## 1 Introduction  
Antennas are rightfully referred to as the electronic eyes and ears of the planet because of their unquestionable significance in wireless communication technology [1]. Microstrip patch antennas (MPAs) have been one of the most revolutionary breakthroughs in the time of downsizing in the ever-growing field of wireless communication technology [2; 3]. Due to their low weight, miniature size, affordability, ease of fabrication, and ability to be printed directly onto circuit boards, they have been widely used in various wireless systems, such as airborne radar, radio telemetry, RFID, mobile communication, navigation systems, and satellite communication [4; 5]. In [6; 7], meta surface-based dual band antennas were investigated, especially for industrial, scientific, and medical (ISM) applications. When the incident angles theta and phi change from \(-90\) to \(90\) and from \(0\) to \(360\) degrees, the unit \"\(1\)\" reflection coefficient amplitude changes from \(0\) to \(1\). A genetic algorithm (GA) optimizes CFMS coding subarray distribution [6]. The S\({}_{11}\) of the antenna is less than \(-10\) dB between \(2.3\)-\(2.62\) GHz and \(4.9\)-\(6.45\) GHz and \(13\%\) and \(27\%\) impedance bandwidth. Additionally, \(6.8\) dB at \(2.45\) GHz and \(9.0\) dB at \(5.8\) GHz [7]. However, the bandwidth and gain of typical microstrip antennas are both low [8; 9], despite their many advantages. Recently, MPAs have been extensively used in X-band applications. An X-band antenna can have both the compact size and the huge bandwidth required to send big data [10; 11]. To increase MPA performance and eliminate numerous drawbacks in the X-band range, substantial research work was conducted accordingly [12; 13; 14; 15; 16; 17]. A tuning fork-shaped MPA having resonance frequencies ranging from \(9\) GHz to \(11\) GHz for X-band radar and satellite applications was presented in [18]. The substrate of Rogers RT/Duroid 5880 in a high-frequency structural simulator (HFSS) simulates and analyzes the antenna characteristics. With total dimensions of \(24\)\(\times\)\(18\)\(\times\)\(1.57\) mm\({}^{3}\), the result generated a maximum gain of \(5.3\) dB. A series-fed microstrip array antenna was also proposed in [19] for X-band applications by using an array structure with a dimension of \(156\)\(\times\)\(9\) mm\({}^{2}\). In [20], a 3D printed corrugated plate antenna with high gain and aperture efficiency was proposed in the work. It is reported that the gain of the antenna is improved with the increment of the number of corrugated structures. The highest gain of \(24.2\) dB was achieved when \(10\) corrugations were implemented in the antenna structure. A proximity coupled technique is also being proposed for microstrip patch antennas (PC-MSPA) in S/C/X-band applications as reported in [21]. The prediction of the impedance response was conducted for a two-layer and single-material design structure. As a result, a new prediction model based on an electric equivalent circuit was introduced accordingly. To achieve the acceptable performance of an antenna using 3D electromagnetic simulation software, such as CST, HFSS, FEKO, and ADS, is a very challenging and time-consuming task. To mitigate these limitations, many researchers apply machine learning (ML) and deep learning (DL) approaches to optimize the antenna design, predict the results, such as resonance frequency (\(f_{r}\)), gain, return loss (s\({}_{11}\)), bandwidth, and so on, and select the antennas for wireless applications [22; 23; 24; 25; 26; 27; 28; 29]. Authors in [30] proposed an artificial neural network (ANN)-based microstrip patch antenna where the antenna dimension and resonance frequencies were predicted. However, the accuracy of the predicted results in terms of percentage of error, such as MSE, MAE, and RMSE, was not considered. Moreover, the prediction results of the proposed ANN model were not compared with the other existing ML models to validate the prediction.