A unified mathematical model for spatial scrambling based secure wireless transmission and its wiretap method

The spatial scrambling based secure wireless transmission methods, such as artificial noise and antenna array weighted randomly, can secure wireless transmission at the physical layer. They have a common physical essence, that is, the private message is transmitted in the desired direction while deliberate interference is transmitted in other orthogonal directions. Unfortunately, the interference is not white in spatial domain due to the limitation of the transmit antenna number. A eavesdropper can eliminate the directional interferences by the aid of multiple antennas. In this paper, a unified mathematical model for the above physical-layer methods is established, based on which, a MUSIC-like wiretap algorithm is proposed by exploiting the finite alphabet property of communication symbols. Simulation results show that if the eavesdropper has more antennas than that of the transmitter, the proposed algorithm can intercept information effectively.