Relative-entropy based beamforming for secret key transmission

In the context of the MISO flat-fading channel, we deal with the transmission of a secret key. More precisely, we seek to find the transmit beamformer to minimize the error probability of the legitimate receivers while maintaining a high (close to one) error probability for the eavesdroppers. To reach this goal, we exploit the popular “artificial noise” strategy which allows to confuse the eavesdroppers while the legitimate receivers are not affected. Under the low noise regime assumption for the eavesdroppers, we first derive the balancing coefficient to reach the constraint of high error probability for the eavesdroppers. Given this value, we find the optimal beamformer which minimizes the error probability of the legitimate receivers. We finally study the behavior of the error probability of the legitimate receivers with respect to the Signal To Noise Ratio and to the number of antennas at the transmission.