Signals are developed for use in a wireless system with multiple transmit and multiple receive antennas so that even in the face of some correlation the most open-loop capacity that can be achieved using a substantially open-loop system with a channel of that level of correlation is obtained. In accordance with the principles of the invention, the signals transmitted from the various antennas are processed so as to improve their ability to convey the maximum amount of information. More specifically, the data to be transmitted is divided into M+1 substreams, where M is the number of transmit antennas. Each transmit antenna is supplied with a combination signal that is made up of a weighted version of a common one of the substreams and a weighted version of a respective one of the substreams that is supplied uniquely for that antenna, so that there are M transmit signals. A receiver having N antennas receives the M transmit signals as combined by the channel and reconstitutes the original data therefrom. This may be achieved using successive decoding techniques. Advantageously, the capacity, i.e., the rate of information that can be conveyed with an arbitrarily small probability of error when the instantaneous forward channel condition is unknown to the transmitter, is maximized.