Complexity analysis and algorithms for the Inter Cell Interference Coordination with fixed transmit powers problem

We study the Inter Cell Interference Coordination problem in a multi-cell OFDMA based cellular network employing universal frequency reuse. In each cell, only a subset of the available subchannels are allocated to mobile stations (MS) 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. Also, we design two heuristic algorithms for the general problem: a greedy distributed algorithm and a simulated annealing based algorithm. The distributed algorithm is fast and requires only message exchanges between neighboring BSs. The simulated annealing based algorithm is centralized and allows a tradeoff between quality of solution and execution time via an appropriate choice of parameters. Finally, we study the performance of the above algorithms via simulations, which show that the distributed algorithm on average achieves an objective function value that is 0.6 times that obtained by the simulated annealing based algorithm using only a small fraction of the number of computations.