Conventional Memory Polynomial Research Articles

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.

Combined kernel with parameter optimization for least squares support vector machine postdistorter in visible light communications

The nonlinearity and memory effects induced by light-emitting diode distort the transmitted signal, which significantly limits the performance of visible light communication (VLC) system. With the characteristics of low computational complexity, fast convergence speed, and strong generalization ability, least squares support vector machine (LSSVM) is investigated in this paper and employed to alleviate the nonlinear effect. Since the performance of LSSVM is largely determined by the type of the adopted kernel functions, we utilize Gaussian and Laplace functions and propose a new combined kernel, which can increase the reproducing kernel Hilbert space and thus enhance the global expressive power compared with conventionally used Gaussian kernel. To further improve the performance, a hybrid parameter optimization algorithm is exploited to optimize the proposed kernel, based on genetic algorithm and particle swarm optimization. The property of the proposed postdistortion method is verified by numerical simulations, and better performance is obtained in VLC systems compared with the Gaussian-kernel LSSVM and conventional memory polynomial method.

A Sparse Neural Network-Based Power Adaptive DPD Design and Its Hardware Implementation

In this paper, an efficient neural-network-based adaptive DPD design which performs well under power varying conditions is presented. The DPD design is derived on the basis of the envelop time-delay neural network (ETDNN). The redefined ETDNN-DPD requires the part of parameter updates, which enables to adapt it to the rapid change of power amplifier (PA) distortion. Additionally, the redefined ETDNN-DPD also maintains the stability of the compensation performances under varying power condition while its structure is pruned by the structured pruning. Furthermore, to verify its practical use, we also propose the weight scaling technique, which reduces multiplications of the redefined ETDNN-DPD, and applied it to the implementation of the redefined ETDNN-DPD on FPGA. Compared FPGA-implemented ETDNN-DPD with FPGA-implemented conventional memory polynomial DPD, we verified that our proposed DPD achieved 3.2 dB better error vector magnitude (EVM) while lower hardware resource utilization at the fixed power level. Moreover, our proposed DPD kept better performance under the varying power condition only by the partial update of its parameters than memory polynomial DPD.

Highly non‐linear and wide‐band mmWave active array OTA linearisation using neural network

This paper proposes a neural network (NN)-based over-the-air (OTA) linearisation technique for a highly non-linear and wide-band mmWave active phased array (APA) transmitter and compares it with the conventional memory polynomial model (MPM)-based technique. The proposed NN effectively learns the distinctive non-linear distortions, which may not easily fit to existing MPM solutions, and can, therefore, successfully cope with the challenges introduced by the high non-linearity and wide bandwidth. The proposed technique has been evaluated using a state-of-the-art 4 × 4 APA operating in highly non-linear regions at 28 GHz with a 100-MHz-wide 3GPP base-station signal as input. Experimental results show the pre-distortion signal generated by the NN exhibits the peak-to-average power ratio (PAPR) much lower than the one generated by MPM and consequently superior linearisation performance in terms of adjacent channel leakage ratio (ACLR) and error vector magnitude (EVM) for high non-linearity cases. Using the proposed NN-based linearisation technique, an improvement of 5-dB ACLR and 7% points in EVM are achieved, which demonstrates the promising potential of this technique for emerging broadband communication systems such as 5G/6G and low Earth orbit (LEO) satellite networks.

2-D Magnitude-Selective Affine Function-Based Digital Predistortion for Concurrent Dual-Band Terminal Power Amplifiers

