This paper experimentally evaluates the Generalized Sinusoidal Frequency Modulated (GSFM) waveform, a generalization of the Sinusoidal Frequency Modulated (SFM) waveform. The Instantaneous Frequency (IF) of the GSFM resembles the time/voltage characteristic of a Linear FM (LFM) chirp waveform. Consequently, the GSFM possesses an Ambiguity Function (AF) that resembles a thumbtack shape. Practical sonar system design must consider two factors beyond the AF. The spectral efficiency (SE), defined as the ratio of energy in an operational frequency band to the total waveform energy, is another important metric for waveform design. The Peak-to-Average-Power Ratio (PAPR) quantifies how close the waveform is to constant amplitude. These measures predict a waveform's energy efficiency and ability to be accurately replicated on practical piezoelectric transducers, which have limits on both their bandwidth and maximum transmit power. This paper explores these design considerations for the GSFM waveform and evaluates its performance against a host of other well established waveforms using simulated and experimental acoustic data. The GSFM possesses superior SE, PAPR, and overall energy efficiency when compared to thumbtack waveforms.

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Pulse compression (PC) active sonar waveforms provide a significant improvement in range resolution over singlefrequency sinusoidal waveforms also known as continuous wave (CW) waveforms. Since their inception in the 1940s, 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 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 autocorrelation 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 paper describes a generalization of the SFM waveform, referred to as the generalized SFM (GSFM) waveform, which modifies the SFM's IF to resemble the time/voltage characteristic of an 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 paper focuses primarily on the properties of the GSFM's thumbtack AF shape and compares it to other well-known waveforms with a similar AF shape. The GSFM waveform achieves zero rangeDoppler coupling for single target measurements which in turn minimizes the variance in jointly estimating target range and velocity and optimizes resolution of multiple point targets in range and velocity. The GSFM's AF peak sidelobe levels, which determine the waveform's ability to detect weak targets in the presence of strong ones, are comparable to other well-established thumbtack AF waveforms such as Costas or phase-coded waveforms over a wide range of time-bandwidth product (TBP) values.

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This paper presents a method for generating a family of waveforms with low in-band Auto/Cross-Correlation Function (ACF/CCF) properties using the Multi-Tone Sinusoidal Frequency Modulated (MTSFM) waveform model. The MTSFM waveform's modulation function is represented using a Fourier series expansion. The Fourier coefficients are utilized as a set of discrete parameters that can be modified to optimize the waveform family's properties. The waveforms' ACF/CCF properties are optimized utilizing a multi-objective optimization problem. Each objective function is weighted to place emphasis on either low ACF or CCF sidelobes. The resulting optimized MTSFM waveforms each possess a thumbtack-like Ambiguity Function in addition to the specifically designed ACF/CCF properties. Most importantly, the resulting MTSFM waveform families possess both ideally low Peak-to-Average Power Ratios (PAPR) and high Spectral Efficiency (SE) making them well suited for transmission on practical radar transmitters.