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Doubly differential modem turns out to be a promising technology for coping with unknown frequency offsets with the pay of signal-to-noise ratio (SNR). In this paper, we propose to compensate the SNR loss by employing the detection-forward cooperative relay. The receiver can employ two kind of combiners to attain the achievable spatial diversity-gain. Performance analysis is carefully investigated for the Rayleigh-fading channel. It is shown that the SNR-compensation is satisfied for the large-SNR range.