Indirect Learning Architecture Research Articles

Machine learning-based methods for piecewise digital predistortion in mmW 5G NR systems

Piecewise linearization techniques require dividing the signal into multiple pieces each linearized individually. Machine learning (ML) is one of the useful tools to perform the automatic division of these pieces. Complexity reduction in the classification of piecewise digital predistortion is possible through carefully constructing features from both the signal statistics and the power amplifier (PA) characteristics. Our paper introduces two low-complex classical ML-based methods that facilitate the classification of baseband input data into distinct segments. These methods effectively linearize PA behavior by employing tailored Volterra models corresponding to each segment. Moreover, we perform an in-depth analysis of the proposed schemes to further optimize their classification and regression complexities. The two proposed low-complexity approaches are validated by laboratory experiments and show up to 4 dB error vector magnitude (EVM) improvement over the conventional approach for a class A PA at 28 GHz. Similarly, the EVM improvement is up to 2 dB over the vector-switched general memory polynomial scheme. With only one indirect learning architecture iteration, the two proposed schemes obey the 5G new radio standard up to 6.5 dB and 7 dB output backoff, respectively.

ADAPTIVE COMPLEX FILTERS BASED TRANSMITTER IQ IMBALANCE REJECTION

This paper presents an efficient method for compensation of frequency-dependent (FD) transmitter In-phase Quadrature (IQ) imbalance. Proposed method compensates imbalance by exploiting indirect learning architecture (ILA) and complex filters whose coefficients are determined in an iterative process. Compensation performance is assessed after the method has been implemented in a Software Defined Radio (SDR) platform, capable of transmitting modulations at different central frequencies. Measured results demonstrate that the imbalance related images are reduced down to the noise floor. After applying the proposed IQ imbalance correction method, the transmitter image rejection ratio (IRR) is increased by 15dB in the case of an SDR transmitter operating at central frequency of 1.7 GHz. The ADC/DAC sampling rate is 61.44MS/s, while the signal bandwidth, for which the compensation is performed, is 30.72MHz. The advantage of the proposed method is low complexity in terms of a reduced number of coefficients. The method is generic and can be utilized for IQ imbalance compensation when wideband signals are transmitted.

An enhanced peak limited digital predistortion based on indirect learning architecture

An enhanced peak limited digital predistortion based on indirect learning architecture

Iterative Learning Control Based Digital Pre-Distortion for Mitigating Impairments in MIMO Wireless Transmitters

Digital pre-distortion (DPD) has recently been developed to compensate for in-phase and quadrature (IQ) imbalance and crosstalk, as well as power amplifier (PA) nonlinearity distortions in multi-input multi-output (MIMO) transmitters (TXs). Despite its limitations, most DPD models still use a simple non-iterative framework called the indirect learning architecture (ILA). This paper proposes a novel integrated DPD solution supported by iterative learning control (ILC) and a neural network (NN) model to compensate for all of these impairments simultaneously. Compared to the state-of-the-art DPD models, our proposed scheme achieves excellent in-band and out-of-band (OOB) performance. In addition, it has a significantly lower running complexity than other polynomial-based models, with 50% fewer floating-point operations (FLOPs).

Digital pre-distortion using a Gauss-Newton-based direct learning architecture for coherent optical transmitters.

Digital pre-distortion (DPD) is a powerful technique to mitigate transmitter nonlinear distortion in optical transmissions. In this Letter, the identification of DPD coefficients based on the direct learning architecture (DLA) using the Gauss-Newton (GN) method is applied in optical communications for the first time. To the best of our knowledge, this is the first time that the DLA has been realized without training an auxiliary neural network to mitigate optical transmitter nonlinear distortion. We describe the principle of the DLA using the GN method and compare the DLA with the indirect learning architecture (ILA) that uses the least-square (LS) method. Extensive numerical and experimental results indicate that the GN-based DLA is superior to the LS-based ILA, especially in a low signal-to-noise ratio scenario.

