  This paper investigates the radar Ambiguity Function (AF) properties of
Constant Envelope Orthogonal Frequency Division Multiplexing (CE-OFDM)
waveforms employing Phase-Shift Keying (PSK). The CE-OFDM is in fact a special
case of the Multi-Tone Sinusoidal Frequency Modulated (MTSFM) waveform which
allows for applying many of the same mathematical techniques of the MTSFM model
to the CE-OFDM model. This results in novel compact closed-form expressions for
the spectrum, AF, and Auto-Correlation Function (ACF) of the CE-OFDM waveform.
The mainlobe structure of the CE-OFDM's AF is characterized by the Ellipse of
Ambigiuity (EOA) model. This produces precise closed-form expressions for the
CE-OFDM's Root-Mean Square (RMS) bandwidth and the degree of range-Doppler
coupling present in the waveform's AF mainlobe. These expressions show that a
CE-OFDM waveform employing PSK as the symbol encoding scheme will possess a
fixed RMS bandwidth for fixed modulation index $h$ and number of sub-carriers
$L$. Additionally, we show that the EOA model predicts that a CE-OFDM waveform
employing PSK encoding will almost always possess a ``Thumbtack-Like'' AF
shape.
