Target Resolution Properties of the Multi-Tone Sinusoidal Frequency Modulatedwaveform

The mainlobe width of a waveform’s Ambiguity Function (AF) determines its ability to resolve multiple closely spaced targets in time-delay (range) and Doppler (range-rate). The contour of the AF’s mainlobe is well approximated by a coupled ellipse known as the Ellipse Of Ambiguity (EOA) whose parameters can be directly calculated in closed form if the waveform’s modulation function is known. The Multi-Tone Sinusoidal Frequency Modulated (MTSFM) waveform possesses a modulation function that is represented using a Fourier series expansion. These Fourier coefficients act as a set of tunable parameters that can be adjusted to synthesize waveforms with desired properties. This paper derives closed form expressions for the EOA parameters of the MTSFM and demonstrates their mainlobe characteristics via simulation.