Analysis of the sensitivity of Karhunen-Loève transform in the secret key establishment

In the secret key establishment using channel characteristics, elements of the measured channel vector are always correlated, which will result in low entropy of the extracted key. Relevant researches has employed Karhunen-Loève transform to decorrelate the measured channel vector in order to furtherly generate secret key with a higher entropy. However, through extensive simulations, we find that the implementation of Karhunen-Loève transform is very sensitive. When Karhunen-Loève transform is independently implemented at two communicating nodes, the bit disagreement ratio of the generated key at two nodes is unusually high. In this paper, we propose to apply lattice whitening filter to do decorrelation instead of Karhunen-Loève transform. Simulation results shows that the decorrelation process with lattice whitening filter can be independently implemented at two nodes without transmission of any information through the public channel.