Fundamental Limitations in Passive Time-Delay Estimation—Part II: Wide-Band Systems

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Abstract

This is the second part of a study which deals with the problem of passive time delay estimation. The focus here is on systems employing wide-band signals and/or arrays of very widely separated receivers. A modified (improved) version of the Ziv-Zakai lower bound (ZZLB) is used to analyze the effect of additive noise and signal ambiguities on the attainable mean-square estimation errors. When the lower bound is plotted as a function of signal-to-noise ratio (SNR), one observes two distinct threshold phenomena dividing the SNR domain into three disjointed segments. At high SNR, the lower bound coincides with the Cramer-Rao lower bound (CRLB). This is the ambiguity-free mode of operation where differential delay estimation is subject only to local errors. At moderate SNR (between the two thresholds), the lower bound exceeds the CRLB by a factor of 12(ω0/w)2where ω0and w are, respectively, the center frequency and signal bandwidth. In this region, the ambiguities in the received signal phases cannot be re-solved; however, a useful estimate of the differential delay can still be obtained using the received signal envelopes. At low SNR, the lower bound approaches a constant level depending only on the a priori search domain of the unknown delay parameter. In this region, signal observations are subject to envelope ambiguities as well, and are thus essentially useless for the delay estimation.

Original languageEnglish
Pages (from-to)1064-1078
Number of pages15
JournalIEEE Transactions on Acoustics, Speech, and Signal Processing
Volume32
Issue number5
DOIs
StatePublished - Oct 1984

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