Behavioral modeling of RF power amplifiers based on pruned volterra series

Behavioral modeling techniques provide a convenient and efficient means to predict system-level performance without the computational complexity of full circuit simulation or physics-level analysis of nonlinear systems, thereby significantly speeding up the analysis process. General Volterra series based models have been successfully applied for radio frequency (RF) power amplifier (PA) behavioral modeling, but their high complexity tends to limit their applications to "weakly" nonlinear systems. To model a PA with strong nonlinearities and long memory effects, for example, the general Volterra model involves a great number of coefficients. In this letter, we propose a new simplified Volterra series based model for RF power amplifiers by employing a "near-diagonality" pruning algorithm to remove the coefficients which are very small, or else not sensitive to the output error, therefore dramatically reducing the complexity of the behavioral model.     

Pruning the Volterra Series for Behavioral Modeling of Power Amplifiers Using Physical Knowledge

This paper presents an efficient and effective approach to pruning the Volterra series for behavioral modeling of RF and microwave power amplifiers. Rather than adopting a pure "black-box" approach, this model pruning technique is derived from a physically meaningful block model, which has a clear linkage to the underlying physical behavior of the device. This allows all essential physical properties of the PA to be retained, but significantly reduces model complexity by removing unnecessary coefficients from the general Volterra series. A reduced-order model of this kind can be easily extracted from standard time/frequency-domain measurements or simulations, and may be simply implemented in system-level simulators. A complete physical analysis and a systematic derivation are presented, together with both computer simulations and experimental validations     

Open-Loop Digital Predistorter for RF Power Amplifiers Using Dynamic Deviation Reduction-Based Volterra Series

In this paper, we propose an efficient open-loop digital predistorter (DPD) derived from the dynamic deviation reduction-based Volterra series that allows compensation for both nonlinear distortion and memory effects induced by RF power amplifiers in wireless transmitters. In this approach, the parameters of the predistorter can be directly extracted from an offline system identification process. This eliminates the usual requirement for a closed-loop real-time parameter adaptation, which dramatically reduces the implementation complexity of the system. It is shown that a further reduction in system complexity can be achieved by applying under-sampling theory in the model extraction and utilizing parameter interpolation in the DPD implementation. Experimental results show that by utilizing this technique with only a small number of parameters, nonlinear distortion induced by the PA can be significantly reduced, as evaluated by both adjacent channel power ratio reduction and normalized root mean square error improvement. A comparison with a memoryless polynomial function based predistorter and an analysis of the impact of decresting are also presented.      

Multi-Lookup Table FPGA Implementation of an Adaptive Digital Predistorter for Linearizing RF Power Amplifiers With Memory Effects

This paper presents a hardware implementation of a digital predistorter (DPD) for linearizing RF power amplifiers (PAs) for wideband applications. The proposed predistortion linearizer is based on a nonlinear auto-regressive moving average (NARMA) structure, which can be derived from the NARMA PA behavioral model and then mapped into a set of scalable lookup tables (LUTs). The linearizer takes advantage of its recursive nature to relax the LUT count needed to compensate memory effects in PAs. Experimental support is provided by the implementation of the proposed NARMA DPD in a field-programmable gate-array device to linearize a 170-W peak power PA, validating the recursive DPD NARMA structure for W-CDMA signals and flexible transmission bandwidth scenarios. To the best of the authors' knowledge, it is the first time that a recursive structure is experimentally validated for DPD purposes. In addition to the results on PA efficiency and linearity, this paper addresses many practical implementation issues related to the use of FPGA in DPD applications, giving an original insight on actual prototyping scenarios. Finally, this study discusses the possibility of further enhancing the overall efficiency by degrading the PA operation mode, provided that DPD may be unavoidable due to the impact of memory effects.     

一种新型数字预失真算法的设计

针对WCDMA系统中功率放大器的非线性特征,设计了一种基于Volterra级数的有记忆数字基带预失真算法,能够自适应地补偿功放的非线性.理论分析和计算机仿真验证了该算法的有效性和实用性.     

