Modeling Of RF Power Amplifiers Research Articles

A Study on Real-Valued Models for Wideband RF Power Amplifier Modeling

A Study on Real-Valued Models for Wideband RF Power Amplifier Modeling

Dynamic behavioral modeling of RF power amplifiers based on decomposed piecewise machine learning technique

AbstractMulti-device radio frequency power amplifiers (PAs) often exhibit strongly non-linear behavior in combination with long-term memory effects, leading to an extremely challenging model development cycle. This paper presents a new, dynamic, behavioral modeling technique, based on a combination of the real-valued decomposed piecewise method and concepts from the field of machine learning. The underlying theory of the proposed modeling technique is provided, along with a detailed modeling procedure. Experimental results show that the proposed decomposed piecewise support vector regression (SVR) model leads to significant performance improvements when compared with standard SVR models for both single transistor and multi-transistor PAs. Different model thresholds are used to test the proposed model performance for both PA types. For the single-transistor PA, modeled using only one partition, an approximately 10 dB normalized mean square error (NMSE) reduction is seen when compared with the standard SVR model. For the same PA, when utilizing two partitions, the reduction improves to 14 dB. When applied to a multi-device Doherty PA, the NMSE between model and measurement data is −50 dB, representing more than 10 dB improvement compared with the standard SVR model.

Evolutionary extreme learning machine for the behavioral modeling of RF power amplifiers

AbstractIn this paper, evolutionary extreme learning machine (E‐ELM) is first introduced for RF power amplifiers (PAs) behavioral modeling. This approach combined differential evolution (DE) and extreme learning machine (ELM) to effectively solve the problem that more neurons of hidden layer are required, and repeated trials are necessary in behavioral modeling PAs by conventional ELM. As revealed in the modeling practices on Class‐AB and Class‐E PAs, fewer hidden layer neurons are used than the condition of conventional ELM. Meanwhile, it is found that ELM's unstable generalization ability in modeling PAs is also significantly improved, thanks to the internal DE method in the E‐ELM.

Design and Modeling of RF Power Amplifiers with Radial Basis Function Artificial Neural Networks

A radial basis function (RBF) artificial neural network model for a designed high efficiency radio frequency class-F power amplifier (PA) is presented in this paper. The presented amplifier is designed at 1.8 GHz operating frequency with 12 dB of gain and 36 dBm of 1dB output compression point. The obtained power added efficiency (PAE) for the presented PA is 76% under 26 dBm input power. The proposed RBF model uses input and DC power of the PA as inputs variables and considers output power as the output variable. The presented RBF network models the designed class-F PA as a block, which could be applied in circuit design. The presented model could be used to model any RF power amplifier. The obtained results show a good agreement between real data and predicted values by RBF model. The results clearly show that the presented RBF network is more precise than multilayer perceptron (MLP) model. According to the results, better than 84% and 92% improvement is achieved in MAE and RMSE, respectively

RF Power Amplifier Behavioral Modeling [Book\/Software Reviews

This book describes the behavioral, or system-level, modeling of RF power amplifiers (PAs) for linearization. It provides a basic background and framework for the nonlinear, dynamical modeling of a PA. These nonlinear modeling techniques can be used to design the digital predistortion linearization algorithm. The author focuses on Volterra series methods to provide a good foundation for understanding how to handle the nonlinear behaviors and dynamic, or time-dependent, effects in the transmitter.

Incorporation of Cross-Terms in Memory Polynomial Using Evolutionary Algorithm for Accurate Behavioral Modeling of RF Power Amplifiers

Incorporation of Cross-Terms in Memory Polynomial Using Evolutionary Algorithm for Accurate Behavioral Modeling of RF Power Amplifiers

Two novel memory polynomial models for modeling of RF power amplifiers

Two novel memory polynomial models are derived based on physical knowledge of a general power amplifier (PA). The derivations are given in detail to facilitate derivations of other model structures. The model error in terms of normalized mean square error (NMSE) and adjacent channel error power ratio (ACEPR) of the novel model structures are compared to that of established models based on the number of parameters using data measured on two different amplifiers, one high-power base-station PA and one low-power general purpose amplifier. The novel models show both lower NMSE and ACEPR for any chosen number of parameters compared to the established models. The low model errors make the novel models suitable candidates for both modeling and digital predistortion.

