Synthesis of Highly Directive Linear Leaky Wave Antennas With Controlled Sidelobe Levels Fed by Nonuniformly Spaced Subarrays

A synthesis procedure for designing linear Fabry–Perot (FP) leaky wave antennas (LWAs) fed with nonuniformly spaced subarrays is presented. First, the array-fed FP LWA is modeled by the superposition of the excited leaky waves that includes the mutual coupling effects. To that end, the dominant leaky mode and the dispersion curves are calculated using the finite element analysis (FEA) of the eigenmode problem without any homogenization approximations. A procedure is proposed to numerically calculate the self-coupling and mutual-coupling coefficients for the excited leaky waves and include them in the model. Finally, a hybrid method based on convex
$\boldsymbol {\ell _{1}}$
-norm minimization and particle swarm optimization (PSO) is applied to the model to group the source array elements into a minimum number of subarrays, while fulfilling the predefined mask-type radiation and element location constraints. Two linear FP LWAs are synthesized at 10 GHz to demonstrate the effectiveness of the model and the optimization tool in designing highly directive antennas with controlled sidelobe levels (SLLs); the first achieves a half power beamwidth (HPBW) of 0.95°, aperture efficiency of 83.4%, and SLL of −19.5 dB using three subarrays, while the second achieves an HPBW of 1.05°, aperture efficiency of 82.9%, and SLL of −29.3 dB using nine subarrays.