Physical Layer Secure Communications over Wireless Channels via Common Zeros

Based on recent results on the challenges of identifiability in blind deconvolution and new methods for blind deconvolution with the knowledge of autocorrelation functions, a novel approach to secure communication over wireless channels is provided by using the Binary Modulation on Conjugated Zeros design. In particular, the blind deconvolution of a transmitted sequence via a wireless channel with Rayleigh fading is rendered impossible through the introduction of common zeros. A signal codebook design is provided as well as a decoding strategy with a shared secret key for the legitimate user. The probability of an eavesdropper guessing the correct key is computed and shown to converge to zero nearly exponentially with an increasing length of the key.