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Decision-feedback differential detection (DFDD) of differential phase-shift keying (DPSK) and differential unitary space-time modulation (DUST) in Rayleigh-fading channels exhibits significant performance improvement over standard single-symbol maximum-likelihood detection. However, knowledge of channel fading correlation and signal-to-noise ratio (SNR) is required at the receiver to compute the feedback coefficients used in DFDD. In this letter, we investigate the robustness of the DFDD to imperfect knowledge of the feedback coefficients by modeling the mismatch between estimated feedback coefficients and ideal coefficients in terms of mismatch between the estimated values of fading correlation and SNR and the true values. Under the assumption of a block-fading channel when nondiagonal DUST constellations are used and a continuous fading channel otherwise, we derive exact and Chernoff bound expressions for pair-wise word-error probability and then use them to approximate the bit-error rate (BER), finding close agreement with simulation results. The relationships between BER performance and various system parameters, e.g., DFDD length and Doppler mismatch, are also explored. Furthermore, the existence of an error floor in the BER-vs-SNR curve is investigated for the infinite-length DFDD. For the special case of Jakes' fading model, it is shown that the error floor can be removed completely even when the Doppler spread is over-estimated.