CPM Training Waveforms with Autocorrelation Sidelobes Close to Zero

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 the 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 correspondence paper, 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.