Throughput and Energy Efficiency in Wireless Ad Hoc Networks with Gaussian Channels

This paper studies the problem of topology control in random wireless ad hoc networks through power assignment for n nodes uniformly distributed in a unit square. We require that the network is strongly connected and look to maximize the minimum throughput (or capacity) link in the case that all the nodes transmit simultaneously. According to the Gaussian channel model, the throughput of a wireless link (u, v) is B log(1 + S/N) bps, where B is the channel bandwidth and S/N is the channel bandwidth. We distinguish between two types of power assignments: homogeneous (all nodes have the same power level) and heterogeneous (nodes may have different power levels) cases. For the homogeneous case we give lower and upper bounds on the minimum capacity link. In the heterogeneous case we develop an energy efficient power assignment algorithm which achieves a minimum throughput of Ω(B log(1 + 1/√n log² n)) and also discuss how to implement this algorithm in a distributed fashion. Finally, we present some simulation results. To the best of our knowledge, these are the first provable bounds for capacity in wireless networks, when nodes are allowed to transmit simultaneously.