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This paper studies the bottleneck link capacity under the Gaussian channel model in strongly connected random wireless ad hoc networks, with n nodes independently and uniformly distributed in a unit square. We assume that each node is equipped with two transceivers (one for transmission and one for reception) and allow all nodes to transmit simultaneously. We draw lower and upper bounds, in terms of bottleneck link capacity, for homogeneous networks (all nodes have the same transmission power level) and propose an energy-efficient power assignment algorithm (CBPA) for heterogeneous networks (nodes may have different power levels), with a provable bottleneck link capacity guarantee of Ω(Blog(1+1/√nlog2n)), where B is the channel bandwidth. In addition, we develop a distributed implementation of CBPA with O(n2) message complexity and provide extensive simulation results.