Consider the joint power and admission control (JPAC) problem for a multi-user single-input singleoutput (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  Chance SINR constraint, group sparse, power and admission control, sample approximation.
To circumvent the difficulty of the chance SINR constraint, REF employed the sample (scenario) approximation scheme to convert the chance constraints into finitely many simple linear constraints.
Sample Approximation-Based Deflation Approaches for Chance SINR Constrained Joint Power and Admission Control
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