Optimal Beamforming in Interference Networks with Perfect Local Channel Information

Abstract

We consider settings in which T multi-antenna transmitters and K single-antenna receivers concurrently utilize the available communication resources. Each transmitter sends useful information only to its intended receivers and can degrade the performance of unintended systems. Here, we assume the performance measures associated with each receiver are monotonic with the received power gains. In general, the systems' joint operation is desired to be Pareto optimal. However, designing Pareto optimal resource allocation schemes is known to be difficult. In order to reduce the complexity of achieving efficient operating points, we show that it is sufficient to consider rank-1 transmit covariance matrices and propose a framework for determining the efficient beamforming vectors. These beamforming vectors are thereby also parameterized by T (K − 1) real-valued parameters each between zero and one. The framework is based on analyzing each transmitter's power gain-region which is composed of all jointly achievable power gains at the receivers. The efficient beamforming vectors are on a specific boundary section of the power gain-region, and in certain scenarios it is shown that it is necessary to perform additional power allocation on the beamforming vectors. Two examples which include broadcast and multicast data as well as a cognitive radio application scenario illustrate the results.

Optimal Resource Allocation in Coordinated Multi-Cell Systems

“…Note that the definition of the channel gain region in Definition 1.5 is different from the definition in [180] because of the feasible transmit strategies. Therefore, the next result which shows that Ω k is compact and convex extends [180,Lemma 1].…”

“…Coordinated beamforming is such an example, because the transmitted signals over each channel component are independent. This is also fulfilled when multiple base stations send multiple independent signals to a given user [180,239], but for simplicity this subsection concentrates on coordinated beamforming.…”

“…Several iterations and rounds of control signaling are generally necessary to achieve the solution, which might not be desirable or feasible in practice. By sacrificing the optimality assurance, noniterative resource allocation algorithms that only utilize local CSI can be obtained; for example, by imitating the structure of optimal beamforming [18,21,23,88,135,142,180,311]. This subsection describes a simple heuristic approach that can be seen as a pragmatic approach to multi-cell coordination but also as a reasonable starting-point for iterative algorithms.…”

Spectrum Leasing via Cooperation for Enhanced Physical-Layer Secrecy

“…In this part, we review the concept and main results related to a power gain region as introduced in [17]. In particular, we introduce a design of beamforming vectors to achieve Pareto boundary points of the power gain region.…”

“…For a design of e e e, e i is set to +1 if the i-th receiver is an intended receiver, while e j = −1 if the j-th receiver is an unintended receiver. By doing so, B e e e Ω becomes a set of Pareto optimal points of the power gain region in direction to maximize its power gain at intended receivers and/or minimizes its power gain at unintended receiver [17].…”