Adaptive and Robust Beamforming
Academic Press Library in Signal Processing
Adaptive beamforming is a versatile approach to detect and estimate the signal-of-interest (SOI) at the output of sensor array using data adaptive spatial or spatio-temporal filtering and interference cancellation    . Being a very central problem of array processing (see  ), adaptive beamforming has found numerous application to radar [5, 6] , sonar , speech processing , radio astronomy [9,10], biomedicine [11, 12] , wireless communications    , cognitive
... tions  , and other fields. The connection of adaptive beamforming to adaptive filtering is emphasized in  . The major differences, however, come from the fact that adaptive filtering is based on temporal processing of a signal, while adaptive beamforming stresses on spatial processing. The latter indicates also that the signal is sampled in space, i.e., the signal is measured/observed by an array of spatially distributed antenna elements/sensors. Electronic beamforming design problem consists of computing optimal (in some sense that will be specified) complex beamforming weights for sensor measurements of the signal. If such complex beamforming weights are optimized based on the input/output array data/measurements, the corresponding beamforming is called adaptive to distinguish it from the conventional beamforming where the beamforming weights do not depend on input/output array data. The traditional approach to the design of adaptive beamforming is to maximize the beamformer output signal-to-interference-plus-noise ratio (SINR) assuming that there is no SOI component in the beamforming training data [2, 3] . Although such SOI-free data assumption may be relevant to certain radar applications, in typical practical applications, the beamforming training snapshots also include the SOI [17, 18] . In the latter case, the SINR performance of adaptive beamforming can severely degrade even in the presence of small signal steering vector errors/mismatches, because the SOI component in the beamformer training data can be mistakenly interpreted by the adaptive beamforming algorithm as an interferer and, consequently, it can be suppressed rather than being protected. The steering vector errors are, however, very common in practice and can be caused by a number of reasons such as signal look direction/pointing errors; array calibration imperfections; non-linearities in amplifiers, A/D converters, modulators and other hardware; distorted antenna shape; Dedicated to the memory of Professor Alex B. Gershman. Academic Press Library in Signal Processing. http://dx.