Power Amplifier Nonlinear Distortion Research Articles

A Novel Specific Emitter Identification Algorithm Based on Amplitude Probability Distribution

We propose a novel specific emitter identification (SEI) algorithm based on amplitude probability distribution (APD). By studying the subtle differences in nonlinear distortion of power amplifiers, the proposed algorithm leverages the real signal amplitude interval probability distribution (AIPD) and analytical signal’s constellation circle interval probability distribution (CIPD) to extract the local distortion features. The simulation results on both the simulated signal and actual signal show that compared to the benchmark methods, the proposed algorithm can achieve significant performance gains with relatively low complexity and has high robustness to training set size and prior information of signal to noise ratio (SNR).

Efficient Neural Network DPD Architecture for Hybrid Beamforming mMIMO

This paper presents several different Neural Network based DPD architectures for hybrid beamforming (HBF) mMIMO applications. They are formulated, tested and compared based on their ability to compensate nonlinear distortion of power amplifiers in a single user (SU) and multiuser (MU) Fully-Connected (FC) HBF mMIMO transmitters. The proof-of-concept is provided with a 64 × 64 FC HBF mMIMO system, with 2 RF chains. The complexity of DPD solution is reduced by using a single Real-Valued Time-Delay Neural Network with two hidden layers (RVTDNN2L) instead of using as many different DPD blocks as there are RF chains in the HBF mMIMO transmitter and it is shown that the proposed architecture better compensates nonlinear distortion compared to the traditional memory polynomial DPD. Two RVTDNN2L DPD architectures are developed and tested for linearization of MU FC HBF mMIMO systems, and it is also shown that the proposed RVTDNN2L DPD architecture efficiently linearizes MU FC HBF mMIMO transmitters in terms of Normalized Mean-Squared Error (NMSE) and Error Vector Magnitude (EVM).

Behavioral Model With Multiple States Based on Deep Neural Network for Power Amplifiers

Digital predistortion is widely used to compensate the nonlinear distortion of power amplifiers (PAs). Among the digital predistortion methods, the polynomial or deep neural networks (DNNs) models are only adopted with one specific state. When the operating conditions of PAs change, it is necessary to retrain and update the coefficients of the PA model. The generalization ability of the DNN models cannot be presented. To address this issue, this letter proposes one new modeling method that can build one generalized PA model with multiple states based on DNN. This method embeds a set of coding vectors representing corresponding states to build the generalized model. Compared with the traditional DNN model, experimental results show that the proposed method can construct the PA model containing multiple states while ensuring good modeling performance.

Spurious Beam Suppression in Dual-Beam Phased Array Transmission by Impedance Tuning

A significant challenge for dual-beam, codesigned systems, such as for simultaneous radar and communications transmission, has been identified as the spurious beams produced by spatial intermodulation from nonlinearities in the transmitter power amplifier. We demonstrate that tuning the load impedance of the power amplifiers can reverse the elementwise power amplifier nonlinear distortion, reducing the magnitude of the unwanted beam transmissions and restoring the integrity of the dual-beam antenna pattern for application to an active electronically scanned array. A comparison to a recently documented predistortion approach for correcting spurious transmissions is provided, and it is shown that impedance tuning can address both element output power and linearity, whereas predistortion addresses only the linearity issue and causes the amplifier gain in many of the array elements to suffer. For multiple dual-beam angle scenarios, simulation results show that impedance tuning is effective at maximizing beam power in both beam directions, maximizing current gain in the element power amplifiers, and minimizing the size of the unwanted spurious beams.

An Upgraded Dual-Band Digital Predistorter Model for Power Amplifiers Linearization

Digital predistortion (DPD) based on Volterra models is commonly employed to counteract the nonlinear distortion of power amplifiers. However, when concurrent dual-band signals are transmitted, 2-D DPD models are required. In this work, upgrading of a standard dual-band model is proposed and justified using multinomial theorem. The linearization performance of the current proposal has been compared to the unextended model. Fifth generation (5G) New Radio signals have been generated to compose a dual-band signal, which later was employed as input signal at Chalmers University of Technology’s RF WebLab. Using coefficient selection techniques, the most relevant regressors are shown, and the importance of the new extension is proven. Linearization results highlight the benefits of this proposal.

Multibeam Digital Predistortion for Millimeter-Wave Analog Beamforming Transmitters

In this letter, a novel multibeam digital predistortion (MB-DPD) technique is proposed to linearize multiple beams simultaneously targeted at the multiuser scenario of millimeter-wave (mmWave) analog beamforming transmitters. It is achieved by effectively constructing the predistorted signal for each beam to remove both the intrinsic nonlinear distortion of power amplifier (PA) and the multibeam interference incurred by all beams except the targeted main beam. To validate the proposed technique, a two-beam test on an analog beamforming transmitter was carried out and the measurement results have shown that the proposed method can effectively realize the multibeam linearization, providing a promising solution for mmWave multiuser applications.

