# Optimization of a Coherent Dual-Beam Array Feed Network for Aperiodic Concentric Ring Antennas
## 3 Numerical Results
In particular, our proposed two-beam C-BFN configuration that feeds an ACRA characterized by subsets of alternated inputs on each C-BFN block in every ring achieves and retains outstanding numerical values of directivity, i.e., an average performance enhancement between 2.5 and 3.5 dB for beam number 1 and 0.9 and 1.9 for beam number 2 (under equal and fair conditions when running the optimization process). Conversely, all the nonequal layout multi-beam experiments (based on Opt. \(\overline{\tau}\)) with the selected coherent system reach higher numerical results of sidelobe level, improving the uniform antenna array, with a performance improvement between \(-4.7\) and \(-6.2\) dB for beam number 1 and \(-2.2\) and \(-3.0\) dB for beam number 2 on average. Furthermore, in this dual-beam configuration, every main beam is shaped and steered to any predefined location utilizing approximately 50% of the input ports (47 input ports for beam number 1 and 45 input ports for beam number 2) for this specific case regarding the total number of radiators (\(N=92\)). Based on the comparative analysis with respect to the dual-beam ACRAs summarized in Table 1. The experimental results prove and confirm that the beamforming network configuration proposal in addition to an ACRA has enhanced performance on each beam compared to a uniform concentric ring array with an equal feeding system regarding the directivity and sidelobe level. Although a predefined direction of maximum radiation is set for each beam in the numerical experiments, the proposed coherent network configuration can generate and scan every beam to any direction of interest beneath the field of view, with a directivity and isolation level with small fluctuations along the azimuthal plane. To establish the maximum performance and for an unbiased analysis in terms of the antenna design trade-off (\(D\) and SLL), including inherent complexity reduction in the network and multi-beam capability, the improvement of a sparseness optimization on the antenna layout has been avoided. Moreover, the optimized circular rings in Figure 5 are considered to be distanced by at least a separation of \(\lambda/2\) plus an additional distance (\(0\leq\Delta_{\lambda}\leq 1.5\lambda\)) among the rings. The novel resulting optimized non-uniform layouts for the multi-beam scenario show a singular compartment where the last and first rings have the biggest radius and with element density in the radial direction; this specific nature is also found in regular non-uniform circular concentric rings and is associated with a low sidelobe amplitude taper. The designed two-beam feeding system found on C-BFN for ACRA benefits from its operational behavior, with improved features over the conventional circular concentric aperture in a phased array with direct feeding. Its clear benefits include sharing paths coherently (i.e., mechanism of coherent coupling), allowing multi-beam features, and also reducing control signal ports. In the configuration proposed in this paper, the dual-beam is scanned and shaped approximately with half of the input ports, i.e., a clear reduction of 50%, only requiring half of the input ports to control each beam compared to the conventional case.