Digital Predistortion Performance Research Articles

A 39-GHz CMOS Bidirectional Doherty Phased- Array Beamformer Using Shared-LUT DPD With Inter-Element Mismatch Compensation Technique for 5G Base Station

This article demonstrates a 39-GHz CMOS phased-array beamformer aiming for power-efficient and area-efficient fifth-generation (5G) dual-polarized multiple-in–multiple-out (DP-MIMO) applications. To address the digital pre-distortion (DPD) implementation issue in the massive beamformer elements with Doherty technique integrated, an inter-element mismatch compensation technique is introduced for improving the shared-lookup table (LUT) DPD performance over the process, voltage and temperature (PVT) variations. A bidirectional Doherty power amplifier (PA)-LNA is proposed to enhance the power back-off (PBO) efficiency regarding the high peak-to-average power ratio (PAPR) 5G signals, meanwhile cost down the system by the unbalanced neutralized bidirectional operation. The proposed phased-array beamformer chip is fabricated in 65-nm CMOS technology and packaged in a wafer-level chip-scale package (WLCSP). Each element occupies only a 0.82-mm2 chip area, including the on-chip low-dropout regulator (LDO). The measured stand-alone Doherty PA-LNA achieves 18.9-dBm saturated output power with 17.8% power-added efficiency (PAE) at 6-dB PBO in PA mode and obtains a 4.8-dB noise figure (NF) at 40 GHz in LNA mode. By utilizing the proposed mismatch compensation, the measured 64-quadrature amplitude modulation (QAM) orthogonal frequency-division multiple access (OFDMA)-mode error vector magnitude (EVM) and adjacent channel leakage ratio (ACLR) with the shared-LUT DPD are improved from −22.4 to −25.0 dB and from −28.7 to −32.1 dBc, respectively. The 64-element module achieves a 55.2-dBm saturated effective isotropic radiated power (EIRP) and supports 21-Gb/s single-carrier (SC) mode data streaming. The measured 64-element transmitter (TX) EVM is −25.2 dB at 43.2 dBm with 3.5-GSymbol/s baud rate in 64 QAM, and the corresponding 64-to-4 elements TX-to-receiver (RX) EVM is −22.5 dB. The consumed power for each element is 402 mW at saturation output point in TX mode and 87 mW in RX mode.

Stable-Sample-Level-Based Digital Predistortion for 2-D Millimeter-Wave Phased Array Steering

This letter proposes a stable-sample-level (SL)-based digital predistortion (DPD) technique for 2-D phased array with fixed-position over-the-air (OTA) feedback (FB) to overcome significant SL fluctuation when the beam is steered. It is achieved by optimizing the phase of the beamformer based on the DPD requirement, which can control the SL at a given value without affecting the main lobe of radiation pattern, relaxing the requirement of FB dynamic range. The radiation pattern and DPD performances are measured on a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4 \times 4$ </tex-math></inline-formula> phased array at 26 GHz. The measured results show that the proposed method can realize the stable SL with good DPD performance.

Experimental demonstration of transport over fiber using 5G NR with performance enhancement using DPD

The article proposes an experimental implementation with a performance comparison of 5G new radio (NR) multiband waveforms utilizing analog radio over fiber (A-RoF) link equipped with performance enhancement via digital predistortion (DPD) methods. An unprecedented convolutional neural network (CNN) is compared with our earlier proposed robust methods such as deep neural network (DNN), magnitude-selective affine (MSA) and generalized memory polynomial (GMP) methods. In circumstances when deep learning is not practicable due to high complexity, we have presented an integrative lightweight convolutional neural network (ILWCNN) approach which is stable over time without the need for DPD coefficient updates. The experimental bench consists of a multiband 5G NR standard at a carrier frequency of 20 GHz with a bandwidth of 50 MHz and a flexible-waveform signal at 3 GHz with a bandwidth of 20 MHz. A 10 km of single-mode fiber is used to transport the signals modulated by a dual-drive Mach Zehnder Modulator. The paper discusses the selection of reduced complexity and robust performance of the ILWCNN-based DPD that eventually outperforms the conventional methods. The proposed ILWCNN reduces the error vector magnitude (EVM) to 1.65% as compared to 4.1%, 3.1%, 1.9% and 7.4% of EVM for GMP, MSA, DNN and non-compensated cases respectively. Similarly, the adjacent channel leakage ratio (ACLR) of −28 dBc uncompensated link is reduced with GMP, MSA and ILWCNN to −40 dBc, −45 dBc and −47 dBc respectively. The suggested ILWCNN approach outperforms the compared methods in terms of ACLR and EVM attaining the 3GPP Release 17 requirements.

