Virtual Sub-Array Beamforming: Two-Level Matrix Reduction
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
The inversion of large matrices becomes intractably difficult for all-digital transmit/receive antenna apertures used in adaptive beamforming algorithms, leading to high computational complexity and impractical power consumption in emerging array processors.
Innovation Solution
A two-level approach using approximate discrete Fourier transform (ADFT) beamformers and adaptive beamformers is employed, reducing computational complexity by using approximate discrete Fourier transform (ADFT) beamformers in subarrays and adaptive beamformers to process signals, thereby reducing matrix inversion complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If all-digital transmit/receive antenna apertures are used for adaptive beamforming algorithms, then beamforming performance is improved, but computational complexity becomes intractably difficult due to large matrix inversions
Solution Approach 1:
The patent divides the large N×N matrix inversion problem into multiple smaller sub-matrix inversion problems by segmenting the antenna array into subarrays. Each subarray processes a portion of the signals independently, reducing the computational burden from O(N³) to O((N/K)³) where K is the number of subarrays, thus resolving the contradiction between maintaining beamforming performance and reducing computational complexity
Solution Approach 2:
The patent introduces a hierarchical processing dimension by organizing the beamforming architecture into multiple levels: first-level ADFT beamformers process signals from individual subarrays, and second-level adaptive beamformers combine these results. This dimensional restructuring transforms a single complex N×N matrix inversion into multiple smaller inversions across different processing levels, reducing overall computational complexity while preserving beamforming effectiveness
2Measurement precision
If large matrix inversions are performed for adaptive beamforming, then accurate beamforming is achieved, but power consumption becomes impractical
Solution Approach 1:
By segmenting the computational task into multiple smaller matrix inversions across subarrays, the patent reduces the total power consumption. Each subarray's smaller matrix inversion requires significantly less power than a single large inversion, and the distributed nature of the computation allows for more efficient power utilization across the system, resolving the contradiction between beamforming accuracy and power consumption
3Measurement precision
If exact discrete Fourier transform beamformers are used, then precise spectral analysis is achieved, but computational complexity increases significantly
Solution Approach 1:
The patent employs approximate discrete Fourier transform (ADFT) beamformers that perform partial DFT operations sufficient for the application's needs. Rather than computing the complete exact DFT, the ADFT computes only the necessary frequency components with acceptable approximation, reducing computational complexity from O(N log N) to O(N) while maintaining sufficient spectral analysis precision for beamforming applications
Data Source
AI summary
Systems and methods are provided for reducing the computational complexity and all-to-all (A2A) communication within virtual sub-arrays (VSAs) while enabling distributed parallel edge processing. This can help solve the beamforming problem described by The United States Defense Advanced Research Projects Agency (DARPA) state of the art array processor (SOAP) unclassified program. The use of all-digital transmit/receive antenna apertures for adaptive beamforming algorithms necessitate inversion of large matrices. The matrix inversions become intractably difficult for emerging all-digital apertures. This complexity problem associated with large all-digital aperture arrays can be solved with a two-level approach.