Predistortion Model Research Articles

A low-power high-performance digital predistorter for wideband power amplifiers

In this paper, we present a low-power high-performance digital predistorter (DPD) for the linearization of wideband RF power amplifiers (PAs). It is based on the novel FIR memory polynomial (FIR-MP) predistorter model, which significantly augments the performance of the conventional memory polynomial predistorter with the use of complex baseband digital FIR filter prior to the memory polynomial. The adjacent channel leakage ratio (ACLR) performance comparison between the conventional MP and the proposed FIR-MP is done based on simulations with multi-carrier modulated signals of 20 and 80 MHz bandwidths. The PA models used for the simulations are extracted from the measurements of a commercial $$1\,\hbox {W}$$ GaAs HBT PA. At the ideal system-level simulations, the improvements in ACLR over the conventional MP are 7.2 and 15.6 dB, respectively, for 20 and 80 MHz signals. The choice of selection of various parameters of the predistorter along with the subsequent digital-to-analog converter (DAC) is presented. The impact of fixed-point representation is assessed using ACLR metrics, which shows that a wordlength of 14 bits is sufficient to obtain ACLR beyond $$45\,\hbox {dBc}$$ with a margin of $$10\,\hbox {dB}$$ . The proposed predistorter is synthesized in $$28\,\hbox {nm}$$ fully-depleted silicon-on-insulator (FDSOI) CMOS process. It is shown that with a fraction of the power and die area of that of the MP a huge improvement in ACLR is attained. With an overall power consumption of 8.2 and 88.8 mW, respectively, for 20 and 80 MHz signals, the FIR-MP DPD proves to be a suitable candidate for small-cell base station PA linearization.

A Novel Algorithm for Determining the Structure of Digital Predistortion Models

The generalized memory polynomial (GMP) model is one of the most commonly used models in digital predistortion to compensate for the nonlinearities and memory effects of power amplifiers (PAs). A very difficult, yet crucial, aspect of behavioral modeling is model dimensioning, i.e., determining nonlinear orders and memory depths. In this paper, we propose an algorithm based on hill-climbing (HC) heuristic to search for a GMP model structure, which provides the best tradeoff between modeling accuracy and complexity with different search criteria. Algorithm performance and convergence are evaluated for two different search criteria. Some optimization methods of the algorithms are then proposed to reduce the execution time by controlling its search path. The algorithm has been evaluated using real measurements from two different Doherty PAs. The solutions of the algorithm are proved robust in linearization of PA on the test bench. The results show that the proposed algorithm allows us to decrease the searching time by a factor typically greater than $10^4$ compared with exhaustive search.

Instantaneous Sample Indexed Magnitude-Selective Affine Function-Based Behavioral Model for Digital Predistortion of RF Power Amplifiers

In this paper, we present a new behavioral model for digital predistortion (DPD) of RF power amplifiers in wireless transmitters. Derived from the decomposed vector rotation model, the new model uses magnitude-selective affine functions as nonlinear operators to construct nonlinear behavior of the model, leading to a highly efficient hardware implementation. Moreover, cross-terms are carefully redesigned based on a new formulation of model structure that not only improves the modeling performance but also significantly lowers the complexity of model extraction. Simulation and experimental results have demonstrated its superior performance and efficient hardware implementation, making this model well suitable for future DPD deployment in 5G small cell base stations where digital hardware resource is highly constrained.

Composite Neural Network Digital Predistortion Model for Joint Mitigation of Crosstalk, $I/Q$ Imbalance, Nonlinearity in MIMO Transmitters

Multi-input multi-output (MIMO) is anticipated to be a prominent technique proposed in the wireless communications to improve the system capacity and data rates of the wireless networks. However, the MIMO transmitter suffers from imperfections, such as crosstalk, power-amplifier (PA) nonlinearity, in-phase and quadrature (I/Q) imbalance, and dc offset. Investigating these effects, this paper proposes neural network (NN)-based digital predistortion (DPD) as an integral solution to compensate for crosstalk, PA nonlinearity, I/Q imbalance, and dc offset imperfections simultaneously in MIMO transmitters. The proposed NN DPD model provides a one-step single-model digital mitigation solution to multibranches of MIMO transmitters. With the increase in the dimensions of MIMO transmitter, the proposed NN-based DPD model provides a better compensation for transmitter imperfections and also reduces the complexity as compared to the state-of-the-art DPD methods. The proof-of-concept is provided with the 2×2 and 3×3 MIMO transmitters in the presence of strong PA nonlinearity, crosstalk, I/Q imbalance, and dc offset for homodyne as well as heterodyne transmitters' cases.

