Abstract-The problem of transmit beamforming to multiple cochannel multicast groups is considered, when the channel state is known at the transmitter and from two viewpoints: minimizing total transmission power while guaranteeing a prescribed minimum signal-to-interference-plus-noise ratio (SINR) at each receiver; and a "fair" approach maximizing the overall minimum SINR under a total power budget. The core problem is a multicast generalization of the multiuser downlink beamforming problem; the difference is that each transmitted stream is directed to multiple receivers, each with its own channel. Such generalization is relevant and timely, e.g., in the context of the emerging WiMAX and UMTS-LTE wireless networks. The joint problem also contains single-group multicast beamforming as a special case. The latter (and therefore also the former) is NP-hard. This motivates the pursuit of computationally efficient quasi-optimal solutions. It is shown that Lagrangian relaxation coupled with suitable randomization/cochannel multicast power control yield computationally efficient high-quality approximate solutions. For a significant fraction of problem instances, the solutions generated this way are exactly optimal. Extensive numerical results using both simulated and measured wireless channels are presented to corroborate our main findings.

The article describes the potential gain by spectrum sharing between cellular operators in terms of network efficiency. The focus of the study is on a specific resource sharing scenario: spectrum sharing between two operators in cellular downlink transmission. If frequency bands are allocated dynamically and exclusively to one operator - a case called orthogonal spectrum sharing - significant gains in terms of achievable throughput (spectrum sharing gains between 50 percent and 100 percent) and user satisfaction are reported for asymmetric scenarios at link and system level as well as from two hardware demonstrators. Additionally, if frequency bands are allocated simultaneously to two operators - a case called non-orthogonal spectrum sharing - further gains are reported. In order to achieve these, different enablers from hardware technologies and base station capabilities are required. However, we argue that all requirements are fulfilled in 3GPP and newer mobile standards. Therefore, the results and conclusions of this overview article encourage to seriously consider the inter-operator spectrum sharing technologies

Abstract-The problem of transmit beamforming to multiple cochannel multicast groups is considered for the important special case when the channel vectors are Vandermonde. This arises when a uniform linear antenna antenna (ULA) array is used at the transmitter under far-field line-of-sight propagation conditions, as provisioned in 802.16e and related wireless backhaul scenarios. Two design approaches are pursued: i) minimizing the total transmitted power subject to providing at least a prescribed received signal-to-interference-plus-noise-ratio (SINR) to each intended receiver; and ii) maximizing the minimum received SINR under a total transmit power budget. Whereas these problems have been recently shown to be NP-hard, in general, it is proven here that for Vandermonde channel vectors, it is possible to recast the optimization in terms of the autocorrelation sequences of the sought beamvectors, yielding an equivalent convex reformulation. This affords efficient optimal solution using modern interior point methods. The optimal beamvectors can then be recovered using spectral factorization. Robust extensions for the case of partial channel state information, where the direction of each receiver is known to lie in an interval, are also developed. Interestingly, these also admit convex reformulation. The various optimal designs are illustrated and contrasted in a suite of pertinent numerical experiments.

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Abstract-We study the achievable ergodic rate region of the two-user multiple-input single-output interference channel, under the assumptions that the receivers treat interference as additive Gaussian noise and the transmitters only have statistical channel knowledge. Initially, we provide a closed-form expression for the ergodic rates and derive the Nash-equilibrium and zero-forcing transmit beamforming strategies. Then, we show that combinations of the aforementioned selfish and altruistic, respectively, strategies achieve Pareto-optimal rate pairs.

In this paper, we study an achievable rate region of the two-user multiple-input single-output (MISO) interference channel. We find the transmit beamforming vectors that achieve Pareto-optimal points. We do so, by deriving a sufficient condition for Pareto optimality. Given the beamforming vector of one transmitter, this condition enables us to determine the beamforming vector of the other transmitter that forms a Pareto-optimal pair. The latter can be done in closed form by solving a cubic equation. The result is validated against state-of-the-art methods via numerical illustrations.

Abstract-We consider the two-user multiple-input singleoutput (MISO) interference channel (IFC) and assume that the receivers treat the interference as additive Gaussian noise. We study the rates that can be achieved in a slow-fading scenario, allowing an outage probability. We introduce three definitions for the outage region of the IFC. The definitions differ on whether the rates are declared in outage jointly or individually and whether there is perfect or statistical information about the channels. Even for the broadcast and the multiple-access channels, which are special cases of the IFC, there exist several definitions of the outage rate regions. We provide interpretations of the definitions and compare the corresponding regions via numerical simulations. Also, we discuss methods for finding the regions. This includes a characterization of the beamforming strategies, which are optimal in the sense that achieve rate pairs on the Pareto boundary of the outage rate region.