Deaf Cooperation for Secrecy With Multiple Antennas at the Helper

In this paper, we investigate the roles of cooperative jamming (CJ) and noise forwarding (NF) in improving the achievable secrecy rates of a Gaussian wiretap channel (GWT) when the helper node is equipped with multiple antennas. We decompose the channel from the helper to the eavesdropper into two orthogonal components: one is aligned in the direction of the channel between the helper and the legitimate receiver (direct component) and the other is in the orthogonal direction to the channel between the helper and the legitimate receiver (orthogonal component). We then propose a strategy in which the helper uses the orthogonal component to transmit pure Gaussian noise as in the CJ strategy while he uses the direct component for either CJ or NF depending on the given channel conditions. We explicitly derive the optimal power control policy for this strategy and give the achievable secrecy rates when the direct component is used to perform CJ or NF. We hence derive the channel conditions where CJ is better than NF over the direct component and vice-versa. Finally, we consider the reversely degraded multiple antenna relay-eavesdropper channel. We show that a simple strategy in which the relay jams with full power along the orthogonal component and transmits nothing in the direct component achieves a secrecy rate that approaches the secrecy capacity of this channel as the relay's average power goes to infinity. Moreover, we show that this result holds almost surely even if the relay-eavesdropper's channel state information is unavailable.