Duality, Polite Water-filling, and Optimization for MIMO B-MAC Interference Networks and iTree Networks

TL;DR

This paper introduces polite water-filling, an optimal network version of water-filling for MIMO B-MAC interference networks, simplifying optimization and improving performance by balancing interference reduction and rate maximization.

Contribution

It develops the concept of polite water-filling for all boundary points of capacity regions in MIMO B-MAC networks, extending rate duality and proposing efficient algorithms.

Findings

Polite water-filling is optimal for boundary points of capacity regions.

Algorithms based on polite water-filling outperform existing methods.

Analysis of iTree networks demonstrates the effectiveness of the approach.

Abstract

This paper gives the long sought network version of water-filling named as polite water-filling. Unlike in single-user MIMO channels, where no one uses general purpose optimization algorithms in place of the simple and optimal water-filling for transmitter optimization, the traditional water-filling is generally far from optimal in networks as simple as MIMO multiaccess channels (MAC) and broadcast channels (BC), where steepest ascent algorithms have been used except for the sum-rate optimization. This is changed by the polite water-filling that is optimal for all boundary points of the capacity regions of MAC and BC and for all boundary points of a set of achievable regions of a more general class of MIMO B-MAC interference networks, which is a combination of multiple interfering broadcast channels, from the transmitter point of view, and multiaccess channels, from the receiver point of view, including MAC, BC, interference channels, X networks, and most practical wireless networks as special case. It is polite because it strikes an optimal balance between reducing interference to others and maximizing a link's own rate. Employing it, the related optimizations can be vastly simplified by taking advantage of the structure of the problems. Deeply connected to the polite water-filling, the rate duality is extended to the forward and reverse links of the B-MAC networks. As a demonstration, weighted sum-rate maximization algorithms based on polite water-filling and duality with superior performance and low complexity are designed for B-MAC networks and are analyzed for Interference Tree (iTree) Networks, a sub-class of the B-MAC networks that possesses promising properties for further information theoretic study.