Directivity of Linear Arrays, Planar Arrays, and Weighted Array Configurations

In array signal processing, directivity refers to an array's capability to respond differently to signals from various directions. Through rational design of array geometry and weight distribution, specific directivity patterns can be achieved to enhance signals from target directions or suppress interference from undesired directions. Implementation typically involves calculating array response vectors and applying digital beamforming algorithms.

Linear arrays represent the simplest configuration where multiple sensor elements are arranged along a straight line. This structure provides symmetric directivity in the horizontal plane, enabling single-direction beamforming. The main lobe width and sidelobe levels can be controlled by adjusting element spacing and quantity. In code implementation, the array response vector for a linear array can be computed using phase shift calculations based on element positions and signal wavelength.

Planar arrays distribute sensors across a two-dimensional plane, enabling simultaneous control of directivity in both horizontal and vertical directions. While this configuration allows more complex beam steering capabilities, it also requires increased computational complexity. Common layouts include rectangular arrays and circular arrays, where the array manifold calculation involves two-dimensional spatial coordinates.

Weighted array configurations optimize directivity by applying different weight coefficients to individual sensors. Common weighting methods include: Uniform weighting: All sensors receive equal weights Tapered weighting: Gradually reduced weights for edge elements to suppress sidelobes Optimal weighting: Weight calculations based on specific optimization criteria like minimum variance distortionless response (MVDR) Code implementation typically involves creating weight vectors and applying them to array output through inner product operations. The choice of weighting strategy directly affects beam pattern characteristics including main lobe width and sidelobe suppression.

These array designs find extensive applications in acoustic signal processing, wireless communications, and radar systems. Through appropriate selection of array configuration and weighting schemes, functions such as directional selectivity, interference suppression, and signal enhancement can be effectively achieved. Practical implementations often combine these techniques with adaptive algorithms for real-time performance optimization.