Optimal Pilot Length for Key Generation in Correlated Wireless Channels

This letter examines the optimal pilot length for key generation in correlated wireless channels. We first deduce the secret key capacity as a function of the pilot length N and other system parameters. Then, derive two fixed-point equations to identify the optimal N with and without an eavesdropper. Our analysis and numerical results confirm the existence of the optimal N that maximizes the secret key capacity, and both results for optimal N are consistent. Furthermore, the optimal N generally decreases with average signal-to-noise ratio and maximum Doppler shift. Our examination can provide useful guidelines in designing practical key generation systems.