  In this paper, we consider the problem of joint secure routing and transmit
power optimization for a multi-hop ad-hoc network under the existence of
randomly distributed eavesdroppers following a Poisson point process (PPP).
Secrecy messages are delivered from a source to a destination through a
multi-hop route connected by multiple legitimate relays in the network. Our
goal is to minimize the end-to-end connection outage probability (COP) under
the constraint of a secrecy outage probability (SOP) threshold, by optimizing
the routing path and the transmit power of each hop jointly. We show that the
globally optimal solution could be obtained by a two-step procedure where the
optimal transmit power has a closed-form and the optimal routing path can be
found by Dijkstra's algorithm. Then a friendly jammer with multiple antennas is
applied to enhance the secrecy performance further, and the optimal transmit
power of the jammer and each hop of the selected route is investigated. This
problem can be solved optimally via an iterative outer polyblock approximation
with one-dimension search algorithm. Furthermore, suboptimal transmit powers
can be derived using the successive convex approximation (SCA) method with a
lower complexity. Simulation results show the performance improvement of the
proposed algorithms for both non-jamming and jamming scenarios, and also reveal
a non-trivial trade-off between the numbers of hops and the transmit power of
each hop for secure routing.