Conventional digital predistortion (DPD) techniques are facing the challenge of complexity in the fifth generation (5G) and beyond concurrent dual-band terminal transmitters. This article proposes novel low-complexity behavior models for the DPD of terminal power amplifiers (PAs). Derived from the conventional memory polynomial (MP) model, the new models utilize magnitude-selective affine (MSA) functions as nonlinear basis functions to greatly decrease the model complexity. The proposed paralleled envelope indexed 2-D MSA (PI-2-D-MSA) model and combined envelope indexed 2-D MSA (CI-2-D-MSA) model take both the in-band intermodulation and cross-band modulation into account and can well compensate for nonlinear distortion in dual-band terminal PAs. Moreover, the proposed models are extended to nonuniform sampling rate (NSR) scenarios, where the aliasing effect for the low sampling rate band is analyzed. Simulations and experimental measurements under the uniform sampling rate and the NSR scenarios were carried out on a 1.7–2.8-GHz wideband Doherty PA and a 4.4–5.0-GHz class-AB terminal PA and demonstrated the linearization performances of the proposed models. The total numbers of floating-point operations (FLOPs) of the PI-2-D-MSA and the CI-2-D-MSA models were 11% and 8% of that of the prior 2-D-MP model, respectively. Even though their linearization accuracy deteriorated, the relaxed linearization standard for terminal transmitters can still be achieved.

Memory aware physically enhanced polynomial model for PAs

In this study, a new behavioural model named memory aware physically enhanced polynomial model is proposed. This modelling approach is based on using a physical analysis of the power amplifier (PA) operation and takes into account the electro-thermal and electrical memory effects as main sources of long-term memory. The physical analysis-based approach allows to select the most relevant coefficients for the model and discards the less significant ones in order to minimise the complexity. In this study, the proposed methodology is demonstrated on a single-stage class-AB PA. Nevertheless, it is applicable for multi-stage PAs. The model accuracy and complexity are evaluated using measurement results from two commercial PAs. Compared to the conventional memory polynomial (MP) model, for, respectively, 20 and 80 MHz long-term evolution signals, the proposed model shows 3 and 5 dB improvement in the normalised mean square error with fewer coefficients 18 instead of 20 for a memory depth of 3. Also, with same accuracy the proposed model has considerably fewer coefficients compared with the PLUME and generalised MP (GMP) models. Applying digital predistortion (DPD), the proposed model outperforms the MP model in terms of performance and the PLUME and GMP models in terms of complexity.

Carrier Aggregated Radio-Over-Fiber Downlink for Achieving 2Gbps for 5G Applications

We demonstrate experimentally, for the first time, a distributed digital predistortion model for radio-over-fiber (RoF) downlink suitable for broadband 5G signals. The model reduces the analog-to-digital converter sampling frequency up to 1/3 of the required sampling in the example of the conventional memory polynomial DPD model, hence reducing demodulator costs and hardware complexity. This model also provides better intercarrier interference by reducing the adjacent channel leakage ratio (ACLR). This leads to reduced crosstalk, which impacts the multi-core and multimode RoF links. Long-term evolution advanced signals of a 256-quadratic-amplitude modulation of different bandwidths are used to validate the model. We achieved an average reduction of 2.5 dB in ACLR for signal bandwidths in the range 100–300 MHz while maintaining minimum error vector magnitude (EVM). The RoF downlink can deliver a peak bit rate of 2.016 Gb/s with a spectral efficiency of 6.72 b/Hz and EVM less than 4%.

A Novel Multi-Band Reduced Sampling Rate and I/Q Compensation Technique for RF Power Amplifiers

In this paper, a novel multi-band reduced sampling rate technique is proposed for power amplifier (PA) linearization system. It is used to enhance performance and reduce hardware costs in spectrum aggregation discontinuous broadband systems and compensate in-phase/quadrature (I/Q) imbalance in the multi-band case. During the feedback loop process of sampling rate, a band-limited filter is introduced, and the frequency band extrapolation is carried out so that the spectrum outside the limited band is compensated effectively. Theoretical analysis is performed to compare the proposed method and the conventional methods. To evaluate the performance of the proposed method, a broadband PA is excited by a tri-band signal composed of a 20 MHz long-term evolution (LTE) signal at 1.31 GHz, a 20 MHz 4-carrier wideband code division multiple access (WCDMA) signal at 2.49 GHz, and a 20 MHz 2-carrier WiMAX signal at 2.58 GHz respectively. The experimental results demonstrate that the normalized mean square error (NMSE) can get high accuracy less than −41 dB, with peak-to-average power ratio (PAPR) equaling 9 dB accompanied by a large reduction in sampling rate. Error vector magnitude (EVM) is 1% better than band-limited memory polynomial (MP) model and 2.3% better than conventional MP model.

