Three-Dimensional Visualization of Directivity for Planar Arrays, Circular Arrays, and Linear Arrays

In wireless communication and radar systems, antenna directivity describes the distribution characteristics of signal radiation or reception strength across different directions. Common array antennas include planar arrays, circular arrays, and linear arrays, each possessing distinct radiation properties. MATLAB enables comprehensive three-dimensional visualization and analysis of these arrays' directivity patterns, including both amplitude and phase distributions. ### 1. Linear Arrays Linear arrays represent the simplest array configuration, consisting of antenna elements arranged along a straight line. Their directivity primarily depends on element spacing and excitation amplitude/phase. For three-dimensional visualization, MATLAB's `pattern` function or custom radiation pattern calculations can be employed, with `surf` or `mesh` functions used to plot three-dimensional amplitude distributions. Phase visualization can be achieved using `quiver3` or `contour` functions to display wavefront propagation characteristics. Key implementation involves calculating array factor through vectorized operations and applying coordinate transformations for spherical radiation patterns. ### 2. Circular Arrays Circular arrays feature antenna elements uniformly distributed along a circumference, making them suitable for omnidirectional or multi-beamforming applications. Their directivity exhibits symmetry characteristics. MATLAB implementation requires polar coordinate transformations to compute radiation intensity in each direction, with `polarplot` combined with three-dimensional projection for amplitude visualization. Phase distribution utilizes complex field calculations to demonstrate beam focusing or divergence properties. Algorithm implementation involves Bessel function expansions for circular array pattern synthesis and phase gradient calculations. ### 3. Planar Arrays Planar arrays (such as rectangular or circular configurations) are widely used in phased array radar systems, offering flexible directivity control in both azimuth and elevation angles. In MATLAB, nested loops can calculate antenna factors for each direction, followed by `surf` or `pcolor` functions for three-dimensional radiation pattern plotting. Phase distribution typically reflects beam scanning angles, which can be intuitively displayed through color mapping. Implementation considerations include efficient matrix operations for large arrays and grating lobe suppression techniques through proper element spacing. ### Implementation Approach Define array geometry (element positions, spacing). Set excitation parameters (amplitude, phase). Compute far-field radiation patterns (incorporating directivity functions). Utilize three-dimensional plotting tools to display amplitude and phase distributions. By adjusting array parameters, observers can analyze beamwidth, sidelobe levels, and steering angle variations, making this approach valuable for antenna design optimization and beamforming research. Code optimization techniques include vectorization for computational efficiency and interactive GUI components for parameter tuning.