  This paper investigates physical layer security for a large-scale WSN with
random multiple access, where each fusion center in the network randomly
schedules a number of sensors to upload their sensed data subject to the
overhearing of randomly distributed eavesdroppers. We propose an uncoordinated
random jamming scheme in which those unscheduled sensors send jamming signals
with a certain probability to defeat the eavesdroppers. With the aid of
stochastic geometry theory and order statistics, we derive analytical
expressions for the connection outage probability and secrecy outage
probability to characterize transmission reliability and secrecy, respectively.
Based on the obtained analytical results, we formulate an optimization problem
for maximizing the sum secrecy throughput subject to both reliability and
secrecy constraints, considering a joint design of the wiretap code rates for
each scheduled sensor and the jamming probability for the unscheduled sensors.
We provide both optimal and low-complexity sub-optimal algorithms to tackle the
above problem, and further reveal various properties on the optimal parameters
which are useful to guide practical designs. In particular, we demonstrate that
the proposed random jamming scheme is beneficial for improving the sum secrecy
throughput, and the optimal jamming probability is the result of trade-off
between secrecy and throughput. We also show that the throughput performance of
the sub-optimal scheme approaches that of the optimal one when facing a
stringent reliability constraint or a loose secrecy constraint.
