Joint Power and Admission Control: Non-Convex Lq Approximation and An Effective Polynomial Time Deflation Approach

In an interference limited network, joint power and admission control (JPAC) aims at supporting a maximum number of links at their specified signal to interference plus noise ratio (SINR) targets while using minimum total transmission power. Various convex approximation deflation approaches have been developed for the JPAC problem. In this paper, we propose an effective polynomial time non-convex approximation deflation approach for solving the problem. The approach is based on the non-convex lq (0 < q < 1) approximation of an equivalent sparse l0 reformulation of the JPAC problem. We show that, for any instance of the JPAC problem, there exists a q̄ ∈ (0, 1) such that it can be exactly solved by solving its lq approximation problem with any q ∈ (0, q̄]. We also show that finding the global solution of the lq approximation problem is NP-hard. Then, we propose a potential reduction interior-point algorithm, which can return an ǫ-KKT solution of the NP-hard lq approximation problem in polynomial time. The returned solution can be used to check the simultaneous supportability of all links in the network and to guide an iterative link removal procedure, resulting in the polynomial time non-convex approximation deflation approach for the JPAC problem. Numerical simulations show that Part of this work was presented in the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Vancouver, Canada, May 26–31, 2013 [25]. Y.-F. Liu and Y.-H. Dai are with the State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China (e-mail: [email protected]; [email protected]). S. Ma is with the Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong (e-mail: [email protected]). October 2, 2014 DRAFT