Direct Learning Architecture Research Articles

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.

A Sparse-Bayesian Approach for the Design of Robust Digital Predistorters Under Power-Varying Operation

In this article, a sparse-Bayesian treatment is proposed to solve the crucial questions posed by power amplifier (PA) and digital predistorter (DPD) modeling. To learn a model, the advanced Bayesian framework includes a group of specific processes that maximize the likelihood of the measured data: regressor pursuit and identification, coefficient estimation, stopping criterion, and regressor deselection. The relevance vector machine (RVM) method is reformulated theoretically to be implemented in complex-valued linear regression. In essence, given an initial set of candidate regressors, the result of this sparse-Bayesian learning approach is the most likely model. Experimental results are provided for the linearization of class AB and class J PAs driven by a 30-MHz fifth-generation new radio signal for a fixed average power, where the evolution of the figures of merit versus the number of active coefficients is examined for the proposed sparse-Bayesian pursuit (SBP) algorithm in comparison to other greedy algorithms. The SBP presents a good performance in terms of linearization capabilities and computational cost. Furthermore, the proposed Bayesian framework enabled the design of a DPD model structure, deselect regressors, and readjust coefficients in a direct learning architecture, demonstrating the robustness to changes in the power level over a 10-dB range.

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.

Under-Sampling Digital Predistortion of Power Amplifier Using Multi-Tone Mixing Feedback Technique

An under-sampling digital predistortion based on a multi-tone mixing feedback technique (MTM-DPD) is presented in this article. In contrast to the under-sampling digital predistortion (DPD) based on conventional receivers, the proposed method could simultaneously reduce the sampling rate and acquisition bandwidth using a multi-tone mixing (MTM)-based feedback channel. The MTM-DPD is implemented with an evolved direct learning architecture, where the coefficients of a predistorter are estimated based on the aliased feedback signal, preprocessed input signal, and preprocessed kernels of the DPD model. To preprocess the input signal and kernels, the behavioral model of the MTM-based feedback channel and its corresponding identification algorithm are analyzed in detailed. Experimental results show that for a gallium nitride (GaN)-based power amplifier (PA) with 40-MHz input, under the excitation of a 17 tone LO signal with frequency interval 7.68 MHz, the MTM-DPD with sampling rate 15.36 MSPS and acquisition bandwidth 15.36 MHz could improve the adjacent channel power ratio (ACPR) from −30.1 to −46.5 dBc and the error vector magnitude (EVM) from 9.13% to 1.76%. Compared with the conventional full sampling DPD (FS-DPD), the MTM-DPD could reduce the cost of analog-to-digital converters (ADCs) in feedback channel significantly while maintaining satisfactory linearization performance.

A Bivariate Volterra Series Model for the Design of Power Amplifier Digital Predistorters.

The operation of the power amplifier (PA) in wireless transmitters presents a trade-off between linearity and power efficiency, being more efficient when the device exhibits the highest nonlinearity. Its modeling and linearization performance depend on the quality of the underlying Volterra models that are characterized by the presence of relevant terms amongst the enormous amount of regressors that these models generate. The presence of PA mechanisms that generate an internal state variable motivates the adoption of a bivariate Volterra series perspective with the aim of enhancing modeling capabilities through the inclussion of beneficial terms. In this paper, the conventional Volterra-based models are enhanced by the addition of terms, including cross products of the input signal and the new internal variable. The bivariate versions of the general full Volterra (FV) model and one of its pruned versions, referred to as the circuit-knowledge based Volterra (CKV) model, are derived by considering the signal envelope as the internal variable and applying the proposed methodology to the univariate models. A comparative assessment of the bivariate models versus their conventional counterparts is experimentally performed for the modeling of two PAs driven by a 30 MHz 5G New Radio signal: a class AB PA and a class J PA. The results for the digital predistortion of the class AB PA under a direct learning architecture reveal the benefits in linearization performance produced by the bivariate CKV model structure compared to that of the univariate CKV model.

A Reduced-Complexity Direct Learning Architecture for Digital Predistortion Through Iterative Pseudoinverse Calculation

In this letter, a novel approach is proposed for digital predistortion (DPD) with direct learning architecture (DLA). Regression of a Volterra behavioral model requires the pseudoinverse of a matrix, which needs many resources due to the inverse operation when the Moore–Penrose pseudoinverse is used. This work substitutes the pseudoinverse calculation by a polynomial expansion (PE) method to obtain a polynomial expansion direct learning architecture (PE-DLA), which attains a pseudoinverse in an iterative fashion avoiding the inverse operation and consequently reducing the algorithm computational complexity. Experimental results show that the number of iterations in the PE-DLA affects the convergence speed. The proposal is benchmarked against other state-of-the-art approaches such as the classic DLA and the covariance matrix DLA (CM-DLA) in the DPD of a commercial class AB power amplifier, concluding that the linearization performance of the current proposal is equivalent to others while featuring simple operations.

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.

