  The performance limits of scalar coding for multiple-input single-output
channels are revisited in this work. By employing randomized beamforming,
Narula et al. demonstrated that the loss of scalar coding is universally
bounded by ~ 2.51 dB (or 0.833 bits/symbol) for any number of antennas and
channel gains. In this work, by using randomized beamforming in conjunction
with space-time codes, it is shown that the bound can be tightened to ~ 1.1 dB
(or 0.39 bits/symbol).