Time-Delay Twin Support Vector Regression- Based Adaptive Predistorter for LED Nonlinearity in Visible Light Communications

The bit error rate (BER) of visible light communications (VLC) based on light emitting diodes (LEDs) has been limited due to the nonlinearity of LED. Artificial neural networks (ANNs) predistorters were applied to mitigate the impacts of LED nonlinearity. However, none of them can efficiently approach the performance of linear VLC systems due to the overfitting issue. In this paper, we for the first time propose a predistorter with adaptive indirect learning architecture based on amplitude time-delay twin support vector regression (ATD-TSVR) for LED nonlinearity in orthogonal frequency division multiplexing(OFDM)-based VLC systems. The experimental results demonstrate the signal distortion caused by LEDs as the major nonlinear source. Moreover, the simulation results show superior BER, amplitude distortion (AM/AM) curves, Power Spectral Density(PSD) and constellation plots in an 80Mbit/s OFDM nonlinear VLC system. Meanwhile, as compared to the traditional SVR approach, the CPU training time of ATD-TSVR can be reduced by more than four times. The adaptive pre-distortion method herein is generally applicable to broadband VLC systems and also proves the application prospect and effectiveness of TSVR in VLC system.

Joint digital pre-distortion model based on Chebyshev expansion

<span>In this paper, a new low complexity model is proposed for the joint digital pre-distortion of in-phase/quadrature-phase (I/Q) imbalance, local oscillator (LO) leakage, and power amplifier nonlinearity in direct-conversion transmitters (DCTs). In this structure, we proposed a set of orthogonal basis functions based on Chebyshev expansion to attenuate the problem of numerical instability created during the conventional model identification method. This robust joint digital pre-distortion (DPD) utilized the indirect learning architecture and updated the coefficients vector based on the recursive least square (RLS) algorithm. To verify the operation and efficiency of the proposed model, an extensive simulation in MATLAB was carried out. The results showed a significant reduction in the conditional number and the coefficient dispersion of the observation matrix. Furthermore, the power of the signal in the adjacent channel decreased by more than 16 dB for the orthogonal frequency division multiplexing (OFDM), 16 QAM input signal. In comparison to the previous digital pre-distorter models, the proposed DPD builds strong numerical stability with the least coefficients.</span>

Closed-form MSE and achievable rate for indirect learning DPD

The digital pre-distortion (DPD) signal processing is an effective way to mitigate the power amplifier (PA) nonlinearity effect. For communication systems containing DPD and PA, 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, the performance is evaluated through intensive simulation. In this paper, we show how one can exploit the results of our recent work to mathematically model the indirect learning architecture (ILA) DPD and efficiently derive important measures in communication systems, e.g. normalized mean square error (NMSE), achievable rate, and signal-to-noise plus distortion ratio (SNDR). The author would like to clarify that this work might be the first one to provide closed-form analysis for DPD systems. We think the provided framework/analysis will open the door to other researchers/engineers to plug their own assumptions and derive the performance metrics. The derived expressions of the performance metrics (NMSE, SNDR, and achievable rate) are validated through Monte Carlo simulations. We also derive a closed-form expression for the achievable rate bound for the transmit chain. Moreover, we analytically study the effect of the thermal noise and the quantization noise, in the analog-digital conversion (ADC) process, on the NMSE and achievable rate. The analytical expressions are validated through numerical simulations.

