Digital Predistortion Algorithm Research Articles

A General Digital Predistortion Linearization Scheme for Hybrid Beamforming System

Hybrid beamforming multiple-input multiple-output (MIMO) system has attracted a lot of attention in recent years since it significantly reduces the hardware cost compared to the fully digital beamforming system. However, with hybrid beamforming, the one-to-one mapping between the radio frequency (RF) chain and the nonlinear power amplifier (PA) is destroyed. The PA nonlinearity cannot be compensated by conventional digital predistortion (DPD) algorithms. In this article, we propose a novel multiple-input DPD model for hybrid beamforming MIMO systems. An extra digital compensation block is introduced in the feedback path. With the feedback compensation block, the proposed DPD can linearize the PA output signal as well as the aggregated far-field signal. What is more, we propose a DPD estimation algorithm with much reduced complexity. Comparing to existing solutions, the proposed scheme achieves satisfactory performance for hybrid beamforming system. It does not rely on the measurement of the channel or the assumption of massive antennas. Simulation results demonstrate the effectiveness of the proposed DPD scheme.

Continual Learning Digital Predistortion of RF Power Amplifier for 6G AI-Empowered Wireless Communication

Artificial intelligence (AI) provides opportunities to enable high-efficiency wireless communication to dynamically adapt to the local environments and user demands. In this article, a continual learning digital predistortion (DPD) algorithm is proposed to linearize radio frequency (RF) power amplifier (PA) in 6G AI-empowered wireless communication. It is achieved by employing the ability of knowledge retention and knowledge transfer to merge the new PA operating state into the previous model, which makes the model more intelligent when dealing with multiple states. In addition, an augmented self-sensing model is proposed to accurately capture the common characteristics and key dynamic characteristics among different PA operating states to improve the knowledge transfer ability during the continual learning process. The experiments were carried out on a Doherty PA with dynamic configurations associated with power, bandwidth, and signal type. The experimental results have shown that the proposed technique can continuously learn when faced with unpredicted new PA operating states and so as to linearize all known states. The proposed DPD method performs with very low complexity in the long term, which is very suitable for the emerging AI-empowered dynamic scenario.

РАЗРАБОТКА ЭНЕРГЕТИЧЕСКИ ЭФФЕКТИВНОЙ СИСТЕМЫ СВЯЗИ В ТРОПОСФЕРНОМ РАДИОКАНАЛЕ НА БАЗЕ OFDM-СИГНАЛОВ

It is known that inter-symbol interference may occur during data transmission in radio relayand tropospheric communication systems. The presence of multipath propagation and frequencyselectivefading in the tropospheric, radio relay channel significantly reduces the energy efficiencyof the communication system as a whole. The aim of the work was to increase the efficiency ofusing the channel for radio relay and tropospheric communication by using OFDM (orthogonalfrequency-division multiplexing using the methods of reducing the peak factor of the OFDM signaland increasing the linearity of the transmission path. To evaluate digital predistortion algorithmsin the Matlab/Simulink environment, a model was developed for the LMS, NLMS, RLS, RPEMmethods and a power amplifier model with real characteristics. Based on the results of modelingalgorithms, RLS was chosen. In addition, in this work, a modified version of the adaptation algorithmbased on the recursive least squares method (RLSm) was developed. The main result of themodification is: a decrease in the number of arithmetic operations per iteration (more than5 times), an increase in the stability of adaptation algorithms, due to the introduction of regularizationmethods, a decrease in the convergence time, due to the introduction of an exponential dependence.Various algorithms for reducing the peak factor of an OFDM signal were investigated,the best result was achieved by combining Tone reservation (TR) and Active constellation extension(ACE). Simulation in the Matlab/Simulink environment showed that the combination of TRand ACE algorithms reduces the peak factor of OFDM signals by ~5dB for BPSK data stream and~4.5dB for 8-PSK, QAM-16, QAM-64, QAM-128 and QAM- 256. To increase the linearity of thetransmission path, the RLSm digital pre-distortion algorithm was selected and upgraded, it madeit possible to reduce the magnitude of the error vector modulus (EVM) by 13.5dB, and also increasethe modulation/error ratio (MER) by 13.6dB.

