Sample Approximation-Based Deflation Approaches for Chance SINR Constrained Joint Power and Admission Control

TL;DR

This paper introduces a novel sample approximation and deflation method for joint power and admission control in interference channels with imperfect CSI, ensuring SINR outage constraints are met efficiently.

Contribution

It develops a new approach using sample approximation and SOCP reformulation to handle chance SINR constraints under imperfect CSI, with an efficient algorithm for supportability testing.

Findings

The proposed method effectively supports links while satisfying outage constraints.

The SOCP-based approach reduces computational complexity.

Simulations demonstrate the approach's efficiency and robustness.

Abstract

Consider the joint power and admission control (JPAC) problem for a multi-user single-input single-output (SISO) interference channel. Most existing works on JPAC assume the perfect instantaneous channel state information (CSI). In this paper, we consider the JPAC problem with the imperfect CSI, that is, we assume that only the channel distribution information (CDI) is available. We formulate the JPAC problem into a chance (probabilistic) constrained program, where each link's SINR outage probability is enforced to be less than or equal to a specified tolerance. To circumvent the computational difficulty of the chance SINR constraints, we propose to use the sample (scenario) approximation scheme to convert them into finitely many simple linear constraints. Furthermore, we reformulate the sample approximation of the chance SINR constrained JPAC problem as a composite group sparse minimization problem and then approximate it by a second-order cone program (SOCP). The solution of the SOCP approximation can be used to check the simultaneous supportability of all links in the network and to guide an iterative link removal procedure (the deflation approach). We exploit the special structure of the SOCP approximation and custom-design an efficient algorithm for solving it. Finally, we illustrate the effectiveness and efficiency of the proposed sample approximation-based deflation approaches by simulations.