Adaptive Predistorters for Linearization of High-Power Amplifiers in OFDM Wireless Communications

Orthogonal frequency division multiplexing (OFDM) has several desirable attributes which make it a prime candidate for a number of emerging wireless communication standards. However, one of the major problems posed by OFDM is its high peak-to-average power ratio (PAPR), which seriously limits the power efficiency of the high-power amplifier (HPA) because of the nonlinear distortion resulting from the high PAPR. We provide a new mixed computational/analytical approach for adaptive compensation of this nonlinear distortion for cases in which the HPA is a traveling wave tube amplifier (TWTA) and solid state power amplifier (SSPA). TWTAs are used in wireless communication systems when high transmission power is required as in the case of the digital satellite channel, and SSPAs are generally used in mobile communication systems. Compared to previous predistorter techniques based on LUT (look-up table) or adaptive schemes, our approach relies on the analytical inversion of Saleh's TWTA model and Rapp's SSPA model in combination with a nonlinear parameter estimation algorithm. This leads to a sparse and yet accurate representation of the predistorter, with the capability of tracking efficiently any rapidly time-varying behavior of the HPA. Computer simulations results illustrate and validate the approach presented.     

A class of signal-processing schemes for reducing the envelope fluctuations of CDMA signals

In this paper, we present a class of nonlinear signal-processing schemes to reduce the envelope fluctuations in the downlink transmission within code-division multiple-access (CDMA) systems. These schemes are compatible with conventional CDMA receivers since they just require some modifications at the transmitter side. The proposed transmitter structure includes a nonlinear operation in the time-domain followed by a linear frequency-domain filtering operation. We also include a semi-analytical statistical characterization of the transmitted signals, which takes advantage of the Gaussian-like nature of CDMA signals with a high number of users. This characterization is used for an analytical performance evaluation of the proposed techniques. A set of performance results is presented showing that we can reduce significantly the envelope fluctuations of the transmitted signals, while maintaining the spectral occupation of the corresponding conventional CDMA signals. Moreover, the performance degradation due to the nonlinear distortion effects on the transmitted signals can be kept relatively low.     

OFDM系统中基于压缩感知恢复由限幅和HPA产生的非线性失真研究

正交频分复用（Orthogonal Frequency Division Multiplexing,OFDM）系统的主要缺点之一就是有较高的峰均功率比（Peak to Average Power Ratio,PAPR）,降低了功率放大器（High Power Amplifier,HPA）的工作效率,同时HPA引入的非线性失真,恶化了系统的误比特率（Bite Error Rate,BER）性能.本文所提算法将限幅和HPA引入的非线性失真视为一个整体来考虑,利用与限幅噪声在时域上的近似稀疏性,对整个非线性过程进行建模.发送端通过限幅降低了OFDM信号的PAPR,在接收端,选取受噪声干扰小的可靠性观测向量,最小化信道噪声的影响,基于非线性模型计算得到的参数,利用压缩感知（Compressive Sensing,CS）算法能有效地恢复总的非线性失真信号,提升了系统的BER性能.     

MQAM 功放器件非线性失真均衡器

本文给出了一种具有记忆能力的自适应非线性失真预均衡器,用于补偿MQAM高功率放大器在非线性区域工作时引入的具有记忆的3阶非线性失真,采用Volterra级数模型分析并补偿这种非线性失真,系统模拟证明这种结构简单的预均衡器对系统的非线性失真具有较好的校正作用。     

An analytic approach for CDMA output of feedforward power amplifier

In this paper, a novel method is introduced to predict the Code-Division Multiple-Access (CDMA) output spectrum of an RF power amplifier linearized with feedforward technique based on transfer function. In this method, an RF power amplifier is modeled mathematically by nonlinear complex envelope transfer function based on AM-AM and AM-PM distortion diagrams. Using this model, analytic expressions of CDMA output spectrum of power amplifier is calculated. Having mathematical model of RF power amplifier leads to derive analytic expressions for InterModulation (IM) products in feedforward amplifier. Based on these expressions, IM products are related to nonlinear complex envelope transfer function of feedforward amplifier. Then, CDMA output spectrum of feedforward linearization technique is predicted. The loops imbalances in feedforward technique are considered in analysis. Finally, the results of derived expressions in MATLAB software are compared with ADS simulations results and good agreements were achieved. Employing this method gives insight for feedforward analysis and loops imbalances effects in feedforward amplifier for CDMA applications.     

