Fast Low-Sidelobe Pattern Synthesis Using the Symmetry of Array Geometry.

Area of Science:

• Electromagnetics and Signal Processing
• Numerical Optimization Techniques

Background:

• Array pattern synthesis aims for low sidelobe levels, crucial in practical applications.
• Numerical optimization is effective but faces high computational complexity with large-scale arrays due to high-dimensional variables.
• Symmetric structures in sensor arrays are often present and can be exploited to accelerate algorithms.

Purpose of the Study:

• To develop a fast pattern synthesis method by utilizing the inherent symmetry of array geometry.
• To formulate the amplitude weighting problem as a second-order cone programming (SOCP) problem, incorporating dynamic range considerations.
• To significantly reduce the computational complexity and number of constraints in the optimization process.

Main Methods:

• Formulating array pattern synthesis as a second-order cone programming (SOCP) problem.
• Exploiting the symmetric properties of array geometry to reduce the dimensionality of optimization variables and constraints.
• Applying the method to uniform rectangular arrays (URA) and uniform hexagonal arrays (UHA).

Main Results:

• Demonstrated significant improvements in computational efficiency for large-scale arrays.
• Achieved a computational efficiency improvement factor of 158 for a 1024-sensor URA.
• Achieved a computational efficiency improvement factor of 284 for a 1261-sensor UHA.

Conclusions:

• The proposed method effectively utilizes array geometry symmetry for accelerated pattern synthesis.
• The SOCP formulation with symmetry exploitation drastically enhances computational efficiency.
• This approach offers a practical solution for designing large-scale sensor arrays with low sidelobe levels.