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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]

This paper studies optimal bandwidth and power allocation in a cognitive radio network where multiple secondary users (SUs) share the licensed spectrum of a primary user (PU) under fading channels using the frequency division multiple access scheme. The sum ergodic capacity of all the SUs is taken as the performance metric of the network. Besides the peak/average transmit power constraints at the SUs and the peak/average interference power constraint imposed by the PU, total bandwidth constraint of the licensed spectrum is also taken into account. Optimal bandwidth allocation is derived in closed-form for any given power allocation. The structures of optimal power allocations are also derived under all possible combinations of the aforementioned power constraints. These structures indicate the possible numbers of users that transmit at nonzero power but below their corresponding peak powers, and show that other users do not transmit or transmit at their corresponding peak powers. Based on these structures, efficient algorithms are developed for finding the optimal power allocations. [ABSTRACT FROM AUTHOR]