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Joint power and admission control via p norm minimization deflation

In an interference network, joint power and admission control aims 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 our previous work, we formulated the joint control problem as a sparse $\ell_0$-minimization problem and relaxed it to a $\ell_1$-minimization problem. In this work, we propose to approximate the $\ell_0$-optimization problem to a p norm minimization problem where $0<p<1$, since intuitively p norm will approximate 0 norm better than 1 norm. We first show that the $\ell_p$-minimization problem is strongly NP-hard and then derive a reformulation of it such that the well developed interior-point algorithms can be applied to solve it. The solution to the $\ell_p$-minimization problem can efficiently guide the link's removals (deflation). Numerical simulations show the proposed heuristic outperforms the existing algorithms.