  Phase Coded (PC) waveforms possess desirable Auto-Correlation Function (ACF)
properties for use in radar and sonar systems. However, their spectra possess
high spectral leakage due to the abrupt phase transitions between the chips in
the waveform. This paper describes a method of Continuous Phase Modulation
(CPM) to reduce a PC waveform's spectral leakage using the Multi-Tone
Sinusoidal Frequency Modulation (MTSFM) model. The MTSFM-CPM model represents
the PC waveform's instantaneous phase as a finite Fourier series. This
representation smooths the abrupt phase transitions between chips resulting in
a spectrally compact waveform. This smoothing of the PC waveform's
instantaneous phase introduces perturbations to the waveform's ACF mainlobe and
sidelobe structure. Adjusting the MTSFM-CPM waveform's parameters refines its
ACF mainlobe and sidelobe structure while also preserving its compact spectral
shape.
