Coprime Planar Array Spectrum Estimation via Block Sampling Tensors
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing spatial spectrum estimation methods for coprime planar arrays lose multi-dimensional spatial structural information and suffer from reduced degree-of-freedom performance due to vectorization of signals and spatial smoothing processes.
Innovation Solution
A spatial spectrum estimation method based on block sampling tensor construction for coprime planar arrays, which uses three-dimensional tensors to represent received signals, calculates second-order cross-correlation tensors, and performs CANDECOMP/PARAFAC decomposition on fourth-order auto-correlation tensors to extract multi-dimensional features and construct a tensor spatial spectrum with enhanced degree-of-freedom.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If traditional vector-based spatial spectrum estimation methods are used, then the processing complexity is reduced, but the multi-dimensional spatial structural information is lost and degree-of-freedom performance deteriorates
Solution Approach 1:
The patent transforms the traditional vector-based signal representation into a three-dimensional tensor structure, adding temporal and spatial dimensions to preserve multi-dimensional spatial structural information. This dimensional transformation allows the system to maintain complete spatial information while enabling advanced tensor decomposition techniques for signal processing.
Solution Approach 2:
The patent constructs a composite tensor model that integrates multiple signal components (steering vectors, signal waveforms, noise) into a unified three-dimensional structure. This composite tensor representation combines spatial, temporal, and statistical information to achieve enhanced degree-of-freedom performance while managing processing complexity through structured decomposition.
2Reliability
If spatial smoothing method is introduced to solve rank deficient problem, then the covariance matrix issue is resolved, but degree-of-freedom performance is reduced
Solution Approach 1:
The patent extracts the essential statistical information directly from the three-dimensional tensor structure through tensor decomposition, bypassing the need for spatial smoothing operations. By taking out the signal subspace information directly from the tensor, the method resolves rank deficiency without the information loss associated with traditional spatial smoothing techniques.
Solution Approach 2:
The patent introduces a tensor decomposition intermediary (CANDECOMP/PARAFAC) that acts as a mediator between the raw tensor data and the final spectrum estimation. This intermediary extracts statistical properties directly from the tensor structure, providing a bridge that resolves covariance matrix issues while preserving degree-of-freedom performance.
3Loss of information
If tensor signal modeling is used to preserve multi-dimensional information, then spatial structural information is retained, but processing complexity increases
Solution Approach 1:
The patent segments the complex tensor processing task into distinct operational phases: tensor construction from array signals, tensor decomposition into component factors, and spectrum estimation from decomposition results. This segmentation manages processing complexity by breaking down the overall task while preserving multi-dimensional information throughout the processing chain.
Solution Approach 2:
The patent changes the fundamental parameter representation from vectors to three-dimensional tensors, fundamentally altering how spatial and temporal information is structured. This parameter change enables the use of tensor-specific decomposition algorithms that efficiently handle the multi-dimensional data structure while managing computational complexity through specialized mathematical operations.
4Loss of information
If block sampling tensor construction is used, then degree-of-freedom is enhanced, but computational load increases
Solution Approach 1:
The patent performs preliminary block sampling and tensor construction before the actual spectrum estimation process. By pre-organizing the data into a three-dimensional tensor structure with appropriate block sampling, the method enhances degree-of-freedom performance while managing computational load by preparing the data structure in advance for efficient decomposition operations.
Data Source
AI summary
Disclosed is a spatial spectrum estimation method with enhanced degree-of-freedom based on block sampling tensor construction for coprime planar array, which mainly solves the multi-dimensional information loss in signals and degree-of-freedom limitation in the existing methods and which is implemented by the following steps: constructing a coprime planar array; modeling block sampling tensors of the coprime planar array; deducing coarray statistics based on the block sampling cross-correlation tensor; obtaining block sampling coarray signals of a virtual uniform array; constructing a three-dimensional block sampling coarray tensor and its fourth-order auto-correlation statistics; constructing signal and noise subspaces based on fourth-order auto-correlation tensor decomposition; estimating a tensor spatial spectrum with enhanced degrees-of-freedom. In the present disclosure, the block sampling tensors of the coprime planar array is constructed, where a coarray tensor is deduced, to realize tensor spatial spectrum estimation with enhanced degrees-of-freedom by extracting signal-to-signal subspace features from the four-order self-correlation tensor.