The Gaussian wiretap channel with noisy public feedback: Breaking the high-SNR ceiling

A multiple-antenna Gaussian wiretap channel in which the number of antennas at the source is not larger than that at the eavesdropper is considered. Without feedback, the secrecy capacity over such a channel generally converges to a constant at high signal-to-noise ratio (SNR). A half-duplex secure protocol allowing the destination to actively broadcast random keys over insecure channels is proposed. It is shown that using multiple antennas at the destination is instrumental in achieving a secrecy rate that grows linearly with log SNR. The pre-log factor of the secrecy rate, i.e. the secure degree of freedom, is characterized, revealing an interesting interplay between the numbers of antennas at the three communication nodes.