A two-step approach for DLA-based digital predistortion using an integrated neural network

In this study, we propose a two-step approach for direct-learning-architecture (DLA) based digital predistortion (DPD) using an integrated neural network. Because solutions to the DLA-based DPD cannot be obtained in closed form, an iterative search, which causes performance degradation and DPD divergence, is required. The proposed method employs an integrated neural network combining two sub-networks, namely, a DPD network and a power amplifier (PA) network, to find unknown solution. A one-dimensional convolutional neural network is adopted as the base structure for the DPD network to consider memory effects. The experimental results demonstrate that the proposed method reduces the adjacent channel leakage ratio by 4.3 dB and the error vector magnitude by 0.07, compared to the conventional method, and is stable over a long period without DPD coefficient update.

Deep learning architecture for direct probability density prediction of small‐scale solar generation

With the increasing penetration of photovoltaic (PV) systems, the problems posed by the inherent intermittency of small-scale PVs are becoming more severe. To address this issue, it is critical to involve the uncertainty of PV generation in the look-ahead periods in a comprehensive framework. To this end, a direct deep learning architecture for probabilistic forecasting of solar generation is proposed in this paper. An end-to-end deep learning architecture as a novel mixture density network (MDN) is designed based on the combination of a convolutional neural network and a gated recurrent unit. Furthermore, a new loss function and training process based on adversarial training is proposed to enhance the accuracy in direct contracting of the probability density function. Then, several deep and shallow networks are implemented, and the results are compared with the proposed architecture. The effectiveness of the proposed MDN in providing complete statistical information is verified through comparison with Monte Carlo dropout, non-parametric kernel density estimation, and the proposed MDN without adversarial training.

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.

Low Computational Complexity Digital Predistortion Based on Direct Learning With Covariance Matrix

This paper proposes a novel approach for digital predistortion, based on direct learning architecture (DLA), to reduce the computational complexity. In power amplifier (PA) behavioral models, the coefficients of a Volterra polynomial or a simplified Volterra polynomial are extracted by calculating the inverse of a time-varying matrix, which is resource-consuming, time-consuming, and power-consuming due to its matrix dimension and inverse operation in a field-programmable gate array. To speed up the computation and save hardware resources, we propose a low computational complexity DLA with covariance matrix that uses the constant covariance matrix to replace the time-varying input signal filled matrix based on a stationary ergodic random process. To verify the proposed method, it was applied to a wideband Doherty gallium nitride (GaN) PA at 2.6 GHz with a 40-MHz orthogonal frequency division multiplexing signal, and to a dual-band Doherty GaN PA at 1.9 and 2.6 GHz with two 20-MHz long-term evolution signals. Experimental results show that the proposed algorithm achieves almost the same performance as the traditional approach, with less than one fifth of the computational quantity.

One-bit in-phase observation for direct learning-based digital predistortion with modified frequency-domain delay estimation and alignment

This article proposes a novel digital predistortion (DPD) implementation method for RF power amplifiers. The new approach adopts only one 1-bit comparator in the feedback path to observe the in-phase (I) or the quadrature (Q) component of the error signal between the input and the output signals. To this end, the theoretical derivation of the in-phase observation based on direct learning architecture (DLA) DPD is first given in this article, by combining the existing 1-bit method and the low-cost in-phase observation. To facilitate the delay estimation and alignment, a modified iterative frequency-domain delay estimation is presented, which only acquires either I or Q components of the output signal to achieve satisfied delay estimation. Experimental results show that the proposed DPD method decreased the normalized mean square error (NMSE) and the adjacent channel power ratio (ACPR) to less than −42 and −51 dB, respectively, which indicates that the proposed DPD system can achieve comparable performance as the existing DPD identification techniques with lower implementation complexity.

1-bit Observation for Direct-Learning-Based Digital Predistortion of RF Power Amplifiers

In this paper, we propose a low-cost data-acquisition approach for model extraction of digital predistortion (DPD) of RF power amplifiers. The proposed approach utilizes only 1-bit-resolution analog-to-digital converters (ADCs) in the observation path to digitize the error signal between the input and output signals. The DPD coefficients are then estimated based on the direct learning architecture using the measured signs of the error signal. The proposed solution is proved feasible in theory, and the experimental results show that the proposed algorithm achieves the performance equivalent to that using the conventional method. Replacing high-resolution ADCs with 1-bit comparators in the feedback path can dramatically reduce the power consumption and cost of the DPD system. The 1-bit solution also makes DPD become practically implementable in future broadband systems since it is relatively straightforward to achieve an ultrahigh sampling speed in data conversion using only simple comparators.

