Behavioral modeling of power amplifiers for wireless applications

In this paper, an improved empirical behavioral model for radio‐frequency power amplifiers (RF‐PAs) is presented. The model was implemented in a commercial nonlinear microwave simulator. It belongs to the category of bandpass PA models, which exhibits memory effects due to the low frequency dependence of bias and temperature. Additionally, it facilitates accurate and efficient system level simulations of RF‐PA large‐signal behaviors such as self‐bias, AM‐AM, AM‐PM, gain expansion effects, and intermodulation distortion (IMD) sweet‐spots. The model was validated using measurement data obtained from a commercial CDMA PA at 1.88 GHz. © 2007 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2007.     

Recurrent neural network technique for behavioral modeling of power amplifier with memory effects

A new technique for behavioral modeling of power amplifier (PA) with short‐ and long‐term memory effects is presented here using recurrent neural networks (RNNs). RNN can be trained directly with only the input–output data without having to know the internal details of the circuit. The trained models can reflect the behavior of nonlinear circuits. In our proposed technique, we extract slow‐changing signals from the inputs and outputs of the PA and use these signals as extra inputs of RNN model to effectively represent long‐term memory effects. The methodology using the proposed RNN for modeling short‐term and long‐term memory effects is discussed. Examples of behavioral modeling of PAs with short‐ and long‐term memory using both the existing dynamic neural networks and the proposed RNNs techniques are shown. © 2014 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:289–298, 2015.     

Interconnect reliability analysis of ULSI using automated model generation algorithm

Fast interconnect reliability analysis is needed with the rapid development of ULSI (Ultra Large Scale Integration). Therefore, we aims to use the automated model generation (AMG) algorithm to analyze the ULSI reliability of metal interconnects. This is the first time to use the AMG algorithm in the field of IC reliability analysis. The AMG algorithm can achieve data generation automatically, determination of data distribution, adaptation of model structure, model training and testing. Using AMG algorithm in the reliability analysis, the number of the training data can be reduced by the adaptive sampling process and the incorporation of interpolation technique. This method can greatly improve the efficiency of the simulation and shorten the time for modeling than the existing manual neural network modeling methods. In this paper, we takes a power amplifier for example to validate the advantage of this technique. © 2016 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:481–488, 2016.     

Surrogate modeling of impedance matching transformers by means of variable‐fidelity electromagnetic simulations and nested cokriging

Accurate performance evaluation of microwave components can be carried out using full‐wave electromagnetic (EM) simulation tools, routinely employed for circuit verification but also in the design process itself. Unfortunately, the computational cost of EM‐driven design may be high. This is especially pertinent to tasks entailing considerable number of simulations (eg, parametric optimization, statistical analysis). A possible way of alleviating these difficulties is utilization of fast replacement models, also referred to as surrogates. Notwithstanding, conventional modeling methods exhibit serious limitations when it comes to handling microwave components. The principal challenges include large number of geometry and material parameters, highly nonlinear characteristics, as well as the necessity of covering wide ranges of operating conditions. The latter is mandatory from the point of view of the surrogate model utility. This article presents a novel modeling approach that incorporates variable‐fidelity EM simulations into the recently reported nested kriging framework. A combination of domain confinement due to nested kriging, and low‐/high‐fidelity EM data blending through cokriging, enables the construction of reliable surrogates at a fraction of cost required by single‐fidelity nested kriging. Our technique is validated using a three‐section miniaturized impedance matching transformer with its surrogate model rendered over wide range of operating frequencies. Comprehensive benchmarking demonstrates superiority of the proposed method over both conventional models and nested kriging.     

Performance‐driven modeling of compact couplers in restricted domains

Fast surrogate models can play an important role in reducing the cost of Electromagnetic (EM)‐driven design closure of miniaturized microwave components. Unfortunately, construction of such models is challenging due to curse of dimensionality and wide range of geometry parameters that need to be included in order to make it practically useful. In this letter, a novel approach to design‐oriented modeling of compact couplers is presented. Our method allows for building surrogates that cover wide range of operating conditions and/or material parameters, which makes them useful for design purposes. At the same time, careful definition of the model domain permits dramatic (volume‐wise) reduction of the of the design space region that needs to be sampled, thus, keeping the number of training data samples at acceptable levels. The proposed technique is demonstrated using a compact rat‐race coupler modeled for operating frequencies from 1 to 2 GHz and power split of ?6 to 0 dB. Benchmarking and application examples for coupler design optimization as well as experimental validation are also provided.     

