In all schemes of unitary space-time modulation (USTM), PSK is used and the data rate is low. In this thesis, we construct USTM with high rate using nonconstant-energy signals. Our schemes are based on pilot symbol-assisted modulation (PSAM). We construct three types of USTM. The data rate of Construction I and Construction II is the same as the training code using 8PSK. The data rate of Construction III is the same as the training code using 16PSK. Codes constructed by our schemes have better minimum distance and frame error performance than codes in the previous schemes.