Memory Polynomial Research Articles

Machine learning-based methods for piecewise digital predistortion in mmW 5G NR systems

AbstractPiecewise linearization techniques require dividing the signal into multiple pieces each linearized individually. Machine learning (ML) is one of the useful tools to perform the automatic division of these pieces. Complexity reduction in the classification of piecewise digital predistortion is possible through carefully constructing features from both the signal statistics and the power amplifier (PA) characteristics. Our paper introduces two low-complex classical ML-based methods that facilitate the classification of baseband input data into distinct segments. These methods effectively linearize PA behavior by employing tailored Volterra models corresponding to each segment. Moreover, we perform an in-depth analysis of the proposed schemes to further optimize their classification and regression complexities. The two proposed low-complexity approaches are validated by laboratory experiments and show up to 4 dB error vector magnitude (EVM) improvement over the conventional approach for a class A PA at 28 GHz. Similarly, the EVM improvement is up to 2 dB over the vector-switched general memory polynomial scheme. With only one indirect learning architecture iteration, the two proposed schemes obey the 5G new radio standard up to 6.5 dB and 7 dB output backoff, respectively.

A Low-Computational-Complexity Digital Predistortion Model for Wideband Power Amplifier

This paper proposes a Composition Piecewise Memory Polynomial (CPMP) digital predistortion model based on a Vector Switched (VS) behavioral model to address the challenges of severe nonlinearity and strong memory effects in wideband power amplifiers (PAs). To tackle this issue, two thresholds are calculated and used to segment the envelope values of the input signal according to the nonlinear distortion characteristics of the PA. In this approach, a Generalized Memory Polynomial (GMP) model is employed for the lower segment, a Memory Polynomial (MP) model is employed for the middle segment, and a higher-order GMP model is employed for the upper segment. By sharing the fundamental MP among the proposed segmented models and leveraging a design methodology that configures different cross terms, memory depths, and polynomial orders for each segment, this model achieves superior linearization performance while simultaneously reducing the computational complexity associated with model extraction. The experimental results demonstrate that the adjacent channel power ratio (ACPR) of the predistorted PA output signal using the proposed model improves from −36 dBc to −54 dBc, matching the performance of the GMP model. Furthermore, this performance is 0.5 dBc better than the Piecewise Dynamic Deviation Reduction (PDDR) and Decomposed Vector Rotation (DVR) models. Notably, the complexity of the proposed parameter extraction process is 28.8% of the DVR model, 21.79% of the GMP model, and 12.83% of the PDDR model.

A hybrid memory polynomial digital predistortion model for RF transmitters

The power amplifier (PA), a key component of the transmitter system, operates near the saturation region, resulting in nonlinear distortion of the output signal, which affects the quality of the transmitter system. For this, a series of linearization techniques are used to compensate for distortion, one of the most effective and widely applied is the digital predistortion (DPD) technique. The traditional DPD models can be categorized into a single model or multiple models cascade or parallel. In this letter, a hybrid memory polynomial (HMP) model is proposed to further enhance the accuracy of the model, which is composed of multiple memory polynomial (MP) models by cascading and parallelizing. The experimental results show that the HMP model has better accuracy than the traditional MP model at the same complexity.

Memory diversity combination algorithm for nonlinear power amplifier in wireless communication systems

The nonlinearity of power amplifier (PA) can lead to performance degradation, so alleviating this adverse effect has been regarded as an essential issue to secure normal transmission for wireless communication systems. For the general nonlinear post-distortion schemes, such as memory polynomial (MP) and power amplifier nonlinearity cancellation (PANC), the memory effect is usually treated similarly as the nonlinearity, which are both removed from the received distorted signal. However, the valid information concealed in the memory could be exploited to supply diversity for detection, so to release this potential, a memory diversity combination (MDC) scheme is proposed to enhance the overall property. In MDC, the memory components are firstly reconstructed using the solution obtained by MP or PANC, which are then combined together, thereby obtaining the diversity. Simulation results show that, MP- and PANC-MDCs can make significant performance improvements over MP and PANC, which is accomplished by merging the memory diversity of PA.