Reduced‐cost microwave filter modeling using a two‐stage Gaussian process regression approach

A technique for the reduced‐cost modeling of microwave filters is presented. Our approach exploits variable‐fidelity electromagnetic (EM) simulations, and Gaussian process regression (GPR) carried out in two stages. In the first stage of the modeling process, a mapping between EM simulation filter models of low and high fidelity is established. The mapping is subsequently used in the second stage, making it possible for the final surrogate model to be constructed from training data obtained using only a fraction of the number of high‐fidelity simulations normally required. As demonstrated using three examples of microstrip filters, the proposed technique allows us to reduce substantially (by up to 80%) the central processing unit (CPU) cost of the filter model setup, as compared to conventional (single‐stage) GPR—the benchmark modeling method in this study. This is achieved without degrading the model generalization capability. The reliability of the two‐stage modeling method is demonstrated through the successful application of the surrogates to surrogate‐based filter design optimization. © 2014 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:453–462, 2015.     

Process structure-based recurrent neural network modeling for model predictive control of nonlinear processes

In this work, physics-based recurrent neural network (RNN) modeling approaches are proposed for a general class of nonlinear dynamic process systems to improve prediction accuracy by incorporating a priori process knowledge. Specifically, a hybrid modeling method is first introduced to integrate first-principles models and RNN models. Subsequently, a partially-connected RNN modeling method that designs the RNN structure based on a priori structural process knowledge, and a weight-constrained RNN modeling method that employs weight constraints in the optimization problem of the RNN training process are developed. The proposed physics-based RNN models are utilized in model predictive controllers and applied to a chemical process network example to demonstrate their improved approximation performance compared to the fully-connected RNN model that is developed as a black box model.     

进化回归神经网络对时序数据和关联数据的建模能力研究

重点研究进化回归神经网络对时序数据和关联数据的建模能力。针对两个标准问题，采用不同形式的建模数据，比较了前向网络和回归神经网络的建模及预测效果，进一步将进化算法用于不同结构回归神经网络的训练并比较了它们的建模能力。仿真结果表明回归神经网络对时序关联数据有很好的建模和预测能力，相比于前向网络，无需过程时序特点的先验知识，可以采用最简单的建模数据形式。而进化算法相比于常规的梯度下降算法，用于训练不同的回归网络结构通用性好，且训练过程不受局部极小问题的困扰，适当规模的训练过程可以获得性能良好的神经网络模型。     

A compound structure and a single‐step identification procedure for I/Q and DC offset impairments and nonlinear distortion modeling and compensation in wireless transmitters

The nonlinear behavior of power amplifiers (PAs) and the in‐phase/quadrature (I/Q) imbalance in I/Q modulators are considered as the main sources of distortions and impairments in radio frequency transmitters. In this article, a compound structure and a single‐step identification procedure are proposed for the modulator's I/Q imbalance and DC offset and the PAs nonlinearity modeling and compensation of wireless transmitters. In fact, the performance of the digital predistortion technique used for PA linearization is adversely affected by the I/Q modulator's impairments that result mainly from gain/phase imbalance and DC offset. The measurement results reveal the robustness of the proposed model in modeling and linearization of the PA in the presence of I/Q modulator imperfections and show its superiority as compared to the generalized memory polynomial model and the dual‐input polynomial model. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2013.     

Robust Recurrent Neural Network Control of Biped Robot

In this paper, a recurrent neural network (RNN) control scheme is proposed for a biped robot trajectory tracking system. An adaptive online training algorithm is optimized to improve the transient response of the network via so-called conic sector theorem. Furthermore, L ₂-stability of weight estimation error of RNN is guaranteed such that the robustness of the controller is ensured in the presence of uncertainties. In consideration of practical applications, the algorithm is developed in the discrete-time domain. Simulations for a seven-link robot model are presented to justify the advantage of the proposed approach. We give comparisons between the standard PD control and the proposed RNN compensation method.     

