR) for the considered schemes. The formulas obtained are valid for the limit in which the number of users per cell, K, and the number of antennas per base station, N, tend to infinity, with fixed ratio β = K N. These theorems also provide expressions for the effective bandwidths occupied by users, and the effective interference caused in the adjacent cell, which allow direct comparisons between the considered schemes.
  @cite_16: In a conventional wireless cellular system, signal processing is performed on a per-cell basis; out-of-cell interference is treated as background noise. This paper considers the benefit of coordinating base-stations across multiple cells in a multi-antenna beamforming system, where multiple base-stations may jointly optimize their respective beamformers to improve the overall system performance. Consider a multicell downlink scenario where base-stations are equipped with multiple transmit antennas employing either linear beamforming or nonlinear dirty-paper coding, and where remote users are equipped with a single antenna each, but where multiple remote users may be active simultaneously in each cell. This paper focuses on the design criteria of minimizing either the total weighted transmitted power or the maximum per-antenna power across the base-stations subject to signal-to-interference-and-noise-ratio (SINR) constraints at the remote users. The main contribution of the paper is an efficient algorithm for finding the joint globally optimal beamformers across all base-stations. The proposed algorithm is based on a generalization of uplink-downlink duality to the multicell setting using the Lagrangian duality theory. An important feature is that it naturally leads to a distributed implementation in time-division duplex (TDD) systems. Simulation results suggest that coordinating the beamforming vectors alone already provide appreciable performance improvements as compared to the conventional per-cell optimized network.
  @cite_20: This paper is concerned with the game theoretical approach in designing the multiuser downlink beamformers in multicell systems. Sharing the same physical resource, the base-station of each cell wishes to minimize its transmit power subject to a set of target signal-to-interference-plus-noise ratios (SINRs) at the multiple users in the cell. In this context, at first, the paper considers a strategic noncooperative game (SNG) where each base-station greedily determines its optimal downlink beamformer strategy in a distributed manner, without any coordination between the cells. Via the game theory framework, it is shown that this game belongs to the framework of standard functions. The conditions guaranteeing the existence and uniqueness of a Nash Equilibrium (NE) in this competitive design are subsequently examined. The paper then makes a revisit to the fully coordinated design in multicell downlink beamforming, where the optimal beamformers are jointly designed between the base-stations. A comparison between the competitive and coordinated designs shows the benefits of applying the former over the latter in terms of each design's distributed implementation. Finally, in order to improve the efficiency of the NE in the competitive design, the paper considers a more cooperative game through a pricing mechanism. The pricing consideration enables a base-station to steer its beamformers in a more cooperative manner, which ultimately limits the interference induced to other cells. The study on the existence and uniqueness of the new game's NE is then given. The paper also presents a condition on the pricing factors that allow the new NE point to approach the performance established by the coordinated design, while retaining the distributed nature of the multicell game.
  @cite_12: This paper addresses coordinated downlink beamforming optimization in multicell time division duplex (TDD) systems where a small number of parameters are exchanged between cells but with no data sharing. With the goal to reach the point on the Pareto boundary with max-min rate fairness, we first develop a two-step centralized optimization algorithm to design the joint beamforming vectors. This algorithm can achieve a further sum-rate improvement over the max-min optimal performance, and is shown to guarantee max-min Pareto optimality for scenarios with two base stations (BSs) each serving a single user. To realize a distributed solution with limited intercell communication, we then propose an iterative algorithm by exploiting an approximate uplink-downlink duality, in which only a small number of positive scalars are shared between cells in each iteration. Simulation results show that the proposed distributed solution achieves a fairness rate performance close to the centralized algorithm while it has a better sum-rate performance, and demonstrates a better tradeoff between sum-rate and fairness than the Nash Bargaining solution especially at high signal-to-noise ratio.
summary: Designing multicell beamformers under the CS CB mode has attracted a lot of research attention, such as @cite_16 @cite_36 @cite_15 @cite_23 @cite_30 @cite_33 @cite_12 @cite_20 . Uplink-downlink duality and iterative fixed-point iteration have been successfully exploited in @cite_16 @cite_30 @cite_33 @cite_12 @cite_36 to obtain optimal beamformers to either minimize the sum transmit power at the BSs or maximize the minimum SINR at the MSs. Different to these previous studies, part of this work examines the application of uplink-downlink duality to optimize the multicell beamformers under the DPS mode.