## 4 Results and Discussions  
This paper describes a technique for correcting radiation pattern distortions in conformal array antennas caused by surface deformities and mutual coupling between antenna radiating elements. The proposed technique is based on constraint convex optimization, a mathematical approach that involves finding the optimal solution to update the complex weights for the array elements subject to certain constraints that ensure that the corrected radiation pattern meets desired mainlobe direction, beamwidth, null locations, and sidelobe levels. In order to evaluate the performance of an optimization algorithm, the antenna array in planar configuration is deformed to the prescribed spherical and cylindrical configurations with varying radii. The spherical and cylindrical configuration both has three different radiuses: \(r=30\,\text{cm}\), \(r=25\,\text{cm}\), and \(r=20\,\text{cm}\), and the result are shown separately for each case. Four prototypes of \(2\times 2\), \(3\times 3\), \(4\times 4\), and \(5\times 5\) conformal array have been chosen for the analysis. The mainlobe radiation pattern having first nulls at \(30^{\circ}\) and \(-30^{\circ}\) has been selected and the inter-element spacing between the array elements is taken as \(0.5\lambda\). The MATLAB is used for the simulation of optimization algorithm, while CST Studio Suite is used for the verification of its accuracy. The proposed experimental structure includes a power combiner/splitter feed network, which is coupled to a high gain power amplifier. Following that, RF variable attenuators and voltage-controlled phase shifters are individually attached to this feed network. The phase shifters and attenuators are supplied the amplitude and phase values, which are regulated by variable power supply. A multi-step process for optimizing the performance of the conformal microstrip antenna arrays is initiated. The first step involves obtaining the position vectors of individual array elements in planar as well as deformed structures of conformal array. Then, the computation of the array factor is carried out utilizing the methodology outlined in Sections 2 and 3 of the study and to obtain the electric field intensity for all the units, preliminary simulations are conducted in CST. The optimization algorithm implemented in MATLAB, outlined by Equations (6) and (8), is  
The result reveals that the performance of the optimization algorithm is highly dependent on the physical configuration and number of radiating elements of the antenna array. It is observed that when the array is bent from its planar arrangement to the prearranged spherical and cylindrical configurations, the spacing and orientation of the radiating elements is significantly altered. This results in loss of mainlobe, null positions, and sidelobe levels, and hence a major distortion of the radiation pattern is realized. However, after the deformed arrays have been subjected to the optimization algorithm, the distorted radiation pattern successfully recovers the sidelobes and nulls, and the mainlobe is observed nearly at the same position as that of the planar array. This demonstrates the effectiveness of the optimization algorithm in recovering desired radiation patterns even when the array is not in its ideal geometry. The conformal array performs better when the array is less deformed (with a radius of curvature of 30 cm), enabling the obtained radiation pattern to closely approximate the desired radiation pattern. In contrast, when the array is more deformed (with a radius of curvature of 20 cm), the obtained radiation pattern deviates more from the desired radiation pattern, indicating that the optimization algorithm is less effective in this case. Additionally, increasing the number of elements increases the degrees of freedom available for the optimization algorithm, allowing for a more precise tuning of the radiation pattern.