Radar Covariance Matrix Padding for SIMD Direction Finding
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Solution Overview
Problem
Radar systems face challenges in efficiently processing matrices of varying dimensions using Single Instruction Multiple Data (SIMD) processing due to branch divergence when calculating pseudo-inverses of covariance matrices with different numbers of columns, which is essential for determining target directions.
Innovation Solution
A method for modifying covariance matrices to ensure they have the same dimensions, allowing simultaneous calculation of pseudo-inverses using a single instruction set on a SIMD processing system, by padding and adjusting matrices to maintain consistent dimensions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional processing methods are used for covariance matrices with different dimensions, then each matrix can be processed individually with accurate results, but processing efficiency is low and branch divergence occurs in SIMD systems
Solution Approach 1:
The patent changes the dimensional parameters of covariance matrices by padding them to a uniform maximum dimension. This allows all matrices to be processed with the same instruction set in SIMD systems, eliminating branch divergence while maintaining processing accuracy through selective use of valid elements.
Solution Approach 2:
The patent segments the processing into two phases: first padding all matrices to uniform dimensions, then processing them collectively using SIMD instructions. This segmentation enables parallel processing of multiple matrices simultaneously, dramatically improving productivity.
2Productivity
If covariance matrices are padded to uniform dimensions for SIMD processing, then processing efficiency increases and branch divergence is eliminated, but additional computational steps are required
Solution Approach 1:
The patent performs preliminary padding of all covariance matrices to their maximum dimension before processing. This preliminary action ensures that subsequent SIMD operations can proceed without branch divergence, and the pseudo-inverse calculation can be performed efficiently using pre-computed padding matrices.
Solution Approach 2:
The patent introduces intermediary padding matrices that facilitate the pseudo-inverse calculation of padded covariance matrices. These intermediary structures enable the mathematical operations to proceed correctly despite the added dimensions, and can be pre-computed to minimize overhead.
3Productivity
If pseudo-inverses are calculated for padded covariance matrices, then SIMD processing can be used for simultaneous calculation, but the calculation complexity increases
Solution Approach 1:
The patent uses copying techniques by creating padded versions of covariance matrices with standardized dimensions. These copied and padded matrices can then be processed using identical SIMD instruction sequences, enabling simultaneous calculation of pseudo-inverses for multiple matrices with different original dimensions.
Data Source
AI summary
The present invention relates to radar systems and associated methods of operation. In one aspect, the present invention relates to an automotive radar system including at least one receiver configured to receive radar signals, a processing system configured to receive from at least one receiver, a received radar signal, process the received radar signal to generate a data frame that has dimensions of M rows by M columns of elements from a covariance matrix, determine a rank N of the data frame. The system is further configured to set all elements in a first subset of columns numbered N through M of the data frame to zero values to create a padded data frame, calculate a pseudo-inverse value of the padded data frame, determine a direction of arrival of at least one target using the pseudo-inverse value, and control an operation of a vehicle using the direction of arrival.