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In this paper, we study the frequency-selective broadcast channel withconfidential messages (BCC) in which the transmitter sends a confidentialmessage to receiver 1 and a common message to receivers 1 and 2. In the case ofa block transmission of N symbols followed by a guard interval of L symbols,the frequency-selective channel can be modeled as a N * (N+L) Toeplitz matrix.For this special type of multiple-input multiple-output (MIMO) channels, wepropose a practical Vandermonde precoding that consists of projecting theconfidential messages in the null space of the channel seen by receiver 2 whilesuperposing the common message. For this scheme, we provide the achievable rateregion, i.e. the rate-tuple of the common and confidential messages, andcharacterize the optimal covariance inputs for some special cases of interest.It is proved that the proposed scheme achieves the optimal degree of freedom(d.o.f) region. More specifically, it enables to send l <= L confidentialmessages and N-l common messages simultaneously over a block of N+L symbols.Interestingly, the proposed scheme can be applied to secured multiuserscenarios such as the K+1-user frequency-selective BCC with K confidentialmessages and the two-user frequency-selective BCC with two confidentialmessages. For each scenario, we provide the achievable secrecy degree offreedom (s.d.o.f.) region of the corresponding frequency-selective BCC andprove the optimality of the Vandermonde precoding. One of the appealingfeatures of the proposed scheme is that it does not require any specificsecrecy encoding technique but can be applied on top of any existing powerfulencoding schemes.

Secured Communication over Frequency-Selective Fading Channels: a practical Vandermonde precoding