Digital Predistortion of an RF Power Amplifier Using a Reduced Volterra Series Model With a Memory Polynomial Estimator

A technique for reducing the number of basis waveforms used in a Volterra series model for digital predistortion (DPD) of radio frequency power amplifiers is proposed. An effective delay is defined for each basis waveform. The DPD model is constrained so that the basis waveforms used have unique delays. When several of the original Volterra terms have a common delay, they are either grouped together to form a single basis waveform or pruned to discard all but the dominant term. It is shown that grouping and pruning produce similar ACLR results when the coefficient estimator notch filters the linear signal bandwidth and applies regularization. Unique delay DPD basis sets are compatible with a fractionally sampled memory polynomial estimator. The basis waveforms within the estimator are specified in the frequency domain as a function of memoryless waveforms and delay operators, thereby reducing the number of fast Fourier transforms needed and allowing for fractional tap spacing that matches the effective delays of Volterra basis waveforms used within the DPD basis set. The approximation associated with using a memory polynomial estimator is sufficiently accurate for a closed-loop estimator to converge to a desired steady state.

Impedance-Dependent Wideband Digital Predistortion of Solid-State Radar Amplifiers

Spectral regrowth and waveform distortion caused by wideband signals input into active phased array antenna systems is the problem this paper addresses. The paper's unique contribution is the development of the impedance-dependent memory polynomial model, capable of solving nonlinear predistortion model parameters for a solid-state high power amplifier with varying load impedance resulting from active electronic beamsteering. Wideband load impedance mismatched tests demonstrate the effectiveness of this technique on a 2.7 GHz, 8 W amplifier.

Compensation of Long-Term Memory Effects on GaN HEMT-Based Power Amplifiers

The long-term memory effects of gallium nitride (GaN) transistors have prevented its use in situations where the modulated envelope signal has a wide amplitude variation over time, such as in time division duplex systems. These long-term memory effects are generally attributed to electron trapping in GaN high electron-mobility transistors (HEMT), which have shown to be very difficult to compensate, especially in cellular base station transmitters known to be subjected to highly restrictive linearity specifications. On top of the electron trapping effects, we show that thermal effects can also induce long-term memory behaviors, which should also be accounted for when linearizing these devices. Because the conventional behavioral modeling approach has been incapable to compensate these long-term memory effects on GaN HEMT-based power amplifiers (PAs), we started by investigating the physical mechanisms responsible for these semiconductor impairments in GaN devices. This physics-based knowledge was then used to design new predistorter models that could effectively compensate those PAs subjected to GaN trapping and thermal effects. In this paper, we describe the new predistortion models for PA linearization, as well as the characterization methods used to determine their parameters. To validate the linearization effectiveness of the proposed model, several high power GaN-based PAs are tested with multicarrier GSM signals, and their linearization results are compared against other state-of-the-art models, evidencing a clear and significant improvement. In fact, to the authors’ knowledge, the proposed approach is the first one to reduce the PA distortion effects due to GaN long-term memory effects to such low levels, allowing a comfortable compliance with the imposed linearity masks.

Deep neural nets based power amplifier non-linear pre-distortion

This paper proposed a novel method based on deep neural networks (auto-encoder) model, to construct the pre-distortion model for non-linear feature of power amplifier. As auto-encoder nets are high non-linear function, with the optimization of object function to tune the weights, the nets can reach any non-linear model. For widely used power amplifier, this method can help setting the pre-distortion model. In this paper, deep (more layers) network structure have been adopted in the auto-encoder model. The experimental results show the effectiveness and efficiency of deep neural network based power amplifier non-linear pre-distortion technique.

Dynamic deviation memory polynomial model for digital predistortion

A dynamic deviation memory polynomial (DDMP) model for digital predistortion is proposed to compensate the non-linear distortion of the power amplifier. It is based on the memory polynomial model and dynamic deviation reduction-based Volterra (DDRV) model. Compared to the DDRV model, the proposed model shows better modelling accuracy under the same complexity. The effectiveness of the DDMP model has been verified by simulation and experiment results.

Concurrent Dual-Band Digital Predistortion Using 2-D Lookup Tables With Bilinear Interpolation and Extrapolation: Direct Least Squares Coefficient Adaptation

In this paper, we present a method to implement concurrent dual-band digital predistortion (DPD) models using 2-D lookup tables (LUTs) with bilinear interpolation and extrapolation. We introduce the required set of basis functions to describe this model. The DPD output is expressed as a linear combination of these basis functions and we show how to directly estimate the coefficients using least squares. We introduce a flexible 2-D bilinear extrapolation scheme that is ideally suited to dual-band signals with high peak-to-average power ratio. We show how these are needed when digital predistortion is implemented in conjunction with automatic gain control. We also introduce example dual-band polynomial models with memory and show how to create a similar memory model based on 2-D lookup tables with bilinear interpolation. One such model is the dual-band generalized memory polynomial model. Laboratory experiments are performed using such a 2-D LUT with bilinear interpolation model.

