Efficient Estimation of Active Element Patterns for 2-D Planar Array Antennas via Directional Decomposition

TL;DR

This work addresses the high computational cost of obtaining accurate active element patterns (AEP) for large 2-D planar arrays by mutual coupling and edge truncation. It introduces a directional decomposition framework using current-based transfer matrices that reduce 2-D problems to 1-D analyses, with 2-D coupling recovered via a Kronecker-product construction. Numerical validation on an 11 by 9 open-ended square-waveguide array at 10 GHz shows excellent agreement with full-wave MoM results (MSE in the main lobe < 0.1 dB) and dramatic efficiency gains, reducing computation time from the conventional method by orders of magnitude (to roughly 0.1% of the original). The approach enables accurate beam synthesis for large arrays and RIS-type platforms, with applicability to more complex antennas and potential future work on dielectric structures.

Abstract

The active element pattern method is widely employed in beam pattern synthesis of array antenna to account for mutual coupling between antenna elements. Calculating the active element patterns for large number of array requires full-wave analyses of total array structure, which is time consuming. To obtain accurate active element patterns efficiently, this letter proposes a method to estimates active element patterns in largely arrayed antenna using directional decomposition approach. Reducing computational cost, proposed method constructs the transfer matrices to reflect both mutual coupling and truncation effects between each antenna element. Numerical validation with open-ended waveguides confirms that the proposed method can estimate active element patterns with high accuracy. The synthesized beam patterns show mean squared errors below 0.1dB in the main lobe region for various beam steering cases. The computational complexity for numerical analysis reduces from $\mathcal{O}(M_B^2(N_x^3 N_y^3))$ to $\mathcal{O}(M_B^2(N_x^3 + N_y^3))$, resulting in a reduction of computation time to under 0.095\% compared to the conventional active element pattern method.

Figures (6)

• Figure 1: Flowchart of obtaining AEP for the conventional full-wave method and the proposed method
• Figure 2: (a) Structure and geometry of 11 $\times$ 9 open-ended square waveguides with port indices (b) Expression of mesh-to-mesh transfer matrices determination
• Figure 3: Averaged current distribution spectrum for 99 cases of unit excitation. (a) MoM results (reference). (b) Predicted results (proposed).
• Figure 4: AEP obtained with proposed method (blue line) and reference obtained with MoM (red dot) for $\phi=0^{\circ}$, $\theta=-90^{\circ}$ to $90^{\circ}$ in (a) normalized magnitude pattern and (b) phase pattern.
• Figure 5: Prediction logarithmic error of synthesized radiation pattern between MoM and PMM-isolated (left), PMM-periodic (center), proposed method (right) for each steering case (a) $\theta=0^{\circ}$, $\phi=0^{\circ}$ and (b) $\theta=25^{\circ}$, $\phi=180^{\circ}$.