Complexity Analysis, Potential Game Characterization and Algorithms for the Inter-Cell Interference Coordination With Fixed Transmit Power Problem

Abstract

We study the inter-cell interference coordination (ICIC) problem in a multicell orthogonal frequency division multiple access based cellular network employing universal frequency reuse. In each cell, only a subset of the available subchannels are allocated to mobile stations (MSs) in a given time slot so as to limit the interference to neighboring cells; also, each base station (BS) uses a fixed transmit power on every allocated subchannel. The objective is to allocate the available subchannels in each cell to the MSs in the cell for downlink transmissions taking into account the channel qualities from BSs to MSs as well as traffic requirements of the MSs so as to maximize the weighted sum of throughputs of all the MSs. First, we show that this problem is NP-complete. Next, we show that when the potential interference levels to each MS on every subchannel are above a threshold (which is a function of the transmit power and the channel gain to the MS from the BS it is associated with), the problem can be optimally solved in polynomial-time via a reduction to the matching problem in bipartite graphs. We also formulate the ICIC problem as a noncooperative game, with each BS being a player, and prove that although it is an ordinal potential game in two special cases, it is not an ordinal potential game in general. Also, we design two heuristic algorithms for the general ICIC problem: a greedy distributed algorithm and a simulated annealing (SA) based algorithm. The distributed algorithm is fast and requires only message exchanges among neighboring BSs. The SA algorithm is centralized and allows a tradeoff between quality of solution and execution time via an appropriate choice of parameters. Our extensive simulations show that the total throughput obtained using the better response (BR) algorithm, which is often used in game theory, is very small compared to those obtained using the SA and greedy algorithms; however, the execution time of the BR algorithm is much smaller than those of the latter two algorithms. Finally, the greedy algorithm outperforms the SA algorithm in dense cellular networks and requires only a small fraction of the number of computations required by the latter algorithm for execution.