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Extra resources for Classical and Modern Direction-of-Arrival Estimation
The more challenging situation is when arrays with a small number of elements and a small aperture must be used either because of cost considerations or because of physical constraints such as limited space to place the antennas in mobile and airborne applications. In this case, the beamwidth and hence the Rayleigh resolution are relatively large. Also, the larger the beamwidth, the higher the probability of having multiple co-channel emitters fall within a beam. 7 Discussion 27 As discussed earlier, the presence of multiple unresolved signal components introduces bias errors that limit the accuracy of the direction-finding system to some significant fraction of a beamwidth.
121). 131), where in this case we substitute f˙ (θ) = b(θ), f (θ) = p(θ), and their noisy ˜ versions f˜˙ (θ) = b(θ), f˜ (θ) = p˜ (θ). 149). 106). 9 Quadratic Interpolation for the MLE Assume that we have computed values of a two-dimensional function d(·, ·) in the neighborhood of a given point (θ0 , θ1 ). Specifically, we have five values of the function: d(θ0 , θ1 ), d(θ0 ± , θ1 ), and d(θ0 , θ1 ± ) for some step size . We further assume that the peak of this function occurs in this neighborhood and we want to calculate the exact peak location.
Wiley. , 1985. Detection of signals by information theoretic criteria. IEEE Trans. Acoust. Speech Signal Process. ASSP-33 (2), 387–392. , 1988. A general class of lower bounds in parameter estimation. IEEE Trans. Inform. Theory. 34 (2), 338–342. , 1989a. Array shape calibration using sources in unknown locations: a maximum likelihood approach. IEEE Trans. Acoust. Speech Signal Process. 37 (12), 1958–1966. , 1989b. Eigenstructure methods for direction finding with sensor gain and phase uncertainties.