Reduced Complexity Sequential Digital Predistortion Technique for 5G Applications

Wireless communication infrastructure is a key enabling technology for smart cities. This paper investigates a novel technique to enhance the performance of 5G base stations by addressing the compensation of nonlinear distortions caused by radiofrequency power amplifiers. For this purpose, a sequential digital predistortion approach that uses twin nonlinear two-box structure along with reduced sampling rates in the feedback path is proposed to implement a linearization system. Such a system is shown to have a correction bandwidth that exceeds the bandwidth of the feedback path. This is achieved by synthesizing the predistortion function in two successive characterization iterations. Both characterizations use the same hardware, which has a reduced sampling rate in the feedback path. Hence, the proposed predistorter scheme does not require any additional hardware compared to standard schemes. Moreover, coarse delay alignment is performed while identifying the memory polynomial function in order to further reduce the computational complexity of the proposed system. Experimental results using an inverse Class-F power amplifier demonstrate the ability of the proposed predistorter to achieve a correction bandwidth of 100 MHz with a feedback sampling rate as low as 25 MSa/s.

Orthogonal Expanded Memory Polynomial Model for Circular Complex Gaussian Processes

Orthogonal Expanded Memory Polynomial Model for Circular Complex Gaussian Processes

Exponential Memory Polynomial Based Nonlinear Equalizer for C-Band IM/DD Systems

Exponential Memory Polynomial Based Nonlinear Equalizer for C-Band IM/DD Systems

Full-Wave Digital Predistortion Linearization Based on Memory Polynomials for HF Power Amplifiers

Full-Wave Digital Predistortion Linearization Based on Memory Polynomials for HF Power Amplifiers

Generalized memory polynomial input neural networks for nonlinear modeling in digital predistortion applications

AbstractThe power amplifiers (PAs) will embody the nonlinear distortion if they work at saturation so as to increase efficiency. The neural network (NN)‐based digital predistortion (DPD) is widely applied for the linearization of the PA in wireless communication. However, the current NN‐based DPD schemes only focus on designing the NN hidden layer and ignore improving the NN input layer, which loses the degree of freedom to fit the DPD. Therefore, this paper first proposes the generalized memory polynomial (GMP) input NN structure. The training data of GMP‐NN outputs are obtained by iterative learning control. The experimental results show that the GMP‐NN presents a great advantage in performance compared with the widely used GMP model and recurrent NN (RNN) model. From the testing data, it is observed that the minimum mean square error (MMSE) of the GMP‐NN is 4 dB lower than the conventional GMP model and is nearly 8 dB lower than the RNN model. The proposed GMP‐NN model is also verified in the DPD application, which shows 2.61 dB improvement in comparison with the GMP DPD model.

GPU versus FPGA implementation of a digital predistortion linearizer for wideband radiofrequency power amplifiers

This paper presents and compares the implementation of a digital predistortion (DPD) linearizer for radiofrequency power amplifiers (PAs) considering two different hardware acceleration platforms. Both graphics processing unit (GPU)-based and field programmable gate arrays (FPGA)-based implementations of the DPD are capable to meet the high throughput requirements for linearizing the PA with current 5G new radio (NR) wideband signals. A comparison in terms of hardware resources usage, precision, throughput and linearization performance is provided for both GPU and FPGA implementations of a DPD based on the generalized memory polynomial (GMP) behavioral model.

