On Secrecy Capacity of the Helper-Assisted Gaussian Wiretap Channel with Multi-Antennas

We investigate the secrecy capacity of Gaussian wiretap channel with a source, an external helper, an eavesdropper and a single-antenna legitimate receiver where the former three terminals are equipped with N_a, N_j and N_e antennas, respectively. Generally, an analytical form of the secrecy capacity in this scenario is difficult to obtain. Instead, we recast the original nonconvex secrecy rate maximization (SRM) problem into a sequence of convex optimization problems. In doing so, the secrecy capacity can be obtained using a combination of convex optimization and a one-dimensional search. On the other hand, to gain more insight into how the secrecy capacity behaves, we study the secure degrees of freedom (s.d.o.f.) and quantify its connection with system parameters, where our result proves that the s.d.o.f. equal to 1 can be achieved if and only if N_e<;N_a+N_j-1. As a by-product, we give a suboptimal but closed-form solution to the original SRM problem for the scenario where N_e<;N_a+N_j-1.Numerical results are presented to validate the theoretical findings and illustrate the efficacy of the proposed schemes.