Parametric modeling of microwave filter using combined MLS‐SVR and pole‐residue‐based transfer functions

In this article, an advanced technique is developed to combine multi‐output least‐squares support vector regression (MLS‐SVR) and pole‐residue‐based transfer function models for microwave filter parametric modeling. MLS‐SVR is trained to learn the relationship between the length of tuning screws and the pole/residues of the transfer function, where MLS‐SVR is an effective method to cope with the multi‐output case unlike the traditional approach. Traditional approach treats the different outputs separately in the multi‐output case and it cannot model the relation between different outputs. Another important element for modeling is feature parameters. Extracted feature parameters have an important influence on the accuracy of modeling. For the purpose of establishing a more accurate model, the complex system poles and residues from Y‐parameters are chosen as the outputs of modeling, which are obtained by vector fitting (VF). Then we give a solution to obtaining pole/residues extracted by VF when the filter is in high detuned. After the proposed modeling process, trained model can be used to provide an accurate and fast prediction of the behavior of microwave filter with the length of tuning screws as variables, and model the electromagnetic simulation (or actual) microwave filter tuning. The methodology is applied to a narrow band coaxial‐resonator filter modeling, and more accurate results are achieved compared with the other methods. An example is presented to illustrate the efficiency of the proposed method.     

Frequency domain data based model extraction for band‐limited digital predistortion of wideband RF power amplifiers

Bandwidth constraints pose significant challenges to linearization of wideband RF power amplifiers (PAs) with digital predistortion (DPD). A recently proposed band‐limited DPD scheme uses a band‐limited modeling technique to eliminate the bandwidth constraints and reduce DPD implementation cost. However, time consuming convolution operations are involved for model extraction in this time domain data based band‐limited modeling method. In this article, band‐limited model extraction is formulated as a generalized least squares problem and investigated from a frequency domain perspective. A frequency domain data based model extraction method is proposed, which greatly reduces the computational complexity for extracting band‐limited DPD model parameters. A 10 W GaN HEMT inverse class‐F PA excited by a 20 MHz four‐carrier WCDMA signal and a 40 MHz two‐carrier LTE signal is tested to validate the method. Experimental results show that the computationally efficient frequency domain data based model extraction method for band‐limited DPD provides as good linearization performance as the time domain data based method. © 2013 Wiley Periodicals, Inc. Int J RF and Microwave CAE 24:412–420, 2014.     

Enhancement of time domain analysis and optimization through neural networks

An efficient computational approach to time domain microwave design and optimization is presented. In particular, artificial neural networks are coupled with a full‐wave time domain simulator in order to model and optimize microwave structures. Furthermore, neural networks are used to predict the late time response from the early time response of a structure to accelerate the convergence of time domain simulations, particularly in the case of high‐Q structures such as filters and resonators. The combination of neural networks with a time domain TLM solver is demonstrated by means of a design example of an iris‐coupled band pass filter. The results demonstrate the dramatic gain in speed and numerical efficiency enabled by this approach to optimizing and modeling microwave devices. © 2007 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2007.     

Robust Adaptive Gradient-Descent Training Algorithm for Recurrent Neural Networks in Discrete Time Domain

For a recurrent neural network (RNN), its transient response is a critical issue, especially for real-time signal processing applications. The conventional RNN training algorithms, such as backpropagation through time (BPTT) and real-time recurrent learning (RTRL), have not adequately addressed this problem because they suffer from low convergence speed. While increasing the learning rate may help to improve the performance of the RNN, it can result in unstable training in terms of weight divergence. Therefore, an optimal tradeoff between RNN training speed and weight convergence is desired. In this paper, a robust adaptive gradient-descent (RAGD) training algorithm of RNN is developed based on a novel RNN hybrid training concept. It switches the training patterns between standard real-time online backpropagation (BP) and RTRL according to the derived convergence and stability conditions. The weight convergence and $L_2$-stability of the algorithm are derived via the conic sector theorem. The optimized adaptive learning maximizes the training speed of the RNN for each weight update without violating the stability and convergence criteria. Computer simulations are carried out to demonstrate the applicability of the theoretical results.      

