Distributed polite water-filling for optimization of MIMO B-MAC interference networks

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. 5 interpretation.Directly applying single-user water-filling to networks is referred to as selfish water-filling here. It is well known to be far from optimal [26]-[28] because it does not control interference to others. Based on selfish water-filling, game-theoretic, distributed, and iterative algorithms have been well studied for DSL [26], [29]-[33], for MIMO interference channels, e.g., [34]-[37], and for multiaccess channels, e.g., [28]. The algorithms converge only under stringent conditions and the performance is not near optimal.The importance of controlling interference to others has been recognized in literature, e.g., [11],[38]- [40]. But a systematic, general, and optimal method has not been found. In interference pricing method, each user maximizes its own utility minus the interference cost determined by the interference prices. With a proper choice of the interference price which can be reverse engineered from the KKT conditions, the interference pricing based method can find a stationary point of the sum utility maximization problem. Several monotonically convergent interference pricing algorithms have been proposed in [41]-[43] for the SISO/MISO interference channels, and the MIMO interference channel with single data stream transmission. Except for the SISO case, all these algorithms update e...

MIMO B-MAC Interference Network Optimization Under Rate Constraints by Polite Water-Filling and Duality

“…It specifies whether interference is completely cancelled or treated as noise: if , after interference cancellation, still causes interference to and otherwise, . The coupling matrices valid for the results of this paper are those for which there exists a transmission and receiving scheme such that each signal is decoded (and possibly cancelled) by no more than one receiver [1]. We give an example of the valid coupling matrices for the B-MAC network in Fig.…”

“…But a valid coupling matrix can serve for an upper or lower bound of the achieved rates. See more discussion in [1].…”

“…However, directly applying traditional water-filling is far from optimal [23]- [25]. In [1], we recently found the long sought network version of water-filling, polite water-filling, which is the optimal input structure of any Pareto rate point, not only the sum-rate optimal point, of the capacity regions of MAC and BC and a large class of achievable regions of a MIMO B-MAC network. Polite water-filling manages the interference to other links through beamforming matrices and power allocation.…”

“…To handle a wide range of interference cancellation, we define a coupling matrix as a function of the interference cancellation scheme [1]. It specifies whether interference is completely cancelled or treated as noise: if , after interference cancellation, still causes interference to and otherwise, .…”

“…W E study the optimization under rate constraints for generalized multiple-input multiple-output (MIMO) interference networks, named MIMO B-MAC networks [1], where each transmitter may send independent data to multiple receivers and each receiver may collect independent data from multiple transmitters. Consequently, the network is a combination of multiple interfering broadcast channels (BC) and multiaccess channels (MAC).…”