Consider the joint power and admission control (JPAC) problem for a multiuser 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, i.e., 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.
Bibliographical noteFunding Information:
The work of Y.-F. Liu was partially supported by the National Natural Science Foundation of China under Grant 11301516, Grant 11331012, and Grant 11571221. The work ofM. Hong was supported in part by NSF under Grant CCF-1526078 and in part by the AFOSR under Grant 15RT0767. The work of E. Song was supported by the National Natural Science Foundation of China under Grant 61473197.
- Chance SINR constraint
- group sparse
- power and admission control
- sample approximation