High SNR BER Comparison of Coherent and Differentially Coherent   Modulation Schemes in Lognormal Fading Channels
  Using an auxiliary random variable technique, we prove that binary differential phase-shift keying and binary phase-shift keying have the same asymptotic bit-error rate performance in lognormal fading channels. We also show that differential quaternary phase-shift keying is exactly 2.32 dB worse than quaternary phase-shift keying over the lognormal fading channels in high signal-to-noise ratio regimes. 
Xuegui Song, Julian Cheng, and Mohamed-Slim Alouini
cs.IT math.IT