Given a set of positions for wireless nodes, the interference minimization problem is to assign a transmission radius (i.e., a power level) to each node such that the resulting communication graph is connected while minimizing the maximum (respectively, average) interference. We consider the model introduced by von Rickenbach (2005), in which each wireless node is represented by a point in Euclidean space on which is centered a transmission range represented by a ball, and edges in the corresponding graph are symmetric. The problem is NP-complete in two or more dimensions (Buchin 2008), and no polynomial-time approximation algorithm is known. We show how to solve the problem efficiently in settings typical for wireless ad hoc networks. If nodes are represented by a set P of n points selected uniformly and independently at random over a d-dimensional rectangular region, then the topology given by the closure of the Euclidean minimum spanning tree of P has O(log n) maximum interference with high probability and O(1) expected interference. We extend the first bound to a general class of communication graphs over a broad set of probability distributions. We present a local algorithm that constructs a graph from this class; this is the first local algorithm to provide an upper bound on expected maximum interference. Finally, we disprove a conjecture of Devroye and Morin (2012) relating the maximum interference of the Euclidean minimum spanning tree to the optimal maximum interference attainable.

We investigate the trade-off between performance and energy efficiency in cooperative cognitive underlay systems. By cooperating, cognitive base stations mitigate the interference and serve their users more effectively at the cost of spending more power. With a flexible cooperation scheme, we thus jointly optimize the clustering and the beamforming to minimize the overall power consumption while satisfying the secondary users' quality of service and respecting the primary users' interference limits. We formulate this problem as a mixed-integer nonlinear program and decompose it into a master problem and a beamforming subproblem. Then, we derive an iterative algorithm based on the generalized Benders decomposition method to find an optimal solution. Moreover, we propose simple techniques to speed up its convergence. When the clusters are fixed and non-overlapping, we also propose a decentralized algorithm with limited signaling schemes using the alternating direction method of multipliers. In contrast to previous works, our distributed algorithm handles the total interference power constraints coupling the cognitive base stations. Through simulations, we analyze the effectiveness and convergence of the proposed algorithms and show the benefits of the cooperation in cognitive wireless networks.