Theoretical analysis and performance of the decorrelating detector for DS-CDMA signals in nonlinear channels

We analyze the effects of the nonlinear distortions, introduced by the transmitting high-power amplifier (HPA), on the performance of the linear decorrelating multiuser detector in direct-sequence code-division multiple-access (DS-CDMA) downlink systems. By assuming and motivating the Gaussian distribution of the nonlinear distortion noise, the symbol-error rate (SER) and the total degradation (TD) has been derived theoretically in additive white Gaussian noise (AWGN) and frequency-flat Rayleigh fading channels. Simulation results show that the analytical model is quite accurate in many scenarios.     

UFMC系统中基于Volterra滤波器的非线性失真补偿方案

为实现通用滤波多载波(UFMC)通信系统高效、可靠的通信性能,需在最大程度上补偿由记忆型高功率放大器(HPA)引起的非线性失真.为解决HPA造成的失真问题,本文提出了一种基于Volterra滤波器的非线性失真补偿(V-NLDC)技术.该技术利用了Volterra级数的稀疏特性和能够模拟任意精度非线性系统的性质以逐次逼近的方式对信号进行预失真.将预失真后的信号传送至HPA,然后采用噪声消除器做进一步噪声消除处理,以达到更小失真度的目的.同时,本研究采用收敛速度快、性能稳定的自适应最小二乘法(RLS),可根据环境变化自适应地计算Volterra滤波器和噪声消除器的系数.通过大量蒙特卡罗仿真实验证实了所提出的非线性失真补偿技术可以很好的补偿由记忆型HPA非线性失真所造成的影响,从而优化系统性能.     

A new analog predistortion criterion with application to highefficiency digital radio links

Describes a new approach for designing analog cubic predistorters in view of minimizing nonlinear distortion introduced by the high power amplifier (HPA) in microwave radio links. The approach is based on a global mean squared error minimization between the input to the predistorter and the output of the power amplifier, rather than on the elimination of the cubic term. In this manner, two advantages are obtained. Firstly, the off-band distortion terms are reduced so that it is possible to eliminate the HF transmission filter. Secondly, the interference produced by the nonlinear distortion can be uniformly distributed over the entire constellation so that it is possible to reduce the back-off value of the HPA. Results of the application of the method proposed to some high spectrally efficient QAM systems, such as the 512-QAM system, are presented     

微波功率放大器非线性特性分析

为判断微波功率放大器非线性失真的主要影响因素,首先,在传统幂级数模型的基础上对功率放大器的非线性幅度失真和相位失真进行拟合,基于包络分析法给出了功率放大器非线性失真与幅度和相位失真间的解析关系;其次,对幅度失真和相位失真引起的非线性失真进行了分析,给出了两者之间的等效失真关系式,据此可对任意给定的功率放大器进行分析,以确定非线性失真的主要影响因素,并用于指导模拟预失真线性化器的设计与调试;最后,通过对一Ka频段行波管放大器的非线性测试及模拟预失真线性化,验证了所提出的功率放大器非线性分析的正确性及幅相等效失真关系式的有效性。     

The Impact of Nonlinear HPA on the Determination of the Impulse Sample Power in IP-OFDM Systems

The recently introduced impulse postfix OFDM (IP-OFDM) system, which performs channel estimation in time-domain by exploiting the IP instead of pilot tones, can achieve the enhanced bit error rate (BER) performance compared to that of conventional OFDM systems. Since there is a peak-to-average power ratio (PAPR) issue of using the IP, however, the decision criteria for determining the power boosting factor (PBF) of IP were proposed to resolve the PAPR issue while achieving the optimum BER performance in the IP-OFDM system with an ideal high power amplifier (HPA). In this paper, a practical IP-OFDM system with a nonlinear HPA is considered and the impact of nonlinear HPA on the determination of the PBF of IP as well as the BER performance are analyzed. The BER lower bound is also derived in the case of QPSK and 16QAM. It is shown that the approximated lower bound approaches to the simulation results as the PBF is increased. According to the analytical results, due to the nonlinearity of the HPA, 1–3dB increased PBF than the ideal PBF is required to achieve the optimum BER performance, which is even deteriorated compared to that of IP-OFDM with an ideal soft envelope limiter.     

