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

The throughput capacity of arbitrary wireless networks under the physical Signal to Interference Plus Noise Ratio (SINR) model has received much attention in recent years. In this paper, 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 in the SINR model. More precisely, we prove that in one-dimensional settings the capacity of a non-uniform assignment exceeds a uniform assignment by at most a factor of O(log Lmax) when the length of the network is Lmax. In two-dimensional settings, the uniform assignment is at most a factor of O(log Pmax) worse than the non-uniform assignment if the maximum power is Pmax. We provide algorithms that reach this capacity in both cases. 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. As a consequence, engineers and researchers may prefer the uniform model due to its simplicity if this degree of performance deterioration is acceptable.