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This paper gives the long sought network version of water-filling named aspolite water-filling. Unlike in single-user MIMO channels, where no one usesgeneral purpose optimization algorithms in place of the simple and optimalwater-filling for transmitter optimization, the traditional water-filling isgenerally far from optimal in networks as simple as MIMO multiaccess channels(MAC) and broadcast channels (BC), where steepest ascent algorithms have beenused except for the sum-rate optimization. This is changed by the politewater-filling that is optimal for all boundary points of the capacity regionsof MAC and BC and for all boundary points of a set of achievable regions of amore general class of MIMO B-MAC interference networks, which is a combinationof 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 asspecial case. It is polite because it strikes an optimal balance betweenreducing interference to others and maximizing a link's own rate. Employing it,the related optimizations can be vastly simplified by taking advantage of thestructure of the problems. Deeply connected to the polite water-filling, therate duality is extended to the forward and reverse links of the B-MACnetworks. As a demonstration, weighted sum-rate maximization algorithms basedon polite water-filling and duality with superior performance and lowcomplexity are designed for B-MAC networks and are analyzed for InterferenceTree (iTree) Networks, a sub-class of the B-MAC networks that possessespromising properties for further information theoretic study.

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