Highly efficient class-F power amplifier with digital predistortion for WCDMA applications

A digital predistorted class-F power amplifier （PA） using Cree GaN HEMT CGH40010 operating at 2. 12 GHz is presented to obtain high efficiency and excellent linearity for wideband code-division multiple access （ WCDMA ） applications. Measurement results with the continuous wave （CW） signals indicate that the designed class-F PA achieves a peak power-added efficiency （PAE） of 75. 2% with an output power of 39.4 dBm. The adjacent channel power ratio （ACPR） of the designed PA after digital predistortion （DPD） decreases from -28. 3 and -27. 5 dBc to -51.9 and -54. 0 dBc, respectively, for a 4-carrier 20 MHz WCDMA signal with 7. 1 dB peak to average power ratio （PAPR）. The drain efficiency （DE） of the PA is 37. 8% at an average output power of 33. 3 dBm. The designed power amplifier can be aoolied in the WCDMA system.

ANALOG PREDISTORTION LINEARIZER ON REDUCING CORRECTED AMPLITUDE OVERSHOOT

This paper presents a dual-nonlinear branch linearizer for reducing the corrected amplitude overshoot of conventional single nonlinear branch linearizer. Theoretical analysis is carried out, the analysis is verified by simulation, and a prototype of Ka band 25.28~26.08 GHz dual nonlinear branch linearizer is achieved. It indicates that the corrected amplitude overshoot is less than 0.5 dB, the C/I3 improvement is more than 10 dB related to a single carrier IBO 9 dB, when it is linked and tested for 50 W spacebrone Travelling Wave Tube Amplifier(TWTA).

Adaptive Digital Predistortion Schemes to Linearize RF Power Amplifiers with Memory Effects

To compensate for nonlinear distortion introduced by RF power amplifiers （PAs） with memory effects, two correlated models, namely an extended memory polynomial （EMP） model and a memory lookup table （LUT） model, are proposed for predistorter design. Two adaptive digital predistortion （ADPD） schemes with indirect learning architecture are presented. One adopts the EMP model and the recursive least square （RLS） algorithm, and the other utilizes the memory LUT model and the least mean square （LMS） algorithm. Simulation results demonstrate that the EMP-based ADPD yields the best linearization performance in terms of suppressing spectral regrowth. It is also shown that the ADPD based on memory LUT makes optimum tradeoff between performance and computational complexity.

Wavelet network based predistortion method for wideband RF power amplifiers exhibiting memory effects

RF power amplifiers (PAs) are usually considered as memoryless devices in most existing predistortion techniques. Nevertheless, in wideband communication systems, PA memory effects can no longer be ignored and memoryless predistortion cannot linearize PAs effectively. After analyzing PA memory effects, a novel predistortion method based on wavelet networks (WNs) is proposed to linearize wideband RF power amplifiers. A complex wavelet network with tapped delay lines is applied to construct the predistorter and then a complex backpropagation algorithm is developed to train the predistorter parameters. The simulation results show that compared with the previously published feed-forward neural network predistortion method, the proposed method provides faster convergence rate and better performance in reducing out-of-band spectral regrowth.

Robust Digital Predistortion for LTE/5G Power Amplifiers Utilizing Negative Feedback Iteration

A robust digital predistortion(DPD)technique utilizing negative feedback iteration is introduced for linearizing power amplifiers(PAs)in long term evolution(LTE)/5G systems.Different from the conventional direct learning and indirect learning structure,the proposed DPD suggests a two-step method to identify the predistortion.Firstly,a negative feedback based iteration is used to estimate the optimal DPD signal.Then the corresponding DPD parameters are extracted by forward modeling with the input signal and optimal DPD signal.The iteration can be applied to both single-band and dual-band PAs,which will achieve superior linear performance than the conventional direct learning DPD while having a relatively low computational complexity.The measurement is carried out on a broadband Doherty PA(DPA)with a 200 MHz bandwidth LTE signal at 2.1 GHz,and on a 5G DPA with two 10 MHz LTE signals at 3.4/3.6 GHz for validation in dual-band scenarios.

Volterra series based predistortion for broadband RF power amplifiers with memory effects

RF power amplifiers （PAs） are usually considered as memoryless devices in most existing predistortion techniques. However, in broadband communication systems, such as WCDMA, the PA memory effects are significant, and memoryless predistortion cannot linearize the PAs effectively. After analyzing the PA memory effects, a novel predistortion method based on the simplified Volterra series is proposed to linearize broadband RF PAs with memory effects. The indirect learning architecture is adopted to design the predistortion scheme and the reeursive least squares algorithm with forgetting factor is applied to identify the parameters of the predistorter. Simulation results show that the proposed predistortion method can compensate the nonlinear distortion and memory effects of broadband RF PAs effectively.

Digital Predistortion and Measurement Method

Digital PreDistortion(DPD)is a very useful method to improve the linearity of Power Amplifiers(PAs)for LTE and upcoming 5 G networks.As the spectrum resources are becoming more and more crowded,and the communications bandwidth are broader,the ACPR(Adjacent Channel Leakage Ratio)is very important to communication systems.DPD is one of the useful means for PA to reduce ACPR.This article demonstrates what DPD is and how DPD is achieved,the measurement of the Digital Distortion of a PA using a vector generator and vector analyzer,and the measurement results has been discussed.

