Frequency-domain correlation: an asymptotically optimum approximation of quadratic likelihood ratio detectors

  • Authors:

  • Wenyi Zhang;H. Vincent Poor;Zhi Quan

  • Affiliations:

  • Department of Electronic Engineering and Information Science, University of Science and Technology of China, Hefei, Anhui, China and Qualcomm Corporate Research and Development, Qualcomm Incorpora ...;Department of Electrical Engineering, Princeton University, Princeton University, NJ;Department of Electrical Engineering, University of California, Los Angeles, CA

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

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Abstract

An approximate implementation is formulated and analyzed for the detection of wide-sense stationary Gaussian stochastic signals in white Gaussian noise. For scalar processes, the approximate detector can be realized as the correlation between the periodogram of the observations and an appropriately selected spectral mask, and thus is termed the frequency-domain correlation detector. Through the asymptotic properties of Toeplitz matrices, it is shown that, as the length of the observation interval grows without bound, the frequency-domain correlation detector and the optimum quadratic detector achieve identical asymptotic performance, characterized by the decay rate of the miss probability under the Neyman-Pearson criterion. The frequency-domain correlation detector is further extended to the detection of vector-valued wide-sense stationary Gaussian stochastic signals, and the asymptotic optimality of its performance is established through the asymptotic properties of block Hermitian Toeplitz matrices.