低复杂度的带限记忆多项式预失真器的设计

提出一种低复杂度的带限记忆多项式模型,通过对由低阶带限滤波器构成的带限记忆多项式模型的建模误差进行前向弥补,可以有效地降低模型所需的滤波器阶数和提高模型的建模精度,从而降低模型的复杂度。实验中,采用一款功率为35W 的AB类GaN功放和带宽为60MHz 的OFDM信号证明这种方法的优越性,实验结果表明,提出的方法与传统的带限记忆多项式模型相比,复杂度更低且精度更高。     

一种基于维度加权盲K近邻算法的数字预失真技术

传统的数字预失真(DPD)模型通常在所有的输入信号功率上采用单一多项式模型和单一记忆深度对功率放大器(PA)进行线性化矫正。然而,功率放大器在不同的功率水平下会呈现出不同的非线性特性,并产生不同的记忆效应。针对这一问题,该文提出一种基于维度加权盲K近邻(KNN)算法的数字预失真模型,所提模型根据功放当前输入信号以及记忆输入信号的幅度进行维度加权的KNN分类,组成维度加权盲KNN记忆多项式(WKMP)模型,并为每一类输入信号序列建立子模型。所提方法用Doherty功率放大器进行实验验证,使用带宽为30 MHz、频点为2.2 GHz的3载波长期演进(LTE)信号作为输入,反馈端使用122.88 MHz的采样率进行采样。实验结果表明,所提维度加权盲KNN分类方法与记忆多项式(MP)模型结合时,功放正向建模效果和数字预失真效果均超过了广义记忆多项式(GMP)模型,并远超记忆多项式模型的效果,实验结果验证了所提模型的优良性能。     

宽带Chrip信号激励下功放数字预失真补偿

功率放大器(power amplifiers, PAs)会对输入的宽带线性调频信号(linear frequency modulated, LFM)引入幅度失真和相位失真,这将导致接收机脉冲压缩处理后的输出信号主瓣展宽,旁瓣电平抬高,从而恶化雷达距离分辨率甚至产生虚假目标。文中提出采用有限冲击响应滤波器(finite impulse response, FIR)模型对宽带LFM信号激励下的功放进行行为建模和数字预失真(digital predistortion, DPD)补偿。利用宽带测试平台对500 MHz 瞬时带宽LFM信号激励下峰值功率15 W 的S波段功放进行验证。实验结果表明,浅饱和和深饱和情况下FIR模型都能准确建模功放的失真特性,浅饱和情况下DPD能够补偿幅度失真和相位失真,而深饱和情况下只能补偿相位失真,经过DPD补偿脉冲压缩后的峰值旁瓣电平都明显降低。     

An Accurate Digital Predistortion for Wideband Power Amplifiers Based on Directly Solving the Inverse Model Function

Digital predistortion (DPD) is one of the most effective techniques that can compensate for the distortions caused by the nonlinearities and memory effects of power amplifiers (PAs). In this paper, a new DPD solution which directly solves the inverse function of a PA model is presented for wideband transmitter applications. The major components of the general memory polynomial (GMP) model are selected to effectively characterize the PA’s nonlinearity and memory effects through model identification. In the direct learning algorithm that followed, the DPD function is obtained by constructing and then solving the reverse function of the identified PA model. Due to the high accuracy of the proposed modeling process and the direct learning algorithm, the DPD function is accurately derived, which could significantly compensate for the nonlinear distortions. Simulations and experiments are performed on wideband long-term evolution (LTE) signals to evaluate the effectiveness of the proposed DPD method. It is demonstrated that a 22-dB adjacent channel leakage ratio improvement is achieved for a 100-MHz LTE-advanced signal, which even outperforms the conventional GMP-based DPD method by about 3 dB.     