A low-power high-performance digital predistorter for wideband power amplifiers

In this paper, we present a low-power high-performance digital predistorter (DPD) for the linearization of wideband RF power amplifiers (PAs). It is based on the novel FIR memory polynomial (FIR-MP) predistorter model, which significantly augments the performance of the conventional memory polynomial predistorter with the use of complex baseband digital FIR filter prior to the memory polynomial. The adjacent channel leakage ratio (ACLR) performance comparison between the conventional MP and the proposed FIR-MP is done based on simulations with multi-carrier modulated signals of 20 and 80 MHz bandwidths. The PA models used for the simulations are extracted from the measurements of a commercial $$1\,\hbox {W}$$ GaAs HBT PA. At the ideal system-level simulations, the improvements in ACLR over the conventional MP are 7.2 and 15.6 dB, respectively, for 20 and 80 MHz signals. The choice of selection of various parameters of the predistorter along with the subsequent digital-to-analog converter (DAC) is presented. The impact of fixed-point representation is assessed using ACLR metrics, which shows that a wordlength of 14 bits is sufficient to obtain ACLR beyond $$45\,\hbox {dBc}$$ with a margin of $$10\,\hbox {dB}$$ . The proposed predistorter is synthesized in $$28\,\hbox {nm}$$ fully-depleted silicon-on-insulator (FDSOI) CMOS process. It is shown that with a fraction of the power and die area of that of the MP a huge improvement in ACLR is attained. With an overall power consumption of 8.2 and 88.8 mW, respectively, for 20 and 80 MHz signals, the FIR-MP DPD proves to be a suitable candidate for small-cell base station PA linearization.

A Novel Weighted Memory Polynomial for Behavioral Modeling and Digital Predistortion of Nonlinear Wireless Transmitters

In this paper, a novel weighted memory polynomial (WMP)-based model is proposed for wireless transmitters and radio-frequency power amplifiers' (PAs) behavioral modeling and predistortion. The new model introduces an instantaneous-power-dependent weight function on the static and dynamic terms of the conventional memory polynomial (MP) model. Experimental validation in both modeling and predistortion contexts was performed on a PA prototype driven by a 20-MHz Long Term Evolution signal. The proposed model was assessed against the standard MP model. The experimental results demonstrate the superiority of the proposed polynomial in behavioral modeling applications as it results in up to 50% (3-dB) improvement in the normalized mean square error for the same number of coefficients. The model robustness was then validated by using a second test signal applied to two Doherty PAs using different transistor technologies. Furthermore, when applied for digital predistortion, the proposed WMP function achieves the same performance as the state-of-art MP while requiring approximately 50% less coefficients.

Concurrent Dual-Band Modeling and Digital Predistortion in the Presence of Unfilterable Harmonic Signal Interference

Motivated by advanced-generation signals and corresponding trends for multiband, broadband, and ultra-wideband transmitters, several models have recently been proposed for digital predistortion in a dual-band concurrent transmission. These state-of-the-art models assume that two frequencies of operation are uncorrelated and harmonic products can be filtered out. However, when the harmonic of one signal falls on the frequency band of another signal, it cannot be removed with filters. This paper proposes a 3-D harmonic memory polynomial based model for the dual-band concurrent transmission in the presence of harmonic interferences. The model is extracted and predistortion is implemented using a low-cost field-programmable gate-array-based system including a transmitter and a feedback receiver. Using the proposed model, a performance improvement up to 22 dB in terms of normalized mean square error and performance improvement up to 20 dB in terms of the adjacent channel power ratio is achieved compared to a conventional dual-band memory polynomial model not including harmonics.

Digital predistortion technique based on non‐uniform MP model and interpolated LUT for linearising PAs with memory effects

A new digital predistortion technique based on a direct learning architecture is proposed for linearising power amplifiers (PAs) with nonlinear memory effects. It is based on the non-uniform memory polynomial (MP) model and with a quadratically interpolated LUT. There are mainly two innovations. First, compared with the conventional MP model, the non-uniform MP model achieves the same modelling accuracy with less coefficients. Secondly, compared with the linearly interpolated LUT, the quadratically interpolated LUT has higher accuracy, which is adopted to realise a part of the mathematical computations in the predistortion. The proposed solution is validated on a real PA ZFL-2500. It reduces the number of the model's coefficients and achieves a spectrum regrowth suppression of about 15 dB with a table size of only 8.

