# On the power of uniform power: capacity of wireless networks with bounded resources

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## Abstract

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 \(O(\log L_{\max })\) when the length of the network is \(L_{\max }\). In two-dimensional settings, the uniform assignment is at most a factor of \(O(\log P_{\max })\) worse than the non-uniform assignment if the maximum power is \(P_{\max }\). We provide algorithms that reach this capacity in both cases. These bounds are tight in the sense that previous work gave examples of networks where the lack of power control causes a performance loss in the order of these factors. To complement our theoretical results and to evaluate our algorithms with concrete input networks, we carry out simulations on random wireless networks. The results demonstrate that the link sets generated by the algorithms contain around 20–35 % of all links. As a consequence, engineers and researchers may prefer the uniform model due to its simplicity if this degree of performance deterioration is acceptable.

## Keywords

Wireless networks SINR Network capacity Power control## Notes

### Acknowledgments

Zvi Lotker: This Research was supported in part by Fondation des Sciences Mathmatiques de Paris and by the Ministry of Science Technology and by Space, Israel, French-Israeli Project MAIMONIDE 31768XL, and by the French-Israeli Laboratory FILOFOCS. Yvonne-Anne Pignolet: Part of this research was done when the author was at ETH Zurich, Switzerland.

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