Digital Predistortion for Envelope-Tracking Power Amplifiers Using Decomposed Piecewise Volterra Series

Due to dynamic changes of supply voltage, envelope-tracking (ET) power amplifiers (PAs) exhibit very distinct characteristics in different power regions. It is very difficult to compensate the distortion induced by these amplifiers by employing conventional digital predistortion techniques. In this paper, by introducing a new piecewise Volterra model based on a vector threshold decomposition technique, we first set several thresholds in the input power level according to the PA characteristics, and decompose the input complex envelope signal into several sub-signals by using these thresholds. We then process each sub-signal separately by employing the dynamic deviation reduction-based Volterra series, and finally recombine them together to produce the predistorted output. Experimental results show that by using this new decomposed piecewise digital predistorter model, the distinct characteristics of the ET system at different signal power levels can be accurately modeled, and thus, the distortion, including both static nonlinearities and memory effects, caused by the amplifier nonlinear behavior can be effectively compensated.     

SSA optimized digital pre-distorter for compensating non-linear distortion in high power amplifier

Telecommunication Systems - We applied the stochastic salp swarm algorithm (SSA) to design high power amplifier (PA) and digital pre-distorter (DPD) using generalized memory polynomial model. This...     

Modeling long term memory effects in microwave power amplifiers for system level simulations

Accurate and dynamic behavioral models of SSPAS become of prime importance in system level analysis and design of modern communication and detection systems. This paper describes a new method to characterize and reproduce nonlinear memory effects in behavioral models ofSspas. We highlight, in a first section, the detailed mathematical development, whose the starting point is the Volterra series expansion, and ends to the nonlinear impulse response notion. The new model extraction relies on envelope transient simulations or time-domain measurements of complex envelopes at externDut reference accesses. This modeling technique is simple and enables a good prediction of nonlinear memory effects and especially long term memory effects and nonlinear transient behaviors. Simulations and measurements based extractions of this model are presented through significant amplifier examples.     

预失真技术在数字电视发射机中的应用研究

根据数字电视OFDM信号对电视发射机功率放大器线性的要求,介绍了一种可识别功放记忆效应的数字预失真器的结构和特点。经过计算机仿真表明,记忆效应预失真结构应用在数字电视发射机功放的线性化中可以取得令人满意的效果。     

An Approximation of Volterra Series Using Delay Envelopes, Applied to Digital Predistortion of RF Power Amplifiers With Memory Effects

In this letter, a new model for digital predistortion (DPD) of radio frequency power amplifiers for wide-band applications is proposed. The model is based on a spline approximation of Volterra series by considering second-order cross-terms. The advantage of the spline cross-term model is a reduction in the number of model parameters. We further reduce the model order by operating on delayed envelope samples, rather than the complex baseband samples. A block of wide-band code-division multiple access signal is sent through a 90 W class-AB power amplifier, based on the freescale LDMOS output device, and the input/output baseband samples were used to identify the DPD parameters.     

Spectral modeling of switched-mode power converters

A new modeling approach for the spectral analysis of pulsewidth modulated (PWM) converters with independent inputs is developed. The key of this approach is to extend the Volterra functional series to nonlinear systems with multiple independent inputs. After formulating the state-space equations describing the dynamical behavior of PWM converters, the Volterra transfer function characterizing the output frequency response can be obtained, which is then symmetrised to form the spectral model. Since the model is developed in a closed form, it is suitable for computer analysis. The modeling approach has been applied to various PWM converters, and the results are verified. The spectral models of different power converters can readily be obtained by using this general approach     

基于偏最小二乘的低复杂度数字预失真

在宽带场景下,传统的数字预失真(DPD)模型需要更高的阶次和更多的系数来校正功率放大器(PA)强非线性和记忆效应,这就会导致极高的计算复杂度和解算系数时的病态问题.文章围绕复杂DPD模型参数辨识和低复杂度DPD算法实现展开深入研究,提出了一种新的基于偏最小二乘(PLS)的低复杂度DPD方法.所提方法根据PA的前逆输入输...     

Impact of Power Amplifier Long Term Memory Effects in Spatial Derivative Superposition Systems

In this letter, the impact of power amplifier (PA) long term memory effects on intermodulation distortion cancellation performance of spatial derivative superposition systems is evaluated. Employing a behavioral model derived from Volterra series analysis, these important nonlinear dynamic effects could be taken into account for evaluating the impairment of the linear characteristics sought in the beam pointing direction. Radiation patterns obtained from simulations of a four-element active array highlight the influence of field effect transistor drain impedance characteristics on the achieved bandwidth. Measurement results, herein reported for the first time, validate the proposed analysis as well as the capability of this technique for improving linearity with spatial selectivity.      

