Threshold Constraints on Symmetric Key Extraction from Rician Fading Estimates

Symmetric key establishment using reciprocal quantization of channel estimates in wireless Rician fading environments is considered. The quantization bits from channel-phase and channel-amplitude are treated as the output of a random number generator. We determine threshold constraints on the required minimal distance of the legitimate communicating parties from a passive eavesdropper, and determine threshold constraints on maximal key establishing rates. The analysis makes use of widely accepted statistical test suites applied to the generated bit streams along with a lemma we define and prove. For distance analysis, the minimal required distance from the eavesdropper to maintain perfect secrecy during key establishment is derived. For key establishing rates, the maximal rates are derived while ensuring the generated bits streams pass the statistical test suites. The work results in generic and clear threshold requirements on distance and rates as function of the Rician factor and quantization bit for any transmission frequency. Clear thresholds are useful for systems operating in a-priori known or estimated propagation environments. In addition, we address the effect of imperfect channel reciprocity on key agreement. Results show practical systems can operate under reciprocal and secure conditions, and that channel-phase estimates perform better than channel-amplitude estimates.