# Modeling of Key Specifications for RF Amplifiers Using the Extreme Learning Machine
## 1 Introduction  
A radio frequency (RF) amplifier is a key component of the RF front-end [1; 2], which has been widely used in various radio systems [3], such as navigation systems [4], radar [5; 6] and satellite communication systems [7], mobile communication systems [8], positioning systems [9], etc. Due to different application scenarios and requirements, the above radio systems usually need to work in various environments. Some radio systems even need to work in very harsh environments [10], such as significant variations in temperature and humidity. As a key component of the above radio system, the performance of the RF amplifier is very sensitive to temperature variations. The performance of the radio system will be affected or even fail with the performance specifications of the RF amplifier change with temperature. It may lead to the radio systems not meeting the requirements of the actual application scenario [10]. In [11], although the RF amplifier has not reached the end of its life at this point, its performance specifications have degraded to the point where it cannot meet the minimum requirements for the proper functioning of the radio system. Therefore, the RF amplifier's performance specifications must be known for a given temperature range to ensure the radio system's proper functioning. Much fruitful work has been carried out previously on the study of amplifier specifications versus temperature variations. For example, [PERSON] et al. [12] proposed a thermal behavioral model for RF power amplifiers (PAs) directly extracted through base-band and RF measurements of an laterally-diffused metal-oxide semiconductor (LDMOS) PA under pulse-modulated RF input-controlled temperature. The presented model accurately predicts the influence of temperature on quasi-static and dynamic characteristics of an LDMOS PA. [PERSON] et al. [13] reported an RF power amplifier behavioral model with temperature effects suitable for predicting the long-term memory effects in standalone and multiple-PA arrays. The model can estimate the PA output power in thepresence of self-heating and for a wide temperature range. [PERSON] et al. [14] focused on the behavioral modeling of thermal effects induced by a power amplifier for system-level simulation to predict better the link budget of RF transmitters for narrow-band radar applications. Finally, [PERSON] et al. [15] presented a new electrothermal behavioral model for power amplifiers. This model, implemented into a circuit simulator, allows predicting the impact of the thermal effects in pulsed-RF mode thanks to an envelope transient analysis. The above studies have investigated the relationship between amplifier specifications and temperature in detail and have developed behavioral models. However, the above studies only focus on the amplifier's thermal effect on its specification, while the actual operating scenarios, where the environment changes (e.g., temperature) also affect the amplifier's specification. Therefore, knowing the relationship between the amplifier specifications and the change in the external operating environment becomes an urgent problem. Currently, there are two main ways to obtain the environmental characteristics of amplifier specifications. On the one hand, the specifications of the RF amplifier at different temperatures are obtained by simulation [16; 17; 18], which is fast. However, the absence of an accurate transistor device model leaves a gap between simulation results and measurement results [19]. However, it is still very effective and convenient for some application scenarios that need to know the trend and range of RF amplifier specifications quickly and qualitatively. On the other hand, another method is to directly obtain the specifications of RF amplifiers at different temperatures by measurement [20]. For example, [PERSON] et al. measured the specifications of power amplifiers at 0 \({}^{\circ}\)C, 50 \({}^{\circ}\)C, 75 \({}^{\circ}\)C and 100 \({}^{\circ}\)C [20; 21], and [PERSON] et al.