Bandwidth formula for Linear FMCW radar waveforms

The International Telecommunications Union provides recommendations regarding spectral emission bounds for primary radar systems. These bounds are currently in review and are defined in terms of spectral occupancy, necessary bandwidth, 40dB bandwidth and out-of-band roll-off rates. Here we derive out-of-band domain spectral envelopes, bandwidth formula and roll-off rates, for various Linear FMCW radar waveforms including sawtooth (LFMCW), Quadratic Phase Coded LFMCW, LFM Pulse Train, and Hann amplitude tapered LFMCW.