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We consider the joint power and admission control problem for a wireless network consisting of multiple interfering links. The goal is to support a maximum number of links at their specified signal to interference plus noise ratio (SINR) targets while using a minimum total transmission power. In this work, we first reformulate this NP-hard problem as a sparse <i>l</i><sub>0</sub>-minimization problem and then relax it to a linear program. Furthermore, we derive two easy-to-check necessary conditions for all links in the network to be simultaneously supported at their target SINR levels, and use them to iteratively remove strong interfering links (deflation). An upper bound on the maximum number of supported links is also given. Numerical simulations show that the proposed approach compares favorably with the existing approaches in terms of the number of supported links, the total transmission power, and the execution time.

Joint Power and Admission Control via Linear Programming Deflation