Secure degrees of freedom for the MIMO wiretap channel with a multiantenna cooperative jammer

A multiple antenna Gaussian wiretap channel with a multiantenna cooperative jammer (CJ) is considered and the secure degrees of freedom (s.d.o.f.), with N antennas at the sender, receiver, and eavesdropper, is derived for all possible values of the number of antennas at the cooperative jammer, K. In particular, the upper and lower bounds for the s.d.o.f. are provided for different ranges of K and shown to coincide. Gaussian signaling both for transmission and jamming is shown to be sufficient to achieve the s.d.o.f. of the channel, when the s.d.o.f. is integer-valued. By contrast, when the channel has a non-integer s.d.o.f., structured signaling and joint signal space and signal scale alignment are employed to achieve the s.d.o.f.