Signal Detection in Fractional Gaussian Noise

Richard J. Barton, H. Vincent Poor

Research output: Contribution to journalArticlepeer-review

118 Scopus citations


Fractional Gaussian noise provides a useful model for phenomena exhibiting strong long-term dependence, such as 1/f noise in oscillators or interference on some communication channels. The problem of detecting signals in the presence of additive fractional Gaussian noise is considered. To facilitate the study of this problem, several results related to the reproducing kernel Hilbert space of fractional Brownian motion are presented. In particular, this reproducing kernel Hilbert space is completely characterized, and an alternative characterization for the restriction of this class of functions to a compact interval [0, T] is given. Infinite- and finite-interval whitening filters for fractional Brownian motion are also developed. Application of these results to the signal detection problem yields necessary and sufficient conditions for a deterministic or stochastic signal to produce a nonsingular shift when embedded in additive fractional Gaussian noise. Finally, a formula for the likelihood ratio corresponding to any deterministic nonsingular shift is developed.

Original languageEnglish (US)
Pages (from-to)943-959
Number of pages17
JournalIEEE Transactions on Information Theory
Issue number5
StatePublished - Sep 1988
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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