A comparative analysis of behavioral models for RF power amplifiers
TL;DR: The models with memory, PH, and RBFNN, showed better cross-validation performance, in terms of lower model errors, than a static polynomial for the hardest cross validation of the 2G PA.
Abstract: A comparative study of nonlinear behavioral models with memory for radio-frequency power amplifier (PAs) is presented. The models are static polynomial, parallel Hammerstein (PH), Volterra, and radial basis-function neural network (RBFNN). Two PAs were investigated: one was designed for the third-generation (3G) mobile telecommunication systems and one was designed for the second-generation (2G). The RBFNN reduced the total model error slightly more than the PH, but the error out of band was significantly lower for the PH. The Volterra was found to give a lower model error than did a PH of the same nonlinear order and memory depth. The PH could give a lower model error than the best Volterra, since the former could be identified with a higher nonlinear order and memory depth. The qualitative conclusions are the same for the 2G and 3G PAs, but the model errors are smaller for the latter. For the 3G PA, a static polynomial gave a low model error as low as the best PH and lower than the RBFNN for the hardest cross validation. The models with memory, PH, and RBFNN, showed better cross-validation performance, in terms of lower model errors, than a static polynomial for the hardest cross validation of the 2G PA
Citations
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TL;DR: A software digital predistortion solution that enables closed-loop wideband linearization was briefly presented with excellent linearization capabilities when amplifying a 12-carrier 60-MHZ wide WCDMA signal.
Abstract: In this article, a thorough overview of behavioral modeling and predistortion of dynamic nonlinearities in RF PAs and transmitters was presented. The sensitivity of the DUT behavior to the characteristics of the stimulus was reviewed to ensure appropriate conditions for accurate observation. Nearly all state-of-the-art behavioral models were described and their relative performance and complexity discussed. Similarities and specifics of behavioral modeling and digital predistortion were presented. Thereby, digital predistortion can be seen as a behavioral modeling problem for which performance assessment is much more straightforward. For DUT behavioral modeling, there is no comprehensive metric that allows the model performance evaluation while taking into account the model accuracy in predicting all the three components of the DUT behavior (in-band distortion, static nonlinearity and memory effects). Finally, a software digital predistortion solution that enables closed-loop wideband linearization was briefly presented with excellent linearization capabilities when amplifying a 12-carrier 60-MHZ wide WCDMA signal.
467 citations
TL;DR: The results show that the generalized memory polynomial behavioral model has the best tradeoff for accuracy versus complexity for both PAs, and can obtain high performance at half of the computational cost of all other models analyzed.
Abstract: A comparative study of state-of-the-art behavioral models for microwave power amplifiers (PAs) is presented in this paper. After establishing a proper definition for accuracy and complexity for PA behavioral models, a short description on various behavioral models is presented. The main focus of this paper is on the modeling accuracy as a function of computational complexity. Data is collected from measurements on two PAs-a general-purpose amplifier and a Doherty PA designed for WiMAX-for different output power levels. The models are characterized in terms of accuracy and complexity for both in-band and out-of-band error. The results show that, among the models studied, the generalized memory polynomial behavioral model has the best tradeoff for accuracy versus complexity for both PAs, and can obtain high performance at half of the computational cost of all other models analyzed.
274 citations
Cites background or methods from "A comparative analysis of behaviora..."
...Many identification methods exist, but in this work, a full search of poles for per each nonlinear order was done as in [34]....
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...It can be seen in this figure that as the number of parameters grow, the amount of improvement gained with excess parameters is limited....
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TL;DR: The findings indicate that deploying the full-duplex principle can indeed also be feasible in mobile devices, and thus be one potential technology in, for example, 5G and beyond radio systems.
Abstract: In this article, we address the challenges of transmitter-receiver isolation in mobile full-duplex devices, building on shared-antenna-based transceiver architecture. First, self-adaptive analog RF cancellation circuitry is required, since the ability to track time-varying self-interference coupling characteristics is of utmost importance in mobile devices. In addition, novel adaptive nonlinear DSP methods are also required for final self-interference suppression at digital baseband, since mobile-scale devices typically operate under highly nonlinear low-cost RF components. In addition to describing the above kind of advanced circuit and signal processing solutions, comprehensive RF measurement results from a complete demonstrator implementation are also provided, evidencing beyond 40 dB of active RF cancellation over an 80 MHz waveform bandwidth with a highly nonlinear transmitter power amplifier. Measured examples also demonstrate the good self-healing characteristics of the developed control loop against fast changes in the coupling channel. Furthermore, when complemented by nonlinear digital cancellation processing, the residual self-interference level is pushed down to the noise floor of the demonstration system, despite the harsh nonlinear nature of the self-interference. These findings indicate that deploying the full-duplex principle can indeed also be feasible in mobile devices, and thus be one potential technology in, for example, 5G and beyond radio systems.
195 citations
Cites background or methods from "A comparative analysis of behaviora..."
...Although the assumed PH model has been shown to be quite accurate for a wide variety of PAs [14], in practice it is not necessarily able to achieve perfect accuracy in modeling an arbitrary PA....
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...This means that the nonlinear residual SI channel follows a parallel Hammerstein (PH) model, whose parameters are relatively straight-forward to estimate and track [14]....