Closed-form MSE and achievable rate for indirect learning DPD

The digital pre-distortion (DPD) signal processing is an effective way to mitigate the power amplifier (PA) nonlinearity effect. For communication systems containing DPD and PA, it is difficult to acquire performance metrics closed-forms for any DPD architecture since there was no mathematical expression for each DPD coefficient. Usually, researchers look for more efficient DPD algorithms for DPD coefficients (compared to the existing ones) in terms of computational complexity, delay, power consumption, etc. Consequently, the performance is evaluated through intensive simulation. In this paper, we show how one can exploit the results of our recent work to mathematically model the indirect learning architecture (ILA) DPD and efficiently derive important measures in communication systems, e.g. normalized mean square error (NMSE), achievable rate, and signal-to-noise plus distortion ratio (SNDR). The author would like to clarify that this work might be the first one to provide closed-form analysis for DPD systems. We think the provided framework/analysis will open the door to other researchers/engineers to plug their own assumptions and derive the performance metrics. The derived expressions of the performance metrics (NMSE, SNDR, and achievable rate) are validated through Monte Carlo simulations. We also derive a closed-form expression for the achievable rate bound for the transmit chain. Moreover, we analytically study the effect of the thermal noise and the quantization noise, in the analog-digital conversion (ADC) process, on the NMSE and achievable rate. The analytical expressions are validated through numerical simulations.

Power Efficiency Model for MIMO Transmitters Including Memory Polynomial Digital Predistortion

Multiple-input multiple-output (MIMO) beamforming array gain can make multi-antenna transmitters (TXs) more power efficient. However, these MIMO TXs require more complex digital predistortion (DPD). In this brief, analytical expressions are derived for the power consumption of both MIMO power amplifier (PA) arrays and their respective DPD, taking into account the effects of precoding on PA output power and peak-to-average power ratio (PAPR). It is shown that for complex DPD algorithms such as cross-over DPD (CO-DPD) in combination with wide bandwidths, the overall DPD power consumption can exceed the overall PA power consumption already for scenarios with more than two antennas.

Very low‐complexity filter lookup‐table design with non‐uniform spacing for SOA linearisation

Non-linearities introduced by power amplifiers in communication systems have been a subject of interest for industry and academia for a long time. On one hand, the search for increased range intrinsically incites operators to boost input power. On the other hand, this leads to stronger non-linear phenomena in amplifiers, which in turn increase the bit error rate. The situation led to the emergence of digital predistortion algorithms that compensate for the power amplifier's non-linearities and improve the overall performance of the link. A rich corpus of literature exists on this topic but it mainly addresses wireless microwave networks. The case of digital predistortion specifically tailored for optical communications is much less explored. This study focuses on predistortion via filter-lookup-tables and tackles the issue of non-uniform spacing. The work is mainly aimed at coherent optical-orthogonal frequency-division multiplexing systems including low-cost semiconductor optical amplifiers.

A Methodology and a Metric for the Assessment of the Linearizability of Broadband Nonlinear Doherty Power Amplifiers

This letter proposes a novel methodology and a metric for the assessment of the linearizability of broadband nonlinear power amplifiers (PAs). Validation of the proposed methodology and the proposed metric on two linearized Doherty PAs (DPAs) using digital predistortion (DPD) technique was carried out and it demonstrated the suitability and appropriateness of the new metric. Different from the iterative optimization procedure between the PA circuit design and the DPD algorithm compensation, the proposed method aims to provide a quantitative criterion on the PA linearizability based on its frequency-dependent amplitude modulation (AM)/AM and AM/phase modulation (PM) characteristics. To verify the effectiveness of the metric, two DPAs were characterized before and after a DPD-based linearization. The average correlation coefficients between the values of the metric and the adjacent channel power ratio after DPD were 0.8763 and 0.9156, and that between the values of the metric and the error vector magnitude after DPD were 0.8618 and 0.7200 for PA1 and PA2, respectively, indicating that the evaluation method and the linearizability metric can be used as a good measure to assess the linearizability of broadband PAs.

The effects of digital predistortion in a CO-OFDM system – a stochastic approach

Digital predistortion is topic of significant interest in telecommunications – both in the wireless radio field and, more recently, in photonics. In the present letter, the authors undertake a sensitivity analysis of various digital predistortion algorithms. Using recent metamodeling techniques designed for efficient stochastic analysis, the authors show that using predistortion not only leads to a reduction of the error vector magnitude in general but can also make the system less sensitive to uncertainties.