A Strong Anti-Jamming Algorithm Based on FPGA for Estimating Loop Delay in Digital Predistortion System

At present what are the key points focused in the research of loop-delay estimation for the digital predistorter in the radio frequency （RF） power amplifier system is reducing its complexity of engineering realization and improving anti-jamming ability and computational speed. Besides, opening up its application scope should be contained. For these targets, a novel method including integer loop delay estimation and fractional part is proposed. The integer part applies amplitude-difference summation function and the fractional one adopts the method of finite impulse response （FIR） linear interpolation. The algorithm finds wide applications. What is more, strong anti-jamming ability and low complexity are also its merits. Simulation results support the above opinion. Digital predistortion （DPD） system based on this algorithm achieves good performance.

A 28GHz Power Amplifier with Analog Predistortion Linearizer in 65nm CMOS

This paper proposes that a radio frequency power amplifier is suitable for a 5G millimeter wave.It adopts a three-stage single-ended structure at 28GHz.An analog predistortion lmearization method is used to improve the linearity of the power amplifier(PA).As a result,there is a significant improvement in power-added efficiency(PAE)and linearity is achieved.The Ka-band PA is implemented in TSMC 65nm CMOS process.At 1.2V supply voltage,the PA proposed in this paper achieves a saturated output power of 15.9dBm and a PAE of 16%.After linearization,the output power at the ldB compression point is increased by 2dBm,with efficient gain compensation performance.

Prediction of the undrained shear strength of remolded soil with non-linear regression,fuzzy logic,and artificial neural network

This study aims to predict the undrained shear strength of remolded soil samples using non-linear regression analyses,fuzzy logic,and artificial neural network modeling.A total of 1306 undrained shear strength results from 230 different remolded soil test settings reported in 21 publications were collected,utilizing six different measurement devices.Although water content,plastic limit,and liquid limit were used as input parameters for fuzzy logic and artificial neural network modeling,liquidity index or water content ratio was considered as an input parameter for non-linear regression analyses.In non-linear regression analyses,12 different regression equations were derived for the prediction of undrained shear strength of remolded soil.Feed-Forward backpropagation and the TANSIG transfer function were used for artificial neural network modeling,while the Mamdani inference system was preferred with trapezoidal and triangular membership functions for fuzzy logic modeling.The experimental results of 914 tests were used for training of the artificial neural network models,196 for validation and 196 for testing.It was observed that the accuracy of the artificial neural network and fuzzy logic modeling was higher than that of the non-linear regression analyses.Furthermore,a simple and reliable regression equation was proposed for assessments of undrained shear strength values with higher coefficients of determination.

Step memory polynomial predistorter for power amplifiers with memory

To reduce the number of digital predistortion coefficients, a step memory polynomial （SMP）predistorter is presented. The number of predistortion coefficients is decreased by adjusting the maximum nonlinear order for different memory orders in the traditional memory polynomial （MP）predistorter. The proposed SNIP predistorter is identified by an offline learning structure on which the coefficients can be extracted directly from the sampled input and output of a PA. Simulation results show that the SMP predistorter is not tied to a particular PA model and is, therefore, robust. The effectiveness of the SMP predistorter is demonstrated by simulations and experiments on an MP model, a parallel Wiener model, a Wiener-Hammerstein model, a sparsedelay memory polynomial model and a real PA which is fabricated based on the Freescale LDMOSFET MRF21030. Compared with the traditional MP predistorter, the SMP predistorter can reduce the number of coefficients by 60%.

The ridgelet transform with non-linear threshold for seismic noise attenuation in marine carbonates

Wavelet transforms have been successfully used in seismic data processing with their ability for local time - frequency analysis. However, identification of directionality is limited because wavelet transform coefficients reveal only three spatial orientations. Whereas the ridgelet transform has a superior capability for direction detection and the ability to process signals with linearly changing characteristics. In this paper, we present the issue of low signal-to-noise ratio （SNR） seismic data processing based on the ridgelet transform. Actual seismic data with low SNR from south China has been processed using ridgelet transforms to improve the SNR and the continuity of seismic events. The results show that the ridgelet transform is better than the wavelet transform for these tasks.

Microstructure evolution of Al-Zn-Mg-Cu alloy during non-linear cooling process

The microstructure evolution and properties of an Al-Zn-Mg-Cu alloy were investigated under different non-linear cooling processes from the solution temperature, combined with in-situ electrical resistivity measurements, selected area diffraction patterns （SADPs）, transmission electron microscopy （TEM）, and tensile tests. The relative resistivity was calculated to characterize the phase transformation of the experimental alloy during different cooling processes. The results show that at high temperatures, the microstructure evolutions change from the directional diffusion of Zn and Mg atoms to the precipitation of S phase, depending on the cooling rate. At medium temperatures, q phase nucleates on A13Zr dispersoids and grain boundaries under fast cooling conditions, while S phase precipitates under the slow cooling conditions. The strength and ductility of the aged alloy suffer a significant deterioration due to the heterogeneous precipitation in medium temperature range. At low temperatures, homogeneously nucleated GP zone, η′ and η phases precipitate.

