Phased Array Nulling via Eigenvalue Decomposition
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Solution Overview
Problem
Conventional methods for placing nulls in array antennas, particularly for large arrays, suffer from poor performance, high computational demands, or infeasibility due to iterative approaches, and deterministic algorithms require excessive computing resources.
Innovation Solution
A closed-form algorithm that uses eigenvalue decomposition of an N×N matrix to place multiple nulls efficiently, allowing for arbitrary depth and proximity without degrading performance, suitable for both signal reception and transmission.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional iterative nulling methods are used, then nulls can be placed in desired directions, but the nulling performance is poor and convergence is slow or fails
Solution Approach 1:
The patent replaces iterative numerical optimization methods with a closed-form deterministic algorithm based on eigenvalue decomposition. This substitution eliminates the iterative convergence process entirely, providing direct computation of optimal nulling weights that achieve deep nulls in a single calculation step, thereby resolving both the poor performance and slow convergence issues of iterative methods.
Solution Approach 2:
The patent changes the computational approach from iterative parameter adjustment to direct eigenvalue-based parameter calculation. By formulating the nulling problem as an eigenvalue decomposition task, the algorithm directly computes the optimal weight parameters without iterative refinement, achieving both fast execution and reliable deep nulling performance.
2Reliability
If deterministic closed-form nulling algorithms are used, then optimized nulling performance is achieved, but computational resources required are excessive for large arrays
Solution Approach 1:
The patent segments the computational task by formulating the nulling problem in terms of eigenvalue decomposition of a matrix constructed from steering vectors. This segmentation allows the algorithm to compute nulling weights for multiple nulls simultaneously through a single eigenvalue decomposition, rather than requiring separate computations for each null, thereby reducing overall computational resources while maintaining optimized nulling performance.
Solution Approach 2:
The patent creates a universal algorithm that handles multiple nulls, arbitrary null depths, and various array configurations through a single eigenvalue decomposition framework. This multi-functional approach eliminates the need for separate specialized algorithms for different nulling scenarios, reducing computational overhead while achieving optimized performance across diverse applications.
3Adaptability or versatility
If multiple nulls are placed close together or near main beam, then coverage of interfering signals is improved, but conventional methods produce degraded nulls or fail to converge
Solution Approach 1:
The patent replaces iterative optimization with closed-form eigenvalue decomposition, which provides a direct mathematical solution that remains stable regardless of null proximity or location near the main beam. This substitution eliminates the convergence failures and null degradation that plague iterative methods when dealing with challenging null configurations, ensuring reliable deep nulling performance across all placement scenarios.
Data Source
AI summary
Systems and method for placing nulls at desired locations within a beam pattern of a phased array antenna are provided. According to embodiments of the present disclosure, a weight vector solution for controlling operating parameters of the M elements of the array antenna such that a beam pattern incorporating one or more desired nulls is obtained by performing operations on an N×N matrix, where N is equal to a number of vectors used to describe the nulls. The nulls can be placed at arbitrary locations within the beam pattern, and can be formed with arbitrary depths.