使用多智能体反馈神经网络实现的数字预失真器

近年来,深度学习（Deep Learning,DL）在通信场景中的应用逐渐兴起,其中就包括射频发射机的数字预失真（Digital Predistortion,DPD）处理。然而,由于射频功率放大器（Power Amplifier,PA）固有的非线性失真和记忆效应特点,如果直接应用传统DL算法去实现DPD会出现拟合效果不佳、自适应性差等现象。针对这个问题,本文提出了一种由多智能体反馈神经网络实现的数字预失真器（Multi-Agent Feedback Enabled Neural Network for Digital Predistortion,MAFENN-DPD）,该网络引入了具有高纠错能力的反馈智能体结构,其主要特点是基于Stackelberg博弈理论去加速网络训练和收敛,同时我们还应用信息瓶颈理论指导网络超参数设计以增强MAFENN-DPD对PA记忆效应变化的动态适应能力。我们进行了一系列的实验来验证MAFENN-DPD的有效性。与使用典型前馈网络实现的DPD方案相比,基于MAFENN-DPD的方案在相邻信道功率比（Adjacent Channel Power Ratio,ACPR）指标上提高了约5 dB。同时,在没有通信过程中的大量先验知识的情况下,MAFENN-DPD实现了与使用记忆多项式方法建模的DPD方案十分接近的ACPR性能。仿真结果说明MAFENN-DPD相比传统神经网络可进一步提升ACPR性能,同时相比记忆多项式方法具有更好的自适应建模能力和通用性,并且具有多智能体反馈结构特征的神经网络未来在其他的通信场景中也具有应用推广的潜力。      

Frequency-Selective Predistortion Linearization of RF Power Amplifiers

This paper presents a frequency-selective RF vector predistortion linearization system for RF multicarrier power amplifiers (PAs) affected by strong differential memory effects. Differential memory effects can be revealed in two-tone experiment by the divergence for increasing tone-spacing of the vector Volterra coefficients associated with the lower and upper intermodulations tones. Using large-signal vector measurement with a large-signal network analyzer, a class-AB LDMOS RF PA is demonstrated to exhibit a strong differential memory effect for modulation bandwidth above 0.3 MHz. New frequency-selective RF and baseband predistortion linearization algorithms are proposed to separately address the linearization requirements of the interband and inband intermodulation products of both the lower and upper sidebands. Theoretical verification of the algorithms are demonstrated with Matlab simulations using a Volterra/Wiener PA model with memory effects. The baseband linearization algorithm is next implemented in a field-programmable gate array and experimentally investigated for the linearization of the class-AB LDMOS PA for two carrier wideband code-division multiple-access signals. The ability of the algorithm to selectively linearize the two interband and four inband intermodulation products is demonstrated. Adjacent channel leakage ratio of up to 45 dBc for inband and interband are demonstrated experimentally at twice the typical fractional bandwidth.     

调整峰值功放电流响应提高效率的LTE-A Doherty 功放*

介绍了一种利用宽带输入匹配网络调整峰值功放输出电流,改善Doherty 功放负载调制效果和带内 效率的设计方法。理论分析表明,Doherty功放中峰值功放C 类偏置情况下带来的带内不一致开启特性会影响输出 电流和负载调制效果。通过引入宽带输入匹配网络,能有效改善它的开启不一致性。为验证分析结果设计了具有 宽带(采用简易实频技术)和窄带两种不同输入匹配网络,用于2.15GHz 频段LTE-A 的Doherty功放。仿真和测试 结果表明,功放的输出功率超过49dBm,在7dB 回退功率处,宽带输入匹配Doherty 功放的带内效率达到42% 以上, 效率波动由10%降低到2%。使用100MHz 宽带LTE-A 信号经过线性化改善后,在40dBm 输出时,宽带输入匹配网 络的Doherty功放上下边带ACLR(adjacent channel leakage ratio)指标为-45.1/-44.9dBc,效率为40.5%,均优于窄带输入匹配网络的Doherty功放。