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

Physical layer security in large-scale random multiple access wireless sensor networks: a stochastic geometry approach