OFDM系统中基于限幅和压缩感知的非线性失真补偿算法

正交频分复用（Orthogonal Frequency Division Multiplexing,OFDM）信号具有较高的峰均功率比（Peak to Average Power Ratio,PAPR）,不仅影响功率放大器（High Power Amplifier,HPA）的工作效率,而且HPA使得OFDM信号产生严重的非线性失真,导致系统的误比特率（Bite Error Rate,BER）增大.本文基于限幅和压缩感知（Compressive Sensing,CS）提出了改进的补偿算法,发送端采用限幅降低信号的PAPR,接收端首先采用改进的逆模型方式减小HPA引入的非线性失真,再采用CS抵消由限幅引入的信号失真.仿真表明,所提方法不仅明显降低了OFDM信号的PAPR,而且有效提高了系统的BER性能.     

EVM simulation and analysis in digital transmitter

The error vector magnitude (EVM) is extensively applied as a metric for digital transmitter signal quality compliance in modern communication systems. This article is focused on the effects of local oscillator (LO) phase noise and nonlinear distortion of power amplifier on EVM. This article contributes to below aspects. First, the relationships between EVM and two effects, LO phase noise and nonlinear distortion of power amplifier, are derived and expressed. Second, to simplify the expression, the third-order intermodulation distortion (IMD3) is used to calculate the EVM. Then, an expression for the EVM is derived based on the digital transmitter model that considers local oscillator phase noise and nonlinear distortion of power amplifier. Finally, the math formula of bit error rate (BER) versus EVM is given which can be easier and more useful to predict BER, according to analysis of the relationship between EVM and signal to noise rate (SNR), inspired by the works of Rishad, Md. Shahriar and AHM, 2006. Simulations are carried out to display the performance of EVM based on these relationships.     

BER Performance of OFDM Signals in Presence of Nonlinear Distortion due to SSPA

Orthogonal frequency division multiplexed signals typically exhibit large dynamic ranges due to superposition of a large number of subcarrier signals. As a result, such signals are highly vulnerable to distortion caused by high power amplifier (HPA) nonlinearity, leading to degradation in bit error rate (BER). In turn, the HPA operating point should be backed off to compensate for such degradation at the expense of the HPA efficiency. In this paper, the considered amplifier chain is a solid state power amplifier of Rapp’s model. We develop the factors contributing to BER degradation in terms of the input back-off (IBO) level assuming quadrature phase shift keying modulation. Consequently, the BER performance for such an amplifier model is developed as a function in IBO. Then, we show how this developed performance can be used to determine the required HPA operating point to achieve a certain required BER. Accordingly, an improvement in the amplifier efficiency is achieved. All developed analytic expressions are compared against simulation measurements, which show that good agreement exists.     

Effects of low noise amplifier non‐linearities on blind adaptive beamforming performance in CDMA wireless systems

We report a new approach to analyse the effects of low noise amplifier (LNA) non‐linear distortions in the code division multiple access (CDMA) wireless communication systems using spatio‐temporal analysis and Volterra series theory. For this purpose, the bit error rate (BER) performance of three blind algorithms is studied based on post correlated model of received signal, and a time‐varying multiple vector channel model which is an extended form of the Gaussian wide sense stationary uncorrelated scattering (GWSSUS) channel. By using the Volterra series theory, an analytical expression for amplitude modulation to phase modulation (AM–PM) conversion is determined as a phase statement of LNA compression. In this approach, by combining the analytical expression for AM–PM conversion and CDMA blind beamforming techniques, we evaluate the AM–PM distortion effects on BER performance of a CDMA system originated from multiple non‐linear LNA blocks. Simulation results show that conditions are found to minimize AM–PM conversion introduced by multiple non‐linear blocks in the system leading to low BER. Copyright © 2006 John Wiley & Sons, Ltd.     

一种有效的自适应预失真算法

自适应预失真技术是一种用于补偿功率放大器引起的非线性失真的技术 ,本文提出了一种改进算法用来加快预失真算法的收敛速度     

An adaptive pre-distorter for the compensation of HPA nonlinearity

A high power amplifier (HPA) is used for the amplification of transmitting communication signals. However, it produces distortions by creating AM/AM and AM/PM modulations in the transmitting signal, Accordingly, this nonlinearity results in bandwidth expansion and nonlinear distortion in the in-band signal. This paper proposes an algorithm for the operation of a pre-distorter, which is composed of a look-up table (LUT), that can compensate for the distortion produced by an HPA. For the fast initialization of the LUT, an estimation algorithm is also proposed for the HPA characteristics. Furthermore, an adaptive algorithm based on the minimization of the mean square error is proposed to compensate for the time-varying property of an HPA. The performance of the proposed algorithm is analyzed by applying the algorithm to an 8-level vestigial sideband (VSB) modulation to be used in the ATSC terrestrial digital TV system     

