The MISO Wiretap Channel with Channel Uncertainty: Asymptotic Perspectives

The N-antenna MISO Gaussian wiretap channel with imperfect channel-state information at the transmitter (CSIT) is studied in terms of secrecy rate scaling versus the signal-to-noise ratio (SNR) and N. Two schemes are considered, beamforming (BF) and artificial noise injection (AN). It is shown that if the CSIT error is independent of SNR, then both schemes do not achieve scaling versus SNR. However, if this error vanishes as SNR increases, then AN achieves the optimal scaling versus SNR, contrary to BF. Scaling can be achieved in BF by increasing N. In fact, BF achieves the optimal scaling versus N. In the AN scheme however, injecting noise in multiple direction deteriorates its scaling versus N. Nevertheless, AN can achieve the optimal scaling if noise is sent in only one direction. This leads to better performance than BF if the CSIT error is smaller than a threshold which is also derived.