Sparse Uniform Array Radar Angle-Finding Without Blind Spots
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Solution Overview
Problem
Radar systems using sparse uniform arrays face computational blind spots and inefficiencies in angle estimation, particularly with unitary ESPRIT algorithms, leading to potential safety issues in automotive applications.
Innovation Solution
A radar system with a processor and sparse uniform antenna arrays that determine signal subspaces and solve invariance equations to estimate angular phases, using a modified angle-finding process that avoids blind spots and reduces computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If sparse uniform arrays are used to reduce the number of antenna elements, then cost and device complexity are reduced, but blind spots appear in angle estimation
Solution Approach 1:
The patent replaces traditional mechanical signal processing methods with a mathematical substitution approach. By substituting the complex covariance matrix with a simplified covariance matrix and replacing standard ESPRIT algorithms with a modified version that uses real-valued computations, the system achieves accurate angle estimation with sparse arrays without requiring dense antenna configurations. This mathematical substitution eliminates blind spots while maintaining the sparse array structure.
Solution Approach 2:
The patent changes key parameters in the angle estimation process by modifying the invariance equation formulation and using real-valued unitary transformation matrices instead of complex ones. These parameter changes in the computational domain allow the system to extract accurate angular information from sparse array data, resolving the blind spot issue without increasing physical antenna density.
2Measurement precision
If standard ESPRIT or unitary ESPRIT algorithms are used with sparse arrays, then angle estimation can be performed, but computational complexity increases and blind spots occur
Solution Approach 1:
The patent extracts and eliminates the computationally intensive components from standard ESPRIT algorithms. By removing the need for complex eigenvalue decomposition and using a simplified covariance matrix approach, the system achieves angle estimation with reduced computational burden. The extraction of only the essential mathematical operations needed for angle estimation eliminates unnecessary complexity while maintaining precision.
Solution Approach 2:
The patent employs computationally efficient approximations that sacrifice minimal accuracy for significant gains in processing speed. The simplified covariance matrix and real-valued computations act as computationally 'cheap' alternatives to the full complex ESPRIT algorithm, providing sufficient angle estimation precision without the high computational cost of traditional methods.
3Measurement precision
If inter-vector sensor spacing exceeds half wavelength to achieve larger aperture, then angular resolution improves, but cyclic phase ambiguities and blind spots increase
Solution Approach 1:
The patent introduces a real-valued unitary transformation matrix as an intermediary that bridges the gap between sparse array measurements and accurate angle estimation. This intermediary transformation enables the system to handle large inter-element spacing without encountering phase ambiguities, as the real-valued computation framework naturally resolves the cyclic phase issues that plague traditional complex-valued approaches.
Data Source
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AI summary
This document describes techniques and systems of a radar system with an angle-finding process for sparse uniform arrays. The described radar system includes a processor and an antenna that can receive electromagnetic energy reflected by objects in the surrounding environment. The antenna includes a one-dimensional (ID) or two-dimensional (2D) sparse array. The processor can determine, using the received electromagnetic energy, a signal subspace associated with the objects that includes an invariance equation. Using an estimated solution to the invariance equation, the processor determines a solution to the invariance equation. The solution to the invariance equation is used to determine angular phases associated with the objects. The processor can then determine, using the angular phases, angles associated with the objects. In this way, the described angle-finding process enables the radar system with a sparse array to efficiently determine angles associated with objects without blind spots.