  This paper investigates generation of a secret key from a reciprocal wireless
channel. In particular we consider wireless channels that exhibit sparse
structure in the wideband regime and the impact of the sparsity on the secret
key capacity. We explore this problem in two steps. First, we study key
generation from a state-dependent discrete memoryless multiple source. The
state of source captures the effect of channel sparsity. Secondly, we consider
a wireless channel model that captures channel sparsity and correlation between
the legitimate users' channel and the eavesdropper's channel. Such dependency
can significantly reduce the secret key capacity.
  According to system delay requirements, two performance measures are
considered: (i) ergodic secret key capacity and (ii) outage probability. We
show that in the wideband regime when a white sounding sequence is adopted, a
sparser channel can achieve a higher ergodic secret key rate than a richer
channel can. For outage performance, we show that if the users generate secret
keys at a fraction of the ergodic capacity, the outage probability will decay
exponentially in signal bandwidth. Moreover, a larger exponent is achieved by a
richer channel.