Vector-switched digital predistortion for concurrent dual-band transmitters with hybrid time-division multiplexing scheme

In a concurrent dual-band digital predistortion (DPD) system, due to the large number of two-dimensional (2D) polynomial-based model coefficients and the existence of cross-modulation terms, the hardware realization usually requires a lot of resources. To alleviate this problem, this paper proposes a hardware-efficient field programmable gate array (FPGA)-based piecewise vector-switched (PVS) DPD method. With the PVS method, a 2D memory polynomial (MP) model with fewer coefficients can be used as a sub predistorter model for each region. Furthermore, a new hybrid time-division multiplexing (HTDM) scheme is proposed for the 2D-MP predistorter architecture, which enables sharing of cross-modulated lookup tables (LUTs) and complex multipliers in a hybrid way. Experimental results show that the proposed method improves the adjacent channel power ratio (ACPR) and normalized mean square error (NMSE) by 18.74 dB and 13.23 dB, respectively, and saves about 30% and 80% of RAM and DSP resources, respectively.

Modified Kramers-Kronig receiver based on memory polynomial compensation for photonics-assisted millimeter-wave communications.

Photonics-assisted millimeter-wave (MMW) wireless communications are advancing rapidly driven by the escalating congestion in the lower-band spectrum and the growing demand for higher data rates. Concurrently, Kramers-Kronig (KK) receivers provide an economical solution ideally suited for cost-sensitive deployment and application. However, the conventional KK receiver is subject to performance degradation due to the nonlinearity and memory effects introduced by practical electronic devices. In this work, the performance degradation of the conventional KK receiver is investigated and quantitatively simulated, showing that the KK receiver exhibits greater sensitivity to nonlinearity and memory effects compared to the conventional coherent receiver. To enhance the performance of KK receivers deployed in MMW communication systems, we propose a modified KK receiver employing memory polynomial compensation, namely MP-KK receiver, capable of effectively compensating memory effects whilst simultaneously addressing nonlinearity. Crucially, the memory polynomial model is employed prior to the KK algorithm to prevent further signal degradation caused by the nonlinear operator in the KK algorithm in the scenario of photonics-assisted MMW wireless communication based on the KK receiver. For verification, we present a 95 GHz W-band MMW wireless transmission demonstration with 20 Gb/s QPSK and 40 Gb/s 16-QAM signals. The experimental results indicate that the MP-KK receiver can achieve more than 3.5 dB improvement in EVM and 71.25% reduction in BER compared to the conventional approaches.

A low‐spur harmonic‐cancelation digital predistortion based on neural network for frequency‐hopping HF transmitters

AbstractHigh frequency (HF) transmitter implemented with the multioctave broadband power amplifier (PA) is always faced with the problem of interfering harmonics because of the nonlinearity of the PA. With the harmonic‐cancelation digital predistortion (HC‐DPD) scheme, the harmonics at lower frequencies can be canceled by the injected components and the harmonics at higher frequencies can be filtered out using a low‐pass filter (LPF). However, the HC‐DPD scheme brings the problem of unwanted spurs while lowering the requirements for sampling rate. In this article, a time‐delay neural network (TDNN) model is used to replace the conventional memory polynomial (MP) model in the forward modeling. Theoretical derivation and simulation results validate the effectiveness of the TDNN model in harmonic cancelation and spur suppression. Further, a frequency‐agile neural network (FANN) model is proposed based on the TDNN model. By adding the carrier frequency to the inputs of the network, the trained model can apply to all the trained carrier frequencies and is more friendly to the frequency‐hopping scenarios. Experiments were carried out on a 2–30 MHz HF transmitter testbench. Measurement results show that the harmonic‐to‐fundamental power ratio, the adjacent channel power ratio (ACPR), and the error vector magnitude (EVM) performances were all improved by more than 20 dB. Compared with the MP model, the unwanted spurs can be suppressed by up to 22 dB. In addition, the number of total model coefficients of the proposed FANN model is only 22% of that of the TDNN model under the frequency‐hopping scenario.

