Characterizing the Ambiguity Function of Constant-Envelope OFDM Waveforms

TL;DR

This paper provides a detailed mathematical characterization of the Ambiguity Function of constant-envelope OFDM waveforms using novel closed-form expressions, revealing their mainlobe structure and range-Doppler coupling properties.

Contribution

It introduces new closed-form formulas for the spectrum, AF, and ACF of CE-OFDM waveforms, and applies the EOA model to analyze their mainlobe structure and bandwidth.

Findings

CE-OFDM has a fixed RMS bandwidth for given parameters.

The AF shape is predicted to be 'Thumbtack-Like' by the EOA model.

Mainlobe structure characterized by the Ellipse of Ambiguity (EOA).

Abstract

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.