Special issue on power amplifier linearization

We are honored to be the guest editors of this Special Issue on linearization and modeling of RF power amplifiers (PAs). In recent years, there has been an upsurge in interest in the behavioral modeling of high-power RF amplifiers, and applying these modeling techniques to the linearization of the PAs using pre-distortion methods, usually applied at baseband frequencies, in the digital domain: hence digital pre-distortion or DPD. This increased interest has been evident in several workshops and focus sessions at the International Microwave Symposium, the European Microwave Conference, and the Radio andWireless Symposium in recent years. To our knowledge, this is the first special issue of a learned journal devoted to the behavioral modeling and linearization of RF PAs. Linearization as a topic is well established, in many fields of endeavor. Notably mathematical in nature, and often in pure form, it is often abstracted from a real application. But here we have a very practical use for the nonlinear mathematics, so it is therefore not a surprise that most of the tools for the linearization of PAs are found in the mathematics of nonlinear dynamical systems, and applied specifically to this interesting problem. Of significant importance, PAs are the backbone of wireless telecommunications systems. They are also the most power hungry devices among the transmitter subsystems. To reduce the power consumption, or, alternatively, to reduce the distortion produced by the PA, not only benefits directly billions of people worldwide using mobile communications by increasing the time of life of their batteries, but also shrinks the bill of the energy consumed in base-stations. This is achieved not only by improving the energy efficiency of the PA itself but also by reducing or removing the need for air conditioning systems in the base-stations, again reducing the energy costs and the carbon footprint of the base station: the behavioral modeling and linearization of PAs support a greener environment. As the demand for increased data over wireless continues to increase, the signal bandwidth, spectral efficiency, and modulation complexity have also increased, and this has raised the interest in PA linearizers significantly, making predistortion a commercial reality. The continued increase in signal bandwidth to cope with this increased data requires a similar increase in the bandwidth of the linearizer, and has promoted research on different technologies and strategies to overcome these bandwidth demands and produce more compact yet effective modeling and linearizing schemes. Such approaches see compromises between bandwidth, memory depth, and overall model complexity to achieve optimum model accuracy and a level of linearization that is sufficient for the given practical application. In this Special Issue of IJMWT, we bring together a collection of papers detailing various aspects of modeling and linearization, from a review of recent model developments and characterization and test methods, to new approaches for model parameter identification and implementation in DPD systems, in the face of the many and varied challenges to deliver more voice and data information, without compromising the quality of service. Such challenges, what is new in PA linearization, and the inventive and robust techniques for defeating them, form the thread of this issue. There are several papers that focus on the fundamentals of the behavioral modeling of RF PAs, with the goal being to produce compact yet effective DPD algorithms. The papers of Braithwaite [1] and Boumaiza [2] both address the issue of determining the appropriate memory description for the PA. Braithwaite analyses the sampling rate requirements, using a Gaussian channel model to make the mathematical treatment tractable, enabling the number and separation of the delay taps to be traded off against the model accuracy to achieve a practical PA model, and hence a pre-distorter that is compact and effective. Boumaiza employs the mathematical method of embedding to determine the memory tap spacing and memory depth, using a variety of techniques to estimate memory characteristic. Again, a compact and effective DPD linearizer is constructed and demonstrated. The paper by Mehdi et al. [3] applies model-order reduction techniques such as Akaike and Bayesian information criteria to reduce the number of model parameters in a systematic manner, again trading off model complexity against accuracy to arrive at the optimum model. This approach has been applied to build pre-distorters for traditional single input– single-output PAs and also multiple input–multiple output (MIMO) PA systems. In Sombrin’s paper [4], non-analytic functions that are invariant elements of the Chebyshev Transform are used to generalize the polynomial nonlinearity theory, producing models that exhibit intermodulation behavior significantly different from that of classical polynomial models, giving theoretical foundation for nonlinearities such as threshold and hard limiter functions. The final modeling paper is by Maziere et al. [5], who used a different approach Corresponding author: John Wood and Eduard Bertran Emails: john.wood@maximintegrated.com; bertran@tsc.upc.edu Maxim Integrated, San Jose, California, USA Universitat Politecnica de Catalunya, Barcelona, Catalonia, Spain

Adaptive Digital Predistortion of Wireless Power Amplifiers/Transmitters Using Dynamic Real-Valued Focused Time-Delay Line Neural Networks