Machine Learning-Based Linearization Schemes for Radio Over Fiber Systems

This work proposes a novel machine learning (ML)-based linearization scheme for radio-over-fiber (RoF) systems with external modulation. The proposed approach has the advantage of not requiring new training campaigns in case the Mach-Zehnder modulator (MZM) parameters are changed over time. Our innovative digital pre-distortion (DPD) was designed to favor enhanced remote areas (eRAC) scenarios, in which the non-linearities introduced by the MZM become more severe. It employs a multi-layer perceptron (MLP) artificial neural network (ANN) to model the RoF system and estimate its post-inverse response, which is then applied to the DPD block. We investigate the ML-based DPD performance in terms of adjacent channel leakage ratio (ACLR), normalized mean square error (NMSE), resultant signal root mean square error vector magnitude error (EVM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_\mathrm{RMS}$</tex-math></inline-formula> ), and complexity. Numerical results demonstrate that the intended DPD method is less complex and outperforms the orthogonal scalar feedback linearization (OSFL) scheme, which has been considered a state-of-the-art DPD technique. The proposal has the potential to effectively and efficiently compensate for the RoF nonlinear distortions, especially in a time-variant system, without needing new training campaigns.

Periodicity-Enabled Size Reduction of Symbol Based Predistortion for High-Order QAM

We experimentally demonstrate a novel size reduction approach for symbol-based look-up table (LUT) digital predistortion (DPD) of the transmitter impairments taking advantage of the periodicity in the pattern-dependent distortions. Compared to other reduced-size LUT schemes, the proposed method can significantly lessen the storage memory requirements with negligible performance penalty for high-order modulation formats. To further alleviate the storage memory restriction, a twice reduced-size LUT scheme is proposed to provide further size reduction. Importantly, given a targeted memory length, we verify the importance of averaging over sufficient occurrences of the patterns to obtain a well-performing LUT. Moreover, it is necessary to evaluate the performance of LUT-based DPD using random data. Finally, we demonstrate a neural network (NN) based nonlinear predistortion technique, which achieves nearly identical performance to the full-size LUT for all employed constellations and is robust against a change of modulation format. The proposed techniques are verified in a back-to-back transmission experiment of 20 Gbaud 64-QAM, 256-QAM, and 1024-QAM signals considering 3 and 5 symbol memory. The performance of the LUT-based DPD is further validated in a noise loading experiment.

Digital Predistortion of RF Power Amplifiers Robust to a Wide Temperature Range and Varying Peak-to-Average Ratio Signals

In this work, a digital predistortion (DPD) model for the linearization of RF power amplifiers (PAs) is presented. The model provides a linearized gain (DPD &#x002B; PA) independent of the instantaneous transistor channel temperature within a predefined temperature window. Channel temperature variations due to varying ambient temperatures or changes in the signal probability density function (PDF) cause long-term memory effects, which results in dispersed (dynamic) AM/AM and AM/PM characteristics. The presented model is used to compensate for the memory effects due to self-heating and external temperature changes by estimating the transistor channel temperature through a linear single-pole Foster thermal network. The DPD model uses a first-order Taylor approximation to cancel out temperature-based nonlinearities. Gaussian pulses are used to extract the PA intrapulse gain at different temperatures without being affected by the signal PDF, thus allowing temperature- and signal-independent PA characterization. The model is validated from <inline-formula> <tex-math notation="LaTeX">$20~^\circ \text{C}$ </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">$80~^\circ \text{C}$ </tex-math></inline-formula> and by considering a class-B 3.75-GHz 10-W gallium nitride (GaN)-on-SiC PA. The DPD performance is evaluated by considering the normalized root-mean-squared error (NRMSE), the output spectra, and adjacent channel power ratio (ACPR) with and without DPD for multiple signals bandwidths and peak-to-average power ratio (PAPR) and finally compared with other approaches.

