chapter  6
48 Pages

Source Estimation

The temporal signals radiated by sources are separated on the principle of non-overlapping or partially overlapping temporal spectral characteristics of the signals. A perfect separation is possible only when the signal spectra are non-overlapping. The spatio-temporal signals possess an additional degree of variability, namely, the spatial spectrum. The differences in the spatial spectra can be used, in addition to the differences in the temporal spectra, for the purpose of signal separation. The signals coming from widely different directions will have non-overlapping spatial spectra and therefore they can be separated using an array of sensors. However, when the signal sources are quite close, perfect separation is not possible. There will be some cross-talk. We shall evaluate the Wiener fi lter, which was derived in Chapter 3, from the point of cross-talk power in relation to the total signal power. Suppression of unwanted signal or interference is achieved by placing a null or a collection of nulls in the spatial frequency band occupied by the interference. The effectiveness of nulls is enhanced when additional constraints are placed on the fi lter; for example, the fi lter response is unity in the direction of useful signal. This leads to the well-known Capon fi lter, which is also known as the minimum variance fi lter. It is found that the Capon fi lter is quite effective when the signal and the interference sources are highly directional. The fi lter will automatically place a null wherever there is a strong interference. Finally, when the direction of interference is known a priori, it is possible to devise a fi lter that will place a sharp null at the spatial frequency corresponding to the direction of arrival (DOA) of the interference. The null can be steered to any desired position, depending upon how the interference is changing its direction. Thus, null steering can be effectively used to suppress slowly varying interference. In Section 6.4, we take up the problem of source estimation in space-time domain leading to wideband adaptive beamformation, and in Section 6.5 we consider frequency invariant (FI) beamformation often used in the estimation of speech signal.