Design of Efficient Power Amplifier Models Using 16-QAM

In this paper a predistorter linearizer is designed to reduce the memory less and also memory effect in different power amplifier models. The proposed method is based on the joint working principle of RLS filter model (polynomial) which compensate intermodulates and the multi-level system excludes the trade-off between precision and adaptation speed. The Predistorter model is validated by utilizing the orthogonal frequency division multiplexing in 16-QAM modulation. The Matlab realization of the proposed system shows 32×–34× faster convergence time than predistorter based on conventional LMS model with same adaptation step.

Non-overlapping conditions to enable multi- dimensional behavioral models/dpds for multi-band or non-continuous carrier aggregation systems

To linearize the multi-band PAs/ transmitters, a serial of multi-band predistortion models based on multi-dimensional architecture have been proposed. However, most of these models work properly only for the signals whose harmonic and intermodulation products of carriers' non-overlap with the interested fundamental bands. In this paper, the non-overlapping conditions for dual-band and tri-band signals are derived and denoted in the form of closed-form expression. It can be used to verify whether a given dual-band/ multi-band signals can be linearized properly by these multi-dimensional behavioral models. Also the conditions can be used to plan the frequency spacing and maximum bandwidth of a multi-band or non-continuous carrier aggregation signal. Several dual-band and triband signals were tested on the same PA, by employing 2-D DPD and 3-D DPD behavioral models. The measurement results show that the signals which don’t satisfy the non-overlapping conditions cannot be linearized well by the multi-dimensional behavioral models which does not take the harmonic and intermodulation products of carriers' into account.

Multi-Band Complexity-Reduced Generalized-Memory-Polynomial Power-Amplifier Digital Predistortion

This paper expounds a complexity-reduced generalized memory polynomial (CR-GMP) model for multi-band power amplifier (PA) digital predistortion (DPD). First, PA block diagrams characterizing the behavior of PAs under multi-band stimulus are proposed. Second, CR-GMP forward models are derived from the feedback block diagrams of the PA, driven with both dual- and tri-band signals, leading to a general formulation for PAs driven with multi-band signals. The resulting models are used to linearize two PAs driven with dual- and tri-band signals. The proposed CR-GMP models are compared to a dual-input digital predistortion (2D-DPD) model and a triple-input digital predistortion (3D-DPD) model and show similar linearization performance while requiring fewer coefficients. Due to the presence of cross terms in the dual-band CR-GMP formulation, the proposed model is robust against time-delay misalignment between dual-band signals, whereas the 2D-DPD is not. With a reduced number of coefficients and the presence of cross terms, the proposed CR-GMP models represent excellent candidates for the linearization of highly nonlinear PAs driven with multi-band signals.

Comparative study of polynomial based predistorters for LTE-radio over fiber applications

In this paper, we are comparative study of performance analysis of polynomial based predistorter technique with three different architectures viz. memory polynomial, envelope memory polynomial and hybrid envelope memory polynomial models for high order of nonlinearity (K=7) and large memory length (Q=3). The nonlinear distortion is a critical issue for radio over fiber link. The predistorter is one of the most important approaches to overcome the nonlinear distortion. In this paper the performance analysis of the two most prevailing predistorters (memory polynomial and envelope memory polynomial) have been compared with the performance of the model (hybrid envelop memory polynomial) developed by the author. The performance of different predistorter model are analyzed for input laser power ranging from −4dBm to 4dBm, input frequency for ∼0.55GHz to ∼3.00GHz and for different type of input signal like m-QAM, orthogonal frequency division multiplex, WiMax and LTE (long term evolution). The performance metrics are adjacent power ratio, error vector magnitude and normalized mean square error. The model have been tested for fiber length up to ∼50km. Whole of the simulation work to compare the performance analysis has been carried out on OptiSystem v13.0 and MATLAB R20013a.