Digital Predistortion for MIMO Transmitters Using Multi-Channel Error Feedback Adaptation

Digital predistortion (DPD) is known as an efficient solution to suppress nonlinear distortion of power amplifiers (PAs) in wireless transmitters to achieve both high linearity and power efficiency. In multiple input and multiple output (MIMO) applications, the power gains of multiple transmitting channels are usually different. Meanwhile, the channel crosstalk cannot be ignored, given the isolations between the physical channels are limited. Accordingly, the linearization performances of the conventional DPD methods are usually degraded. In this article, we propose a novel DPD method for MIMO transmitters, where both the crosstalk and different power gains of multiple channels are considered. In this method, the expected predistorted signals, which would be used to train the DPD model, are firstly obtained by an iterative algorithm derived from the contraction mapping theorem. Then, the coefficients of a MIMO-DPD model are extracted by fitting the DPD model to the obtained predistorted signal. Experimental results verify that the extracted coefficients can achieve an improved linearization performance for the MIMO transmitter with crosstalk between the channels, especially in the case where the channel gains are different. Specifically, for a $2 \times 2$ MIMO transmitter with -20 dB crosstalk and 1.2 dB difference between the two channel gains, the proposed DPD improves the adjacent channel power ratio (ACPR) from -31.4 dBc to -47.1 dBc, which outperforms the conventional DPD by 6.8 dB.

MIMO and Massive MIMO Transmitter Crosstalk

The effects of hardware-induced crosstalk in MIMO transmitters, subject to nonlinear power amplifier distortion, are considered in this paper. A methodology that provides tractable results and a clear understanding of the effects of crosstalk on transmitter performance is introduced and applied to different transmitter models. In particular, a physically motivated $2 \times 2$ MIMO transmitter model, which is subjected to input and output crosstalk, is studied in detail, as well as a behavior motivated transmitter model, which is subjected to linear crosstalk. For the latter structure, asymptotic results, when the number of transmitters tends to infinity, are derived. These results provide insight into different 1D and 2D transmitter structures in the massive MIMO scenario. The methodology provides tractable analytical results of the performance of the transmitter. It is shown that the transmitter crosstalk degrades the performance in terms of normalized mean squared error with 3 dB going from a $2\times 2$ set-up to a 1D array of a massive amount of transmitters, and an additional 3 dB loss going from a 1D to 2D transmitter structure. Transmitter input power back-off optimization is further studied, with back-off determination that takes the effects of MIMO crosstalk into account in order to increase the energy efficiency of the transmitter.

Linearization of a Directional Modulation Transmitter Using Low-Complexity Cascaded Digital Predistortion

Directional modulation (DM) implemented at the transmitter side is a physical layer security technology based on the multi-antenna structure. Current DM methods paid little attention to the issue of the nonlinear distortion of power amplifiers (PAs), which may lead to poor amplifier efficiency and worsen the signal’s error vector magnitude (EVM). For the first time, we consider linearization of a DM transmitter using the digital predistortion (DPD) technique. We modify the paralleled DM DPD model to a novel cascaded model based on the characteristics of the DM transmitter. This modified method applies a common DPD to mitigate the nonlinear distortion of all paths and an auxiliary DPD to fine-tune each path, so as to significantly reduce the complexity. In order to validate this idea, two-element uniform linear array (ULA) and four-element ULA experiments were performed, in which 16QAM 20-MHz bandwidth signals with a peak-to-average power ratio (PAPR) of about 8.0 dB were generated for commercial part PAs. Experimental results show that the modified approach has almost the same linearization performance as the paralleled DM DPD technique but reduces the computational complexity significantly.

Saleh Model and Digital Predistortion for Power Amplifiers in Wireless Communications Using the Third-Order Intercept Point

This paper presents a novel approach for estimating the Saleh model’s parameters using the gain and third-order intercept point (IP3) of a power amplifier. The IP3 is a widely used technical parameter for describing the nonlinearity of the power amplifier in wireless communications. The proposed approach minimizes an objective function of error between the third-order Taylor series and the Saleh Amplitude-to-Amplitude (AM/AM) model. This approach of the parameters estimation is also used for identifying the Digital Predistortion (DPD) to compensate for the memoryless AM/AM nonlinear distortion of power amplifiers in wireless communications. Finally, the Saleh model accuracy and DPD linearization are validated based on the WCDMA measurement signal.

