A Combinatorial Auction based Subcarrier Allocation Algorithm for multiuser OFDMA Ioannis N. Stiakogiannakis , Dimitra I. Kaklamani School of Electrical and Computer Engineering National Technical University of Athens istiak@ieee.org , dkaklam@mail.ntua.gr Abstract—The margin adaptive problem for the downlink of Orthogonal Frequency Division Multiple Access is tackled in this work. A subcarrier allocation algorithm is presented, which formulates the issue of subcarrier allocation as a combinatorial auction, where the base station auctions the OFDM subcarriers and the users compete for their allocation. A major feature of the proposed algorithm is its distributed nature, since each user decides independently which subcarriers to bid for, informs the base station for his preferences, and the base station is the entity that makes the decision on the allocation, based on power criteria. The presentation of the algorithm is followed by a series of simulations. The simulations indicate that the performance of the proposed algorithm approaches the performance of the optimal, Hungarian algorithm: the offered bit rate is at least 98.77% of the optimal while the transmit power lies within the range 0.20dB-1.62dB higher than the optimal one. Additionally, based on execution time measurements, it is shown that the necessary execution time is much lower than that of the optimal algorithm, indicating thus a much lower computational complexity. I. I NTRODUCTION The prevalence of Orthogonal Frequency Division Multiple Access (OFDMA) as the multiple access technique for the wireless networks of the next generation, has triggered the past few years the research interest in radio resource management (RRM) for multicarrier systems. Both IEEE [1] and ETSI [2], through their standardisation committees and working groups, have recognised not only the unquestionable advantages of OFDM as a physical layer technique, such as immunity to inter-symbol interference thanks to cyclic prefix, but also the flexibility that offers in MAC layer. OFDMA provides the RRM with additional degrees of freedom by converting the allocation problem from 1D (Frequency, Time and Code Division Multiple Access) to 2D. Furthermore, OFDMA takes advantage of the frequency selective characteristics of the channel by exploiting the multiuser diversity. As a result, frequency selectivity is not any more an undesirable prop- erty of the channel but it becomes a means of performance improvement. The formulation of the OFDMA RRM problem can be roughly divided into two main classes, namely margin and rate adaptive formulation [3]. On the one hand, the margin adaptive formulation aims at minimising the total transmit power while satisfying certain constraints for Bit Rate (BR) and Bit Error Rate (BER) for each user. On the other hand, the rate adaptive formulation aims at maximising the total bit rate of the network under the constraint of total transmit power. Different approaches have been proposed aiming at solving efficiently the RRM problem for either formulation, inspired by diverse areas, such as optimization theory [4], game theory [5] and biological processes [6]. This work aspires to present an approach to the margin adaptive formulation of the RRM problem based on combinatorial auctions. The subcarrier al- location problem can be seen as an auction, where the base station (BS) is the owner of the subcarriers and auctions them to potential buyers, the users. The choice of combinatorial auctions instead of simple auctions was based on the fact that each user needs, in general, more than one subcarrier. As a consequence, the modelling should allow the user to express preference on and bid for bundle of subcarriers. The remainder of this work is organised as follows; in section II, the system model is introduced and the margin adaptive formulation is described. Afterwards, the algorithms conducting the RRM functions are discussed in brief. Section III focuses on the proposed subcarrier allocation algorithm based on combinatorial auctions. Thereafter, in section IV, the simulation parameters are presented, followed by the simulation results and the corresponding analysis on them. Finally, the presented work is summarised and the conclusions are drawn in section V. II. SYSTEM MODEL &PROBLEM FORMULATION A. System Model The OFDMA system under consideration encompasses one BS, with total available power P max BS , and U users (u ∈ U = {1,...,U }). Each user u requires BR R u under BER Pe u . The available bandwidth BW is divided into N OFDM subcarriers (n ∈N = {1,...,N }) and each subcarrier occupies bandwidth Δf = BW/N . The margin adaptive formulation for the radio resource management problem is based on the definition of three allocation matrices: • Subcarrier allocation matrix C = [C u,n ]. C u,n = 1 (C u,n =0) indicates that subcarrier n is (not) allocated to user u. Each subcarrier is allocated to a single user since it has been proven to be an optimal practice [7], formally ∑ U u=1 C u,n ≤ 1, ∀n ∈N . • Bit loading vector B =[b n ]. b n ∈{b min ,...,b max } indicates the number of bits that the BS loads to subcar- rier n. b min (b max ) stands for the minimum (maximum) modulation level that can be employed. In order to