Matrix Completion for Sparse Automotive Radar Arrays
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Solution Overview
Problem
Automotive radars face challenges in achieving high angle discrimination and small package size while maintaining low cost, particularly with virtual sparse linear arrays (SLAs) that introduce grating lobes and angle ambiguity due to irregular element spacing, and existing methods like compressive sensing suffer from off-grid issues and SNR loss.
Innovation Solution
The method employs matrix completion techniques to recover missing elements in the Hankel matrix of virtual ULAs, allowing for high-resolution angle finding without grating lobes and SNR loss, by constructing a Hankel matrix from subarrays and using nuclear-norm minimization to ensure identifiable matrix completion.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If virtual sparse linear arrays (SLAs) are used to reduce hardware cost and package size, then the number of antennas and cost are reduced, but grating lobes are introduced causing angle ambiguity
Solution Approach 1:
The patent introduces matrix completion techniques as an intermediary method to recover the full array response from sparse measurements. By constructing a Hankel matrix from the limited SLA measurements and completing it using nuclear-norm minimization, the system recovers the virtual ULA response without grating lobes, thus maintaining angle discrimination precision while using fewer antennas
Solution Approach 2:
The patent replaces the physical mechanical system of densely packed antennas with a mathematical processing system. Instead of physically deploying a full ULA to avoid grating lobes, the system uses matrix completion algorithms to synthesize the full array response from sparse measurements, substituting physical density with computational reconstruction
2Device complexity
If compressive sensing is used for angle finding in SLAs, then angle finding can be performed with reduced antennas, but off-grid issues and SNR loss occur
Solution Approach 1:
The patent substitutes compressive sensing with matrix completion techniques. Instead of using CS methods that discretize the field of view and suffer from off-grid issues, the system constructs a continuous Hankel matrix model and completes it using nuclear-norm minimization, providing a more reliable solution that preserves SNR while still enabling angle finding with reduced antennas
3Device complexity
If interpolation or extrapolation techniques are used to fill holes in SLA, then angle finding can be performed, but accurate interpolation is difficult when SLAs are irregular or have many holes
Solution Approach 1:
The patent introduces matrix completion as an intermediary approach between sparse measurements and full array processing. Instead of directly interpolating missing elements in irregular SLA configurations, the system uses Hankel matrix construction and nuclear-norm minimization to automatically handle the completion process, making it computationally tractable even for irregular configurations with many missing elements
Data Source
AI summary
In an embodiment, a method for completing measurements for a uniform linear array from measurements from a sparse linear array is provided. The method includes: receiving a first set of measurements for a sparse linear array by a computing device; generating a second set of measurements for a uniform linear array from the first set of measurements by the computing device; and using matrix completion to determine values for a plurality of missing elements of the generated second set of measurements for the uniform linear array by the computing device.