Consider a multiuser communication system in a frequency selective environment whereby users share a common spectrum and can interfere with each other. Assuming Gaussian signaling and no interference cancelation, we study optimal spectrum sharing strategies for the maximization of sum-rate under separate power constraints for individual users. Since the sum-rate function is nonconcave in terms of the users' power allocations, there can be multiple local maxima for the sum-rate maximization problem in general. In this paper, we show that, if the normalized crosstalk coefficients are larger than a given threshold (roughly equal to1/2), then the optimal spectrum sharing strategy is frequency division multiple access (FDMA). In case of arbitrary positive crosstalk coefficients, if each user's power budget exceeds a given threshold, then FDMA is again sum-rate optimal, at least in a local sense. In addition, we show that the problem of finding the optimal FDMA spectrum allocation is NP-hard, implying that the general problem of maximizing sum-rate is also NP-hard, even in the case of two users. We also propose several simple distributed spectrum allocation algorithms that can approximately maximize sum-rates. Numerical results indicate that these algorithms are efficient and can achieve substantially larger sum-rates than the existing Iterative Waterfilling solutions, either in an interference-rich environment or when the users' power budgets are sufficiently high.

Consider a multiuser communication system in a frequency selective environment whereby users share a common spectrum and can interfere with each other. Assuming Gaussian signaling and treating interference as noise, we study optimal spectrum sharing strategies for the maximization of weighted sum-rate. In this work, we show that, if the normalized crosstalk gains are larger than a given threshold (roughly equal to 1/2), then the optimal spectrum sharing strategy is frequency division multiple access (FDMA). We also propose several simple distributed spectrum allocation algorithms that can approximately maximize weighted sum-rates. Numerical simulation of DSL applications shows that these algorithms are efficient and can achieve substantially larger weighted sumrates than those obtained by the existing iterative waterfilling algorithm.