The performance of a burst QPSK differential detector with a noise-reduced reference is analyzed, and shows the 3 dB performance penalty of a differential detector can be reduced to less than 1 dB. In presence of a small frequency offset, the proposed circuit outperforms the conventional differential detector by at least 1.7 dB for E_b/N₀ in the 14 to 20 dB range. Another contribution in this paper is a closed form expression for the probability of a symbol error.