  This paper studies the secrecy rate maximization problem of a secure wireless
communication system, in the presence of multiple eavesdroppers. The security
of the communication link is enhanced through cooperative jamming, with the
help of multiple jammers. First, a feasibility condition is derived to achieve
a positive secrecy rate at the destination. Then, we solve the original secrecy
rate maximization problem, which is not convex in terms of power allocation at
the jammers. To circumvent this non-convexity, the achievable secrecy rate is
approximated for a given power allocation at the jammers and the approximated
problem is formulated into a geometric programming one. Based on this
approximation, an iterative algorithm has been developed to obtain the optimal
power allocation at the jammers. Next, we provide a bisection approach, based
on one-dimensional search, to validate the optimality of the proposed
algorithm. In addition, by assuming Rayleigh fading, the secrecy outage
probability (SOP) of the proposed cooperative jamming scheme is analyzed. More
specifically, a single-integral form expression for SOP is derived for the most
general case as well as a closed-form expression for the special case of two
cooperative jammers and one eavesdropper. Simulation results have been provided
to validate the convergence and the optimality of the proposed algorithm as
well as the theoretical derivations of the presented SOP analysis.
