Radiation Pattern Analysis of Uniform Linear Arrays and 2D Patterns of Uniform Circular Arrays

Uniform Linear Array Radiation Pattern Analysis Uniform Linear Array (ULA) represents one of the most fundamental structures in array signal processing, where all array elements are equally spaced along a straight line. The radiation pattern (beam response) characterizes the array's gain response to signals arriving from different incident angles. The theoretical foundation of linear array patterns lies in the phase differences caused by wave path discrepancies. When signals arrive at specific angles, the inter-element spacing creates wave path differences, resulting in varying phase responses at different elements. By adjusting the weighting coefficients of array elements (such as uniform weighting), beams with main lobes pointing in specific directions can be formed. The core MATLAB implementation for ULA patterns involves calculating the Array Steering Vector, which represents the collective phase response of all array elements to the same signal. Pattern visualization typically involves computing array gains corresponding to varying incident angles, ultimately displayed in polar or Cartesian coordinates. Key functions include calculating element positions using linspace() and constructing steering vectors with exp() and phase accumulation. Two-Dimensional Radiation Patterns of Uniform Circular Arrays Uniform Circular Arrays (UCA) feature elements equally distributed along a circle's circumference. Compared to linear arrays, UCA patterns exhibit omnidirectional symmetry characteristics, making them suitable for beamforming in two-dimensional planes. Mathematical modeling of circular array patterns requires consideration of two-dimensional geometric relationships. Due to the circular distribution of elements, the phase difference calculation for array steering vectors involves polar coordinate transformations. UCA's beamforming capability is controllable in both azimuth and elevation dimensions, hence patterns are often presented as 2D polar plots or 3D surface plots. In MATLAB implementations, UCA pattern generation requires computing each element's coordinates in the 2D plane using trigonometric functions (cos() and sin()), and reconstructing phase difference matrices based on incident directions. By adjusting beam pointing angles, one can observe main lobe and sidelobe distribution characteristics to analyze the array's spatial resolution capability. The pattern calculation typically involves matrix operations and angle sweeping loops. Extension Considerations Pattern Optimization: Non-uniform weighting techniques (like Chebyshev weighting) can suppress sidelobes and improve beam quality through optimized coefficient calculations. Multi-beam Formation: UCAs can achieve simultaneous multi-beam scanning, particularly suitable for MIMO systems using phase shifting algorithms. Practical Constraints: Element spacing must be less than half-wavelength to avoid grating lobes, while mutual coupling effects between elements may affect pattern symmetry, requiring electromagnetic simulation validation.