The Secure Degrees of Freedom of the MIMO BC and MIMO MAC with Multiple Unknown Eavesdroppers

Abstract

We investigate the secure degrees of freedom (SDoF) of a two-transmitter Gaussian multiple access channel with multiple antennas at the transmitters, a legitimate receiver and an unknown number of eavesdroppers each with a number of antennas less than or equal to a known value NE. The channel matrices between the legitimate transmitters and the receiver are available everywhere, while the legitimate pair have no information about the fading eavesdroppers' channels. We provide the exact sum SDoF for the considered system. We show that it is equal to min(M1 + M2 ? NE, 1/2(max(M1;N2 + max(M2;N) ? NE,N). A new comprehensive upperbound is deduced and a new achievable scheme based on utilizing jamming is exploited. We prove that Cooperative Jamming is SDoF optimal even without the eavesdropper CSI available at the transmitters.