Multiuser Water-filling in the Presence of Crosstalk

Spectrum optimization is an important part of the design of interference-limited multiuser communication systems. While traditional water-filling provides a closed-form solution to the transmit optimization problem in a single-user system, the multiuser version of the problem often leads to nonconvex problem formulations which are difficult to solve. Motivated by high-speed parallel-link and digital subscriber line applications, this paper investigates two practical multiuser settings in which global or local optimal solutions to the multiuser spectrum optimization problems can be found efficiently. The first part of this paper considers a high-speed transmission system in which practical (but suboptimal) minimum-mean-squared-error linear equalizers (MMSE-LEs) are used at the receiver. The optimal single-user transmit spectrum in this case involves a modified water-filling solution. Surprisingly, such a modified water-filling spectrum can be shown to be near-optimal in a multiuser setting as well, if the direct-link and the crosstalk characteristics are symmetric and if crosstalk is reasonably small. Thus, for practical parallel-link systems using MMSE linear equalizers, the optimal single-user and multiuser spectra are nearly identical. The second part of this paper considers numerical techniques for solving a nonconvex multiuser rate maximization problem for digital subscriber line applications. A new ingredient in the proposed approach is a taxation scheme that takes into account the effect of interference between neighboring lines. This leads to a modified iterative water-filling algorithm which is capable of finding local optimum solutions to the multiuser spectrum optimization problem efficiently.