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DOA Estimation Fundamentals 186 6. Multilayer Structures 6 Multilayer Structures Fig. 6.1.1 Multilayer dielectric slab structure. Higher-order transfer functions of the type of Eq. (5.7.2) can achieve broader reflectionless notches and are used in the design of thin-film antireflection coatings, dielectric mirrors, and optical interference filters [615–677,737–770], and in the design of broadband terminations of transmission lines [805–815]. They are also used in the analysis, synthesis, and simulation of fiber Bragg gratings [771–791], in the design of narrow-band transmission filters for wavelength-division multiplexing (WDM), and in other fiber-optic signal processing systems [801–804]. They are used routinely in making acoustic tube. | 69 CHAPTER 5 DOA Estimation Fundamentals In many practical signal processing problems the objective is to estimate from a collection of noise contaminated measurements a set of constant parameters upon which the underlying true signals depend 21 . Moreover as clearly understood from the previous chapter the accurate estimation of the direction of arrival of all signals transmitted to the adaptive array antenna contributes to the maximization of its performance with respect to recovering the signal of interest and suppressing any present interfering signals. The same problem of determining the DOAs of impinging wavefronts given the set of signals received at an antenna array from multiple emitters arises also in a number of radar sonar electronic surveillance and seismic exploration applications. The resolution properties of antenna arrays have been extensively investigated by many researchers. A significant portion of these efforts has been devoted to the estimation of performance bounds for any given array geometry. The reason is the comparison of the performance of the DOA estimation and beamforming methods to several basic array geometries. The theoretical performance bound studies are concerned mostly with the derivation of the Cramér-Rao lower bound CRLB for DOA estimation variance given an arbitrary array geometry. The CRLB gives the variance lower bound of the unbiased estimator of a parameter or parameter vector 110 . In 114 there are detailed discussions and derivations as well of the CRLB for various scenarios. In the case of the DOA estimation the CRLB provides the metric to compare the arrays in an algorithm-independent way because specific algorithms may exploit special properties of certain geometries and thus performance comparisons using any given algorithm cannot be considered conclusive. In the studies by Messer et al. 115 and Mirkin and Sibul 116 as well CRLB expressions for azimuth and elevation angles estimates of a single source using .