Deep Neural Network-Based Digital Pre-Distortion for High Baudrate Optical Coherent Transmission

High-symbol-rate coherentoptical transceivers suffer more from the critical responses of transceiver components at high frequency, especially when applying a higher order modulation format. We recently proposed a neural network (NN)-based digital pre-distortion (DPD) technique trained to mitigate the transceiver response of a 128 GBaud optical coherent transmission system. In this paper, we further detail this work and assess the NN-based DPD by training it using either a direct learning architecture (DLA) or an indirect learning architecture (ILA), and compare performance against a Volterra series-based ILA DPD and a linear DPD. Furthermore, we deliberately increase the transmitter nonlinearity and compare the performance of the three DPDs schemes. The proposed NN-based DPD trained using DLA performs the best among the three contenders. In comparison to a linear DPD, it provides more than 1 dB signal-to-noise ratio (SNR) gains at the output of a conventional coherent receiver DSP for uniform 64-quadrature amplitude modulation (QAM) and PCS-256-QAM signals. Finally, the NN-based DPD enables achieving a record 1.61 Tb/s net rate transmission on a single channel after 80 km of standard single mode fiber (SSMF).

A Digital Predistortion for Concurrent Dual-Band Power Amplifier Linearization Based on Periodically Nonuniform Sampling Theory

In this article, we propose a novel technique of digital predistortion (DPD) for dual-band power amplifiers (PAs) based on the periodically nonuniform sampling (PNS) theory. In contrast to conventional dual-band DPD (2-D-DPD) models, the proposed periodically nonuniform sampled DPD (PNS-DPD) has only a single input, which can largely reduce the model complexity. We fold the two stimuli with aliasing and feed them to a simple single-band DPD model. The desired predistorted signals are reconstructed from aliased DPD output through the PNS theory. Compared with conventional multi-input models that include numerous intermodulation products of the input signals, the complexity of the proposed single-input PNS-DPD model is hugely decreased. The model coefficients of the proposed PNS-DPD can be easily extracted with conventional direct or indirect learning architecture. We experimentally evaluate the proposed DPD on a test bench and compare it with other DPD techniques in the literature. The implementation complexity can be reduced by over 30%, and the identification complexity is also largely reduced.

A Frequency-Selective Digital Predistortion Method Based on a Generalized Indirect Learning Architecture

Frequency-selective (FS) digital predistortion (DPD), which focuses on suppressing the nonlinear distortion at a specific band, has gained increased interest in recent years. However, there is a lack of a general FS DPD approach that is applicable to most scenarios and is suitable for practical implementation. This paper proposes an FS DPD method based on a generalized indirect learning architecture (GILA). Our work on this GILA-based FS DPD method is composed of two contributions. First, an FS Volterra series model structure, which consists of a basic linear part and a partial-band pre-compensation part, is proposed to construct an FS predistorter. Second, a GILA-based identification method is proposed to extract coefficients of the FS predistorter with the FS Volterra series model structure. The proposed GILA-based FS DPD is a general method with low complexity for implementation. Both simulations and experiments verify that the target band of the DPD linearization is arbitrary for the proposed GILA-based FS DPD method. As a special case, when using the proposed method to focus on suppressing the out-of-band distortion, the adjacent channel power ratio performance of the proposed method can be 7.1 dB better than that of the conventional full-band DPD.

Closed-form analysis for indirect learning digital pre-distorter for wideband wireless systems

Indirect learning architecture (ILA) for digital pre-distortion (DPD) is commonly used to linearize power amplifiers (PA). To the author’s best knowledge, most of the DPD results in the literature obtain the matrix form of the least-square solution in order to get the DPD coefficients numerically. There exists no explicit closed-form for these coefficients that can be used as plug-and-play in simulations, or used for further closed-form analysis of important measures such as signal-to-noise ratio (SNR) and mean square error (MSE), bit-error rate (BER), …etc. In this paper, we analyze the ILA-DPD system for general memory-polynomial PA models. We provide a closed-form solution for the DPD coefficients. We first present the analytical methodology for deriving the mathematical expressions for each DPD coefficient and then introduce an open-access code that generates the DPD coefficients in symbolic form that is used to mathematically model the DPD. We consider case studies for PA and show that the analytical DPD solution matches the Monte Carlo simulations. Moreover, we also provide a closed-form solution for the iterative adaptive ILA-DPD. Our analysis shows that in the case of a large training block length the non-iterative DPD achieves approximately the same performance as an iterative DPD with a shorter training block length. System impairments are also considered, e.g. the thermal noise and the quantization noise in analog–digital conversion (ADC). We derive the normalized mean square error (NMSE) for the transmit chain in the presence of these impairments. The NMSE expression is verified through numerical simulations.

