Sparse Array DOA Estimation via Vandermonde Reconstruction
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Solution Overview
Problem
Existing DOA estimation methods using sparse arrays face challenges such as basis mismatch and poor estimation performance for signals with small angular intervals, particularly in sparse signal reconstruction (SSR), virtual array-based interpolation (VAI), and structured Nyquist correlation reconstruction (SNCR) algorithms.
Innovation Solution
A DOA estimation method and system based on Vandermonde decomposition reconstruction, involving covariance matrix completion optimization using nuclear norm and alternating direction multiplier method to enhance spatial resolution and utilize extra degrees of freedom in sparse arrays.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If sparse array is used to provide larger aperture and extra degree of freedom, then spatial resolution is improved, but basis mismatch occurs and estimation performance deteriorates for signal sources with small angular interval
Solution Approach 1:
The patent changes the mathematical parameters of the covariance matrix representation by introducing Vandermonde decomposition. Instead of using conventional covariance matrix approaches that lead to basis mismatch, the method decomposes the covariance matrix into Vandermonde structure, enabling accurate representation of sparse array signals and resolving the basis mismatch issue while maintaining high spatial resolution
Solution Approach 2:
The patent introduces an intermediary variable (Vandermonde matrix) to bridge the sparse array signals and the covariance matrix. This intermediary structure allows the system to utilize the extra degree of freedom from sparse arrays while avoiding the basis mismatch problem, serving as a mediator between the sparse array configuration and the signal processing algorithm
2Productivity
If conventional covariance matrix methods are used, then computation is simple, but basis mismatch prevents maximum utilization of extra degree of freedom
Solution Approach 1:
The patent transforms the covariance matrix into a Vandermonde-decomposed form, changing the mathematical parameters to enable proper utilization of sparse array degrees of freedom. This parameter transformation allows the system to adapt to the specific structure of sparse array signals while maintaining computational feasibility through the optimized decomposition approach
Data Source
AI summary
Provided are a direction of arrival (DOA) estimation method and system for a sparse array based on Vandermonde decomposition reconstruction, relating to the technical field of array signal processing. The method includes: constructing a covariance matrix completion optimization model based on sparse array signals and uniform linear array signals, and performing Vandermonde decomposition by using characteristics of a uniform linear array; introducing a nuclear norm to optimize a rank function in the model, and updating the covariance matrix completion optimization model; and introducing an auxiliary variable to transform the model into a solvable optimization problem, and solving the problem by an alternating direction multiplier method to obtain an optimal estimation value. The DOA is estimated using a root multiple signal classification algorithm.