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A wireless relay network allows relays to cooperate with each other, emulate a virtual array of transmit antennas, and perform distributed space-time modulation of the source signals. In this paper, two types of relay networks are considered-one with no channel state information (CSI) (i.e., the noncoherent networks) and one with only the information of the relay-to-destination channels (i.e., the partially coherent networks) at the destination. First, a new optimal power-allocation (PA) scheme is derived to maximize the average signal-to-noise ratio (SNR) at the destination while minimizing the amount of fading experienced over the network. Second, the Fourier-based unitary space-time modulation (USTM), which was originally proposed for multiple colocated transmit antennas, is applied to wireless relay networks. The receivers for such distributed USTM over noncoherent and partially coherent networks are developed, and their error performances are shown to be asymptotically the same. The impact of different PA schemes on the error performance of distributed USTM is thoroughly illustrated with simulation results.