Linear transceiver design for a MIMO interfering broadcast channel achieving max–min fairness

Abstract

We consider the problem of linear transceiver design to achieve max-min fairness in a downlink MIMO multicell network. This problem can be formulated as maximizing the minimum rate among all the users in an interfering broadcast channel (IBC). In this paper we show that when the number of antennas is at least two at each of the transmitters and the receivers, the min rate maximization problem is NP-hard in the number of users. Moreover, we develop a low-complexity algorithm for this problem by iteratively solving a sequence of convex subproblems, and establish its global convergence to a stationary point of the original minimum rate maximization problem. Numerical simulations show that this algorithm is efficient in achieving fairness among all the users. I. INTRODUCTIONWe consider the linear transceiver design problem in a MIMO-IBC, in which a set of Base Stations (BSs) send data to their intended users. Both the BSs and the users are equipped with multiple antennas, and they share the same time/frequency resource for transmission. The objective is to maximize the minimum rate among all the users in the network, in order to achieve network-wide fairness.Providing max-min fairness has long been considered as an important design criterion for wireless networks. Hence various algorithms that optimize the min-rate utility in different network settings have been proposed in the literature. References [20], [21] are early works that studied the max-min signal to interference plus noise ratio (SINR) power control problem and a related SINR feasibility problem in a scalar interference channel (IC). It was shown in [20], [21] that for randomly generated scalar ICs, with probability one there exists a unique optimal solution to the max-min problem. The proposed algorithm with an additional binary search can be used to solve the max-min fairness problem efficiently. Recently reference [17] derived a set of algorithms based on nonlinear Perron-Frobenius theory for the same network setting. Differently from [20], [21], the proposed algorithms can also deal with individual users' power constraints. Apart from the scalar IC case, there have been many published results [1], [3], [4], [8], [14], [18], [19] on the min rate maximization problem in a multiple input single output (MISO) network, in which the BSs are equipped with multiple antennas and the users are only equipped with a single antenna. Reference [19] utilized the nonnegnative matrix theory to study the related power control problem when the beamformers are known and fixed. When optimizing the transmit power and the beamformers jointly, M. Razaviyayn, M. Hong, and Z.-Q. Luo are with the

Robust Transmission in Downlink Multiuser MISO Systems: A Rate-Splitting Approach

“…,μ M have finite supports [52], [53]. Now, we observe that problems (7) and (25) are instances of problems (60) and (61) respectively, with continuously differentiable objective and constraint functions [28], [37]. Also, P lies in the compact set given by P | tr PP H ≤ P t .…”

“…Even a sampled instance of the problem with a finite number of constraints is highly intractable in its current form due to the non-convex coupled nature of the sum-rate expressions embedded in each user's achievable rate. We start this section by introducing the WMMSE approach, initially proposed in [27] and then further established in [28], [37] with more rigorous convergence proofs. This approach is heavily employed throughout this paper due to its effectiveness in solving problems featuring sum-rate expressions.…”

“…The convergence of WMMSE algorithms to stationary (KKT) points was established for the sum-rate problem [28] and the max-min fair problem [37] in the context of the MIMO Interfering BC (IBC) under prefect CSI and NoRS. It was later shown that the WMMSE algorithm belongs to a class of inexact BCDs, known as Successive Upper-bound Minimization (SUM), and more general analysis and proofs were established in [42], [43].…”

Optimal Resource Allocation in Coordinated Multi-Cell Systems

“…Therefore, it is significantly more difficult to analyze and optimize the performance of a MIMO interference channel. In fact, even the resource allocation problem with fixed QoS requirements is provably NP-hard in the MIMO case [158,210]. As this is the computationally simplest problem in the MISO case, we cannot expect to solve any multi-cell single-stream MIMO resource allocation problem to global optimally in practice.…”

Optimization algorithms for big data with application in wireless networks

“…Therefore the previous analysis ofBSUM in Section 3.2.3 does not apply. Fortunately by carefully studying the optimality conditions of the resulting subproblems, one can still show that the iterates {vUlj converge to the set of stationary solutions of problem (3.37); see [56] for detailed analysis .…”