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Two-Channel Matched Subspace Detectors

In: Coherence

Author

Listed:
  • David Ramírez

    (Universidad Carlos III de Madrid)

  • Ignacio Santamaría

    (Universidad de Cantabria)

  • Louis Scharf

    (Colorado State University)

Abstract

This chapter considers the detection of a common subspace signal in two multi-sensor channels. This problem is usually referred to as passive detection. We study second-order detectors where the unknown transmitted signal is modeled as a zero-mean Gaussian and averaged out or marginalized and first-order detectors where the unknown transmitted signal appears in the mean of the observations with no prior distribution assigned to it. The signal subspaces at the two sensor arrays may be known or unknown but with known dimension. In the first case, the resulting detectors are termed matched subspace detectors; in the second case, they are matched direction detectors. We study different noise models ranging from spatially white noises with identical variances to arbitrarily correlated Gaussian noises. For each noise and signal model, the invariances of the hypothesis testing problem and its GLR are established. Maximum likelihood estimation of unknown signal and noise parameters leads to a variety of coherence statistics.

Suggested Citation

  • David Ramírez & Ignacio Santamaría & Louis Scharf, 2022. "Two-Channel Matched Subspace Detectors," Springer Books, in: Coherence, chapter 7, pages 203-234, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-13331-2_7
    DOI: 10.1007/978-3-031-13331-2_7
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