Extended logarithmic frequency domain rulers for joint radar-communications

This paper studies the design and performance of a new class of Doppler estimation capable waveforms called Extended Logarithmic Frequency Domain Rulers (E-LFDRs) for joint radar-communications. E-LFDRs are multicarrier wave-forms whose carriers are spaced according to an Extended Golomb Ruler after a logarithmic warping of the frequency axis. The multiplicative Doppler shift additively translates the waveform's logarithmically warped spectrum, which allows simultaneous signal detection and Doppler shift estimation via convolutional matched filtering of the logarithmically warped power spectrum. We propose to use these waveforms for communications by phase modulating the carriers and using the estimated Doppler shift to adjust a pilot tone time domain matched filter for fine symbol synchronization. The synchronized waveform is then sent to a communications module for symbol decoding. This paper gives an example of these waveforms, details their design, illustrates a receiver, and explores their bit error rate in AWGN and multipath.