Robust Formulation
It is important to incorporate robustness into broadband beamformer designs for them to work in the practical environment. This is because errors and mismatches between the practical environment and theoretical model can be detrimental to the operation of
- PDF / 1,414,787 Bytes
- 25 Pages / 439.37 x 666.142 pts Page_size
- 97 Downloads / 180 Views
Robust Formulation
Abstract It is important to incorporate robustness into broadband beamformer designs for them to work in the practical environment. This is because errors and mismatches between the practical environment and theoretical model can be detrimental to the operation of beamformers. This chapter discusses a robust beamformer design formulation by modelling practical errors and mismatches as random variables. The beamformers are then optimised based on the mean of these stochastic models, resulting in robust beamformers. Keywords Robust beamformer · Stochastic error models
5.1 Introduction In practice, it is impossible to have a completely error-free model for designing a beamformer. Hence, robustness to such errors is a major consideration in the design of a practical beamformer. Beamformers, especially super-directive beamformers and small array beamformers, are known to be very sensitive to slight errors and deviation between the presumed and actual models [1–5]. Any violation of the underlying assumptions can significantly degrade their performance. Causes for such violations can be due to mismatches between the presumed and actual array element characteristics [6], imperfect array calibration [7], error in the sensor positions [8], electronic self-noise, medium inhomogeneity [9], nearfield–farfield mismatch [10], mutual coupling between sensors [11], local scattering and source spreading [12–15], to name a few. One such example is shown in Sects. 3.6 and 4.7 where the nearfield-only beamformers and farfield-only beamformers are evaluated for the value of r that is outside their design specifications. The significance of these errors depends heavily on the type of sensor array used as well as the area of application. For example, the effect of mutual coupling between sensors is often negligible in acoustic beamforming but not in radio antenna beamforming [16]. A major issue in acoustic broadband beamformers is that at low frequencies, they behave like super-directive or small array beamformers. In these beamformers, the element spacings are normally small relative to the operating signal wavelength © The Author(s) 2017 C.C. Lai et al., A Study into the Design of Steerable Microphone Arrays, SpringerBriefs in Signal Processing, DOI 10.1007/978-981-10-1691-2_5
77
78
5 Robust Formulation
[1–5]. As a result, the array aperture size is not sufficient to provide good signal directivity and every array element essentially “sees” the same signal sample. In order to achieve high directivity in such beamformers, the dynamic range of the beamformer weights needs to be very large. Although these large weights can increase the beamformer’s gain theoretically, which is desired, it causes the beamformers to be extremely sensitive to errors and perturbations which exist in practice. The most common method to introduce robustness to such errors is to include a white noise gain (WNG) constraint in beamformer weights design. This is equivalent to the diagonal loading method if the designs are expressed in matri
Data Loading...
