Physical layer key generation methods for arbitrary fading channels

Two methods are developed that can be applied to generate secret keys automatically from fading propagation channels that are reciprocal but have arbitrary (i.e. non Gaussian) statistics. Such methods may be necessary for physical-layer key generation in cases where the line-of-sight (LOS) component produces Rician channel statistics, not only because channel quantization based on Gaussian statistics will not provide equally probable symbols, but also because the symbol error rate (SER) and efficiency analysis based on Gaussian channels does not reflect true performance. An improved channel quantization method compared to [1], [2] is developed, where the empirical cumulative distribution function (cdf) of the channel is used directly to ensure equal probability of the key symbols. The results show that LOS channels can have slightly better SER performance than strictly Gaussian channels, especially at low SNR. Second, the idea of positional coding is developed, where a secret key can be transmitted by dividing empirical channel observations into multiple codewords and conveying a secret message from Alice to Bob in the sequence of channels fed forward from Alice to Bob. Analysis of the method illustrates that key mismatch rate can be made arbitrarily low by properly selecting the codeword length.