Digital Predistorter for Short-Wave Power Amplifier With Improving Index Accuracy of Lookup Table Based on FPGA

The method of function approximation to improve index accuracy of the lookup table (LUT) of digital predistortion (DPD) is proposed in this paper. The algorithm utilizes Taylor Series method for LUT approximation. The power value of a forward signal is divided into an integer and a decimal to index corresponding LUT respectively, and the indexed predistortion value of the forward signal is approached by fitting according to Taylor series, which makes the LUT index precision obviously increased. Experiment shows that comparing with the traditional Memory Polynomial Model (MPM) DPD LUT method, this model can improve Adjacent Channels Power Ratio (ACPR) over 15 dB for high frequency (HF) power amplifier’s output signal, compensate for short-wave power amplifier nonlinear distortion effectively, and improve the short-wave radio communication quality greatly.

Digital Self-Interference Cancellation for Asynchronous In-Band Full-Duplex Underwater Acoustic Communication.

To improve the throughput of underwater acoustic (UWA) networking, the In-band full-duplex (IBFD) communication is one of the most vital pieces of research. The major drawback of IBFD-UWA communication is Self-Interference (SI). This paper presents a digital SI cancellation algorithm for asynchronous IBFD-UWA communication system. We focus on two issues: one is asynchronous communication dissimilar to IBFD radio communication, the other is nonlinear distortion caused by power amplifier (PA). First, we discuss asynchronous IBFD-UWA signal model with the nonlinear distortion of PA. Then, we design a scheme for asynchronous IBFD-UWA communication utilizing the non-overlapping region between SI and intended signal to estimate the nonlinear SI channel. To cancel the nonlinear distortion caused by PA, we propose an Over-Parameterization based Recursive Least Squares (RLS) algorithm (OPRLS) to estimate the nonlinear SI channel. Furthermore, we present the OPRLS with a sparse constraint to estimate the SI channel, which reduces the requirement of the length of the non-overlapping region. Finally, we verify our concept through simulation and the pool experiment. Results demonstrate that the proposed digital SI cancellation scheme can cancel SI efficiently.

The Polarization Modulation Based Self-Interference Cancellation for Full Duplex

In full duplex systems, self-interference (SI) cancellation amounts is limited by the power amplifier (PA) nonlinear distortion. In this paper, to cancel the nonlinear SI induced by the PA, a SI cancellation scheme based on polarization modulation is proposed. The proposed scheme uses polarization state as the information-bearing parameter and can let the PA work in its nonlinear region without suffering distortion. The simulation results and analysis show that the proposed SI cancellation scheme can improve the bit error rate (BER) performance significantly when the PA nonlinear distortion exists in the system.

Polarization oblique projection based self-interference cancellation against PA nonlinear distortion in MIMO full duplex system

In MIMO full duplex system, power amplifier (PA) nonlinearity limits the self-interference (SI) cancellation seriously. Most existing methods need to model and estimate the PA nonlinearity in order to reconstruct the SI, however the estimation error caused by the mismatch between the estimated PA model and the actual PA property still impacts the cancellation ability, especially when the transmit power is high. In this paper we propose a polarization oblique projection based self-interference cancellation method which does not need to estimate the PA nonlinearity coefficients. It exploits the polarization state information of the signals which is immune to the PA nonlinearity, and establishes an oblique projection operator to cancel the SI. Numerical results and analysis demonstrate that it can cancel the nonlinear SI effectively. Moreover the signal to interfere plus noise ratio (SINR) and the achievable sum rate do not deteriorate when the transmit power is high. Further, the upper bound of the achievable sum rate can be more than twice that of the half duplex.

A low complexity SI sequence estimator for pilot-aided SLM–OFDM systems

Selected mapping (SLM) is a well-known method for reducing peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. However, as a consequence of implementing SLM, OFDM receivers often require estimation of some side information (SI) in order to achieve successful data recovery. Existing SI estimation schemes have very high computational complexities that put additional constraints on limited resources and increase system complexity. To address this problem, an alternative SLM approach that facilitates estimation of SI in the form of phase detection is presented. Simulations show that this modified SLM approach produces similar PAPR reduction performance when compared to conventional SLM. With no amplifier distortion and in the presence of non-linear power amplifier distortion, the proposed SI estimation approach achieves similar data recovery performance as both standard SLM–OFDM (with perfect SI estimation) and also when SI estimation is implemented through the use of an existing frequency-domain correlation (FDC) decision metric. In addition, the proposed method significantly reduces computational complexity compared with the FDC scheme and an ML estimation scheme.

