Adaptive Digital Predistortion Research Articles

Regularization of the RLS algorithm for adaptive digital predistortion

Problem statement. Modern digital pre-image input systems, as a rule, involve the use of adaptation algorithms to correct their parameters. Adaptation algorithms are solutions based on LMS and RLS methods. At the same time, the efficiency, in terms of the convergence rate and the accuracy of the solution, of RLS methods is significantly higher. This is due to the presence of a covariance matrix as part of the solution based on the RLS method. However, when using RLS algorithms (an adaptation algorithm using the RLS method), problems may arise related to poor conditionality of the covariance matrix resulting from signal noise, high inertia of the nonlinear properties of the power amplifier, limited accuracy of parameter calculation, etc. To solve this problem, it is advisable to use the regularization procedure of the RLS algorithm, taking into account the specifics of the digital predistortion systems. Objective. Creation and analysis of the regularization procedure of the RLS algorithm for adaptive input systems of digital presets. Results. The paper presents the implementation of the regularization procedure of the RLS algorithm for adaptive input systems of digital presets. Using the regularization procedure of the RLS algorithm avoids the state of poor conditionality of the covariance matrix, thereby ensuring stable operation of the digital pre-order input system. The state of the covariance matrix is monitored at each iteration of the RLS algorithm by evaluating the trace of the matrix. Practical importance. The proposed solution can be used to stabilize the parameters of adaptive systems for entering pre-orders based on RLS algorithms.

Adaptive digital predistortion based on Feedback–Wiener Model for aeronautical applications

AbstractIn this work, a new adaptive digital predistorter (DPD) is proposed to linearize radio frequency power amplifiers (PA). The DPD structure is composed of two sub-models. A Feedback–Wiener sub-model, describing the main inverse nonlinearities of the PA, combined with a second sub-model based on a memory polynomial (MP) model. The interest of this structure is that only the MP model is identified in real time to compensate deviations from the initial behavior and thus further improve the linearization. The identification architecture combines offline measurement and online parameter estimation with small number of coefficients in the MP sub-model to track the changes in the PA characteristics. The proposed structure is used to linearize a class AB 75 W PA, designed by Telerad society for aeronautical communications in Ultra High Frequency (UHF) / Very High Frequency (VHF) bands. The obtained results, in terms of identification of optimal DPD and the performances of the digital processing, show a good trade-off between linearization performances and computational complexity.

Training Data Selection and Dimensionality Reduction for Polynomial and Artificial Neural Network MIMO Adaptive Digital Predistortion

In 5G and beyond radios, the increased bandwidth, the fast-changing waveform scenarios, and the operation of large array multiple-input multiple-output (MIMO) transmitter architectures have challenged both the polynomial and the artificial neural network (ANN) MIMO adaptive digital predistortion (DPD) schemes. This article proposes training data selection methods and dimensionality reduction techniques that can be combined to enable relevant reductions of the DPD training time and the implementation complexity for MIMO transmitter architectures. In this work, the combination of an efficient uncorrelated equation selection (UES) mechanism together with orthogonal least squares (OLS) is proposed to reduce the training data length and the number of basis functions at every behavioral modeling matrix in the polynomial MIMO DPD scheme. For ANN MIMO DPD architectures, applying UES and principal component analysis (PCA) is proposed to reduce the input dataset length and features, respectively. The UES-OLS and the UES-PCA techniques are experimentally validated for a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2 \,\times \, 2$ </tex-math></inline-formula> MIMO test setup with strong power amplifier (PA) input and output crosstalk.

Reconfigurable DPD Based on ANNs for Wideband Load Modulated Balanced Amplifiers Under Dynamic Operation From 1.8 to 2.4 GHz

This article proposes a methodology to ensure linear amplification of a load modulated balanced amplifier (LMBA) while keeping the power efficiency as high as possible over a frequency band ranging from 1.8 to 2.4 GHz and where the transmitted signals can present different bandwidth (BW) configurations. The proposed reconfigurable linearization methodology consists of, in a first step, tuning some free parameters (with dependence on the signal BW and frequency of operation) of the LMBA to trade-off linearity and power efficiency. In a second step, two multipurpose adaptive digital predistortion (DPD) linearizers are considered, properly combined with crest factor reduction (CFR) techniques, to meet the required linearity specifications. Either a DPD based on artificial neural networks or a DPD based on polynomials can be selected taking into account the compromise between computational complexity and linearization performance. Experimental results will validate the proposed methodology to guarantee the linearity levels (ACPR <−45 dBc and EVM <1%) with high power efficiency in an LMBA under dynamic transmission, where both the signal BW (from 20 and up to 200-MHz instantaneous BW) and frequency of operation (in the range of 1.8–2.4 GHz) change.

