Joint power and admission control via p norm minimization deflation

TL;DR

This paper introduces a p norm minimization approach (0<p<1) for joint power and admission control in interference networks, aiming to better approximate sparsity and improve link support efficiency.

Contribution

It proposes a novel p norm minimization formulation for joint control, demonstrating its strong NP-hardness and providing an interior-point algorithm-based solution.

Findings

The p norm approach better approximates the zero-norm than the l1 norm.

The proposed heuristic outperforms existing algorithms in simulations.

The method effectively guides link removals to optimize network performance.

Abstract

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.