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
${\bar C_N}$
of Gaussian wiretap channel and the average secrecy rate
${\bar R_N}$
achieved by the null-space jamming scheme is investigated, and we prove that
${\bar R_N} \leq {\bar C_N} \leq {\bar R_{N + 1}}$
. 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
$N \leq M - 1$
, there exists a performance ceiling on it.