Wireless physical-layer security via transmit precoding over dispersive channels: optimum linear eavesdropping

Multi-layer security and information assurance frameworks will become essential as potential attackers´ resources continue to grow. Due to its growing use and obvious vulnerability, wireless communication is in particular need of protection. As available computational power increases, transmitters will be able to implement sophisticated precoding to increase transmission security. We consider the security-enhancing capability of algebraic channel decomposition multiplexing (ACDM), a form of multipulse spread-spectrum precoding for dispersive wireless channels that results in orthogonal signaling at the receiver. In ACDM, the transmit code vectors are determined from the SVD of the convolution matrix describing the channel between the transmitter and desired receiver. Since any potential transmitter-eavesdropper channel is going to have a different multipath structure, the eavesdropper´s ability to detect and decode the transmissions can be severely reduced. We develop semi-analytical formulae for the performance penalty experienced by an eavesdropper employing the optimum linear MMSE receiver under the worst-case assumptions that it has perfect knowledge of the transmit code set and its own channel response. Using realistic channel models, we demonstrate that such an eavesdropper experiences a significant performance degradation, and show that this degradation is due to a combination of diversity loss and inter-code interference.