Array Antenna Synthesis Using Hilbert Transform Phase Derivation
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Solution Overview
Problem
Existing methods for designing array antennas require knowledge of the target radiation pattern in both amplitude and phase, which is often not fully known, limiting their effectiveness in synthesizing array factors based on arbitrary target curves specified by designers.
Innovation Solution
The method employs the Least Mean Square (LMS) algorithm to synthesize the array factor of an array antenna by deriving a complex function from a target array factor amplitude mask, using the Hilbert transform to calculate the phase, allowing for optimization and implementation with limited designer supervision.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If traditional synthesis methods (Dolph-Chebyshev, Taylor, Fourier series, Woodward-Lawson) are used, then the radiation pattern can be synthesized with known amplitude and phase information, but the method cannot handle arbitrary target curves where phase information is not initially known
Solution Approach 1:
The system performs self-service by automatically deriving the phase information from the amplitude mask through the Hilbert transform relationship, eliminating the need for external phase specification. The complex target function is constructed internally using the analytic signal property where the phase is obtained as the Hilbert transform of the amplitude's natural logarithm.
Solution Approach 2:
The Hilbert transform acts as an intermediary mathematical operator that converts the amplitude mask into the corresponding phase information. This intermediary process enables the transition from incomplete target specification (amplitude only) to complete target function (amplitude and phase) required by the LMS algorithm.
2Reliability
If the LMS algorithm is applied directly without deriving phase from amplitude, then the algorithm cannot converge to the correct solution, but deriving phase through Hilbert transform enables successful synthesis
Solution Approach 1:
The phase information is derived in advance through the Hilbert transform before the LMS optimization process begins. This preliminary action of constructing the complex target function with both amplitude and phase ensures that the LMS algorithm has complete information needed for reliable convergence, rather than attempting to solve for phase during optimization.
3Manufacturing precision
If complete target radiation pattern (amplitude and phase) is specified, then synthesis accuracy is improved, but the ease of operation is reduced as designers need thorough knowledge of target pattern
Solution Approach 1:
The system performs self-service by automatically deriving the phase information from the amplitude mask through the Hilbert transform relationship, eliminating the need for external phase specification. The complex target function is constructed internally using the analytic signal property where the phase is obtained as the Hilbert transform of the amplitude's natural logarithm.
Data Source
Figure 1A~1B
Figure 1C
Figure 2
AI summary
A method for synthesizing an array factor for an array antenna based on a target shape of an array factor amplitude, comprising: calculating an array factor phase based on the target shape of the array factor amplitude, and calculating array antenna weight coefficients using the Least Mean Square method, where a target function used in the LMS method is a complex function composed by said target shape of the array factor amplitude and the calculated array factor phase, wherein the calculated weight coefficients determine the array factor.