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.

Behavioral modeling and predistortion

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

A comparative analysis of behavioral models for RF power amplifiers

In this paper, systematic neural network modeling techniques are presented for microwave modeling and design using the concept of inverse modeling where the inputs to the inverse model are electrical parameters and outputs are geometrical parameters. Training the neural network inverse model directly may become difficult due to the nonuniqueness of the input-output relationship in the inverse model. We propose a new method to solve such a problem by detecting multivalued solutions in training data. The data containing multivalued solutions are divided into groups according to derivative information using a neural network forward model such that individual groups do not have the problem of multivalued solutions. Multiple inverse models are built based on divided data groups, and are then combined to form a complete model. A comprehensive modeling methodology is proposed, which includes direct inverse modeling, segmentation, derivative division, and model combining techniques. The methodology is applied to waveguide filter modeling and more accurate results are achieved compared to the direct neural network inverse modeling method. Full electromagnetic simulation and measurement results of Ku-band circular waveguide dual-mode pseudoelliptic bandpass filters are presented to demonstrate the efficiency of the proposed neural network inverse modeling methodology.

/pdf/neural-network-inverse-modeling-and-applications-to-59svabkg4a.pdf

Neural Network Inverse Modeling and Applications to Microwave Filter Design

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.

https://publications.lib.chalmers.se/records/fulltext/local_121905.pdf

A Comparative Analysis of the Complexity/Accuracy Tradeoff in Power Amplifier Behavioral Models

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.

Full-duplex mobile device: pushing the limits

A radial-basis function neural network (RBFNN) has been used for modeling the dynamic nonlinear behavior of an RF power amplifier for third generation. In the model, the signal's envelope is used. The model requires less training than a model using IQ data. Sampled input and output signals were used for identification and validation. Noise-like signals with bandwidths of 4 and 20 MHz were used. The RBFNN is compared to a parallel Hammerstein (PH) model. The two model types have similar performance when no memory is used. For the 4-MHz signal, the RBFNN has better in-band performance, whereas the PH is better out-of-band, when memory is used. For the 20-MHz signal, the models have similar performance in- and out-of-band. Used as a digital-predistortion algorithm, the best RBFNN with memory suppressed the lower (upper) adjacent channel power 7 dB (4 dB) compared to a memoryless nonlinear predistorter and 11 dB (13 dB) compared to the case of no predistortion for the same output power for a 4-MHz-wide signal.

Wide-band dynamic modeling of power amplifiers using radial-basis function neural networks

In this paper, a method for increasing the bandwidth of a test bed for dynamic characterization of power amplifiers (PAs) is described. The technique is readily implemented using commercially available instruments, which makes it suitable for, e.g., production testing. The bandwidth extension technique is combined with coherent averaging of the measurements in order to simultaneously increase the bandwidth and dynamic range of the test bed. The errors in the obtained wideband signal are also estimated. The method is evaluated experimentally on a base station PA for the third-generation wideband code division multiple access system and on a Doherty amplifier. A tenfold increase in bandwidth to a total of 144 MHz and a more than 10-dB increase in dynamic range to 78 dB were obtained in practice. In addition, the obtained wideband signal is used for behavioral amplifier modeling.

A Technique to Extend the Bandwidth of an RF Power Amplifier Test Bed

In this paper, a novel method to measure the amplitude and phase of two-tone third-order intermodulation products generated in a high-power amplifier is presented. The method is based on the sampled input and output signals of the amplifier. The presented measurement setup and the associated algorithms for the calculation of the amplitudes and phases are considerably faster and simpler than the current methods. By making use of the sampled input and output signals of the amplifier and the signal processing techniques, the need for a nonlinear reference, a tunable attenuator, and a phase shifter in the existing measurement setups is eliminated, which makes it simple and easy to use. Hence, this is a substantial simplification of the measurement setup compared to what has been reported earlier. The proposed measurement setup is also suitable for fast automated measurements, which is of interest for many applications that are both laboratory and production oriented. In addition, a method to increase the bandwidth of the measured signal is used to overcome the bandwidth limitation set by the Nyquist criteria for sampled systems. Measurements are done on two base-station high-power amplifiers and are found to be in agreement with theory and reference measurements.

Characterization of Memory Effects in Power Amplifiers Using Digital Two-Tone Measurements

A stepped three-tone measurement technique based on digitally modulated baseband signals is used in characterizing radio-frequency power amplifiers (PAs). The bandwidths of the stepped measurement were 8.8 MHz for the input signal and 26.4 MHz for the output signal. A PA designed for third-generation mobile telecommunication system was analyzed. The amplitude and phase of the third-order Volterra kernel were determined from the identified intermodulation products. The properties of the Volterra kernel along certain paths in the 3-D frequency space were analyzed and compared to some box models for nonlinear systems. The main symmetry of the third-order Volterra kernel of this PA was found to be of the type given by the cascaded quadratic nonlinearities with a linear filter in between (a Hammerstein-Wiener system), and frequency dependence, i.e., memory effects, was found to be due to the effects at the baseband.

David Wisell

Papers

A comparative analysis of behavioral models for RF power amplifiers

Wide-band dynamic modeling of power amplifiers using radial-basis function neural networks

A Technique to Extend the Bandwidth of an RF Power Amplifier Test Bed

Characterization of Memory Effects in Power Amplifiers Using Digital Two-Tone Measurements

Three-Tone Characterization of Nonlinear Memory Effects in Radio-Frequency Power Amplifiers