Modeling and compensation of transmitter nonlinearity in coherent optical OFDM

We present a comprehensive study of nonlinear distortions from an optical OFDM transmitter. Nonlinearities are introduced by the combination of effects from the digital-to-analog converter (DAC), electrical power amplifier (PA) and optical modulator in the presence of high peak-to-average power ratio (PAPR). We introduce parameters to quantify the transmitter nonlinearity. High input backoff avoids OFDM signal compression from the PA, but incurs high penalties in power efficiency. At low input backoff, common PAPR reduction techniques are not effective in suppressing the PA nonlinear distortion. A bit error distribution investigation shows a technique combining nonlinear predistortion with PAPR mitigation could achieve good power efficiency by allowing low input backoff. We use training symbols to extract the transmitter nonlinear function. We show that piecewise linear interpolation (PLI) leads to an accurate transmitter nonlinearity characterization. We derive a semi-analytical solution for bit error rate (BER) that validates the PLI approximation accurately captures transmitter nonlinearity. The inverse of the PLI estimate of the nonlinear function is used as a predistorter to suppress transmitter nonlinearity. We investigate performance of the proposed scheme by Monte Carlo simulations. Our simulations show that when DAC resolution is more than 4 bits, BER below forward error correction limit of 3.8 × 10(-3) can be achieved by using predistortion with very low input power backoff for electrical PA and optical modulator.

Cascade Structure of Digital Predistorter for Power Amplifier Linearization

In this paper, a cascade structure of nonlinear digital predistorter (DPD) synthesized by the direct learn- ing adaptive algorithm is represented. DPD is used for linearization of the power amplifier (PA) characteristics, namely for compensation of PA nonlinear distortion. Blocks of the cascade DPD are described by different models: the functional link artificial neural network (FLANN), the polynomial perceptron network (PPN) and the radially pruned Volterra model (RPVM). At synthesis of the cascade DPD there is possibility to overcome the ill conditionality problem due to reducing the dimension of the DPD nonlinear operator approximation. Results of compensating nonlinear distortion in Wiener-Hammer- stein model of PA at the GSM-signal with four carriers are shown. The highest accuracy of PA linearization is pro- duced by the cascade DPD containing PPN and RPVM.

TSK type self-organising online fuzzy equalisation to mitigate nonlinear power amplifier distortions in OFDM systems

This paper presents a first order Takagi-Sugeno-Kang TSK type self-constructing, adaptive, online, transversal, fuzzy equaliser to mitigate nonlinear power amplifier distortion effects from received signal in orthogonal frequency division multiplexing OFDM systems. Here, the proposed SOTSKFS equaliser, that attempts to compensate the nonlinear distortions in single-antenna and/or multi-antenna OFDM systems, produces most compact fuzzy rule base with less number of rules in comparison to other online fuzzy equalisers, viz. FSCFNN and SCRFNN. Computer simulations show improved bit-error-rate BER and mean-square-error MSE performances of this proposed evolving fuzzy equalisation technique, when compared to that of the latest power amplifier nonlinearity cancellation techniques in OFDM receiver.

Widely linear digital self-interference cancellation in direct-conversion full-duplex transceiver

This paper addresses the modeling and cancellation of self-interference in full-duplex direct-conversion radio transceivers, operating under practical imperfect radio frequency (RF) components. First, detailed self-interference signal modeling is carried out, taking into account the most important RF imperfections, namely, transmitter power amplifier nonlinear distortion as well as transmitter and receiver IQ mixer amplitude and phase imbalances. The analysis shows that after realistic antenna isolation and RF cancellation, the dominant self-interference waveform at the receiver digital baseband can be modeled through a widely linear transformation of the original transmit data, opposed to classical purely linear models. Such widely linear self-interference waveform is physically stemming from the transmitter and receiver IQ imaging and cannot be efficiently suppressed by classical linear digital cancellation. Motivated by this, novel widely linear digital self-interference cancellation processing is then proposed and formulated, combined with efficient parameter estimation methods. Extensive simulation results demonstrate that the proposed widely linear cancellation processing clearly outperforms the existing linear solutions, hence enabling the use of practical low-cost RF front ends utilizing IQ mixing in full-duplex transceivers.

FPGA Implementation of a Real-Time NARMA-Based Digital Adaptive Predistorter

This paper presents the design of a nonlinear autoregressive moving average (NARMA) digital adaptive predistorter (DAPD) for power amplifier (PA) linearization consisting of a low-complex closed-loop architecture. Both the predistortion function and the adaptation algorithm are fully implemented in a field-programmable gate array (FPGA) device, without the need for using any additional coprocessor. The proposed predistortion architecture is capable to compensate for both the PA nonlinear distortion and memory effects. Moreover, this DAPD allows almost real-time adaptation without interrupting the normal transmission. The computational complexity introduced by this DAPD is studied in this paper. The proposed theoretical design is implemented in an FPGA, whereas the linearization performance of the DAPD is validated through simulated and experimental results.