Secured Communication over Frequency-Selective Fading Channels: A Practical Vandermonde Precoding

We study the frequency-selective broadcast channel with confidential messages (BCC) where the transmitter sends a confidential message to receiver 1 and a common message to receivers 1 and 2. In the case of a block transmission of [inline-graphic not available: see fulltext] symbols followed by a guard interval of [inline-graphic not available: see fulltext] symbols, the frequency-selective channel can be modeled as a [inline-graphic not available: see fulltext] Toeplitz matrix. For this special type of multiple-input multiple-output channels, we propose a practical Vandermonde precoding that projects the confidential messages in the null space of the channel seen by receiver 2 while superposing the common message. For this scheme, we provide the achievable rate region and characterize the optimal covariance for some special cases of interest. Interestingly, the proposed scheme can be applied to other multiuser scenarios such as the [inline-graphic not available: see fulltext]-user frequency-selective BCC with [inline-graphic not available: see fulltext] confidential messages and the two-user frequency-selective BCC with two confidential messages. For each scenario, we provide the secrecy degree of freedom (s.d.o.f.) region of the corresponding channel and prove the optimality of the Vandermonde precoding. One of the appealing features of the proposed scheme is that it does not require any specific secrecy encoding technique but can be applied on top of any existing powerful encoding schemes.