Neural Computation
Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
Proceedings of the 1998 conference on Advances in neural information processing systems II
Sparse bayesian learning and the relevance vector machine
The Journal of Machine Learning Research
Bayesian methods for finding sparse representations
Bayesian methods for finding sparse representations
Review of user parameter-free robust adaptive beamforming algorithms
Digital Signal Processing
Cognitive spatial degrees of freedom estimation via compressive sensing
Proceedings of the 2010 ACM workshop on Cognitive radio networks
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Beamformers are spatial filters that pass source signals in particular focused locations while suppressing interference from elsewhere. The widely-used minimum variance adaptive beamformer (MVAB) creates such filters using a sample covariance estimate; however, the quality of this estimate deteriorates when the sources are correlated or the number of samples n is small. Herein, a modified beamformer is derived that replaces this problematic sample covariance with a robust maximum likelihood estimate obtained using the relevance vector machine (RVM), a Bayesian method for learning sparse models from possibly overcomplete feature sets. We prove that this substitution has the natural ability to remove the undesirable effects of correlations or limited data. When n becomes large and assuming uncorrelated sources, this method reduces to the exact MVAB. Simulations using direction-of-arrival data support these conclusions. Additionally, RVMs can potentially enhance a variety of traditional signal processing methods that rely on robust sample covariance estimates.