Wave Field Analysis Device Using Low-Rank Array Response
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Solution Overview
Problem
Existing methods for analyzing wave fields require significant computing effort and storage space, especially when using compact receiving device arrangements for electromagnetic waves with wavelengths in the mm to cm range in inhomogeneous environments, leading to reduced resolution and susceptibility to environmental influences.
Innovation Solution
The method employs a set of 2×a dimensional matrices for the array response, allowing for decorrelated measurements and reducing the complexity of calculations by projecting multidimensional objects, thereby saving computing time and memory while maintaining high analysis accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional array response methods are used to analyze wave fields, then measurement precision can be achieved, but computing effort and storage space requirements increase significantly
Solution Approach 1:
The patent segments the traditional high-dimensional array response into multiple low-rank components that can be processed separately. By decomposing the array response matrix into lower-rank approximations, the computing complexity and storage requirements are significantly reduced while maintaining the essential information for wave field analysis.
Solution Approach 2:
The patent changes the parameter representation from full-rank array responses to low-rank approximations characterized by fewer parameters. This parameter reduction allows the same measurement precision to be achieved with significantly reduced computing effort and storage space by focusing on the dominant modes of the wave field.
2Volume of moving object
If compact receiving device arrangements are used, then device portability is improved, but resolution deteriorates due to spatial constraints
Solution Approach 1:
The patent transitions from spatial dimension exploitation to dimensional decomposition in the signal processing domain. By using low-rank approximation and separating the array response into dominant modes, the system can achieve high resolution with compact physical arrangements, effectively moving the resolution enhancement from physical space to mathematical space.
Solution Approach 2:
The patent changes the approach from relying on physical aperture size to relying on the effective rank of the signal subspace. By identifying and processing only the dominant low-rank components, the system achieves resolution comparable to larger arrays using compact receiving device arrangements.
3Loss of information
If traditional array response storage is used, then complete wave field information is preserved, but memory usage increases significantly
Solution Approach 1:
The patent extracts only the essential low-rank components from the full array response matrix, storing only these dominant modes rather than the complete high-dimensional data. This extraction process retains the critical wave field information while discarding redundant components, significantly reducing memory usage.
Solution Approach 2:
The patent changes the storage parameter from full-rank matrix elements to low-rank approximation parameters. By storing fewer parameters that characterize the dominant signal subspace, the system preserves wave field information completeness while dramatically reducing the quantity of stored data.
Data Source
Figure 1
AI summary
The invention relates to a method for the analysis of a wave field, wherein an autocorrelation matrix calculated from measured values and an array response obtained by way of computation or calibration measurements are used in order to determine to determine the direction of incidence, polarization, phase and/or curvature of one or more wave field fractions by way of distance computation, particularly projection, and to a device for the analysis of a wave field. By using a multi-dimensional array response according to the invention, or by computing the upper performance limits according to the invention on the basis of the eigenvalues of the autocorrelation matrix of measured values, it is possible to save computation time and storage space and as a result to compute better analyses of wave fields more cost effectively and/or on a smaller space.