Optimal waveform design using Multi-Tone Sinusoidal Frequency Modulation

This paper presents an optimal waveform design method using Multi-Tone Sinusoidal Frequency Modulation (MTSFM). The MTSFM waveform's modulation function is represented using a Fourier series expansion. This representation results in a constant amplitude waveform with a continuous modulation function whose spectrum, Auto-Correlation Function, and Ambiguity Function shapes can be modified by adapting the Fourier Series coefficients of the waveform's modulation function. The MTSFM waveforms additionally possesses a low Peak-to-Average Power Ratio (PAPR) and high Spectral Efficiency (SE) making them well-suited for transmission on practical piezoelectric devices.