Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
Uniformly most powerful cyclic permutation invariant detection for discrete-time signals
ICASSP '01 Proceedings of the Acoustics, Speech, and Signal Processing, 2001. on IEEE International Conference - Volume 05
Optimal invariant detection of a sinusoid with unknown parameters
IEEE Transactions on Signal Processing
Spatial diversity in radars-models and detection performance
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
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The Uniformly Most Powerful (UMP) test, which is one with the highest probability of detection over all unknown parameters in a composite hypothesis test, does not exist in the most practical problems. It is common to derive the suboptimal Generalize Likelihood Ratio (GLR) detector, that is shown to perform close to optimal invariant tests in some problems. The Uniformly Most Powerful Invariant (UMPI) test is the one that is used for the performance evaluation of the GLR detector. However, the GLR or UMPI detectors are not simply derivable in many problems. In this paper, we suggest that the problem be transformed to a new space. We derive the conditions of the transformation, such that the detectors for the original problem and the transformed ones become equivalent. In addition, using this method, we discuss two practical problems (one in radar and other in communication) and derive the GLR detectors. We also find the UMPI detectors in these problems to verify the performance of the derived GLR detector.