This is an investigation of the adaptive and robust design of transmit signals for wireless transmission paths. The objective is to determine fundamental design methods that will allow reliable transmission at data rates several times faster than are presently achievable by adaptively contouring the transmit signals to match channel conditions. Time-varying and/or broadcast wireless transmission paths create special challenges for such adaptive transmission design that at present have not been solved. The project first studies transmission on fixed broadcast channels where feedback to the transmitter is not allowed and principles of robust signal design need to be derived to improve reliably transmitted data rates. Study then encompasses time-variation through both well known and new models for both broadcast and interactive time-varying (mobile) channels. The focus then shifts to generalization to multiuser coordinated transmission technologies. Extension and generalization of multi-tone waveforms which are very successful on wireline channels will be treated in these new and more challenging contexts.