On the Ambiguity Function of Spiral Modulated Waveforms

In recent studies, spiral modulation (SM) has been found to be effective in reducing bit error rates in high order digital modulation. In addition to time, frequency, and phase modulations, SM leverages its time and rotational reversals to increase degrees of freedom for modulation. In this paper, we investigate the sensing capabilities of SM in terms of its ambiguity function (AF). We derive a closed form expression of the AF for a basic SM waveform and compare it with the AF of a rectangular pulse. Our analysis shows that the basic SM waveform provides the same range and Doppler resolutions as that of the rectangular pulse. In contrast to chirp waveforms, SM does not provide any pulse compression gain. We exploit the time and rotational reversal properties of SM to transmit information carrying symbols in each pulse. Finally, we analyze the corresponding range and Doppler sidelobe levels to those in the case of standard chirps.