Secrecy outage of Nakagami-m MISO channels with randomly located receivers

We perform an analysis of the secrecy outage of random networks under Nakagami-m fading with multiple transmit antennas. Specifically, using a network model that accounts for uncertainties both in node locations (distances) and channel coefficients (fading), we derive the distribution of the best path gain of eavesdroppers using Probability Generating Functional property of Poisson Point Process (PPP). Using this result, the secrecy outage probability and the conditional secrecy outage probability of random networks with multiple eavesdroppers are obtained, with basic factors such as the density of eavesdropping nodes, the number of transmit antennas and the fading coefficient all accounted for by explicit parameters. The impact of transmission factors, including number of transmit antennas, fading figure, legitimate node distance and node density are studied and analysed in numerical results.