Secrecy capacity of MISO Gaussian wiretap channel with a cooperative jammer

We study the Gaussian MISO wiretap channel with a transmitter, a legitimate receiver, an eavesdropper and an external helper, where the transmitter and the helper have an arbitrary number of antennas but the intended receiver and the eavesdropper have only one antenna. The transmitter sends confidential messages to its intended receiver, while the helper transmits jamming signals independent of the source message to confuse the eavesdropper. The jamming signal is assumed to be treated as noise at both the intended receiver and the eavesdropper. Assuming Gaussian signaling at the helper, we obtain the optimal beamformers at the transmitter and the helper that achieve the secrecy capacity.