Design of a memory polynomial predistorter for wideband envelope tracking amplifiers

Efficiency and linearity of the microwave power amplifier are critical elements for mobile communication systems. A memory polynomial baseband predistorter based on an indirect learning architecture is presented for improving the linearity of an envelope tracing （ET） amplifier with application to a wireless transmitter. To deal with large peak-to-average ratio （PAR） problem, a clipping procedure for the input signal is employed. Then the system performance is verified by simulation results. For a single carrier wideband code division multiple access （WCDMA） signal of 16-quadrature amplitude modulation （16-QAM）, about 2% improvement of the error vector magnitude （EVM） is achieved at an average output power of 45.5 dBm and gain of 10.6 dB, with adjacent channel leakage ratio （ACLR） of -64.55 dBc at offset frequency of 5 MHz. Moreover, a three-carrier WCDMA signal and a third-generation （3G） long term evolution （LTE） signal are used as test signals to demonstrate the performance of the proposed linearization scheme under different bandwidth signals.

Robust power amplifier predistorter by using memory polynomials

In memory polynomial predistorter design, the coefficient estimation algorithm based on normalized least mean square is sensitive to initialization parameters. A predistorter based on generalized normalized gradient descent algorithm is proposed. The merit of the GNGD algorithm is that its learning rate provides compensation for the independent assumptions in the derivation of NLMS, thus its stability is improved. Computer simulation shows that the proposed predistorter is very robust. It can overcome the sensitivity of initialization parameters and get a better linearization performance.

NON-LINEAR FORCED VIBRATION OF AXIALLY MOVING VISCOELASTIC BEAMS

The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near- and exact-resonant steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.

Characteristics of the Main Journal Bearings of an Engine Based on Non-linear Dynamics

Many simple nonlinear main journal bearing models have been studied theoretically, but the connection to existing engineering system has not been equally investigated. The consideration of the characteristics of engine main journal bearings may provide a prediction of the bearing load and lubrication. Due to the strong non-linear features in bearing lubrication procedure, it is difficult to predict those characteristics. A non-linear dynamic model is described for analyzing the characteristics of engine main journal bearings. Components such as crankshaft, main journals and con rods are found by applying the finite element method. Non-linear spring/dampers are introduced to imitate the constraint and supporting functions provided by the main bearing and oil film. The engine gas pressure is imposed as excitation on the model via the engine piston, con rod, etc. The bearing reaction force is calculated over one engine cycle, and meanwhile, the oil film thickness and pressure distribution are obtained based on Reynolds differential equation. It can be found that the maximum bearing reaction force always occurs when the maximum cylinder pressure arises in the cylinder adjacent to that bearing. The simulated minimum oil film thickness, which is 3 μm, demonstrates the reliability of the main journal bearings. This non-linear dynamic analysis may save computing efforts of engine main bearing design and also is of good precision and close connection to actual engine main journal bearing conditions.

Microsphere femtosecond laser sub-50 nm structuring in far field via non-linear absorption

Creation of arbitrary features with high resolution is critically important in the fabrication of nano-optoelectronic devices.Here,sub-50 nm surface structuring is achieved directly on Sb2S3 thin films via microsphere femtosecond laser irradi-ation in far field.By varying laser fluence and scanning speed,nano-feature sizes can be flexibly tuned.Such small patterns are attributed to the co-effect of microsphere focusing,two-photons absorption,top threshold effect,and high-repetition-rate femtosecond laser-induced incubation effect.The minimum feature size can be reduced down to~30 nm(λ/26)by manipulating film thickness.The fitting analysis between the ablation width and depth predicts that the feature size can be down to~15 nm at the film thickness of~10 nm.A nano-grating is fabricated,which demonstrates desirable beam diffraction performance.This nano-scale resolution would be highly attractive for next-generation laser nano-lithography in far field and in ambient air.

A Non-linear Non-ideal Model of Simulated Moving Bed Chromatography for Chiral Separations

A non-linear non-ideal model, taking into account non-linear competitive isotherms, axial dispersion, film mass transfer, intraparticle diffusion, and port periodic switching, was developed to simulate the dynamics of simulated moving bed chromatography (SMBC). The model equations were solved by a new efficient numerical technique of orthogonal collocation on finite elements with periodical movement of concentration vector. The simulated SMBC performance is in accordance with the experimental results reported in the literature for separation of l,1'-bi-2-naphthol enantiomers using SMBC. This model is useful for design, operation, optimization and scale-up of non-linear SMBC for chiral separations with significant non-ideal effects, especially for high solute concentration and small intraparticle diffusion coefficient or large chiral stationary phase particle.

ON THE HOLOMORPHIC SOLUTION OF NON-LINEAR TOTALLY CHARACTERISTIC EQUATIONS WITH SEVERAL SPACE VARIABLES

In this paper the authors study a class of non-linear singular partial differential equation in complex domain C-t x C-x(n). Under certain assumptions, they prove the existence and uniqueness of holomorphic solution near origin of C-t x C-x(n).