Optimal Correlators and Waveforms for Mismatched Detection

Research output: Contribution to journalArticlepeer-review


We consider the classical Neymann–Pearson hypothesis testing problem of signal detection, where under the null hypothesis (H0), the received signal is white Gaussian noise, and under the alternative hypothesis (H1), the received signal includes also an additional non–Gaussian random signal, which in turn can be viewed as a deterministic waveform plus zero–mean, non-Gaussian noise. However, instead of the classical likelihood ratio test detector, which might be difficult to implement, in general, we impose a (mismatched) correlation detector, which is relatively easy to implement, and we characterize the optimal correlator weights in the sense of the best trade-off between the false-alarm error exponent and the missed-detection error exponent. Those optimal correlator weights depend (non-linearly, in general) on the underlying deterministic waveform under H1. We then assume that the deterministic waveform may also be free to be optimized (subject to a power constraint), jointly with the correlator, and show that both the optimal waveform and the optimal correlator weights may take on values in a small finite set of typically no more than two to four levels, depending on the distribution of the non-Gaussian noise component. Finally, we outline an extension of the scope to a wider class of detectors that are based on linear combinations of the correlation and the energy of the received signal.

Original languageEnglish
Pages (from-to)8342-8354
Number of pages13
JournalIEEE Transactions on Information Theory
Issue number12
StatePublished - 1 Dec 2022


  • Correlation
  • Correlators
  • Detectors
  • Probability density function
  • Signal detection
  • Testing
  • Uncertainty
  • correlation–detection
  • error exponent
  • hypothesis testing
  • signal detection

All Science Journal Classification (ASJC) codes

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


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