# Directly Matching an MMIC Amplifier Integrated with MIMO Antenna through DNNs for Future Networks
## 2 Proposed Optimization Method
### LSTM-Based DNN for Modeling Antenna (Phase-1)  
Antennas play important role in both transmitting and receiving signals in communication systems. They can either radiate or receive electromagnetic waves as the essential data. Hence, strong and high-performance antennas are required, essentially enabling us to convert electrical energy into electromagnetic waves and vice versa. Figure 2 presents the PA and antenna as active, and passive devices are the essential blocks in the communication systems. Matching the antenna to the drain's optimal impedance such that the performance specifications are high is challenging. Hence, a strong method is needed for modeling the antenna to facilitate the overall performance of the amplifier. Intelligent-based methods that include DNNs are the most promising methods for modeling RF designs [31; 32]. Therein, modeling the antennas, especially with complex structures, can be executed through DNNs. From another perspective, the antenna coupling can  
Figure 1: Comprehensive overview around the proposed methodology where two LSTM-based DNNs are employed for modeling antenna and PA.  
Figure 2: A typical structure of any communication system includes PAs and antennas. amplifiers, and some antenna elements can recognize negative impedances [33]. In this case, a well-designed amplifier that is matched with optimal drain impedances through LSTM-based DNNs can be a good solution. Figure 3 describes the antenna modeling approach for predicting the load impedances, including real and imaginary parts, over the large frequency band. In this paper, as the first phase, we present antenna modeling procedure through LSTM-based DNN. As all the proposed methodology is performed automatically and based on the DNN constructions, a combination between EDA tools and numerical analyzer is required. Hence, for modeling the antenna, an automated environment between Microwave Studio (Dassault Systemes) and MATLAB are created (Step-1). Afterwards, the initial structure of antenna is developed by means of the CST tool (Step-2). Determining the design parameters after constructing the initial configuration of antenna is a major concern allowing us to influence the output specification of the antenna. In this case, we employ the GA method that is based on the natural selection, and continuously alters the population of individual possibilities [34; 35; 36] (Step-3). After constructing the configuration of the antenna and finding the optimal design parameters, it is time to train the LSTM-based regression DNN, aiming to predict the extended load impedances of antenna in the interested frequency band. The main requirement of DNN construction is to provide a suitable sized dataset that includes training and testing data. For this case, a parametric sweep (i.e., random iteration) is employed for altering the design parameters and achieving the outcomes as \(S_{11}\), gain, radiation patterns in E-plane and H-plane and load impedances (i.e., real and imaginary parts) for half of the full targeted bandwidth (Step-4). Another significant process in DNN construction is finding the hyperparameters. To achieve the optimal hyperparameters, we employ the BO method that enables us to achieve the optimal number of hidden layers with number of neurons in each layer. The BO is applied due to its capability in doing optimization over the continuous domains [37; 38; 39; 40] (Step-5). As Figure 3 shows, each  
Figure 3: LSTM-based DNN for modeling the antenna and predicting the extended impedances in the frequency domain. neural network structure consists of three sections, namely as input layer, hidden layers, and output layer. In our proposed DNN, the input layer defines important characteristics of antenna as S\({}_{11}\)of IMD levels are calculated for the third, fifth, and seventh orders as presented in (3)-(5). Afterwards, we propose using the 'Multivariate Newton's Method' [27] for providing the approximate function (i.e., representation) of linearity specification.