The Fourier-based unitary space-time modulation (USTM) originally proposed for multiple co-located transmit antennas is applied to wireless relay networks. The scheme allows the relays cooperate with each other, emulate a virtual array of transmit antennas, and perform distributed USTM (DUSTM) of the source signals. It is assumed that the relays have no information of all the channels, while the destination might have the information of the relay-to-destination channels (i.e., in the partially coherent networks) or no channel information at all (i.e., in the noncoherent networks). For such systems, a new optimal power allocation scheme is derived to maximize the average SNR at the destination. The receivers for DUSTM over these two types of relay networks are developed and their performances are shown to be asymptotically the same.
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