Multi-rate convolution for LFM and NLFM

High resolution radar using linear frequency modulation (LFM) and non-linear frequency modulation (NLFM) transmit a wideband pulse to achieve a narrow range resolution. We consider digital multi-rate implementation of LFM and NLFM pulse compression. For the LFM case, we consider short-length fixed-point fast Fourier transform (FFT) within the multi-rate structure as a way to increase speed and reduce power while obtaining the ideal compression gain. It is shown that the multi-rate method is robust to the compression gain and suited for fixed-point processors. For the NLFM case, we reduce the number of match filter coefficients using the frequency selectivity of the filter banks while maintaining the desired performance parameters. For a particular case, we demonstrate that the complex multiplication per output sample per sub-band is smaller than an overlap-save fast convolution. Performance metrics and computational complexity of the NLFM multi-rate implementation are compared to the ideal case.