Secrecy capacity limits of multiple antenna multiple eavesdropper multicast

In this paper we study the scaling laws of achievable secrecy rates for multicast communication scenarios with a single multiple antenna transmitter and multiple eavesdropper. First we prove bounds on the achievable secrecy rate. Then we use these bounds to analyze the scaling of the system in three asymptotic regimes, 1) increasing the number of legitimate users while keeping the number of eavesdroppers and antennas constant, 2) increasing the number of eavesdroppers for a fixed number of legitimate users and antennas, and 3) increasing the number of transmit antennas with a constant number of users. Next, we derive the probability of outage for some special cases. In the last part, the theoretical analysis is justified by simulations.