Joint Optimization of Preamble Selection and Access Barring for Random Access in MTC with General Device Activities

Most existing random access schemes for MTC simply adopt a uniform preamble selection distribution, irrespective of the underlying device activity distributions. Hence, they may yield unsatisfactory access efficiency, especially for correlated device activities. In this paper, we model device activities for MTC with a general MVB distribution and optimize preamble selection and access barring for random access in MTC according to the underlying device activity distribution. We investigate three cases of the general joint device activity distribution, i.e., the cases of perfect, imperfect, and unknown joint device activity distributions, and formulate the average, worst-case average, and sample average throughput maximization problems, respectively. The problems in the three cases are challenging nonconvex problems. In the case of perfect joint device activity distribution, we develop an iterative algorithm and a low-complexity iterative algorithm to obtain stationary points of the original problem and an approximate problem, respectively. In the case of imperfect joint device activity distribution, we develop an iterative algorithm and a low-complexity iterative algorithm to obtain a KKT point of an equivalent problem and a stationary point of an approximate problem, respectively. In the case of unknown joint device activity distribution, we develop an iterative algorithm to obtain a stationary point.