[Paper Review] The Generalized Sinusoidal Frequency Modulated Waveform for Active Sonar Systems

David A. Hague|arXiv (Cornell University)|Sep 28, 2018

Structural Health Monitoring Techniques3 citations

TL;DR

This paper introduces the Generalized Sinusoidal Frequency Modulated (GSFM) waveform, a novel active sonar waveform that preserves the Doppler sensitivity of traditional Sinusoidal FM (SFM) waveforms while drastically reducing range sidelobes by modifying the instantaneous frequency to resemble a chirp. The result is an ambiguity function (AF) that approaches a thumbtack shape, significantly improving target resolution and reverberation suppression in sonar systems.

ABSTRACT

Pulse Compression (PC) active sonar waveforms provide a significant improvement in range resolution over single frequency sinusoidal waveforms also known as Continuous Wave (CW) waveforms. Since their inception in the 1940's, a wide variety of PC waveforms have been designed using either Frequency Modulation (FM), phase coding, or frequency hopping to suite particular sonar applications. The Sinusoidal FM (SFM) waveform modulates its Instantaneous Frequency (IF) by a single frequency sinusoid to achieve high Doppler sensitivity which also aids in suppressing reverberation. This allows the SFM waveform to resolve target velocities. While the SFM's resolution in range is inversely proportional to its bandwidth, the SFM's Auto-Correlation Function (ACF) contains many large sidelobes. The periodicity of the SFM's IF creates these sidelobes and impairs the SFM's ability to clearly distinguish multiple targets in range. This dissertation describes a generalization of the SFM waveform, referred to as the Generalized SFM (GSFM) waveform, that modifies the IF to resemble the time/voltage characteristic of a FM chirp waveform. As a result of this modification, the Doppler sensitivity of the SFM is preserved while substantially reducing the high range sidelobes producing a waveform whose Ambiguity Function (AF) approaches a thumbtack shape. This dissertation describes the properties of the GSFM's thumbtack AF shape, compares it to other well known waveforms with a similar AF shape, and additionally considers some of the practical considerations of active sonar systems including transmitting the GSFM on piezoelectric transducers and the GSFM's ability to suppress reverberation. Lastly, this dissertation also describes designing a family of in-band nearly orthogonal waveforms with potential applications to Continuous Active Sonar (CAS).

Motivation & Objective

• To address the high range sidelobe problem in conventional Sinusoidal FM (SFM) waveforms, which limits target resolution in active sonar.
• To develop a generalized waveform that maintains the Doppler sensitivity of SFM while achieving a thumbtack-shaped ambiguity function.
• To enable practical implementation of GSFM on piezoelectric transducers and evaluate its reverberation suppression capabilities.
• To design a family of in-band nearly orthogonal GSFM waveforms for Continuous Active Sonar (CAS) applications.
• To explore pulse train designs that allow frequent target scene revisiting while balancing CPI, TBP, and acceleration tolerance.

Proposed method

• Generalize the SFM waveform by modifying its instantaneous frequency (IF) to follow a chirp-like trajectory, reducing periodicity-induced sidelobes.
• Use a Fourier series representation of the phase function to model the GSFM’s spectrum and ambiguity function (AF).
• Apply time and frequency tapering to suppress off-axis sidelobes in the AF, improving resolution in delay-Doppler space.
• Design linear frequency-hopped pulse trains to reduce cross-correlations between pulses and suppress range sidelobes.
• Implement a processing framework that revisits the target scene every PRI, enabling high PRF operation with unambiguous range measurements.
• Utilize the GSFM’s constant envelope and low peak-to-average power ratio (PAPR) to ensure compatibility with practical piezoelectric transducers.

Experimental results

Research questions

• RQ1 Can the GSFM waveform achieve a thumbtack-shaped ambiguity function while preserving the Doppler sensitivity of SFM?
• RQ2 How does the GSFM’s AF performance compare to other well-known waveforms such as linear FM and stepped-frequency waveforms?
• RQ3 What are the practical limitations of transmitting GSFM waveforms on piezoelectric transducers in real sonar systems?
• RQ4 Can GSFM pulse train designs effectively suppress multiple-target range sidelobes while enabling high PRF operation?
• RQ5 Can the Fourier series representation of the GSFM phase be optimized to synthesize waveforms with user-defined spectral and AF properties?

Key findings

• The GSFM waveform achieves a thumbtack-shaped ambiguity function, significantly reducing range sidelobes compared to conventional SFM waveforms.
• The GSFM maintains high Doppler sensitivity, enabling effective velocity resolution and reverberation suppression in active sonar.
• The GSFM’s constant envelope and low PAPR make it suitable for transmission on piezoelectric transducers without distortion.
• Linear frequency-hopped GSFM pulse trains reduce cross-correlation between pulses, effectively suppressing multiple-target range sidelobes.
• The GSFM waveform design allows for high PRF operation with unambiguous range measurements, overcoming a key limitation in Pulse-Doppler radar and ultrasound systems.
• The Fourier series representation of the GSFM phase enables systematic analysis and potential optimization for custom spectral and AF responses.