Threshold IBO of HPA in the predistorted OFDM communication system

Orthogonal frequency division modulation (OFDM) system is very useful for the multi-path channel and highly bandwidth-efficient system. However, OFDM signal shows the high peak to average power ratio (PAPR) so that nonlinear distortion can happen in the high power amplifier (HPA). This paper studies BER performance variation according to input back off (IBO) values when the predistorter is used for the compensation for the HPA nonlinearity. In the case of the solid state power amplifier (SSPA) of nonlinearity parameter p=0.5 and IBO=0 dB, the system with predistorter is poorer than the one without predistorter. But this situation is inverted, if IBO is increased from 0 dB to 3 dB. So, we can find that there is a threshold value of IBO for the predistorter to effectively compensate for the nonlinear SSPA when the sub-carrier number and p value are changed. This threshold IBO value is proportional to the nonlinearity parameter p value but it is nearly independent of the sub-carrier number because amplitude and distribution are normalized. The OFDM system with predistorter can be improved only when thee IBO value is higher than the threshold value.     

前向信道CDMA信号频谱增生的算法与仿真实验

利用幂级数和高阶累计量的统计方法,推导出基于IS-95模型前向信道的CDMA(码分多址)信号通过弱非线性RF功率放大器产生的频谱增生的严谨表达式,通过仿真验证其正确性.并由此获得了经该放大器特征模型变换的输出信号自相关函数的解析表达式.用三阶截断点IP3表示了包含带内和带外电抗的记忆效应三阶非线性.频谱增生的分析结果可直接用于工程计算,这对于确定射频功率放大器最佳的工作条件是十分有价值的.根据推导出的算法进行仿真,并与ADS软件进行仿真结果进行比较,以说明其正确性.     

Novel Adaptive Nonlinear Predistorters Based on the Direct Learning Algorithm

The adaptive nonlinear predistorter is an effective technique to compensate for the nonlinear distortion existing in digital communication and control systems. However, available adaptive nonlinear predistorters using indirect learning are sensitive to measurement noise and do not perform optimally. Other available types are either slow to converge, complicated in structure and computationally expensive, or do not consider the memory effects in nonlinear systems such as a high power amplifier (HPA). In this paper, we first propose several novel adaptive nonlinear predistorters based on direct learning algorithms - the nonlinear filtered-x RLS (NFXRLS) algorithm, the nonlinear adjoint LMS (NALMS) algorithm, and the nonlinear adjoint RLS (NARLS) algorithm. Using these new learning algorithms, we design adaptive nonlinear predistorters for an HPA with memory effects or for an HPA following a linear system. Because of the direct learning algorithm, these novel adaptive predistorters outperform nonlinear predistorters that are based on the indirect learning method in the sense of normalized mean square error (NMSE), bit error rate (BER), and spectral regrowth. Moreover, our developed adaptive nonlinear predistorters are computationally efficient and/or converge rapidly when compared to other adaptive nonlinear predistorters that use direct learning, and furthermore can be easily implemented. We further simplify our proposed algorithms by exploring the robustness of our proposed algorithm as well as by examining the statistical properties of what we call the "instantaneous equivalent linear" (IEL) filter. Simulation results confirm the effectiveness of our proposed algorithms     

Blind downlink channel estimation for TDD‐based multiuser massive MIMO in the presence of nonlinear HPA

In time division duplex (TDD)‐based multiuser massive multiple input multiple output (MIMO) systems, the uplink channel is estimated and the results are used in downlink for signal detection. Owing to noisy uplink channel estimation, the downlink channel should also be estimated for accurate signal detection. Therefore, recently, a blind method was developed, which assumes the use of a linear high‐power amplifier (HPA) in the base station (BS). In this study, we extend this method to a scenario with a nonlinear HPA in the BS, where the Bussgang decomposition is used for HPA modeling. In the proposed method, the average power of the received signal for each user is a function of channel gain, large‐scale fading, and nonlinear distortion variance. Therefore, the channel gain is estimated, which is required for signal detection. The performance of the proposed method is analyzed theoretically. The simulation results show superior performance of the proposed method compared to that of the other methods in the literature.