Ultra wideband transceivers promise multi-gigabit per second performance at power consumptions commensurate with portable devices. Future products are likely to adopt multiple antennas to maximize performance. Severe FCC EIRP restrictions impose an interesting system design constraint. In this paper, capacity optimal multiple antenna transmission schemes are investigated for EIRP restricted systems under the assumption that the channel is known at the transmitter. It is shown that per subcarrier antenna power allocation, which reduces to antenna selection at low SNR or when using one receive antenna, is optimal for some transmitter configurations. The improvements in capacity are quantified for representative channels.