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Constraining the output interference-plus-noise power to unity is similarly trivial; for any weight vector w, use instead the weight vector A weight vector optimizing the SINR and satisfying the output noise power constraint of Eq. (136) may be obtained by applying the method of Lagrange multipliers to the problem The augmented function to be optimized may be expressed as Adaptive Degrees of Freedom and Nulling Performance The number of adaptive degrees of freedom, that is, the number N of elements in the adaptive weight vector w = (w1 , w2 , .
The log likelihood surface [Eq. (213)] for quiescent and clutter environments (SNR = 20 dB). Space–time adaptivity distorts the mainlobe seen on the right. formance advantages in terms of additional sampling and resolution [Bliss (55)], [Fishler (57)]. 36. 37. 38. 39. NOTATION 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. CN Re Im a* xT zH tr A x⊗y x y v t w R N M fd PRI or Tr PRF CPI SNR CNR JNR SINR PD PFA Complex N-space Real part Imaginary part Complex conjugation of a Transpose of x Hermitian transpose of z Trace of the square matrix A Tensor (Kronecker) product of x and y Schur–Hadamard product of x and y Steering vector 40.
The conditional distribution of ϒ is CN(0, 1) under H0 and CN((a/|a|)(x )1/2 , 1) under H1 , given the loss factor . Therefore, the GLRT test is equivalent to the test Adaptive Detectors Generalized Likelihood Ratio. Using the generalized likelihood ratio test (GLRT) approach (24) under a multivariate complex Gaussian assumption, Kelly (39, 40) derived the equivalent GLRTs which yields a noncentral F distribution (27) conditioned on the loss factor . This test is comparable to a classical CFAR detector (42).