Hermetic Transform for Phased-Array Beamforming
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Solution Overview
Problem
Conventional beamforming methods struggle to achieve narrow main-lobes and effective noise rejection in directional reception, especially with arrays smaller than half-wavelength spacing, leading to reduced discrimination of signals from desired directions and increased interference from other directions.
Innovation Solution
The Hermetic Transform, a decomposable linear transformation combining a matched filter matrix and a weight matrix, is used to improve beamforming by designing a weight matrix that minimizes sidelobe levels and mainlobe width, while a noise conditioning matrix is applied to reduce internal noise impact, allowing for the creation of more nulls in the spatial transfer function.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If conventional beamforming methods are used, then the system is simpler to implement, but the main-lobe width is wider and noise rejection is poorer
Solution Approach 1:
The patent transforms the beamforming problem by changing the mathematical parameters and transformation approach. Instead of conventional beamforming parameters, it uses a linear transformation matrix with specific structural constraints (first column as matched filter, remaining columns as orthogonal vectors). This parameter transformation enables narrower main-lobes while maintaining implementation feasibility through structured matrix design.
Solution Approach 2:
The transformation matrix is segmented into distinct functional components: the first column represents the matched filter for the desired signal direction, while the remaining columns represent orthogonal vectors that form nulls in other directions. This segmentation allows independent optimization of main-lobe characteristics and sidelobe suppression, achieving narrow main-lobes with effective noise rejection.
2Length of stationary object
If arrays with spacing less than half-wavelength are used, then the physical size is reduced, but the discrimination of signals from desired directions is reduced
Solution Approach 1:
The patent changes the mathematical parameters of the array response through a linear transformation that compensates for the reduced physical aperture. By designing the transformation matrix with specific orthogonality constraints and matched filter properties, it achieves direction discrimination performance equivalent to larger arrays, effectively decoupling discrimination capability from physical size constraints.
Solution Approach 2:
The transformation matrix creates a mathematical copy or representation of the ideal beamforming response that would be achieved with larger arrays. Through the linear transformation with orthogonal columns, it reproduces the directional discrimination characteristics of half-wavelength spaced arrays even when physical elements are closer together, effectively copying the performance characteristics without the physical constraints.
3Object-affected harmful factors
If more nulls are placed in the spatial transfer function, then noise and interference rejection is improved, but the system complexity increases
Solution Approach 1:
The transformation matrix columns are segmented to represent different null directions independently. Each column beyond the first can be designed to create a null in a specific interference direction while maintaining orthogonality to other columns. This segmentation allows systematic placement of multiple nulls without requiring complex iterative optimization, as each column can be designed independently with simple orthogonality constraints.
Solution Approach 2:
The linear transformation matrix serves multiple functions simultaneously: it creates the matched filter for the desired signal, places nulls in multiple interference directions, and maintains orthogonality across all transformation vectors. This multi-functionality is achieved through the universal structure of the matrix where each column contributes to both signal enhancement and interference rejection, reducing overall system complexity despite the multiple objectives.
Data Source
AI summary
Systems and methods are described using a Hermetic Transform, as well as related transforms, for applications such as directional reception and/or transmit of signals using phased-array devices and systems. The systems and methods an include identifying a direction of arrival for a mobile communicating device. The systems and methods also include the use of a noise conditioning matrix.