  The role of multiple antennas for secure communication is investigated within
the framework of Wyner's wiretap channel. We characterize the secrecy capacity
in terms of generalized eigenvalues when the sender and eavesdropper have
multiple antennas, the intended receiver has a single antenna, and the channel
matrices are fixed and known to all the terminals, and show that a beamforming
strategy is capacity-achieving. In addition, we show that in the high
signal-to-noise (SNR) ratio regime the penalty for not knowing eavesdropper's
channel is small--a simple ``secure space-time code'' that can be thought of as
masked beamforming and radiates power isotropically attains near-optimal
performance. In the limit of large number of antennas, we obtain a
realization-independent characterization of the secrecy capacity as a function
of the number $\beta$: the number of eavesdropper antennas per sender antenna.
We show that the eavesdropper is comparatively ineffective when $\beta<1$, but
that for $\beta\ge2$ the eavesdropper can drive the secrecy capacity to zero,
thereby blocking secure communication to the intended receiver. Extensions to
ergodic fading channels are also provided.