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TL;DR: In this paper, a digital predistorter structure for joint estimation and mitigation of frequency-dependent power amplifier and in-phase and quadrature (I/Q) modulator impairments in direct-conversion radio transmitters is presented.
Abstract: In this paper, we present a novel digital predistorter structure for joint mitigation of frequency-dependent power amplifier (PA) and in-phase and quadrature (I/Q) modulator impairments in direct-conversion radio transmitters. The predistorter is based on an extended parallel Hammerstein structure, yielding a predistorter that is fully linear in the parameters. In the parameter estimation stage, the indirect learning architecture is utilized. The proposed technique is the first technique in the literature to consider the joint estimation and mitigation of frequency-dependent PA and I/Q modulator impairments. Extensive simulation and measurement analysis is carried out to verify the operation and efficacy of the proposed predistortion structure. It is shown that the adjacent channel power ratio is increased by more than 20 dB in all experiments when using the proposed method, and that the performance of the reference techniques is clearly exceeded.
173 citations
TL;DR: The proposed switched behavioral model considering memory effects with a special focus on “difficult” amplifier architectures is proposed and is shown to be very low-complex and linearly identifiable and to outperform other state-of-the-art models and digital predistorters in terms of computational complexity.
Abstract: A switched behavioral model considering memory effects with a special focus on “difficult” amplifier architectures is proposed in this paper. The proposed model is shown to be very low-complex and linearly identifiable. A digital predistorter based on the proposed model is implemented for a 100-W 2.6-GHz Doherty power amplifier that has been considered difficult in other reports, and it is shown that the proposed models can successfully linearize the amplifier, both for a WCDMA signal and a more wideband long-term evolution signal. In particular, the proposed model and the digital predistorter is shown to outperform other state-of-the-art models and digital predistorters in terms of computational complexity for a given desired accuracy.
133 citations
References
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Book•
01 Jan 1987
TL;DR: Das Buch behandelt die Systemidentifizierung in dem theoretischen Bereich, der direkte Auswirkungen auf Verstaendnis and praktische Anwendung der verschiedenen Verfahren zur IdentifIZierung hat.
Abstract: Das Buch behandelt die Systemidentifizierung in dem theoretischen Bereich, der direkte Auswirkungen auf Verstaendnis und praktische Anwendung der verschiedenen Verfahren zur Identifizierung hat. Da ...
20,436 citations
Book•
01 Jan 1980
TL;DR: In this article, a complete and detailed development of the analysis, design and characterization of non-linear systems using the Volterra and Wiener theories, as well as gate functions, is presented.
Abstract: This text presents a complete and detailed development of the analysis, design and characterization of non-linear systems using the Volterra and Wiener theories, as well as gate functions, thus yielding new insights and a better comprehension of the subject. The Volterra and Wiener theories are useful in the study of systems in biological, mechanical, and electrical fields.
2,210 citations
"A comparative analysis of behaviora..." refers background in this paper
...Nonlinear dynamic behavioral PA models can, in most cases, be categorized as either neural networks (NNs) [20] or Volterra models [21]....
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TL;DR: A frequencydependent quadrature model is proposed whose parameters are obtainable from single-tone measurements and is shown to fit measured data very well.
Abstract: Simple two-parameter formulas are presented for the functions involved in the amplitude-phase and the quadrature nonlinear models of a TWT amplifier, and are shown to fit measured data very well. Also, a closed-form expression is derived for the output signal of a TWT amplifier excited by two phase-modulated carriers, and an expression containing a single integral is given when more than two such earriers are involved. Finally, a frequencydependent quadrature model is proposed whose parameters are obtainable from single-tone measurements.
1,442 citations
"A comparative analysis of behaviora..." refers methods in this paper
...In [11], an extension of the Wiener model was presented, in which parallel Wiener systems of different order are added; each one of the parallel systems has a linear filter....
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TL;DR: In this paper, memory effects in the power amplifier limit the performance of digital predistortion for wideband signals, and novel algorithms that take into account such effects are proposed to solve the problem.
Abstract: Memory effects in the power amplifier limit the performance of digital predistortion for wideband signals. Novel algorithms that take into account such effects are proposed. Measured results are presented for single and multicarrier UMTS signals to demonstrate the effectiveness of the new approach.
934 citations
"A comparative analysis of behaviora..." refers methods in this paper
...The model can be identified by minimizing the mean square error of the modeled and measured output signal using the nonlinear least-squares techniques [9], [13], [25]....
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Book•
30 Sep 2000
TL;DR: This is the first single comprehensive guide to examine and directly compare all major RF power amplifier linearization techniques in detail and save you valuable design time while helping to avoid costly design errors.
Abstract: From the Publisher:
Based on the author's real-world design experience in this key emerging area, this is the first single comprehensive guide to examine and directly compare all major RF power amplifier linearization techniques in detail. Packed with practical tips, more than 250 illustrations, and over 600 verified equations, the book saves you valuable design time while helping you avoid costly design errors. It covers the modeling and measurement of amplifier non-linearity, and describes the main methods for overcoming non-linearity in a wide range of applications, including:
> base stations using feedforward and predistortion
> mobile communications systems and handsets using RF or digital predistortion, cartesian loop, LINC and envelope elimination and restoration (EE&R )
> satellite systems using any of these techniques
689 citations