How many antennas does a cooperative Jammer need for achieving the degrees of freedom of multiple antenna Gaussian channels in the presence of an eavesdropper?

In this work, multiple antenna Gaussian wiretap channels with a multiantenna cooperative jammer are considered. In particular, the focus is on identifying the spatial resources needed at the cooperative jammer in order to achieve a secure degrees of freedom (s.d.o.f.) for the channel in question equal to the degrees of freedom (d.o.f.). In order to accomplish this goal, the cooperative jammer sets out to send correlated jamming signals. Simultaneously, the legitimate transmitter chooses a precoder that perfectly aligns its information signals over the jamming ones at the eavesdropper. Both terminals use structured signaling, i.e., discrete constellations. The proposed approach is shown to achieve full d.o.f. for the channel at hand as long as the cooperative jammer has twice the antennas of the eavesdropper. It is also shown that within 1/2 of the d.o.f. is achievable with one less antenna at the cooperative jammer.