Secure Space-Time Communications over Rayleigh Flat Fading Channels

In this paper, we consider the wire-tap channel model consisting of three users, namely, a transmitter, a legal receiver, and an eavesdropper, where the eavesdropper has possible unlimited centralized or distributed multiple antennas, while the legal user has just a single antenna. With this model, we study the realization of strict positive secrecy rate through Rayleigh flat fading channels using M-ary phase shift keying (PSK) and orthogonal space-time block code (OSTBC) based on channel reciprocal principle. We demonstrate that the information rate at the eavesdropper can be reduced to zero and a positive communication rate at the legal receiver can be realized if the transmitter employs a proper phase precoder based on the channel reciprocal, and uses OSTBC and M-ary PSK modulations for data transmissions. Application examples of space-time codes for positive secrecy rate are illustrated. As we have given the eavesdropper more capabilities than the legal receiver and thus captured a worst case scenario, any positive secrecy rate that is achieved serves as a lower bound on the secrecy capacity.