Neural networks and volterra series for time‐domain power amplifier behavioral models

This paper presents a black‐box model that can be applied to characterize the nonlinear dynamic behavior of power amplifiers (PAs), including strong nonlinearities and memory effects. Feedforward time‐delay Neural Networks (TDNN) are used to extract the model from a large‐signal input‐output time‐domain characterization in a given bandwidth; furthermore, explicit formulas to derive Volterra kernels from the TDNN parameters are also presented. The TDNN and related Volterra models can predict the amplifier response to different frequency excitations in the same bandwidth and power sweep. As a case study, a PA, characterized with a two‐tone power swept excitation, is modeled and simulations are found in good agreement with training measurements; moreover, a model validation with two tones of different frequencies and spacing is also performed. © 2007 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2007.     

A regime-switching recurrent neural network model applied to wind time series

This paper proposes a regime-switching recurrent network model (RS-RNN) for non-stationary time series. The RS-RNN model emits a mixture density with dynamic nonlinear regimes that fit flexibly data distributions with non-Gaussian shapes. The key novelties are: development of an original representation of the means of the component distributions by dynamic nonlinear recurrent networks, and derivation of a corresponding expectation maximization (EM) training algorithm for finding the model parameters. The results show that the RS-RNN applied to a real-world wind speed time series achieves standardized residuals similar to popular previous models, but it is more accurate distribution forecasting than other linear switching (MS-AR) and nonlinear neural network (MLP and RNN) models.     

Microstrip antenna design using artificial neural networks

Neural‐network computational modules have recently gained recognition as an unconventional and useful tool for RF and microwave modeling and design. Neural networks can be trained to learn the behavior of passive/active components/circuits. This work describes the fundamental concepts in this emerging area aimed at teaching RF/microwave engineers what neural networks are, why they are useful, when they can be used, and how to use them to model microstrip patch antenna. This work studies in‐depth different designs and analysis methods of microstrip patch antenna using artificial neural‐network and different network structure are also described from the RF/microwave designer's perspective. This article also illustrates two examples of microstrip antenna design and validating the utility of ANN in the area of microstrip antenna design. © 2009 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2010.     

Extracting finite-state representations from recurrent neuralnetworks trained on chaotic symbolic sequences

Concerns neural-based modeling of symbolic chaotic time series. We investigate the knowledge induction process associated with training recurrent mural nets (RNN) on single long chaotic symbolic sequences. Even though training RNN to predict the next symbol leaves the standard performance measures such as the mean square error on the network output virtually unchanged, the nets extract a lot of knowledge. We monitor the knowledge extraction process by considering the nets stochastic sources and letting them generate sequences which are then confronted with the training sequence via information theoretic entropy and cross-entropy measures. We also study the possibility of reformulating the knowledge gained by RNN in a compact easy-to-analyze form of finite-state stochastic machines. The experiments are performed on two sequences with different complexities measured by the size and state transition structure of the induced Crutchfield's epsilon-machines (1991, 1994). The extracted machines can achieve comparable or even better entropy and cross-entropy performance. They reflect the training sequence complexity in their dynamical state representations that can be reformulated using finite-state means. The findings are confirmed by a much more detailed analysis of model generated sequences. We also introduce a visual representation of allowed block structure in the studied sequences that allows for an illustrative insight into both RNN training and finite-state stochastic machine extraction processes.     

一类非线性周期时间序列模型

为了描述周期时间序列中的偏倚和多峰等非线性特征,结合有限混合模型方法,提出混合周期自回归滑动平均时间序列模型（MPARMA）,给出了MPARMA模型的平稳性条件,讨论了期望最大化（EM）算法的应用,通过PM10浓度序列分析,评估了MPARMA模型的表现。