Coprime Planar Array Direction-of-Arrival Estimation via Structured Coarray Tensor
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Solution Overview
Problem
Existing two-dimensional direction-of-arrival estimation methods for coprime planar arrays face challenges with loss of degrees-of-freedom and structural information due to vectorization, leading to reduced accuracy and resolution in underdetermined cases.
Innovation Solution
A two-dimensional direction-of-arrival estimation method based on structured coarray tensor processing, which represents received signals as tensors, performs cross-correlation analysis, and applies CANDECOMP/PARAFAC decomposition to derive coarray tensors, effectively increasing the degrees-of-freedom and retaining structural information.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If vectorization is used to derive coarray signals from coprime array second-order correlation statistics, then the one-dimensional direction-of-arrival estimation method can be extended to two-dimensional scenarios, but the multidimensional structural information of the received signals is destroyed and the coarray signals encounter large scale challenges
Solution Approach 1:
The patent transitions from traditional vectorized second-order correlation statistics to a fourth-order coarray tensor that preserves multidimensional structure. By constructing the tensor with dimensions corresponding to different array subarrays and lag vectors, the method maintains the inherent two-dimensional spatial structure while enabling direction-of-arrival estimation in underdetermined scenarios.
Solution Approach 2:
The patent creates a composite tensor structure by combining multiple correlation matrices from different array subarrays (uniform rectangular subarray and coprime planar subarray) into a single coarray tensor. This composite structure integrates the strengths of different array configurations while preserving the complete multidimensional signal characteristics.
2Measurement precision
If traditional coarray signal processing is used for coprime planar arrays, then direction-of-arrival estimation can be performed, but the degrees-of-freedom are limited by the number of physical sensors
Solution Approach 1:
The patent introduces a virtual coarray tensor as an intermediary that expands the effective aperture beyond the physical sensor array. By computing fourth-order correlations and constructing virtual sensor positions through tensor operations, the method creates a virtual array with more elements than the physical array, thereby increasing degrees-of-freedom without adding physical sensors.
Solution Approach 2:
The patent utilizes the fourth-order tensor structure to create additional dimensional information from the same physical sensors. By organizing correlation statistics into a tensor with multiple lag dimensions corresponding to different subarrays, the method effectively increases the number of independent signal paths that can be processed.
3Measurement precision
If the coprime planar array uses more physical sensors to increase degrees-of-freedom, then better resolution and accuracy can be achieved, but the system complexity and cost increase
Solution Approach 1:
The patent creates virtual copies of the physical array through mathematical operations on the received signals. By computing fourth-order correlations and mapping them to virtual sensor positions in the coarray tensor, the method generates additional virtual sensors that replicate the functionality of physical sensors without the associated hardware complexity and cost.
Data Source
AI summary
A two-dimensional direction-of-arrival estimation method for a coprime planar array based on structured coarray tensor processing, the method includes: deploying a coprime planar array; modeling a tensor of the received signals; deriving the second-order equivalent signals of an augmented virtual array based on cross-correlation tensor transformation; deploying a three-dimensional coarray tensor of the virtual array; deploying a five-dimensional coarray tensor based on a coarray tensor dimension extension strategy; forming a structured coarray tensor including three-dimensional spatial information; and achieving two-dimensional direction-of-arrival estimation through CANDECOMP/PARACFAC decomposition. The present disclosure constructs a processing framework of a structured coarray tensor based on statistical analysis of coprime planar array tensor signals, to achieve multi-source two-dimensional direction-of-arrival estimation in the underdetermined case on the basis of ensuring the performance such as resolution and estimation accuracy, and can be used for multi-target positioning.