MATLAB Code Implementation for Drawing Hexagonal Cellular Networks

Cellular networks are widely used in wireless communications due to their efficient coverage capabilities. When drawing cellular networks in MATLAB to cover a specified circular area, the key lies in the geometric construction and spatial arrangement of hexagonal cells. Here is the implementation approach:

Hexagonal Cell Modeling Each cell is a regular hexagon generated by calculating vertex coordinates. Given the hexagon side length `r`, the circumradius is also `r`. Using polar coordinate transformation, the 6 vertices are evenly distributed on a circle at 60° intervals. MATLAB implementation typically involves creating vertex arrays using trigonometric functions like `sin()` and `cos()` with angle increments of pi/3 radians.

Grid Tiling Strategy A staggered arrangement is employed where odd and even rows have horizontal offsets of half a side length. By iterating through center coordinates, hexagonal cells cover the target circular domain. Coverage range requires dynamic calculation to avoid redundant drawing. The algorithm involves nested loops for row and column indices with coordinate transformations using hexagonal grid mathematics.

Circular Boundary Handling Only hexagons with centers located inside the target circular domain are retained. Distance calculation between hexagon centers and the domain center filters qualifying cells. This can be extended to partial coverage through hexagonal clipping, though it requires more complex geometric computations using polygon intersection algorithms.

Visualization Optimization MATLAB's `patch` function draws hexagons through batch generation in loops. Adjusting colors and transparency helps distinguish adjacent cells or mark central station locations. Implementation can include colormap assignments and alpha properties for enhanced visual differentiation.

Extension Ideas Dynamic adjustment of cell radii for non-uniform coverage Integration with signal attenuation models to render coverage intensity heatmaps Using `voronoi` function to generate more complex heterogeneous network layouts through Voronoi tessellation algorithms