Transmit beamforming to multiple cochannel multicast groups

Abstract

The major contribution of this thesis is on the problem of transmit beamforming to multiple cochannel multicast groups. Two viewpoints are considered: i) minimizing total transmission power while guaranteeing a prescribed minimum signal-to-interference-plus-noise ratio (SINR) at each receiver; and ii) 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 multicast beamforming problem is in general NP-hard, motivating the pursuit of computationally efficient quasi-optimal solutions. In chapter 1, it is shown that semidefinite relaxation coupled with suitable randomization/cochannel multicast power control yield computationally efficient high-quality approximate solutions. The multicast beamforming problem is revisited in chapter 2 for the important special case when the channel vectors are Vandermonde. This arises when a uniform linear antenna array is used at the transmitter under far-field line-of-sight propagation conditions, as provisioned in 802.16e and related wireless backhaul scenarios. It is shown 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. Chapter 3 considers the joint scheduling, admission, and power control problem under quality-of-service (QoS) constraints and a general formulation that incorporates multi-casting, cochannel or orthogonal transmission modalities, and access point selection. Several special cases are well-known to be NP-hard, yet important for QoS provisioning and bandwidth-efficient operation of existing and emerging cellular and overlay/underlay networks. Approximate solutions to the original problem are generated following a disciplined approach. The general problem is first concisely formulated as constrained optimization. A geometric programming approximation is then developed, which forms the core of a heuristic, yet well-motivated centralized algorithm. Chapter 4 considers the throughput maximization problem in the context of wireless networks. One is given a directed multi-hop network between a source and a destination, with edge capacities that are a function of transmission powers. Each node may split its aggregate incoming flow to multiple outgoing flows, and the objective is to select flows to maximize the end-to-end flow from source to destination. Power control can be used to obtain a favorable ‘topology’ from the throughput maximization viewpoint. This suggests a joint max-flow power control problem that is basic, yet has not been considered in the cross-layer network optimization literature. Alternatively, power control may be coupled with dynamic routing by means of differential queue lengths information. Both approaches are sketched and convex approximations, in the high SINR regime, are provided for these cross-layer power control problems.