Analog Predistorter Averaged Digital Predistortion for Power Amplifiers in Hybrid Beam-Forming Multi-Input Multi-Output Transmitter

For higher data throughput, the Massive Multi-input Multi-output (MIMO) system has been widely used in modern communication systems. Due to the circuit size and power consumption, it is difficult to integrate one Radio Frequency (RF) chain for each power amplifier (PA). As a result, MIMO transmitters with hybrid beam-forming don't have enough RF chains, and this demands the digital predistortion (DPD) block to deal with several power amplifiers (PA) simultaneously, which causes a shared DPD problem. This article presents an Analog Predistorter Averaged DPD (A 2 -DPD) for hybrid beam-forming massive MIMO transmitters. To linearize more than one PAs with one shared digital predistortion unit, continuously tunable Analog Predistortion (APD) modules are employed to uniform the nonlinear behavior of PAs in each channel. Based on iterative learning control (ILC) technique, crossed normalized mean square error (CNMSE) is derived to judge the uniformity of PAs. By comparing the CNMSE of each PAs, the best similarity state of PAs can be found. The nonlinear behavior of PAs can be adjusted to a similar state by tuning the APD control voltage. The adjustment makes PAs easier to be linearized by a shared DPD. Furthermore, an averaged DPD algorithm is proposed to improve the total linearity performance for each PA. Simulations are performed to study the relationship between CNMSE and PA uniformity and further simulations show the ability of A 2 -DPD to deal with a multi-PA scenario. In the end, to verify the feasibility of the proposed A 2 -DPD, two class-AB PAs with operating frequency at 3.5 GHz with the same type transistor and similar design are tested. Experimental results show the proposed A 2 -DPD can significantly improve the uniformity of PAs and the Adjacent Channel Power Ratio (ACPR) can be improved by 8 dB compared with using the DPD parameter of the other PA.

Analysis on predistortion algorithm for improving adjacent channel leakage ratio of radio over fiber systems

AbstractNonlinear distortion introduced by optoelectronic components imposes serious limitations on the performance of radio over fiber (RoF) systems, such as dynamic range and adjacent channel leakage ratio (ACLR). In this article, we focus on the impact of digital predistortion (DPD) on the ACLR improvement in a wideband RoF system with multiple carriers. Three key factors, that is, the order of DPD algorithm, the initial phases of carriers, and the processing bandwidth of the predistortion module, are all taken into account in investigating the influence of predistortion on the ACLR performance of RoF systems. A preliminary experiment verifies the effectiveness of predistortion technique for improving the ACLR performance. Quantitative simulation results demonstrate that with the increase in the order of DPD algorithm, the ACLR performance can be significantly improved while the phase randomness within 10 carriers leads to an ACLR fluctuation up to 5 dB. The dependence of the ACLR improvement on the processing bandwidth of the predistortion module, which is very important in practical application, has also been quantitatively studied.

A Full-Duplex Quadrature Balanced RF Front End With Digital Pre-PA Self-Interference Cancellation

This article presents a quadrature balanced radio-frequency (RF) front-end transmitter (TX) architecture assisted by a digital self-interference cancellation (SIC) algorithm for simultaneous transmission and reception in next-generation full-duplex radios. The proposed quadrature balanced power amplifier (QBPA) topology is a four-port circuit with an embedded passive primary isolation (PI) between the antenna and the receiver (RX) low-noise amplifier (LNA), along with a very low power SIC injection mechanism that reuses the TX’s gain. A transmit–receive (TR) isolation of >57 dB is measured for continuous-wave (CW) signals over an 80 MHz bandwidth (BW). A TR isolation of >50 and >56 dB is demonstrated for an 80 MHz 802.11ac orthogonal frequency-division multiplexing (OFDM) signal at 10- and 20 dB backoff from 30 dBm peak TX power ( $P_{\text {TX,max}}$ ), respectively, within the 2.4 GHz Wi-Fi band. A digital predistortion algorithm is applied to linearize the TX at the high output power case, achieving error vector magnitude (EVM) lower than −34.7 dB for concurrent TX-SIC operation. A simultaneous TR scenario is demonstrated, measuring an RX signal EVM of −22 dB, while $P_{\text {TX,max}}\,\,=$ 30 dBm. Measured RX loss is lower than 1.8 dB within the operating frequency band.