One-Shot Blind Frequency-Domain Nonlinear Equalization for Millimeter-Wave Fiber-Wireless IFoF Mobile Fronthaul System

Nonlinear equalization (NE) plays a pivotal role in the analog intermediate-frequency over fiber (IFoF) mobile fronthaul (MFH) system demanding a high signal fidelity. This work proposes and experimentally validates a novel blind frequency-domain NE (FD-NE) approach for millimeter-wave (MMW) fiber-wireless (FiWi) IFoF MFH systems. This proposed blind FD-NE scheme relies on the FD two-block cascade Hammerstein NE structure and particular pairs of M-ary phase shift keying (MPSK) and M-ary amplitude shift keying (MASK) subcarriers. It features lower computational complexity, higher transmission capacity, and comparable equalization performances to the widely-employed training-assisted memory polynomial (MP) NE schemes. Moreover, it only requires a small fraction of subcarriers in a single received signal block to be modulation-format constrained, which renders one-shot blind learning of NE coefficients and thus achieves symbol-by-symbol channel tracking. The performance of the proposed NE method is experimentally evaluated in MMW FiWi IFoF MFH systems operating at 5G NR frequency range 2-1 (FR2-1) n258 band (24.25 GHz to 27.50 GHz) and FR2-2 (52.6 GHz to 71 GHz). The obtained experimental results show that our proposal can effectively improve the nonlinearity tolerances of coherent 25-GHz and non-coherent 60-GHz FiWi IFoF MFH systems transmitting multiple 64QAM/256QAM IF OFDM signals.

Optimized MSA DPD method for improving 5G multiband optical fronthaul performance

AbstractA modified optimized magnitude‐selective affine (OMSA) model‐based digital predistortion (DPD) is presented that introduces the weighting function into our earlier proposed magnitude‐selective affine (MSA) method with an aim to further reduce the complexity overheads without affecting performance compared to the MSA method. This model utilizes a power‐reliant weighted function rather than the summation of MSA quantities for improving the multiband 5G new radio (NR) analog radio over fiber system performance. The OMSA‐DPD method is tested using 5G NR signals which are transmitted over a 10‐km fiber length. The performance of the OMSA‐DPD method is assessed in comparison to MSA and generalized memory polynomial (GMP) methods in terms of adjacent channel power ratio, error vector magnitude, and complexity. The experimental results show that the OMSA‐DPD method achieves better performance with lower complexity compared to the MSA and GMP models, meeting the 3GPP limits.

Attention mechanism based bidirectional LSTM model for broadband power amplifier linearization

AbstractIn this letter, a novel digital predistortion (DPD) model for broadband power amplifier (PA) linearization is proposed, namely Attention Mechanism based Bidirectional Long Short‐term Memory Network (AM‐BiLSTM) model. In order to verify the linearization performance of the AM‐BiLSTM model in digital predistortion process, a 100 MHz bandwidth 5G new radio (5G NR) signal is employed to test a sub‐6G PA operating at 2.6‐GHz. The experimental results show that the adjacent channel power ratio (ACPR) of the PA with AM‐BiLSTM model can be improved by 24 dB which is 6 dB and 3 dB better than the generalized memory polynomial (GMP) model and the Chebyshev polynomials LSTM (CP‐LSTM) model in ref [1], repspectively. Therefore, the proposed AM‐BiLSTM model is very effective for the DPD linearization of broadband PAs.

Effective Digital Predistortion (DPD) on a Broadband Millimeter-Wave GaN Power Amplifier Using LTE 64-QAM Waveforms

We demonstrate in this work effective linearization on a millimeter-wave (mm-Wave) broadband monolithic gallium nitride (GaN) power amplifier (PA) using digital predistortion (DPD). The PA used is a two-stage common-source (CS)/2-stack PA that operates in the mm-Wave 5G FR2 band, and it is linearized with the generalized memory polynomial (GMP) DPD and tested using 4G (4th generation) long-term-evolution (LTE) 64-QAM (quadrature amplitude modulation) modulated signals with a PAPR (peak-to-average power ratio) of 8 dB. Measurement results after implementing GMP DPD indicate considerable broadband improvement in the adjacent channel leakage power ratio (ACLR) of 16.9 dB/17.3 dB/16.5 dB/15.1 dB at 24 GHz/28 GHz/37 GHz/39 GHz, respectively, with a common average POUT of 15 dBm using a 100 MHz LTE 64-QAM input signal. At a fixed frequency of 28 GHz, the GaN PA after GMP DPD achieved signal bandwidth-dependent ACLR improvement and root-mean-square (rms) EVM (error vector magnitude) reduction using 20 MHz/40 MHz/80 MHz/100 MHz LTE 64-QAM waveforms with a common average POUT of 15 dBm. The GaN PA thus achieved very good linearization results compared to that in other state-of-the-art mm-Wave PA DPD studies in the literature, suggesting that GMP DPD should be rather effective for linearizing mm-Wave 5G broadband GaN PAs to improve POUT, Linear.

