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In this paper, low-complexity joint power assignment algorithms are developed for multi-source multi-destination relay networks where multiple sources share a common relay that forwards all received signals simultaneously to destinations. In particular, we consider the following power optimization strategies: (i) Minimization of the total transmission power of the sources and the relay under the constraint that the signal-to-interference-plus-noise ratio (SINR) requirement of each source-destination pair is satisfied, and (ii) Maximization of the minimum SINR among all source-destination pairs subject to any given total power budget. Both optimization problems involve K power variables, where K is the number of source-destination pairs in the network, and an exhaustive search is prohibitive for large K. In this work, we develop a methodology that allows us to obtain an asymptotically tight approximation of the SINR and reformulate the original optimization problems to single-variable optimization problems, which can be easily solved by numerical search of the single variable. Then, the corresponding optimal transmission power at each source and relay can be calculated directly. The proposed optimization schemes are scalable and lead to power assignment algorithms that exhibit the same optimization complexity for any number (K) of source-destination pairs in the network. Moreover, we apply the methodology that we developed to solve a related max-min SINR based optimization problem in which we determine power assignment for the sources and the relay to maximize the minimum SINR among all source-destination pairs subject to any given total power budget. Extensive numerical studies illustrate and validate our theoretical developments. [ABSTRACT FROM AUTHOR]

Distributed network utility maximization (NUM) has received an increasing intensity of interest over the past few years. Distributed solutions (e.g., the primal-dual gradient method) have been intensively investigated under fading channels. As such distributed solutions involve iterative updating and explicit message passing, it is unrealistic to assume that the wireless channel remains unchanged during the iterations. Unfortunately, the behavior of those distributed solutions under time-varying channels is in general unknown. In this paper, we shall investigate the convergence behavior and tracking errors of the iterative primal-dual scaled gradient algorithm (PDSGA) with dynamic scaling matrices (DSC) for solving distributive NUM problems under time-varying fading channels. We shall also study a specific application example, namely the multicommodity flow control and multicarrier power allocation problem in multihop ad hoc networks. Our analysis shows that the PDSGA converges to a limit region rather than a single point under the finite state Markov chain (FSMC) fading channels. We also show that the order of growth of the tracking errors is given by \cal O\left(\bar T/\bar N\right), where \bar T and \bar N are the update interval and the average sojourn time of the FSMC, respectively. Based on this analysis, we derive a low complexity distributive adaptation algorithm for determining the adaptive scaling matrices, which can be implemented distributively at each transmitter. The numerical results show the superior performance of the proposed dynamic scaling matrix algorithm over several baseline schemes, such as the regular primal-dual gradient algorithm. [ABSTRACT FROM AUTHOR]