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- Hyberg, Per, 1945-
(författare)
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Antenna array mapping for DOA estimation in radio signal reconnaissance
- 2005
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- To counter radio signal reconnaissance, an efficient way of covert communication is to use subsecond duration burst transmissions in the congested HF band. Against this background, the present thesis treats fast direction finding (DF) using antenna arrays with known response only in a few calibration directions. In such scenarios the known method of array mapping (interpolation) may be used to transform the output data vectors from the existing array onto the corresponding output vectors of another (virtual) array that is mathematically defined and optimally chosen. But in signal reconnaissance the emitters are initially unknown and the mapping matrix must be designed as a compromise over a wide sector of DOAs. This compromise may result in large DOA estimate errors, both deterministic and random. Analyzing, analytically describing, and minimizing these DOA errors, is the main theme of the present thesis. The first part of the thesis analyzes the deterministic mapping errors, the DOA estimate bias, that is caused by dissimilarity between the two array geometries. It is shown that in a typical signal reconnaissance application DOA estimate bias can dominate over DOA estimate variance. Using a Taylor series expansion of the DOA estimator cost function an analytical expression for the bias is derived and a first order zero bias condition is identified. This condition is general, estimator independent, and can be applied to any type of data pre-processing. A design algorithm for the mapping matrix is thereafter presented that notably reduces mapped DOA estimate bias. A special version is also given with the additional property of reducing the higher order Taylor terms and thus the residual bias. Simulations demonstrate a bias reduction factor exceeding 100 in some scenarios. A version based on signal subspace mapping rather than array manifold mapping is also given. This version is of large practical interest since the mapping matrix can be designed directly from calibration data. In the second part of the thesis the derived bias minimization theory is extended into Mean Square Error (MSE) minimization, i.e. measurement noise is introduced. Expressions for DOA error variance and DOA MSE under general pre-processing are derived, and a design algorithm for the mapping matrix is formulated by which mapped DOA estimate MSE can be minimized. Simulations demonstrate improved robustness and performance for this algorithm, especially in low SNR scenarios. In the third and final part of the thesis the theoretical results are supported by experimental data. For an 8 element circular array mapped onto a virtual ULA across a 600 sector it is shown that the mapped DOA estimate errors can be suppressed down to the Cramér-Rao level.
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| 2. |
- Hyberg, Per, et al.
(författare)
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Array interpolation and DOA MSE reduction
- 2005
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Ingår i: IEEE Transactions on Signal Processing. - : IEEE Signal Processing Society. - 1053-587X .- 1941-0476. ; 53:12, s. 4464-4471
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Tidskriftsartikel (refereegranskat)abstract
- Interpolation or mapping of data from a given real array to data from a virtual array of more suitable geometry is well known in array signal processing. This operation allows arrays of any geometry to be used with fast direction-of-arrival (DOA) estimators designed for linear arrays. In an earlier companion paper [21], a first-order condition for zero DOA bias under such mapping was derived and was also used to construct a design algorithm for the mapping matrix that minimized the DOA estimate bias. This bias-minimizing theory is now extended to minimize not only bias, but also to consider finite sample effects due to noise and reduce the DOA mean-square error (MSE). An analytical first-order expression for mapped DOA MSE is derived, and a design algorithm for the transformation matrix that minimizes this MSE is proposed. Generally, DOA MSE is not reduced by minimizing the size of the mapping errors but instead by rotating these errors and the associated noise subspace into optimal directions relative to a certain gradient of the DOA estimator criterion function. The analytical MSE expression and the design algorithm are supported by simulations that show not only conspicuous MSE,improvements in relevant scenarios, but also a more robust preprocessing for low signal-to-noise ratios (SNRs) as compared with the pure bias-minimizing design developed in the previous paper.
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| 3. |
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| 4. |
- Hyberg, Per, et al.
(författare)
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Array Mapping : Optimal Transformation Matrix Design
- 2002
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Ingår i: Proceedings IEEE International Conference on Acoustics, Speech, and Signal Processing. - : IEEE. ; , s. 2905-2908
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Konferensbidrag (refereegranskat)abstract
- Mapping of the data output vector from an existing antenna array onto the data vector of an imaginary array of more suitable configuration is well known in array signal processing. By mapping onto an array manifold of lower dimension or uniform structure for example., processing speed can be improved. Conditions for the retaining of DOA error variance under such mapping have been formulated by several authors but the equally important systematic mapping errors, the bias, has been less treated to date. This paper uses a geometrical interpretation of a Taylor expansion of the DOA estimator cost function to derive an alternative design of the mapping matrix that almost completely removes the bias. The key feature of the proposed design is that it takes the orthogonality between the manifold mapping errors and certain gradients of the estimator cost function into account.
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