Development of hybrid envelop memory polynomial based predistorter for RoF system

Radio over Fiber (RoF), an empowering innovation for dissemination of wireless broadband service signals through simple optical connections experiences non-linear distortion. We have designed and implemented a novel predistorter model to reduce nonlinear distortion using hybrid envelop memory polynomial (HEMPM) for the RoF system. The link gives satisfactory performance in the range of GHz signal. The designed algorithm is superior to popular approaches like memory polynomial model (MPM) and envelop memory polynomial model (EMPM) in terms of order of the memory and degree of nonlinearity. As per author's the best knowledge, this is exclusively first time result obtained for HEMPM technique for RoF link and also, for MPM, EMPM based predistorter for RoF link using MATLAB – OptiSystem co-simulation. The results shows that adjacent channel power (ACP) is suppressed by ∼0.45dBm, ∼28.4dBm and ∼7.65dBm of MPM & EMPM and HEMPM model for K=5 &Q=2 whereas for K=7 &Q=3 the value of suppressed power is ∼36.3dBm, ∼47.7dB and ∼05.8dBm, respectively as compared to input signal. NMSEs for (K=7) and memory length (Q=3) reduced by ∼−5.003dBm for HEMPM model and increased by ∼−4.13dBm for MPM model. The EVM is increased from ∼1.56% to ∼1.96% for HEMPM model and increased from ∼4.38% to ∼14.73% for MPM model for K=7 &Q=3.

A Novel Model for Digital Predistortion of Discrete Level Supply-Modulated RF Power Amplifiers

The linearization of a discrete level supply modulated RF power amplifier using digital predistortion (DPD) is investigated. The characteristics of the system are evaluated and a novel DPD model, capable of handling the switching dynamics of the system, is developed and presented. The model is tested for an RF power amplifier operating at 2.65 GHz with a 16 MHz modulated signal. It is shown that modeling the supply voltage transitions with the novel model significantly improves linearity by up to 1.6 dB NMSE and 3.3 dB in ACLR. With the novel model DPD on the supply modulated PA can achieve similar linearity as a single supply PA but with much improved PAE.

Experimental demonstration of digital predistortion for orthogonal frequency‐division multiplexing‐radio over fibre links near laser resonance

Radio over fibre (RoF), an enabling technology for distribution of wireless broadband service signals through analogue optical links, suffers from non-linear distortion. Digital predistortion has been demonstrated as an effective approach to overcome the RoF non-linearity. However, questions remain as to how the approach performs close to laser resonance, a region of significant dynamic non-linearity, and how resilient the approach is to changes in input signal and link operating conditions. In this work, the performance of a digital predistortion approach is studied for directly modulated orthogonal frequency-division multiplexing RoF links operating from 2.47 to 3.7 GHz. It extends previous works to higher frequencies, and to higher quadrature amplitude modulation (QAM) levels. In addition, the resilience of the predistortion approach to changes in modulation level of QAM schemes, and average power levels are investigated, and a novel predistortion training approach is proposed and demonstrated. Both memoryless and memory polynomial predistorter models, and a simple off-line least-squares-based identification method, are used, with excellent performance improvements demonstrated up to 3.0 GHz.

An Average Power Tracking Method for Wideband Highly Nonlinear Power Amplifiers

An accurate average power tracking method is presented to track and compensate the fluctuation of power amplifier (PA) output during updates of digital predistorter. Firstly, joint distortion probability distribution (JDPD) of the predistorter input signal and PA compression state is presented to extract the average power gain fluctuation related to the nonlinearity of the PA. The accurate PA compression state is extracted by linear-zone-reposition technique. Then, the average power gain fluctuation related to PA memory is obtained assisted by the predistortion model. The PA output power fluctuation is well controlled through the proposed method. Results from experiments show that the performance of DPD improves at least 3 dB for long time experiments when the proposed method is used for wideband highly nonlinear PA.

Decomposed Vector Rotation-Based Behavioral Modeling for Digital Predistortion <newline/>of RF Power Amplifiers

A new behavioral model for digital predistortion of radio frequency (RF) power amplifiers (PAs) is proposed in this paper. It is derived from a modified form of the canonical piecewise-linear (CPWL) functions using a decomposed vector rotation (DVR) technique. In this model, the nonlinear basis function is constructed from piecewise vector decomposition, which is completely different from that used in the conventional Volterra series. Theoretical analysis has shown that this model is much more flexible in modeling RF PAs with non-Volterra-like behavior, and experimental results confirmed that the new model can produce excellent performance with a relatively small number of coefficients when compared to conventional models.

Research on the Application of Linearization Pre-Distortion Technique for Memoryless Power Amplifier

In order to improve the nonlinear problems of power amplifier, this paper discussed about the nonlinear characteristic of power amplifier without memory and put forward a kind of new pre-distortion model. The MATLAB simulation process was being used to obtain the input and output amplitude curves, and calculated the normalized mean square error NMES and error vector magnitude EVM, the results show that the power amplifier linearization improved after pre-distortion processing.