Multidimensional Magnitude-Selective Affine-Function-Based Behavioral Model for Multiband Digital Predistortion of RF Power Amplifiers

A kind of novel general multiband digital predistortion (DPD) model is proposed for the linearization of the multifrequency transmitters. By the theoretical analysis, we extend the existing instantaneous sample indexed magnitude-selective affine (IMSA) function-based model to multidimensional cases, which includes the 2-D-IMSA model and the 3-D-IMSA model for concurrent dual-band and triband scenarios, respectively. The core of the new models is to use the multidimensional IMSA function to replace the complex basis function of the classic multiband model through the method of segmentation and approximation. After segmentation, the proposed models have a simple linear structure in each small area, which greatly reduces the model complexity. Experiments show that the proposed models can give similar normalized mean square error and DPD performance in comparison with existing classic models when a power amplifier is excited by two 20-MHz signals in the concurrent dual-band scenario and by three 20-MHz signals in the concurrent triband scenario.

Performance of digital predistorter in system with analogue to digital converter

The baseband digital pre-distortion (DPD) signal processing technique is the most cost-effective linearisation method among other techniques to address the nonlinearity effect of the power amplifier. For communication systems containing DPD and power amplifier, it is difficult to acquire performance metrics closed-forms for any DPD architecture since there was no mathematical expression for each DPD coefficient. Usually, researchers look for more efficient DPD algorithms for DPD coefficients (compared to the existing ones) in terms of computational complexity, delay, power consumption etc. Consequently, performance is evaluated through intensive simulation. In this paper, it is shown how one can exploit the results of the recent work to mathematically model the indirect learning architecture DPD and efficiently derive important measures in communication systems. Expressions of the normalised mean square error (NMSE) and achievable rate for the OFDM communication system are derived. The DPD is modelled mathematically by exploiting the DPD coefficients closed-form expressions. The derived expressions of the NMSE and achievable rate are verified through numerical simulations. Furthermore, closed-form expressions for the NMSE and achievable rate bounds for the OFDM communication system are derived. The performance measures bounds are found assuming a perfect linearisation scenario. The analytical expressions are validated through numerical simulations.

Reducing Power Consumption of Digital Predistortion for RF Power Amplifiers Using Real-Time Model Switching

In this article, we propose a new behavioral modeling method to reduce the running complexity and power consumption of digital predistortion (DPD) models for radio frequency power amplifiers. By employing the proposed method, different cross terms in a DPD model can be switched dynamically in real time. Each cross-term branch can further choose the model coefficients from multiple coefficient sets, which improves the DPD performance with little extra complexity. The switch of both cross-term branches and model coefficients is realized using a decision tree-based switch controller, leading to very low run-time complexity. By optimizing the selection process, different input samples can choose the most suitable model configuration that contributes most to the linearization performance. As only one branch is activated at a time, the power consumption can be greatly reduced. Based on the experimental results, the proposed method can achieve excellent linearization performance with significantly reduced power consumption.

A Band-Limited Magnitude-Selective Affine Function-Based Model for Digital Predistortion of 5G Broadband Power Amplifiers

A band-limited magnitude-selective affine (MSA) function-based model is proposed for digital predistortion (DPD) of broadband power amplifiers (PAs) in 5G millimeter-wave frequency band. The new model is derived from the band-limited canonical piecewise linear function-based model by employing MSA functions, which can obviously reduce the number of multiplication operations and the model complexity. Experimental results show that the proposed model gives better normalized mean square error and DPD performance in comparison with some existing models when a broadband PA is excited by a 5G new radio (NR) signal of 400-MHz bandwidth at 28-GHz band.

A Low Sampling Rate Memory-Grouped Method for Digital Predistortion With Constrained Acquisition Bandwidth

A novel memory-grouped method is proposed for digital predistortion (DPD) of power amplifiers (PAs) with constrained acquisition bandwidth (BW) and extremely low sampling rate. By grouping the basis functions with different memory delays, a two-step algorithm can reduce overfitting in the constrained-BW technique. As a result, excellent DPD performance can be achieved even when the acquisition BW is constrained to several times narrower than the BW of the original input signal. Thus, using the memory-grouped method, a very low-speed analog-to-digital converter (ADC) can be used to sample the constrained feedback signal without aliasing, significantly reducing the cost of configuring a high-speed ADC. The performance of the proposed method is compared with the existing methods in different scenarios. Experimental results show that when the feedback BW is less than the BW of the original input signal, the proposed method can still achieve good performance, while the traditional methods fail to work. The experiment results also imply that the memory-grouped method can reduce the sampling rate by more than ten times.