Dither Signal of Feedback Channel Quantization in Adaptive Digital Predistorter

The amplification of signals with fluctuating envelopes leads to distortion inevitably because of nonlinear behavior of the power amplifier (PA). Digital predistortion (DPD) can be used to counteract these nonlinear effects. For improving feedback signal distortion of a DPD system, the method of quantization noise and feedback channel dither signal is presented in this paper. Before quantization, the technique of injecting a feedback channel dither signal to reduce these effects of feedback signal distortion of DPD and be filtered by the digital filter after digital converter (ADC). Experiment shows that this method can used to obtain more accurate data to estimate the PA behavior for effective DPD.

A Combined Approach of DPD and CFR in F-OFDM System

The nonlinear distortion of the power amplifier (PA) is studied for Filtered Orthogonal Frequency Division Multiplexing (F-OFDM) systems, which will be adopted in the fifth generation (5G) mobile communication systems. The peak to average power ratio (PAPR) of F-OFDM signal may make the PAs work in the saturation region and result into extremely serious nonlinear saturation distortion, and the nonlinear saturation distortion is usually compensated by predistortion technology. A digital predistortion (DPD) structure is designed to compensate the nonlinear characteristics of the PA in the article. Firstly, repeated iterative clipping revision (RICR) algorithm is used to reduce the PAPR, which makes the working region of PA infinitely close to the saturation region, and as a result, the efficiency is improved. Furthermore, an integrated structure combining crest factor reduction (CFR) and DPD is employed. The experimental results show that the performance of the proposed CFR joint adaptive DPD lowers the PAPR of the predistorted signal by 2dB. The combined CFR & DPD reduces the ACPR of the transmitter by 3dB compared with the unlinearized PA.

Linearization of RF Power Amplifiers in Wideband Communication Systems by Adaptive Indirect Learning Using RPEM Algorithm

This paper proposes a new approach of digital predistortion (DPD) technique based on the adaptive indirect learning architecture (ILA) by using a recursive prediction error minimization (RPEM) algorithm for linearizing radio frequency (RF) power amplifiers (PAs) in emerging wideband communication systems. In the proposed RPEM-based linearization approach, the forgetting factor varies with time and is less sensitive to noise. Therefore, the predistorter (PD) parameter estimates become more consistent and accurate in steady state so that the mean square errors can be reduced. Both the error vector magnitude (EVM) and the adjacent channel power ratio (ACPR) are used to evaluate the DPD technique in RF PAs employing the proposed linearization. The efficiency validation of the proposed method is based on a simulated PA Wiener model. The simulation results have clarified the improvement of the proposed adaptive ILA-based DPD with RPEM algorithm in terms of both EVM and ACPR.

Software-Defined Radio Transceiver Design Using FPGA-Based System-on-Chip Embedded Platform With Adaptive Digital Predistortion

In this paper, a software-defined radio (SDR) based transceiver system is designed and implemented on the system-on-chip (SoC) platform, which consists of a high-speed Arm embedded processor and a reconfigurable field-programmable gate array (FPGA). In the proposed SDR transceiver, the real-time baseband signal generation and adaptive digital predistortion (ADPD) units are implemented on the SoC platform. Memory polynomial model based ADPD solution is implemented to linearize the radio frequency (RF) power amplifiers (PAs). The implementation of the ADPD on a reconfigurable FPGA platform makes the system flexible and cost-effective. The PA characterization, in terms of model extraction and coefficient calculation, is done in real-time. These calculated coefficients are updated in the transmission path to precondition the transmitted signal before it is applied to the PA. The proposed ADPD is applied at the baseband level. Therefore, it can be used for different classes of PA operating at different RF carrier frequencies. A long-term evolution (LTE) signal with 20 MHz bandwidth and 11 dB peak to average power ratio (PAPR) is used for simulation and measurement purposes. The LTE signal is amplified using a GaN-based harmonically tuned continuous Class-F PA in measurement. The performance of the implemented ADPD scheme is analyzed in terms of NMSE, ACPR and EVM.

