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Joint channel and rate allocation with power minimization in orthogonal frequency-division multiple access (OFDMA) has attracted extensive attention. Most of the research has dealt with the development of suboptimal but low-complexity algorithms. In this paper, the contributions comprise new insights from revisiting tractability aspects of computing the optimum solution. Previous complexity analyses have been limited by assumptions of fixed power on each subcarrier or power-rate functions that locally grow arbitrarily fast. The analysis under the former assumption does not generalize to problem tractability with variable power, whereas the latter assumption prohibits the result from being applicable to well-behaved power-rate functions. As the first contribution, we overcome the previous limitations by rigorously proving the problem's NP-hardness for the representative logarithmic rate function. Next, we extend the proof to reach a much stronger result, namely, that the problem remains NP-hard, even if the channels allocated to each user are restricted to be a consecutive block with given size. We also prove that, under these restrictions, there is a special case with polynomial-time tractability. Then, we treat the problem class where the channels can be partitioned into an arbitrarily large but constant number of groups, each having uniform gain for every individual user. For this problem class, we present a polynomial-time algorithm and provide its optimality guarantee. In addition, we prove that the recognition of this class is polynomial-time solvable. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the problem of fair resource allocation based on the Nash bargaining solution (NBS) over wireless amplify-and-forward (AF) relay networks in which variable-rate users and constant-rate users coexist. Via the dual decomposition method, a distributed algorithm, including relay selection, relay power allocation, and rate adaptation, is proposed. When the number of users is large and/or the rate constraints are stringent, the problem becomes infeasible, and admission control is necessary. We formulate the admission control and fair resource allocation problem as a two-stage optimization problem, aiming to first find the maximal number of users the network can support with guaranteed rates and then allocate resources based on NBS for the admitted users. Since the problem is combinatorially hard, we transform it into an equivalent one-stage optimization problem, which can be solved by existing methods but with a higher computational complexity. To further reduce the computational complexity, a suboptimal algorithm is then developed. Simulations verify the convergence and fairness of the distributed algorithm. Simulations also show that the suboptimal algorithm achieves an approximate optimal performance but with a significant running time reduction. [ABSTRACT FROM PUBLISHER]

In this paper, the average rate maximization problem given transmission power constraints in a decode-and-forward (DF) relay network over slow fading channels is studied. For the problem, either a long- or short-term power constraint is imposed on the source and relays. In each combination of the power constraints at the source and relays, the original optimization problem is decomposed into subproblems, each corresponding to a specific channel gain realization. For each subproblem, a fast algorithm with closed-form solutions is provided. The case with additional peak power spectrum density constraints is also investigated. Numerical results are presented to demonstrate the effectiveness of the algorithms. [ABSTRACT FROM PUBLISHER]