On the secrecy capacity of frequency-selective fading channels: A practical Vandermonde precoding

We study the secrecy capacity of the frequency-selective wiretap channel. Assuming that a guard interval of L symbols is inserted to avoid the inter-block interference and these symbols are discarded at the receiver, the single-carrier frequency-selective channel is modeled as a multiple-input multiple-output Toeplitz matrix. For this special case of the MIMO wiretap channel and under the assumption of perfect channel knowledge at transmitter (CSIT), we propose a practical Vandermonde precoding scheme that transmits the confidential messages on the zeros of the eavesdropper channel. It is proved that this Vandermonde precoding achieves the full multiplexing gain offered by the frequency-selective wiretap channel in the high SNR regime. For a more realistic case where the transmitter only knows the legitime channel we consider the "mask beamforming" scheme where the artificial noise is sent on the zeros of the legitime channel via the Vandermonde precoding. This mask beam-forming is shown to achieve the same multiplexing gain as the perfect CSIT.