On Tractability Aspects of Optimal Resource Allocation in OFDMA Systems

Abstract

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 is restricted to 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. Index Termsorthogonal frequency-division multiple access, resource allocation, tractability.

On Power Minimization for Non-orthogonal Multiple Access (NOMA)

“…The NP-hardness of the former has been proved in [12]. For L = 1, we conclude that NPM is NP-hard since it is equivalent to MPCA.…”

“…Thus the UEs in K require more power than p * on each subchannel. Therefore, a special case NPM S is equivalent to MPCA in [12], and NPM is NP-hard and intractable.…”

“…For example, the algorithm idea in [6] does not fit into the problem of power minimization. For OMA, we refer to [10]- [12] and the references therein for papers that perform either rate adaptive or margin adaptive optimization. For NOMA, margin adaptive optimization schemes remain a significant topic of study.…”

“…To accurately evaluate the potential improvement of NOMA over OMA, we consider scenarios with K = N for which OMA power minimization is polynomial-time solvable as in this case it reduces to bi-partite matching [12]. Here, K = N = 10.…”

A Unified Graph Labeling Algorithm for Consecutive-Block Channel Allocation in SC-FDMA

“…Many algorithms have been proposed for OFDMA channel allocation with the objective of maximizing the sum utility or minimizing the power (e.g., [3]- [5]). The algorithms are mainly heuristics, justified by that OFDMA resource allocation is in general NPhard even if the rate function is well-behaved [6], [7].…”