研究目的
To propose an optimal method for designing frequency-invariant beamformers for circular arrays, focusing on deriving closed-form weighting vectors and solving a multi-constraint optimization problem to achieve optimal performance.
研究成果
The proposed method effectively designs frequency-invariant beamformers for circular arrays by deriving closed-form weighting vectors and solving multi-constraint optimization problems. Simulations and experiments show good performance in terms of directivity, robustness, and frequency-invariance, providing a flexible approach for optimal beamformer design.
研究不足
The method is specific to circular arrays and may not generalize to other array configurations. Cases where N >= M/2 for even M or N > (M-1)/2 for odd M are not considered, potentially limiting applicability. The optimization relies on preset constraints, which might not cover all practical scenarios.
1：Experimental Design and Method Selection:
The methodology involves expressing the desired beampattern in a complex-weighted general form, deriving weighting vectors using minimum mean square error (MMSE) approximation, formulating a multi-constraint optimization problem, and computing weighting vectors at other frequencies based on analytical functions. Theoretical models include signal models for circular arrays and optimization techniques.
2：Sample Selection and Data Sources:
Simulations use a 12-element circular array with specific parameters (e.g., M=12, N=2, ka range [0.1,6]). Experimental data is collected from a 12-hydrophone circular array in a lake experiment, with manifold vectors obtained from measured data.
3：1,6]). Experimental data is collected from a 12-hydrophone circular array in a lake experiment, with manifold vectors obtained from measured data.
List of Experimental Equipment and Materials:
3. List of Experimental Equipment and Materials: A circular array of 12 omnidirectional hydrophones with a diameter of 3 m is used for data collection. Software tools include CVX or SeDuMi for solving optimization problems.
4：Experimental Procedures and Operational Workflow:
Steps include defining the desired beampattern, deriving weighting vectors, solving the optimization problem to find optimal desired weighting vectors, computing weighting vectors at different frequencies, and validating through simulations and practical experiments.
5：Data Analysis Methods:
Performance is evaluated using directivity factor (DF), sensitivity function (SF), and mean square error (MMSE). Data is analyzed through simulations and comparison with experimental results to demonstrate frequency-invariance and robustness.
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