Expanded Mathematical Treatment for "Spectral Bias in Adaptive Beamforming with Narrowband Interference''
spetral bias, adaptive beamforming, narrowband interference
This technical note presents extended versions of some mathematical derivations found in the paper Spectral Bias in Adaptive Beamforming with Narrowband Interference which is under review for publication in IEEE Signal Processing Letters. Though the SP Letters paper is self contained and complete, this note provides intermediate steps for some of the equation derivations to assist the interested readers who would like to re-create the results.
Original Publication Citation
Brian D. Jeffs and Karly F. Warnick. "Expanded Mathematical Treatment for 'Spectral Bias in Adaptive Beamforming with Narrowband Interference'," IEEE Signal Processing Letters, 2008.
BYU ScholarsArchive Citation
Jeffs, Brian D. and Warnick, Karl F., "Expanded Mathematical Treatment for "Spectral Bias in Adaptive Beamforming with Narrowband Interference''" (2008). Faculty Publications. 1326.
Ira A. Fulton College of Engineering and Technology
Electrical and Computer Engineering
© 2008 Brian D. Jeffs and Karl F. Warnick
Copyright Use Information
This work was funded by National Science Foundation under grant number AST - 0352705. This demonstration software shows how an adaptive beamformers (LCMV and subspace projection) in the presence of narrowband interference, cause a "spectral scooping" null in the PSD estimate for signal and noise. This code supports the results found in the paper "Spectral Bias in Adaptive Beamforming with Narrowband Interference," submitted to IEEE SP Letters. It is shown in that paper that adaptive canceling arrays which track interference by regular updates of the beamformer weights can introduce a spectral null at the excised interference frequency. This PSD estimation bias effect we call 'spectral scooping' is most prominent for narrowband interference. Scooping is problematic in radio astronomy where bias in either the weak signal or noise floor spectra can corrupt the observation. The mathematical basis for scooping is derived, and an algorithm to eliminate it is proposed. Both simulated and real data experiments demonstrate the effectiveness of the proposed algorithm.