Directed Graph Navigated Digital Predistortion of mmWave Power Amplifiers for 6G Hopping Applications

To exploit the limited communication resources, the real-time carrier frequency of the power amplifier (PA) may hop, which will result in rapid change in PA’s nonlinear behavior and bring huge challenge to make the digital predistortion (DPD) response in a timely manner. Different from the conventional methods that attempt to shorten the DPD updating time, a novel scheme of controlling its nonlinear variation is proposed. By analyzing PA’s various behaviors using graph model and extracting a directed graph to navigate its power adjustments, the variation in nonlinear behavior induced by hopping carrier frequency can be effectively compensated, which will mitigate the DPD performance deterioration when there is not enough time for DPD update. Finally, the proposed method was validated by experiments on a 100-MHz modulated signal stimulated millimeter-wave (mmWave) PA operating at five hopping carrier frequencies from 26.4 to 28 GHz, with the step of 400 MHz.

Neural Network DPD for Aggrandizing SM-VCSEL-SSMF-Based Radio over Fiber Link Performance

This paper demonstrates an unprecedented novel neural network (NN)-based digital predistortion (DPD) solution to overcome the signal impairments and nonlinearities in Analog Optical fronthauls using radio over fiber (RoF) systems. DPD is realized with Volterra-based procedures that utilize indirect learning architecture (ILA) and direct learning architecture (DLA) that becomes quite complex. The proposed method using NNs evades issues associated with ILA and utilizes an NN to first model the RoF link and then trains an NN-based predistorter by backpropagating through the RoF NN model. Furthermore, the experimental evaluation is carried out for Long Term Evolution 20 MHz 256 quadraturre amplitude modulation (QAM) modulation signal using an 850 nm Single Mode VCSEL and Standard Single Mode Fiber to establish a comparison between the NN-based RoF link and Volterra-based Memory Polynomial and Generalized Memory Polynomial using ILA. The efficacy of the DPD is examined by reporting the Adjacent Channel Power Ratio and Error Vector Magnitude. The experimental findings imply that NN-DPD convincingly learns the RoF nonlinearities which may not suit a Volterra-based model, and hence may offer a favorable trade-off in terms of computational overhead and DPD performance.

Enhancing distributed feedback‐standard single mode fiber‐radio over fiber links performance by neural network digital predistortion

AbstractThis letter presents a novel neural network (NN) based digital predistortion (DPD) technique to obliterate the signal impairments and nonlinearities in radio over fiber (RoF) systems. DPD is generally performed with volterra based procedures that utilizes indirect learning architecture (ILA) that can become complex and expensive computationally. The proposed method using NNs evades issues associated with ILA and utilizes a NN to first model the RoF link and then training a NN based predistorter by backpropagating through the RoF NN model. Furthermore, the experimental evaluation is carried out for long term evolution 20‐MHz 256‐QAM modulation signal using 1310 nm distributed feedback laser, and standard single‐mode fiber to establish a comparison between NN based RoF link and volterra based generalized memory polynomial using ILA. The efficacy of the DPD is examined by reporting adjacent channel power ratio, mean square error, and error vector magnitude. The experimental findings imply that NN‐DPD convincingly learns the RoF nonlinearities which may not suit a volterra based model, and hence may offer a favorable trade‐off in terms of computational overhead and DPD performance.

Digital Predistortion Utilizing Over-the-Air Feedback for Phased Arrays

In this paper, an efficient digital predistortion (DPD) architecture utilizing over-the-air (OTA) feedback is presented to linearize phased array transmitters. It places one additional observation antenna (OA) in the far field to capture the combined signal of the array outputs and uses the combined signal to build a nonlinear model that describes the joint nonlinear distortions of all the power amplifiers (PAs) in the phased array. Then, a corresponding DPD model is extracted by the typical indirect learning method to linearize the phased array. After introducing this DPD architecture, the relationship between the OA position and the performance of the extracted DPD model is specifically explored, and two significant results are found. First, when the OA is perfectly colocated in the main beam direction, the DPD coefficients extracted with an arbitrary steering angle for the phased array are also applicable to any other steering angle. Second, when the OA is not perfectly placed in the main beam direction, the linearization performance for the extracted DPD coefficients will degrade as the OA placement mismatch increases, and the phased array has an optimum steering angle at which the OA placement mismatch has a minimal influence on the DPD performance. Based on the above two results, a new DPD training strategy is proposed, which extracts only one set of DPD coefficients by making the phased array point at the optimum steering angle. The advantages of the proposed strategy are that the OA can be placed in a relatively wide range of positions and that the extracted coefficients will be applicable to any other steering angle. The two results and the proposed DPD training strategy are verified by simulations, which are conducted on a 1 × 4 uniform linear array (ULA) and a 4 × 4 uniform rectangular array (URA).

