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The use of differentially coherent combining is proposed to improve the performance of a double-dwell acquisition system by increasing the reliability of a decision in the verification stage. The detection and mean acquisition time performance of the acquisition scheme with the proposed combining scheme is analyzed in frequency-selective Rayleigh fading channels, and compared with that of two previously published double-dwell acquisition schemes based on long correlation intervals and noncoherent combining. It is shown that the proposed acquisition scheme outperforms the previous ones, and that the performance improvement increases as the frequency offset increases.