This paper considers the transmission of confidential messages over noisy wireless ad hoc networks, where both background noise and interference from concurrent transmitters affect the received signals. For the random networks where the legitimate nodes and the eavesdroppers are distributed as Poisson point processes, we study the secrecy transmission capacity (STC), as well as the connection outage probability and secrecy outage probability, based on the physical layer security. We first consider the basic fixed transmission distance model, and establish a theoretical model of the STC. We then extend the above results to a more realistic random distance transmission model, namely nearest receiver transmission. Finally, extensive simulation and numerical results are provided to validate the efficiency of our theoretical results and illustrate how the STC is affected by noise, connection and secrecy outage probabilities, transmitter and eavesdropper densities, and other system parameters. Remarkably, our results reveal that a proper amount of noise is helpful to the secrecy transmission capacity.
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