  Fundamental limits of secret-key agreement over reciprocal wireless channels
are investigated. We consider a two-way block-fading channel where the channel
gains in the forward and reverse links between the legitimate terminals are
correlated. The channel gains between the legitimate terminals are not revealed
to any terminal, whereas the channel gains of the eavesdropper are revealed to
the eavesdropper. We propose a two-phase transmission scheme, that reserves a
certain portion of each coherence block for channel estimation, and the
remainder of the coherence block for correlated source generation. The
resulting secret-key involves contributions of both channel sequences and
source sequences, with the contribution of the latter becoming dominant as the
coherence period increases. We also establish an upper bound on the secret-key
capacity, which has a form structurally similar to the lower bound. Our upper
and lower bounds coincide in the limit of high signal-to-noise-ratio (SNR) and
large coherence period, thus establishing the secret-key agreement capacity in
this asymptotic regime. Numerical results indicate that the proposed scheme
achieves significant gains over training-only schemes, even for moderate SNR
and small coherence periods, thus implying the necessity of randomness-sharing
in practical secret-key generation systems.
