Robust Adaptive Beamforming

A common problem in spatial signal processing is to locate signal source positions by using an array of passive sensors (cf. the problem of finding frequencies in a temporal signal). This problem can be solved by constructing spatial filters, which try to pass the signal coming from a certain spatial position while surpressing the signals and noise from all other positions. This type of approach is commonly known as beamforming. The positions for which the filter output is "large" are then likely to contain sources. Similarly, beamforming can also be used to transmit signals in a directed manner.

Data dependent beamformers, or adaptive beamformers, (where the spatial filter depends on the received data) have attracted lots of attention due to their potential to adaptively suppress interference and noise in an optimal manner. In particular, the minimum variance beamformer, or the standard Capon beamformer (SCB), appears to be fundamental in the sense that it can be derived from several different starting points. However, the interference rejection capabilities of the SCB can in some cases lead to cancellation of the signal of interest. This happens, e.g., when the array is not perfectly calibrated and when the covariance matrix is estimated from data with the desired signal present. The latter is sometimes unavoidable, e.g., in spatial spectral estimation. In such a case, also a limited number of data snapshots or signal correlated interferences can lead to severe signal cancellation.

Our group performs research on how to "robustify" beamformers against errors in the array calibration or in the data covariance matrix. Some contributions include the Robust Capon Beamformer [1], [2], [5], and some approaches to automatic robust adaptive beamforming (i.e., without the selection of any user parameters) [4].

Selected Publications

H He, P Stoica and J Li, Wideband MIMO systems: signal design for transmit beampattern synthesis. IEEE Trans Signal Process, vol 59, 618-628, 2011.
L Du, L Xu, J Li, B Guo, P Stoica, C Bahr and L Cattafesta, Covariance-based approaches to aeroacoustic noise source analysis. J Acoust Soc of America, vol 128, 2877-2887, 2010.

1. Fully automatic computation of diagonal loading levels for robust adaptive beamforming. Lin Du, Jian Li, and Peter Stoica. In IEEE Transactions on Aerospace and Electronic Systems, volume 46, number 1, pp 449-458, 2010. (DOI).
2. Review of user parameter-free robust adaptive beamforming algorithms. Lin Du, Tarik Yardibi, Jian Li, and Peter Stoica. In Digital signal processing (Print), volume 19, number 4, pp 567-582, 2009. (DOI).
3. Automatic robust adaptive beamforming via ridge regression. Yngve Selén, Richard Abrahamsson, and Peter Stoica. In Signal Processing, volume 88, number 1, pp 33-49, 2008. (DOI).
4. Enhanced covariance matrix estimators in adaptive beamforming. Richard Abrahamsson, Yngve Selén, and Peter Stoica. In 2007 IEEE International Conference on Acoustics, Speech, and Signal Processing, Vol II, Pts 1-3, volume 2 of International Conference on Acoustics Speech and Signal Processing (ICASSP), pp 969-972, 2007.
5. On robust Capon beamforming and diagonal loading. J. Li, P. Stoica, and Z. Wang. In IEEE Trans Signal Process, volume 51, number 1702-1715, 2003.