  By exploiting multipath fading channels as a source of common randomness,
physical layer (PHY) based key generation protocols allow two terminals with
correlated observations to generate secret keys with information-theoretical
security. The state of the art, however, still suffers from major limitations,
e.g., low key generation rate, lower entropy of key bits and a high reliance on
node mobility. In this paper, a novel cooperative key generation protocol is
developed to facilitate high-rate key generation in narrowband fading channels,
where two keying nodes extract the phase randomness of the fading channel with
the aid of relay node(s). For the first time, we explicitly consider the effect
of estimation methods on the extraction of secret key bits from the underlying
fading channels and focus on a popular statistical method--maximum likelihood
estimation (MLE). The performance of the cooperative key generation scheme is
extensively evaluated theoretically. We successfully establish both a
theoretical upper bound on the maximum secret key rate from mutual information
of correlated random sources and a more practical upper bound from Cramer-Rao
bound (CRB) in estimation theory. Numerical examples and simulation studies are
also presented to demonstrate the performance of the cooperative key generation
system. The results show that the key rate can be improved by a couple of
orders of magnitude compared to the existing approaches.
