On Secrecy Capacity of Gaussian Wiretap Channel Aided by A Cooperative Jammer

We study the secrecy capacity of Gaussian wiretap channel aided by an external jammer/helper. Both the transmitter and the intended receiver are equipped with a single antenna, while the eavesdropper and the jammer are equipped with M and N antennas, respectively. Generally, an analytical form of the secrecy capacity in this scenario is difficult to obtain. Instead, we consider a null-space jamming scheme which totally nulls out the jamming signal at the legitimate receiver, and derive lower and upper bounds on its maximal achievable secrecy rate R_N. The relationship between the average secrecy capacity C̅_N of Gaussian wiretap channel and the average secrecy rate R̅_N achieved by the null-space jamming scheme is investigated, and we prove that R̅_N ≤ C̅_N ≤ R̅_N+1. Based on this inequality and the derived lower and upper bounds on R_N, the upper and lower bounds on the average secrecy capacity of Gaussian wiretap channel aided by an external jammer can be obtained, where our result shows that when N > M, the average secrecy capacity increases linearly with the total transmit power; while when N ≤ M - 1, there exists a performance ceiling on it.