  Most existing random access schemes for machine-type communications (MTC)
simply adopt a uniform preamble selection distribution, irrespective of the
underlying device activity distributions. Hence, they may yield unsatisfactory
access efficiency. In this paper, we model device activities for MTC as
multiple Bernoulli random variables following an arbitrary multivariate
Bernoulli distribution which can reflect both dependent and independent device
activities. Then, we optimize preamble selection and access barring for random
access in MTC according to the underlying joint device activity distribution.
Specifically, we investigate three cases of the 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 Karush-Kuhn-Tucker (KKT) point
of an equivalent problem and a stationary point of an approximate problem,
respectively. Finally, in the case of unknown joint device activity
distribution, we develop an iterative algorithm to obtain a stationary point.
The proposed solutions are widely applicable and outperform existing solutions
for dependent and independent device activities.