A 2-D Predistortion Based on Profile Inversion for Fully Digital Cartesian Transmitter

A novel 2-D digital predistortion (DPD) algorithm for fully digital Cartesian transmitter is proposed. The nonlinearity of the digital power amplifier in the digital transmitter necessitates DPD for linearization. In order to shorten the setup time of predistortion coefficients in the lookup table (LUT), a profile inversion-based method is adopted. Compared to the traditional adaptive iterative method, the profile inversion method for DPD in this paper shortens the setup time to $15~\mu \text{s}$ , which is possible for Long Term Evolution (LTE) time division duplex digital transmitter system to execute calibration within every frame. The algorithm is experimentally verified in a fully digital transmitter implemented in 65-nm general process CMOS technology with LUT size of 0.19 mm2, chip size of 2.7 mm2. The digital transmitter has achieved −35- and −32-dBc adjacent channel leakage ratio with 10-MHz LTE and 20-MHz 802.11g WiFi baseband feed in signals, respectively. The DPD improves the linearity of the transmitter by 21 dB for a 2-D constellation signal.

An enhanced digital predistortion algorithm based on polynomial model identification

To improve the accuracy of the nonlinear distortion correction for the radio frequency (RF) power amplifier (PA), it is necessary to precisely obtain the reverse function of the PA nonlinear model. However, the direct inversion of the PA nonlinear model involves solving a high-order univariate polynomial, which is difficult to apply in engineering. In this study, based on the envelope memory polynomial (EMP) model, the high-order terms of the nonlinear model are approximated by their previously calculated values through iterations and considered as known constants in the polynomial solution finding process, thereby resulting in a significant reduction in computational complexity. Compared with the direct inversion method, model of a 9th-order nonlinear, the proposed method reduces the calculation time in the coordinated rotation digital computer (CORDIC) algorithm by at least 80%. The simulation results show that for a long-term evolution (LTE) downlink signal, the results obtained by the proposed simplified method agree well with those obtained by direct inversion method.

Orthogonal Scalar Feedback Digital Pre-Distortion Linearization

Digital pre-distortion (DPD) systems are employed to reduce intermodulation at the output of intrinsic non-linear RF power amplifiers. Typical DPD algorithms use time-domain linear regression to calculate the model coefficients used to compensate the amplifier’s distortion. This solution has high complexity and limited performance. This paper presents an innovative DPD system where the feedback information is a scalar measurement taken from the feedback signal. Different feedback information can be obtained from the distorted signal, e.g., the adjacent channel leakage rejection or the spectral mask margin. The DPD model coefficients estimation becomes a generic numerical optimization problem and is conducted iteratively in a coefficient-by-coefficient basis. A new coefficient orthogonalization algorithm removes the interaction between orders, resulting in a faster convergence time and lower output power variation across the iterations. The numerical optimization problem is simplified, since the nonlinear model becomes orthogonal in the intermodulation domain, i.e., the adjustment of given coefficient does not affect the others. Simulations and experimental results show that the proposed algorithm can effectively and efficiently compensate the nonlinear distortion and reduce the spectral regrowth.

Amplifier-Coupled Tone Reservation for Minimization of OFDM Nonlinear Distortion

Nonlinear distortion of an OFDM signal is a serious problem when it comes to energy-efficient Power Amplifier(PA) utilization. Typically, Peak-to-Average Power Ratio(PAPR) reduction algorithms and digital predistortion algorithms are used independently to fight the same phenomenon. This paper proposes an Amplifier-Coupled Tone Reservation (ACTR)algorithm for the reduction of nonlinear distortion power, utilizing knowledge on thep redistorted PA characteristic. The optimization problem is defined. Its convexity is proved. A computationally-efficient solution is presented. Finally, its performance is compared against two state-of-the-art TR algorithms by means of simulations and measurements. The results show the proposed solution is advantageous, both in terms of nonlinear distortion power and the required number of computations.

A Direct Learning Digital Predistortion Algorithm to Accurately Compensate for the Power Amplifier Nonlinearity

The conventional digital predistortion (DPD) algorithm based on model identification involves approximations, which introduce an ineligible calculation error, and hence cause performance degradation. In this paper, we present a novel direct learning predistortion algorithm which identifies the power amplifier (PA) model using the least square (LS) algorithm and accurately calculates the predistortion function by a new method. The method constructs a univariate polynomial and finds its roots to obtain the accurate value of the DPD function. Although the proposed algorithm will require additional calculations, it can compensate the PA nonlinearity more precisely. Simulation results demonstrate that the new algorithm outperforms the conventional algorithm in both the adjacent channel leakage ratio (ACLR) and normalized mean square error (NMSE) performance.