Non‐linear modelling and distortion compensation in optical Fast‐orthogonal frequency division multiplexing systems

AbstractFast‐OFDM‐based intensity‐modulation and direct‐detection (IM/DD) has been proposed for deployment of cost‐efficient optical access networks, due to its implementation simplicity and high spectral efficiency. In this article, the accuracy of the generalised memory polynomial (GMP) for the non‐linear modelling of optical Fast‐OFDM links is studied, including memory effects and considering different model parameters. After model validation using measured data of a 10 km single mode fibre link, the GMP is used for performance investigations of a distortion compensation approach to optical Fast‐OFDM, for up to 16PAM modulation formats and different number of Fast‐OFDM subcarriers. This study firstly reports the performance results of optical 16PAM‐Fast‐OFDM systems using either 2PAM‐ or 4PAM‐based training signals for digital post‐distortion and FFT‐based channel estimation, and firstly investigates the influence of the zero padding (ZP) length on the performance of optical Fast‐OFDM. Excellent performance improvements are achieved using the proposed distortion compensation scheme, relative to conventional system implementation.

Digital Predistortion Linearization of a GaN HEMT Push-Pull Power Amplifier for Cable Applications With High Fractional Bandwidth

This paper presents two linearization strategies for a custom-designed wideband push-pull (PP) power amplifier (PA) for wired communication applications such as, for example, cable TV. Two digital predistortion (DPD) behavioral models are proposed to meet the in-band and out-of-band linearity requirements when efficiently amplifying wideband DOCSIS signals with high fractional bandwidth (FBW). A radiofrequency (RF) DPD linearizer based on a band-pass generalized memory polynomial (BP-GMP) behavioral model and a baseband (BB) I-Q DPD linearizer based on a harmonic distortion GMP (HD-GMP) behavioral model are proposed. Both DPD models take into account the harmonic distortion typical of high FBW amplification. Experimental results will show high efficient and linear amplification of a 4 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times$</tex-math> </inline-formula> 192 MHz composite DOCSIS signal by properly combining a crest factor reduction (CFR) technique and the proposed DPD strategies.

A Novel Digital Predistortion Identification Algorithm Based on Variable Forgetting Factor Recursive Least Square Method

The transmitting signal of wireless communication system is impaired by the nonlinearity of RF power amplifier (PA) which leads to signal distortion and spectrum spillover, by which the signal transmission quality is affected. Digital predistortion (DPD) is an efficient and economical way to correct the nonlinear effects of power amplifiers. The recursive least square (RLS) recognition algorithm is commonly used to extract the correction coefficients of the DPD model, and the accuracy of the extraction directly affects the system performance. In this paper, a new variable forgetting factor identification algorithm (new variable forgetting factor recursive least square, NVFFRLS) is proposed for recursive least square (RLS) identification algorithm. The 64-QAM signal is combined with a memory polynomial (MP) predistortion model for predistortion system simulation. The experimental results show that, compared with the RLS identification algorithm and two kinds of variable forgetting factor RLS identification algorithms, the algorithm has smaller estimation error, faster convergence, and better tracking capability, stability, and adaptability; the predistortion system based on NVFFRLS identification algorithm can compensate the nonlinear memory effects of power amplifier more effectively.