Stabilization of a Modified LMS Algorithm for Canceling Nonlinear Memory Effects

The least-mean-square (LMS) is promising in a system whose signal statistics are time-varying, and it is preferred in adaptive digital predistortion techniques. In a nonlinear memory system, it is found that the high nonlinearity, the finite sampling rate and the finite number of digits will introduce colored noise that is dependent on signals. In this paper, the long-term stability of the conventional LMS in the presence of signal-dependent noise is analyzed using perturbation analysis. It is revealed that the cumulative effect of the signal-dependent noise may lead to a divergence of the conventional LMS, and a properly selected leaky coefficient is needed to suppress the divergence. Unfortunately, the compensation performance may be harmed by enlarging the leaky coefficient. To address this problem, a modified LMS (MLMS) algorithm is proposed. By adjusting the updating strategy in the iterations, the long-term stability of the algorithm is guaranteed, without harming the linearization performance. Numerical simulations verify that the MLMS outperforms the conventional LMS both in stability and compensation performance.

MADS: A Framework for Design and Implementation of Adaptive Digital Predistortion Systems

Digital predistortion (DPD) has important applications in wireless communication for smart systems, such as, for example, in Internet of Things (IoT) applications for smart cities. DPD is used in wireless communication transmitters to counteract distortions that arise from nonlinearities, such as those related to amplifier characteristics and local oscillator leakage. In this paper, we propose an algorithm-architecture-integrated framework for design and implementation of adaptive DPD systems. The proposed framework provides energy-efficient, real-time DPD performance, and enables efficient reconfiguration of DPD architectures so that communication can be dynamically optimized based on time-varying communication requirements. Our adaptive DPD design framework applies Markov Decision Processes (MDPs) in novel ways to generate optimized runtime control policies for DPD systems. We present a GPU-based adaptive DPD system that is derived using our design framework, and demonstrate its efficiency through extensive experiments.

Spectral Re-Growth Suppression in the FBMC-OQAM Signal Under the Non-linear Behavior of a Power Amplifier

Typically, the filter bank multicarrier with offset quadrature amplitude modulation (FBMC-OQAM) bears some impressive properties that make it popular as one of the substitutes to orthogonal frequency division multiplexing (OFDM) for the upcoming technology of broadband wireless communication systems. Although FBMC-OQAM preserves the multicarrier modulation (MCM) features, its spectrum usually suffers from impairments when subjected to the nonlinear behavior of a power amplifier (PA) which results in spectral re-growth. Due to the spectrum limitation and low energy efficiency foreseen in the forthcoming 5G networks, it is vital to confine the spectrum of the FBMC-OQAM signal within the allocated band of interest. In this paper, the suppression of the spectral re-growth experienced on the FBMC-OQAM signal due to the nonlinear distortion effects introduced by the PA is investigated. The crest factor reduction (CFR) method in combination with an adaptive digital pre-distortion (DPD) are used. The peak windowing technique based on sequential asymmetric superposition windowing (SASW) algorithm is used in the CFR part while the least square estimation with QR-decomposition (LSE/QR) has been used as the coefficient’s estimator and adaptation algorithm in the DPD part. The performance of the two combined techniques has been evaluated on SystemVue2018 simulation platform. The adjacent channel leakage ratio (ACLR) and the error vector magnitude (EVM) have been considered as the performance merits. The simulation results show that the proposed techniques significantly improve the spectrum, first by reducing the PAPR of the FBMC-OQAM signal by about 1.5dB. Secondly, the spectral re-growth has been reduced by about -45.74dB adjacent channel leakage suppression and the error vector magnitude measure has been obtained to be about 7.12%. (-22.95dB). These values lead to better average input power of the FBMC-OQAM signal and improvement in the spectral efficiency and they are in accordance with the 3GPP standard for wideband signals in nonlinear systems.

