We study the secrecy rate and secrecy outage probability in Multiple-Input-Single-Output (MISO) Gaussian broadcast channels at the limit of a large number of legitimate users and eavesdroppers. In particular, we analyze the asymptotic achievable secrecy rates and outage, when only statistical knowledge on the wiretap channels is available to the transmitter.
Since the emergence of multiple antenna technologies to state-of-the-art wireless standards, many studies have explored the potential gains in exploiting the multiple antenna technology not only to boost the network throughput but also for attaining secrecy in various setups. Most of these studies examine a basic communications setup, in which a transmitter is transmitting data to a specific receiver in the presence of one or more eavesdroppers, under various configurations. However, in many instances, the transmitter is serving multiple users and can select (schedule) the users for transmission opportunistically. In this study, we consider this user diversity model and analyze the secrecy outage probability when there are multiple legitimate users, and the transmitter selects the users for transmission opportunistically. Specifically, we consider the Gaussian MISO wiretap channel model, where a t transmitter with antennas is serving K legitimate users in the presence of M anonymous eavesdroppers. We assume that CSI is available from all legitimate users, yet only channel statistics are available on the eavesdroppers. We assume that the transmitter is transmitting (beamforming) in the direction of the selected user, which is optimal when the transmitter has only statistical information on the wiretap channel, and artificial noise is not an option. We analyze the secrecy outage probability as a function of t, K and M, and explore the subtle relation (tradeoff) between these numbers, i.e., the secrecy outage probability as a function of antennas, users and eavesdroppers. Our analysis provides exact expressions for the reduction in the secrecy rate as the number of eavesdroppers grows, compared to the boost in the secrecy rate as the number of legitimate users grows.