  Continuous phase modulation (CPM) plays an important role in wireless
communications due to its constant envelope signal property and tight spectrum
confinement capability. Although CPM has been studied for many years, CPM
training waveforms having autocorrelations with zero sidelobes have not been
reported before, to the best of our knowledge. Existing works on CPM system
design mostly assume that the channel fading coefficients are either perfectly
known at the receiver or estimated using random CPM training waveforms. In this
work, we propose a novel class of CPM training waveforms displaying
autocorrelation sidelobes close to zero. The key idea of our construction is to
apply differential encoding to Golay complementary pair having perfect
aperiodic autocorrelation sum properties.
