Joint Optimization of Array Element Distribution and Wideband Signal Beamforming Using Genetic Algorithm and Convex Optimization

The joint optimization of genetic algorithms and convex optimization represents an efficient hybrid methodology particularly suitable for solving array element distribution and wideband signal beamforming problems. This strategy leverages the complementary advantages of both optimization techniques to find near-globally optimal solutions within complex search spaces.

Genetic Algorithm (GA) excels at solving non-convex, nonlinear optimization problems by simulating natural selection mechanisms (selection, crossover, mutation) to explore the solution space. In array element distribution optimization, GA can flexibly adjust parameters such as element positions and spacing to improve array directivity and sidelobe suppression performance. Implementation typically involves encoding array configurations as chromosomes, where each gene represents an element's position parameter, and defining fitness functions based on array performance metrics.

Convex optimization addresses subproblems with convex properties, such as weight allocation in beamforming. For wideband signal processing, convex optimization ensures that beam responses satisfy constraints like interference minimization and signal-to-interference-plus-noise ratio (SINR) maximization under given array distributions. This is commonly implemented using quadratic programming or semidefinite programming solvers to compute optimal weighting coefficients across frequency bands.

The joint optimization workflow typically follows these steps: Genetic Algorithm optimizes array layout and generates candidate solutions. Each candidate array configuration is passed to the convex optimization module to calculate optimal beamforming weights. Beamforming performance metrics (such as mainlobe width and sidelobe levels) provide fitness feedback to guide GA's evolutionary process for subsequent generations.

This approach is particularly advantageous for wideband signal processing since broadband beamforming requires frequency-domain consistency optimization. Genetic algorithms help avoid local optima traps, while convex optimization efficiently solves weight calculation problems. The joint optimization ultimately enhances overall array system performance, including improved anti-jamming capability and higher target resolution. Code implementation often involves MATLAB optimization toolbox functions for convex optimization coupled with custom GA routines for array configuration search.