Neural networks (NNs) are becoming an increasingly attractive solution for power amplifier (PA) behavioral modeling, due to their excellent approximation capability. Recently, different topologies have been proposed for linearizing PAs using neural based digital predistortion, but most of the previously reported results have been simulation based and addressed the issue of linearizing static or mildly nonlinear PA models. For the first time, a realistic and experimentally validated approach towards adaptive predistortion technique, which takes advantage of the superior dynamic modeling capability of a real-valued focused time-delay neural network (RVFTDNN) for the linearization of third-generation PAs, is proposed in this paper. A comparative study of RVFTDNN and a real-valued recurrent NN has been carried out to establish RVFTDNN as an effective, robust, and easy-to-implement baseband model, which is suitable for inverse modeling of RF PAs and wireless transmitters, to be used as an effective digital predistorter. Efforts have also been made on the selection of the most efficient training algorithm during the reverse modeling of PA, based on the selected NN. The proposed model has been validated for linearizing a mildly nonlinear class AB amplifier and a strongly nonlinear Doherty PA with wideband code-division multiple access (WCDMA) signals for single- and multiple-carrier applications. The effects of memory consideration on linearization are clearly shown in the measurement results. An adjacent channel leakage ratio correction of up to 20 dB is reported due to linearization where approximately 5-dB correction is observed due to memory effect nullification for wideband multicarrier WCDMA signals.

Measurement-based memory polynomial behavioral modeling of RF power amplifiers

Measurement-based memory polynomial behavioral modeling of RF power amplifiers

On the Continuous-Time Model for Nonlinear-Memory Modeling of RF Power Amplifiers

The RF front-end in modern communication systems is faced with variable envelope and large bandwidth signals (including desired signals and large interferers), which require the behavioral model of the amplifying unit (either in Tx or Rx) to accurately account for nonlinear memory effects. Important advancements have been made on the subject; however it is still challenging to derive a model that performs equally well with all possible input stimuli. This paper gives a concise overview of the recent developments that have been made on the continuous-time modeling approach for the behavioral modeling of nonlinear memory in power amplifiers, as opposed to the explicit discrete-time modeling approach.

Implementation of electrothermal system-level model for RF power amplifiers in Scilab/Scicos environment

This paper presents a behavioral electrothermal model implementation for high RF power amplifiers dedicated to the simulation of radar application in the Scilab/Scicos environment. This model, based on the direct coupling between a behavioral electrical model and a physics-based reduced thermal model, allows to predict nonlinear effects, high-frequency memory effects, and thermal effects due to the amplifier self-heating. System model implementation in Scilab/Scicos platform allows fast time domain simulation with very good convergence properties.

A Data-Based Nested LUT Model for RF Power Amplifiers Exhibiting Memory Effects

In this letter, a new model is proposed for radio frequency power amplifiers exhibiting memory effects. The model is based on nested look-up tables that compute the estimated amplifier output signal, based on the current input sample and the preceding ones. The model is validated experimentally, using input and output waveforms of a high-power LDMOS based amplifier driven by a multicarrier WCDMA signal. It is shown that the performance of the proposed model is comparable to that of the conventional memory polynomial model. However, the nested look-up table based model significantly reduces the complexity of the identification of the model's parameters, as well as the computational complexity in calculating the estimated output signal.

A parameter-reduced volterra model for dynamic RF power amplifier modeling based on orthonormal basis functions

A nonlinear dynamic behavioral model for radio frequency power amplifiers is presented. It uses orthonormal basis functions, Kautz functions, with complex poles that are different for each nonlinea ...

Dynamic Deviation Reduction-Based Volterra Behavioral Modeling of RF Power Amplifiers

A new representation of the Volterra series is proposed, which is derived from a previously introduced modified Volterra series, but adapted to the discrete time domain and reformulated in a novel way. Based on this representation, an efficient model-pruning approach, called dynamic deviation reduction, is introduced to simplify the structure of Volterra-series-based RF power amplifier behavioral models aimed at significantly reducing the complexity of the model, but without incurring loss of model fidelity. Both static nonlinearities and different orders of dynamic behavior can be separately identified and the proposed representation retains the important property of linearity with respect to series coefficients. This model can, therefore, be easily extracted directly from the measured time domain of input and output samples of an amplifier by employing simple linear system identification algorithms. A systematic mathematical derivation is presented, together with validation of the proposed method using both computer simulation and experiment

Quantifying memory effects in RF power amplifiers

This paper proposes a system-level behavioral model for RF power amplifiers (PAs), which exhibit memory effects, that is based on the parallel Wiener system. The model extraction is performed using two-tone intermodulation distortion (IMD) measurements with different tone frequency spacings and power levels. It is found that by using such a model, more accurate adjacent-channel power-ratio levels may be predicted for high PAS close to the carrier frequency. This is validated using IS-95B CDMA signals on a low-power (0.5 W) class-AB PA, and on a high-power (45 W) class-B PA. The model also provides a means to quantify memory effects in terms of a figure-of-merit that calculates the relative contribution to the IMD of the memoryless and memory portion of the PA nonlinearity. This figure-of-merit is useful in providing an estimate of the amount of correction that a memoryless predistortion system may have on PAS that exhibit memory effects.