On the Power of Uniform Power: Capacity of Wireless Networks with Bounded Resources

Abstract. The throughput capacity of arbitrary wireless networks under the physical Signal to Inter-ference Plus Noise Ratio (SINR) model has received a greater deal of attention in recent years. It has been shown that power control can increase the capacity of a network significantly compared to the case where all transmitters emit signals of uniform power. However, the published examples exhibit one common property: they usually position the nodes in an area of exponential size in the number of nodes and they require transmission power levels that differ by a factor exponential in the number of nodes. In this paper, we quantify the gap induced by the ability to adjust the transmission power if the available resources are bounded. We investigate the question of how much the worst-case performance of uniform and non-uniform power assignments differ under constraints such as a bound on the area where nodes are distributed or restrictions on the maximum power available. We determine the maximum factor by which a non-uniform power assignment can outperform the uniform case. More precisely, the uniform assignment is at most a factor of O(logPmax) worse than the non-uniform assignment if the maximum power is Pmax. If the length of the network is Lmax, the capacity of a non-uniform assignment exceeds a uniform assignment by at most a factor of O(logLmax) in a one-dimensional setting. Due to lower bound examples in previous work, these results are tight in the sense that there are networks where the lack of power control causes a performance loss in the order of these factors. In contrast to earlier work our arguments do not rely on the assumption that the path-loss exponent α exceeds two, i.e., our results are valid for positive α ≤ 2 as well. As a consequence, engineers and researchers may prefer the uniform model due to its simplicity if this degree of performance deterioration is acceptable. Both results are tight.