On the Modeling and Compensation of Backward Crosstalk in MIMO Transmitters

In this letter, the impact of backward crosstalk at the output of power amplifiers (PAs) on the behavioral model of the multi-input multi-output (MIMO) transmitter is investigated. In this case, the interference signal from other branches leaks into the output of PA and changes the PA behavioral model. A novel generalized memory polynomial is proposed to model the nonlinear distortion caused by this type of crosstalk. Moreover, it is shown that a digital predistortion (DPD) algorithm based on a 2-D generalized memory polynomial can efficiently compensate for the nonlinearity and backward crosstalk impairment effects in MIMO transmitter. The experimental results validate the performance of the proposed model and the DPD method in four different scenarios. An adjusted channel power ratio of less than -50 dBc for the linearized output signal in the presence of -15/-10 dB crosstalk is achieved.

System-Level Design Considerations for Digital Pre-Distortion of Wireless Base Station Transmitters

Over the past 25 years or so there has been much interest in the use of digital pre-distortion (DPD) techniques for the linearization of RF and microwave power amplifiers. In this paper, we describe the important system and hardware requirements for the four main subsystems found in the DPD linearized transmitter: RF/analog, data converters, digital signal processing, and the DPD architecture and algorithms, and illustrate how the overall DPD system architecture is influenced by the design choices that may be made in each of these subsystems. We shall also consider the challenges presented to future applications of DPD systems for wireless communications, such as higher operating frequencies, wider signal bandwidths, greater spectral efficiency signals, resulting in higher peak-to-average power ratios, multiband and multimode operation, lower power consumption requirements, faster adaption, and how these affect the system design choices.

A Digital Polar Transmitter With DC–DC Converter Supporting 256-QAM WLAN and 40-MHz LTE-A Carrier Aggregation

A digital polar transmitter is introduced using 9-b thermometer-coded uniform cells for wideband signal. By analyzing amplitude and phase paths impairment which causes both in-band and out-of-band distortions, a 960-MHz delay tuner is designed for precise amplitude and phase alignment. Furthermore, two digital pre-distortion algorithms for digital power amplifier (DPA) are implemented and compared. Importantly, an on-chip dc–dc converter is included for direct battery connection and output power control. Boosted cascode gate bias improves PA efficiency at low power region. The proposed design is fabricated using a 55-nm RF CMOS technology. This DPA including digital amplitude modulation (AM) filtering achieves peak power of +21.9 dBm with 41% drain efficiency in continuous-wave measurements. It achieves EVM of 2.9% with 20-MHz IEEE 802.11ac compliance of 256-QAM OFDM signal, and also achieves EVM of 4.5% (CC0)/4.8% (CC1) with 40-MHz LTE-A carrier aggregation compliance of 64-QAM OFDM signal.

An Ultra-Wideband Digitally Programmable Power Amplifier With Efficiency Enhancement for Cellular and Emerging Wireless Communication Standards

The design and measurements of a fabricated novel digitally programmable wideband power amplifier (PA) are presented. The PA is made suitable for use in all communication standards, including GSM, 3G, LTE and Femto-cells, offering a bandwidth of several octaves covering presently 300 MHz to 3.5 GHz. It meets power, efficiency and linearity specifications. The amplifier showed excellent performances. The uniquely linear and high power SONY GaAs J-PHEMT process along with novel output-stage multiple cascode topology structure are discussed. This enabled a distinctive larger output impedance and power and low voltage operation. The output stage offered 15–20 dB of gain without a driver. The circuit requires only little output or input matching for gain or impedance, depending on the application. In order to obtain higher gain and optimal application specific performance, a driver stage was added on the same die. A digitally programmable tuning chip was incorporated to the solution to optimize the performance for large bandwidths exceeding 40%. For smaller bandwidths no digital tuning was required. Digital pre-distortion algorithm was tested for better linearization. To the best knowledge of the authors, this is the first comprehensive plug-and-play solution for multi-band and multi-mode handset transmitters with the single chip one PA.