Digital Predistortion of Phased-Array Transmitter With Shared Feedback and Far-Field Calibration

Digital predistortion (DPD) of a phased array requires that multiple transmit paths must be measured by a feedback (FB) receiver (Rx). In this article, we propose an FB concept for DPD in a time-division-duplex (TDD) phased arrays. We use a single FB line to collect the waveform samples from the parallel transmit paths to the FB Rx. The TDD switches are used to enable and disable individual transmit paths. The FB is calibrated by comparing the FB outputs from individual power amplifiers (PAs) to over-the-air (OTA) measurement reference performed with a frequency-modulated continuous-wave (FMCW) signal. The individual PA measurements are postequalized before the DPD training to model the far-field signal. Three alternative strategies are considered for training the DPD through the calibrated FB line and compared with the OTA DPD. The performance is verified by OTA measurements of a 28-GHz phased-array transmitter and with fifth-generation new radio waveform in terms of total radiated adjacent channel power ratio (TRACPR), cumulative absolute ACP (CACP), and main lobe error vector magnitude (EVM). The best EVM and ACPR performance is achieved by the strategy where the individual PA responses are treated independently. The methods were comparable to the OTA DPD performance, achieving all < −37-dB TRACPR, −29-dBm/MHz CACP, and ≤7 % EVM.

Beyond the Moore-Penrose Inverse: Strategies for the Estimation of Digital Predistortion Linearization Parameters

Digital predistortion (DPD) is the linearization technique most often used to cope with the inherent tradeoff between linearity and efficiency in power amplifiers (PAs). Adaptation is needed to optimize DPD performance. This article reviews strategies for estimating the parameters controlling the DPD linearizer.

Piecewise Digital Predistortion for mmWave Active Antenna Arrays: Algorithms and Measurements

In this paper, we describe a novel framework for digital predistortion (DPD) based linearization of strongly nonlinear millimeter-wave active antenna arrays. Specifically, we formulate a piecewise (PW) closed-loop (CL) DPD solution and low-complexity gradient-adaptive parameter learning algorithms, together with a region partitioning method, that can efficiently handle deep compression of the PA units. The impact of beamsteering on the DPD performance is studied, showing strong beam-dependence, thus necessitating frequent updating of the DPD. In order to facilitate fast adaptation, an inexpensive, non-iterative, pruning algorithm is introduced, which allows to significantly reduce the amount of model coefficients. The proposed methods are validated with extensive over-the-air RF measurements on a 64-element active antenna array transmitter operating at 28 GHz carrier frequency and transmitting a 400 MHz 5G New Radio (NR) standard-compliant orthogonal frequency division multiplexing waveform. The obtained results demonstrate the excellent linearization capabilities of the proposed solution, conforming to the new 5G NR requirements for frequency range 2 (FR2) in terms of both inband waveform quality and out-of-band emissions. The proposed PW-CL DPD is shown to outperform the state-of-the-art PW DPD based on the indirect learning architecture, as well as the classical single-polynomial based DPD solutions in terms of linearization performance and computational complexity by a clear margin.

Grading Optimization for Dimensions-Reduced Orthogonal Volterra DPD

High-speed optical communication systems may suffer from a combination of impairments such as memory effect and nonlinear behavior of the optoelectronic components. Nonlinear digital pre-distortion (DPD) is one of the well-known technique to alleviate these effects. As typical implementation of Volterra-based DPD is considered complex and consumes high power, more efficient orthogonal-based Volterra series representation has been proposed. Previous works offered ways to perform efficient grading of the most dominant dimensions based on the combination of the dimensions variances and the signal projection. Here, it is shown that normalization of the data dynamic range further improves this method and decreases significantly the number of required dimensions. Using normalization combined with the previous methods, maximizes the DPD performance by means of error vector magnitude (EVM) and bit error rate (BER), while minimizing the DPD complexity in the terms of required series dimensions. Extensive simulation and lab measurements indicate a potential saving of up to 87% in the number of dimensions with a negligible performance penalty.

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.