Subcarrier Allocation in Multiuser OFDM Systems: Complexity and Approximability

Abstract

Abstract-We consider a number of related problem formulations pertaining to adaptive subcarrier allocation in multiuser Orthogonal Frequency-Division Multiplexing (OFDM) systems, and prove that they are NP-hard. Thus there exist no known algorithms that can provide optimal solutions for all instances of these problems in polynomial time. We further prove that these problems are hard to approximate in polynomial time. Finally, we discuss qualitatively the settings under which worstcase performance is likely to be observed.

A Novel Subcarrier Allocation Algorithm for MC–CDMA Systems

“…Literature has several studies concerning the subcarrier allocation matter [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Studies [3,4] performed assignments taking into consideration the channel gains in algorithms used during the allocation processes.…”

“…[7] presents an algorithm that reduces the system complexity in order for the user to achieve the desired speed. [8] suggests an algorithm that performs allocation in proportion to the user gains.…”

On Tractability Aspects of Optimal Resource Allocation in OFDMA Systems

“…In contrast to the significant amount of research on algorithms, investigations along the line of tractability analysis have been few [10], [11]. The edge of fundamental understanding of problem tractability is formed in respect of the following limitations.…”

“…Thus the result does not apply to the problem where powers are optimization variables. In [11], the resource allocation problem is shown to be NP-hard for one particular type of rate function r mn (P ) ∈ C inc , where r mn (P ) is the rate as a function of power P for the mth user and nth subcarrier, and C inc is the set of all increasing functions such that r mn (0) = 0. By this result, there exists some (but possibly ill-behaved 1 ) function in C inc for which the problem is NP-hard.…”

“…Indeed, it is very commonly assumed that the rate function is given by r mn (P ) = log(1+ g mn P ), with g mn > 0. For the hierarchy C linear ⊂ C concave ⊂ C inc , the result in [11] applies to C inc \C concave . We investigate the complexity for the representative logarithmic function case of C concave , and, if the problem is NP-hard for the function, examine to what extent restrictions on input structure (e.g., assuming the number of subcarrier for each user is given in the input) will admit better tractability.…”