An Adaptive Cascaded ILA- and DLA-Based Digital Predistorter for Linearizing an RF Power Amplifier

This paper presents a novel adaptive digital predistortion (DPD) technique based on a cascade of an adaptive indirect learning architecture (ILA) and a static direct learning architecture (DLA) using a linear interpolation look-up-table (LILUT). The static LILUT-DLA-based DPD is designed to identify the inverse of a radio-frequency power amplifier (PA) model. The cascaded system of the DLA-based predistorter (PD) and PA is theoretically linear. However, in real-time applications, the PA characteristics change with time due to process, supply voltage, and temperature variations, making this cascaded system not strictly linear, which results in some residual nonlinear distortion at the PA output. This residual distortion is effectively compensated by an additional adaptive ILA-based PD using least mean squares or recursive least squares. Thanks to the incorporation of the static DLA, the proposed DPD approach is less sensitive to the PA output noise, ensuring a better preinverse of the PA and also requiring a smaller number of adaptive coefficients than either the adaptive stand-alone DLA- or ILA-based DPDs. The experimental results show that the proposed DPD technique effectively linearizes the PA, even if its characteristics change, and obtains better linearization performance than either the classical stand-alone DLA- or stand-alone ILA-based DPDs.

A Delay Spread Cancelling Waveform Characterizer for RF Power Amplifiers

A two channel 65-nm CMOS RF-waveform characterizer is presented that enables multi-harmonic adaptive matching networks or adaptive digital pre-distortion in RF-power amplifiers. The characterizer measures the dc component and the first 3 harmonics of RF signals by applying a DFT to 8 (ideally) equally spaced quasi-dc output voltages. Conventionally in these types of systems accuracy is limited by sample timing accuracies, which in our case are mainly due to delay cell mismatch. We introduce a novel way to cancel delay cell mismatch, that significantly increases measurement accuracy at the cost of only a small power and area increase. The RF-waveform characterizer achieves 6.8-bit measurement linearity together with a (clock feedthrough limited) 24 dB SFDR. The measured power consumption for our proof-of-principle demonstrator is 18.6 mW at a maximum input signal frequency of 1.1 GHz under continuous operation.

Compressive sensing‐based adaptive sparse predistorter design for power amplifier linearization

SummaryGreedy algorithms in the compressive sensing theory have been formed the essential method for pruning power amplifier (PA) behavioral models and digital predistorters (DPDs). However, the inherent batch mode of these algorithms limits their application in adaptive digital predistortion framework. In this paper, a powerful subspace pursuit greedy scheme combined with stochastic gradient descent adaptive algorithm is proposed to design a class of adaptive sparse DPDs. According to the given sparsity level, the proposed approach can obtain the sparse terms of DPDs and extract the corresponding coefficients adaptively. Performance improvement of the proposed method is validated by simulation results on the adaptive DPD excited by 15‐MHz 3‐carrier Long‐Term Evolution signals and 50‐MHz 16 amplitude/phase‐shift keying signals. Meanwhile, measurement results on a Doherty PA excited by 30‐MHz 3‐carrier Long‐Term Evolution signals are also performed to verify the advantage of the proposed approach. Simulation and experimental results show that proposed algorithm can efficiently construct the adaptive sparse DPD models with only a small number of parameters; both nonlinear distortions and memory effects in the PA can be almost completely removed. A comparison with the nonsparsity aware DPD techniques and batch mode compressive sensing pruning techniques has been demonstrated that the proposed method exhibit faster convergence, improving tracking capabilities and reduced computational complexity.

Low-complexity, Multi Sub-band Digital Predistortion

The nonlinearities of power amplifiers combined with non-contiguous transmissions found in modern, frequency-agile, wireless standards create undesirable spurious emissions through the nearby spectrum of data carriers. Digital predistortion (DPD) is an effective way of combating spurious emission violations without the need for a significant power reduction in the transmitter leading to better power efficiency and network coverage. In this paper, an iterative, multi sub-band version of the sub-band DPD, proposed earlier by the authors, is presented. The DPD learning is iterated over intermodulation distortion (IMD) sub-bands until a satisfactory performance is achieved for each of them. A sequential DPD learning procedure is also presented to reduce the hardware complexity when higher order nonlinearities are incorporated in the DPD learning. Improvements in the convergence speed of the adaptive DPD learning are also achieved via incorporating a variable learning rate and interpolation of previously trained DPD coefficients. A WarpLab implementation of the proposed DPD is also shown with excellent suppression of the targeted spurious emissions.

