A receiver for frequency hopping logarithmic frequency domain ruler codes

This paper studies a receiver for a new class of Doppler detection capable frequency hopping radar waveforms. These waveforms use a frequency set spaced according to a Golomb ruler after a logarithmic warping of the frequency axis. This gives the transmitted waveform Doppler detection capability while preserving the Golomb ruler's autocorrelation. An incoming waveform is detected via a running Chirp Z-Transform followed by squaring, frequency warping and matched filtering in the warped frequency domain, which also allows estimation of the Doppler shift. Code sets are constructed via orthogonal time-frequency patterns. Decoding is done by mapping the frequency hopping waveform onto its multicarrier equivalent and performing the detection process again. This paper gives an example of these waveforms and their code sets, derives the optimal detector and decoder, illustrates their performance, and exhibits the receiver's ambiguity function and Doppler estimation accuracy.