  We establish in closed-form the capacity and the optimal signaling scheme for
a MISO channel with per-antenna power constraint. Two cases of channel state
information are considered: constant channel known at both the transmitter and
receiver, and Rayleigh fading channel known only at the receiver. For the first
case, the optimal signaling scheme is beamforming with the phases of the beam
weights matched to the phases of the channel coefficients, but the amplitudes
independent of the channel coefficients and dependent only on the constrained
powers. For the second case, the optimal scheme is to send independent signals
from the antennas with the constrained powers. In both cases, the capacity with
per-antenna power constraint is usually less than that with sum power
constraint.