GaN Power Amplifier Digital Predistortion by Multi-Objective Optimization for Maximum RF Output Power

While digital predistortion (DPD) usually targets only the linearity performance of the radio–frequency (RF) power amplifier (PA), this work addresses more than a single PA performance metric exploiting a multi-objective optimization approach. We present a predistorer learning procedure based on a constrained optimization algorithm that maximizes the RF output power, while guaranteeing a prescribed linearity level, i.e., a maximum normalized mean square error (NMSE) or adjacent-channel power ratio (ACPR). Experimental results on a Gallium Nitride (GaN) PA show that the proposed approach outperforms the classical indirect learning architecture (ILA), yet using the same predistorter structure with predetermined nonlinearity and memory orders.

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.

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.

Theory and experiments of a low sampling frequency broadband digital predistortion with cyclostationarity

SummaryTo reduce the sampling rate from analog to digital converter for the feedback loop of digital predistortion (DPD) in a microwave power amplifier (MPA), a model was proposed and used to obtain the formulae for the cyclostationarity of the digital modulation signal, which shows that the nonlinear parameter of the MPA model is only determined by the correlation matrix of the signal and can be estimated with the under‐sampled output signal. The output signal of the MPA, similar to a high sampling rate, can be recovered by combining the nonlinear parameter with the input signal. Then the DPD of the MPA is implemented through indirect learning architecture to realize its linearization. A Ka‐band traveling wave tube amplifier is used to the circuit for performing a low sampling rate DPD process to validate the rationality of the proposed model and formulae.

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.

Impact evaluation of DC operating condition on DPD linearizability and power efficiency in GaN-based power amplifiers

AbstractThe paper presents the results of studies on the effect of transistor DC operating conditions on GaN power amplifiers’ (PAs) power efficiency and linearity improved by digital predistortion (DPD). The single-ended 10 W (ISM2.45 GHz) and 150 W (3.4/3.6 GHz) GaN HEMT PAs excited by wideband LTE20 E-TM1.1 signal were tested. To check the applicability of the small-signal approach for designing of LTE signals’ PAs, the 150 W PA using transistor model extracted from S-parameters measured at the properly selected operating points was designed. The conventional DPD based on the indirect learning architecture and the memory polynomial model of PA non-linearity was implemented. The results of the research show that in case of class A and B PAs operating up to several dozen watts, an additional improvement in adjacent channel leakage ratio (ACLR) of the order of a few dB only by an increase in the quiescent drain current of PA transistor can be achieved. However, a noticeable ACLR improvement with a coincident increase in power-added efficiency (PAE) can be obtained by choosing the compromise DC operating point and using DPD. In the case of high-PAs, the linearity and efficiency are strongly dependent on the load of a transistor, thus the role of DPD is significantly increased.

Digital Predistortion for Linearity Improvement of VCSEL-SSMF-Based Radio-Over-Fiber Links

This letter unfolds a digital predistortion (DPD) technique that improves the linearity of limited range mobile front haul links for the contemporary long-term evolution (LTE) and future (5G) networks. In particular, the proposed technique is applied to radio-over-fiber links based on single-mode (SM) vertical cavity surface emitting lasers emitting at 850 nm and standard SM fibers. Both the memory and generalized memory polynomial models are exploited for the predistorter and identified by utilizing indirect learning architecture. The impact of the DPD technique is observed by the link performance improvement in terms of normalized mean square error and adjacent channel power ratio, referring to complete LTE frames of 10 ms occupying 5-MHz bandwidth and having 64-quadrature amplitude modulation format. Furthermore, the effectiveness of the DPD approach, when varying input power levels, is investigated. The experimental results demonstrate the capability of the proposed DPD technique to achieve promising linearization performance.