Ziv-Zakai time-delay estimation bounds for frequency-hopping waveforms under frequency-selective fading

  • Authors:

  • Ning Liu;Zhengyuan Xu;Brian M. Sadler

  • Affiliations:

  • Department of Electrical Engineering, University of California, Riverside, CA;Department of Electrical Engineering, University of California, Riverside, CA;Army Research Laboratory, Adelphi, MD

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 2010

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Abstract

Ziv-Zakai Bayesian lower bounds on time-delay estimation (TDE) are developed for frequency hopping waveforms. These wideband waveforms are readily employed for both communications and TDE. We consider random frequency-selective fading channels, described by a Gaussian tapped delay line model with inter-hop correlation. The receiver does not know the channel realization to assist in estimating the time delay but does know the channel statistics. The development incorporates a random uniform prior on the delay. The bounds provide tight mean-square error prediction for the maximum a posteriori (MAP) estimator performance over a large range of signal-to-noise ratios (SNRs). They also accurately predict the TDE frequency diversity gain from multi-frequency transmission in fading channels. The special case of independent fading is discussed, including both flat Rician and Rayleigh fading, and closed-form expressions enable easy study of the effects of SNR, frequency diversity, and channel statistics on TDE.