Digital Predistortion of Power Amplifier using Quadratic Rotation Method

In this paper, the task of design and implementation of digital pre-distortion technique has been divided into two parts. The behavioural model of power amplifier has been developed and digital predistorters module has been developed. AM-AM characterstics for the proposed model is presented and power spectral density (PSD) have been considered as the major parameters to check the performance and modelling accuracy. Parameter estimation and their automatic adjustment is a key issue in adaptive digital predistorter design.

Adaptive Digital Predistortion Based on Hybrid Indirect Learning Structure with Variable Step-Size for Wideband HPA

Adaptive digital predistortion is one of the most promising linearization technique, which leads to more efficient and cost-effective high power amplifier (HPA). In this paper, a fast-converging variable step-size least mean square algorithm based on hybrid indirect learning structure is presented to provide an unbiased predistortion identification in the non-stationary signal condition for wideband HPA. By using a variable step-size strategy, the proposed identifying algorithm can adapt its learning rate according to the dynamic range of input signal. Thus, more stable learning convergence and lower steady-state mis-adjustment error are obtained simultaneously. A comprehensive theoretical analysis is presented, and some important results including learning stability, convergence behavior, and selection criteria for initialization parameter setting are derived. Both its superiority and robustness are well confirmed through extensive numerical simulations.

An adaptive digital predistortion for compensating nonlinear distortions in RF power amplifier with memory effects

In this paper, an adaptive digital predistortion based on a memory polynomial model is proposed in order to linearize the power amplifier with memory effect. The coefficients of the power amplifier model have been extracted using a least square method and those of predistortion have been identified by applying an indirect learning structure. Finally, the performance of digital predistortion has been demonstrated using the simulation of the power amplifier and the digital predistortion excited by a modulated 16 QAM signal in Matlab software. According to the simulation results, the criterion of adjacent channel power ratio (ACPR) declined by around 15dB and the input/output power spectrum density of the power amplifier has quite similar curves. The linearized power amplifier output spectrum demonstrates the superiority of the proposed predistorter in eliminating the spectral regrowth which is caused by the memory effect in comparison to the other linearization methods.

Learning Aided Behavioral Modeling and Adaptive Digital Predistortion Design for Nonlinear Power Amplifier

A new learning-based structure is defined for the identification of nonlinear attributes of a baseband power amplifier (PA) and design of an adaptive digital pre-distorter for application in wireless channels. Analytically and experimentally, generalized memory polynomial (GMP) model is derived from the transmit–receive conditions and the learning network structure. The test data are a sequences of 16-quadrature amplitude modulation (QAM) and 64-QAM complex symbols. In simulation, unknown GMP models of different order are used as a baseband PA model for identification. Minicircuits ZHL-4240 radio frequency PA modules along with NI USRP 2920 units are employed for experimental verification of the concept. The learning aspect is governed by a specially designed artificial neural network structure called real valued focused time delay neural network. Simulation and empirical results agree with analytical derivation.

Power amplifier linearisation using digital predistortion and multi‐port techniques

Power amplifiers are essential components in communication systems and are inherently non-linear. The non-linearity creates spectral growth (broadening) beyond the signal bandwidth, which interferes with adjacent channels. It also causes distortions within the signal bandwidth, which decreases the bit error rate at the receiver. This study reports an adaptive digital predistorter with fast convergence rate and low complexity and cost to alleviate these problems. In this design, a lookup table-based adaptive digital predistortion (DPD) technique using a five-port receiver instead of traditional heterodyne and homodyne architectures is proposed to realise the linearisation loop for this amplifier. The five-port receiver is implemented by use of passive microwave circuits and detector diodes. This approach highly reduces the cost and complexity of the linearisation system. Simulation and measurement results obtained are presented for a laterally diffused metal–oxide–semiconductor-based high-power amplifier biased in class AB operation with wideband code-division multiple access input signal to demonstrate the effectiveness of this novel DPD design. Moreover, these results are compared with DPD technique using homodyne receiver in feedback path.