  In this paper, we consider the problem of resource allocation in the
orthogonal frequency division multiple access system with single source and M
untrusted users in presence of a friendly jammer. The jammer is used to improve
either the weighted sum secure rate or the overall system fairness. The
formulated optimization problem in both the cases is a mixed integer non-linear
programming problem, belonging to the class of NP-hard. In the sum secure rate
maximization scenario, we decouple the problem and first obtain the subcarrier
allocation at source and the decision for jammer power utilization on a
per-subcarrier basis. Then, we do joint source and jammer power allocation
using primal decomposition and alternating optimization framework. Next, we
consider fair resource allocation by introducing a novel concept of subcarrier
snatching with the help of jammer. We propose two schemes for jammer power
utilization, called proactively fair allocation (PFA) and on-demand allocation
(ODA). PFA considers equitable distribution of jammer power among the
subcarriers, while ODA distributes jammer power based on the user demand. In
both cases of jammer usage, we also present suboptimal solutions that solve the
power allocation at a highly reduced complexity. Asymptotically optimal
solutions are derived to benchmark optimality of the proposed schemes. We
compare the performance of our proposed schemes with equal power allocation at
source and jammer. Our simulation results demonstrate that the jammer can
indeed help in improving either the sum secure rate or the overall system
fairness.
