Zak-OTFS for Identification of Linear Time-Varying Systems

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Abstract
Linear time-varying (LTV) systems model radar scenes where each reflector/target applies a delay, Doppler shift and complex amplitude scaling to a transmitted waveform. The receiver processes the received signal using the transmitted signal as a reference. The self-ambiguity function of the transmitted signal captures the cross-correlation of delay and Doppler shifts of the transmitted waveform. It acts as a blur that limits resolution, at the receiver, of the delay and Doppler shifts of targets in close proximity. This paper considers resolution of multiple targets and compares performance of traditional chirp waveforms with the Zak-OTFS waveform. The self-ambiguity function of a chirp is a line in the delay-Doppler domain, whereas the self-ambiguity function of the Zak-OTFS waveform is a lattice. The advantage of lattices over lines is better localization, and we show lattices provide superior noise-free estimation of the range and velocity of multiple targets. When the delay spread of the radar scene is less than the delay period of the Zak-OTFS modulation, and the Doppler spread is less than the Doppler period, we describe how to localize targets by calculating cross-ambiguities in the delay-Doppler domain. We show that the signal processing complexity of our approach is superior to the traditional approach of computing cross-ambiguities in the continuous time / frequency domain.
Funding Information
  • Department of Science and Technology, Ministry of Science and Technology, India (e-50660)
  • Department of Science and Technology, Ministry of Science and Technology, India (TPN-96226)
  • Jai Gupta Chair at I.I.T. Delhi. The work of Ananthanarayanan Chockalingam
  • J.C. Bose National Fellowship
  • NSF-DST project (International Cooperation Division), Department of Science and Technology, Government of India
  • National Science Foundation (2342690)
  • National Science Foundation (2148212)
  • Federal Agency and Industry Partners as specified in the Resilient and Intelligent NextG Systems (RINGSs) Program
  • Air Force Office of Scientific Research (FA 8750-20-2-0504)
  • Air Force Office of Scientific Research (FA 9550-23-1-0249)