Characterizing the Ambiguity Function of Constant-Envelope OFDM Waveforms

This paper investigates the radarAmbiguity Function (AF) properties of Constant Envelope Orthogonal FrequencyDivision Multiplexing (CE-OFDM) waveforms employing Phase-Shift Keying (PSK).The CE-OFDM is in fact a special case of the Multi-Tone Sinusoidal FrequencyModulated (MTSFM) waveform which allows for applying many of the samemathematical techniques of the MTSFM model to the CE-OFDM model. This resultsin novel compact closed-form expressions for the spectrum, AF, andAuto-Correlation Function (ACF) of the CE-OFDM waveform. The mainlobe structureof the CEOFDM's AF is characterized by the Ellipse of Ambigiuity (EOA) model.This produces precise closed-form expressions for the CEOFDM's Root-Mean Square(RMS) bandwidth and the degree of range-Doppler coupling present in thewaveform's AF mainlobe. These expressions show that a CE-OFDM waveformemploying PSK as the symbol encoding scheme will possess a fixed RMS bandwidthfor 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.