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And equality holds if and only if w is a scalar multiple of v. For the problem of optimizing the SINR, take w, v def ≡ wH Rv; then SINR = |a|2 | w, R−1 v |2 / w, w . Thus the SINR is maximized if and only if for an arbitrary complex constant α. The maximum SINR is Like Eq. (95), Eq. (103) is called the adaptive filter equation, and the components of w are called adaptive weights. Maximum Likelihood Estimate of Target Amplitude The adaptive filter equation is also a consequence of the maximum likelihood estimate of the target amplitude.

91) is viewed as an estimation loss due to the unknown covariance. This estimation loss is comparable to the CFAR loss encountered in nonadaptive radars (14–53). Because we do not have an optimality criterion to drive our choice of adaptive detector, the selection is done with the following goals in mind: Low Estimation Loss The estimation loss, compared to the optimum known covariance detection performance, should be small, say a few decibels or less. CFAR Property The detection performance should be independent of the interference and noise scenario, that is, it should be independent of the underlying 22 Radar, Adaptive covariance matrix R.

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. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. Target steering vector Adaptive weight vector Interference-plus-noise covariance matrix Number of adaptive degrees of freedom or antenna elements Number of radar pulses Doppler frequency Pulse repetition interval Pulse repetition frequency Coherent processing interval Signal-to-noise ratio Clutter-to-noise ratio Jammer-to-noise ratio Signal-to-interference-plus-noise ratio Probability of detection Probability of false alarm BIBLIOGRAPHY 1.

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