Iterative Learning Control for RF Power Amplifier Linearization

This paper proposes a new technique to identify the parameters of a digital predistorter based on iterative learning control (ILC). ILC is a well-established control theory technique that can obtain the inverse of a system. Instead of focusing on identifying the predistorter parameters, the technique proposed here first uses an iterative learning algorithm to identify the optimal power amplifier (PA) input signal that drives the PA to the desired linear output response. Once the optimal PA input signal is identified, the parameters of the predistorter are estimated using standard modeling approaches, e.g., least squares. To this end, in this paper, we present a complete derivation of an ILC scheme suitable for the linearization of PAs, which includes convergence conditions and the derivation of two learning algorithms. The proposed ILC scheme and parameter identification technique were demonstrated experimentally and compared with the indirect learning architecture (ILA) and direct learning architecture (DLA). The experimental results show that, even for the most difficult cases, the proposed ILC scheme can successfully linearize the PA. The experimental results also indicate that the proposed parameter identification technique is more robust to measurement noise than ILA and can provide better linearity performance when the PA nonlinearities are strong. In addition, the proposed parameter identification technique can achieve similar or better linearity performance than DLA but with a simpler identification process.

Analysis on LUT based digital predistortion using direct learning architecture for linearizing power amplifiers

In modern wireless communication system, power amplifier (PA) is an important component which is expected to be operated at the region of high power efficiency, but in this region, PA is inherently nonlinear. Thus, the linearization of high power efficient PA is necessary. In this paper, direct learning architecture (DLA) and indirect learning architecture (ILA) are firstly compared. It shows that DLA is more robust than ILA. Then a baseband digital predistortion (DPD) method with DLA is proposed for power amplifier linearization based on combined look-up tables (LUT) and memory polynomial (MP) model. The main innovation is that a LUT-based approach is proposed to calculate directly the complex-valued predistorted signal. Moreover, some interpolation techniques are introduced to reduce the LUT size. The proposed DPDs are validated experimentally. Additionally, the influences of some important parameters in experimental setup, such as the number of bits of analog-to-digital converter (ADC) and the instrument bandwidth, are analyzed.

Digital predistortion method combining memory polynomial and feed‐forward neural network

A baseband digital predistortion (DPD) technique based on a feed-forward neural network (FFNN) is presented. The process of memory polynomial (MP) DPD is time consuming because of the large number of mathematical calculations. The FFNN is adopted to realise the mathematical calculations in MP DPD with direct learning architecture (DLA). The training samples of the FFNN are derived from MP DPD with DLA. It guarantees the accuracy of imitating the MP DPD. Although the training of the FFNN is time consuming, the trained FFNN DPD is less time consuming than MP DPD. This solution is validated based on a power amplifier (PA) ZFL-2500 driven by a wideband code division multiple access (WCDMA) signal with 3.84 MHz bandwidth. The experimental results show that the FFNN can mimic the behaviour of the MP DPD. The proposed DPD achieves a significant improvement in linearity and is stable.

Digital predistortion technique based on non‐uniform MP model and interpolated LUT for linearising PAs with memory effects

A new digital predistortion technique based on a direct learning architecture is proposed for linearising power amplifiers (PAs) with nonlinear memory effects. It is based on the non-uniform memory polynomial (MP) model and with a quadratically interpolated LUT. There are mainly two innovations. First, compared with the conventional MP model, the non-uniform MP model achieves the same modelling accuracy with less coefficients. Secondly, compared with the linearly interpolated LUT, the quadratically interpolated LUT has higher accuracy, which is adopted to realise a part of the mathematical computations in the predistortion. The proposed solution is validated on a real PA ZFL-2500. It reduces the number of the model's coefficients and achieves a spectrum regrowth suppression of about 15 dB with a table size of only 8.

A New Digital Predistortion for Wideband Power Amplifiers With Constrained Feedback Bandwidth

This letter presents a new digital predistortion (DPD) solution for wideband power amplifiers (PAs) with restricted feedback bandwidth and relatively low sampling rate. By integrating a microwave cavity filter into the feedback path, the feedback bandwidth is reduced efficiently. A PA parameter extraction method is then proposed to identify the PA model, using the bandwidth-constrained signals. By applying the extracted parameters to the direct learning architecture, the DPD function can be obtained, which can linearize nonlinear distortion over the sampling bandwidth. Experiments demonstrate that a 22 dB adjacent channel leakage ratio improvement is acquired for a 100 MHz Long Term Evolution-advanced signal, even when the feedback bandwidth is restricted from 500 MHz to 100 MHz, which remarkably reduces the ADC sampling rate from 1105.92 Msps to 368.64 Msps.

An Improved Direct Learning Architecture for Satellite High Power Amplifiers Pre-Distortion

The pre-distortion techniques based on traditional direct learning architecture (DLA) are commonly used to linearize high power amplifiers (HPAs) settled in ground-station or on board satellite merely, which cannot achieve a satisfying linearization. In this paper, an improved DLA, considering the satellite channel features with two HPAs in the loop, is put forward. Nonlinear polynomial with 7 order and 4 memory depth is utilized as pre-distorter and recursive least square (RLS) algorithm is adopted for its parameters updating. Simulation results show that with pre-distortion the power spectrum density (PSD) of 16APSK signal achieves about 7.2dB improvement, the EVM of signal constellation is greatly improved up to 61.83%, and desirable system linearization performance is acquired.