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By Simon Haykin

This collaborative paintings offers the result of over 20 years of pioneering examine by means of Professor Simon Haykin and his colleagues, facing using adaptive radar sign processing to account for the nonstationary nature of our surroundings. those effects have profound implications for defense-related sign processing and distant sensing. References are supplied in each one bankruptcy guiding the reader to the unique examine on which this ebook is predicated.

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8W. A larger boundary results in a larger mismatch of the power levels between the known signal components. Note the detail of the composite spectrum despite the larger spectral window. 7 F-Test for the Line Components 35 features that are of interest. Thomson [39] recommends that W be between 1/N and 20/N, with a time–bandwidth product of 4 or 5 being a common starting point. 3 are not expected to be good estimates, since we know that line components exist and that the spectrum estimation techniques developed have implicitly assumed none.

80], and the other, ||y − Axˆ ||2, due to residual errors. Each of these 36 Chapter 2 Angle-of-Arrival Estimation in the Presence of Multipath components has associated with it a number of degrees of freedom, ν1 and ν2, respectively. For K complex data points, the total number of degrees of freedom is ν1 + ν2 = 2 K It turns out now that, provided the errors are independent and zero-mean Gaussian random variables, each of the two variance components follows a χ2-distribution with ν1 or ν2 degrees of freedom, respectively.

D2 df = . . = λk k =0 K −1 N −1 N −1 ∑ ∑ ∑ υ(nk ) υ(mk )e j 2π(n− m)( f − f ) 2 1 sin 2 π ( n − m ) W π (n − m ) k =0 n=0 m=0 N −1 K −1 f1 +W 2 λ k υ(nk ) e j 2 πn( f2 − f1 ) cdf = . . = f1 −W n=0 k =0 N −1 K −1 f1 +W 2 c1df = . . = λ k υ(nk ) x ( n ) e − j 2 πnf1 f1 −W n=0 k =0 K −1 N −1 N −1 f1 +W c2 df = . . 47). We just have to set f0 = f1. 60) tests the existence of two lines only. If again, we let f1 vary over the entire frequency range, f2 will vary in (f1 − W, f1 + W). As we can see from Figs.

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