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We propose the generalized quadratic receivers (GQRs) for unitary space-time modulation over flat Rayleigh fading channels. The GQRs realize the performance improvement potential, known to be approximately 2-4 dB, between the quadratic receiver (QR) and the coherent receiver (CR), by performing channel estimation without the help of additional training signals that consume additional bandwidth. They are designed for various unitary space-time constellations (USTC) in which signal matrices may or may not contain explicit inherent training blocks, and may be orthogonal or nonorthogonal to one another. As the channel memory span exploited for channel estimation increases, the error probability of the GQRs reduces from that of the QR to that of the CR. The GQRs work well for both slow and fast fading channels, and the performance improvement increases as the channel fade rate decreases. For a class of USTC with the orthogonal design structure, the GQR is simplified to a form whose complexity can be less than the complexity of the QR or even that of the simplified form of the QR.