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In this paper, we propose a bit-by-bit interleaved trellis coded 16DAPSK modulation with differential detection. The performance of the proposed system is evaluated on Rayleigh fading channels in terms of the bit error rate (BER) by numerical analysis and computer simulation. As the bit-by-bit interleaving induces more diversity effect than the symbol-by-symbol interleaving, the proposed system shows better BER performance than that of the conventional symbol-by-symbol interleaved trellis coded system. Moreover, at high Eb/No, the BER of the proposed system is better than that of the symbol-by-symbol interleaved system based on coherent detection with perfect channel state information (CSI) in spite of fact that the proposed system requires no CSI.