| 1. |
- Lundberg, Magnus, et al.
(författare)
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Multi-rank Capon beamforming
- 2004
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Ingår i: Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers. - : IEEE Communications Society. - 0780386221 ; , s. 2335-2339
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Konferensbidrag (refereegranskat)abstract
- This paper presents a multi-rank extension of the Capon beamformer. By expanding the rank of the beamformer it is possible to fully exploit situations in which signals lie in multi-dimensional subspaces, as opposed to the standard point source case. Such situations are commonly caused by array mismatches and scattered or distributed sources. The extension involves the design of a constraint matrix which can be interpreted in terms of signal power. Three possible choices for the constraint are proposed. These correspond to one non-adaptive choice, one choice that is dependent on the signal covariance structure only, and one choice that is both signal and data adaptive. Simulation examples are presented that show the promise of the idea of multi-rank Capon beamforming. Especially the signal- and data adaptive constraint appears very promising.
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| 2. |
- Pezeshki, Ali, et al.
(författare)
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Eigenvalue beamforming using a multirank MVDR beamformer and subspace selection
- 2008
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Ingår i: IEEE Transactions on Signal Processing. - 1053-587X .- 1941-0476. ; 56:5, s. 1954-1967
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Tidskriftsartikel (refereegranskat)abstract
- We derive eigenvalue beamformers to resolve an unknown signal of interest whose spatial signature lies in a known subspace, but whose orientation in that subspace is otherwise unknown. The unknown orientation may be fixed, in which case the signal covariance is rank-1, or it may be random, in which case the signal covariance is multirank. We present a systematic treatment of such signal models and explain their relevance for modeling signal uncertainties. We then present a multirank generalization of the MVDR beamformer. The idea is to minimize the power at the output of a matrix beamformer, while enforcing a data dependent distortionless constraint in the signal subspace, which we design based on the type of signal we wish to resolve. We show that the eigenvalues of an error covariance matrix are fundamental for resolving signals of interest. Signals with rank-1 covariances are resolved by the largest eigenvalues of the error covariance, while signals with multirank covariances are resolved by the smallest eigenvalues. Thus, the beamformers we design are eigenvalue beamformers, which extract signal information from eigenmodes of an error covariance. We address the tradeoff between angular resolution of eigenvalue beamformers and the fraction of the signal power they capture.
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| 3. |
- Pezeshki, Ali, et al.
(författare)
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Empirical canonical correlation analysis in subspaces
- 2004
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Ingår i: Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers. - : IEEE Communications Society. - 0780386221 ; , s. 994-997
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Konferensbidrag (refereegranskat)abstract
- This paper addresses canonical correlation analysis of two-channel data, when channel covariances are estimated from a limited number of samples, and are not necessarily full-rank. We show that empirical canonical correlations measure the cosines of the principal angles between the row spaces of the data matrices for the two channels. When the number of samples is smaller than the sum of the ranks of the two data matrices, some of the empirical canonical correlations become one, regardless of the two-channel model that generates the samples. In such cases, the empirical canonical correlations may not be used as estimates of correlation between random variables.
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| 4. |
- Scharf, Louis L., et al.
(författare)
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Multi-rank adaptive beamforming
- 2005
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Ingår i: 2005 IEEE/SP 13th Workshop on Statistical Signal Processing. - Piscataway, NJ : IEEE Communications Society. - 0780394046 ; , s. 307-312
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Konferensbidrag (refereegranskat)abstract
- This paper presents a multi-rank generalization of the Capon beamformer to accommodate model mismatch in situations where the unknown signal of interest lies in a multidimensional subspace. By expanding the beamforming subspace robustness (or diversity) is achieved at the expense of resolution. The generalization involves solving a quadratically-constrained quadratic minimization problem, and designing a constraint matrix. Three strategies for designing this constraint matrix are discussed. Simulation examples are presented to demonstrate the performance of the multi-rank Capon beamformer.
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