Digital Predistortion for Concurrent Dual-Band Transmitters Using 2-D Modified Memory Polynomials

Cross-band modulation effects in the concurrent dual-band transmitters are quite noticeable for the linearization. This paper proposes a novel two-dimensional modified memory polynomial (2D-MMP) technique to compensate for nonlinear distortion in the concurrent dual-band transmitters. By taking into account the cross-band modulation effects, the 2D-MMP model is developed by properly modifying the envelope terms of the conventional memory polynomial (MP) model. This makes the model complexity of the 2D-MMP model significantly reduced compared to the prior 2D-DPD model in previous work. However, the linearization ability of the 2D-MMP model is still retained. Simulations prove that the 2D-MMP model is quite robust to different PA models. Experimental measurements were carried out for a dual-band class-AB PA exhibiting mild nonlinearity and a highly nonlinear dual-band Doherty PA. The results show that the 2D-MMP model can achieve nearly the same linearization accuracy compared to the 2D-DPD model, with much less coefficients. Less than -52 dBc adjacent channel power ratios (ACPRs) for the dual-band class-AB power amplifiers (PAs) and -50 dBc ACPRs for the dual-band Doherty PA in the dual bands were achieved.

Complex-Chebyshev Functional Link Neural Network Behavioral Model for Broadband Wireless Power Amplifiers

The Neural Network (NN) based models are commonly used in power amplifier modeling and predistorter design, and seen as a potential alternative to model and compensate broadband power amplifiers (PAs) having medium- to-strong memory effects along with high-order nonlinearity. In this paper, we propose a novel computationally efficient behavior model based on complex-Chebyshev functional link neural network (CCFLNN) suitable for dynamic modeling of wireless PAs. The CCFLNN exhibits a simpler compact structure than the previously reported NNs and can require less computational burden during the learning process since it uses the complex-valued topology and does not need the hidden layers, which exist in most of the conventional neural-network-based models. The proposed approach utilizes the complex-valued inverse QR-decomposition-based recursive least square algorithm to update the weighting coefficients of the CCFLNN model. The proposed model is comparatively compared with a real-valued focused time-delay NN model and a conventional memory polynomial model with respect to computation complexities and modeling performance. The accurate modeling capacity of the CCFLNN model is demonstrated through a full characteristic (working in the strongly nonlinear region) 170-W class AB amplifier driven by a multicarrier WCDMA signal. Furthermore, the proposed model has been applied for linearizing a real PA in multicarrier application. Results obtained from the measurement clearly show that the proposed digital predistorter can eliminate various intensity in-band and out-of band distortions.

An open-loop digital predistorter based on memory polynomial inverses for linearization of RF power amplifier

Digital Predistorter is a cost-effective solution to compensate for the nonlinear distortions appearing in the RF power amplifiers (PAs). The indirect learning scheme is widely implemented because of its flexibility to eliminate the requirement for building a closed-loop real time system, which dramatically reduces the complexity for measurement setup. However, such scheme is sensitive to the measurement noise that may cause biasing in the coefficients estimation. To minimize the influence of measurement noise and simultaneously enable the open-loop implementation, we propose a predistortion technique that first model the PA and then generates predistorted signal iteratively through a feedback configured structure to avoid using the noisy signal when performing the inverse model estimation. Unlike the indirect learning which estimates the postinverse of the PA, our predistortion is based on the preinverse of the PA. Both simulations and measurements show that utilizing the proposed predistortion can obtain adjacent channel power ratio (ACPR) improvement in wideband code division multiple access (WCDMA) signal test compared with the conventional memory polynomial predistortion based on indirect learning. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011.

Robust Fractional Order Memory Polynomial Based Pre-Distorter

In this paper, a robust fractional order memory polynomial pre-distorter with two novel schemes to conduct digital base-band power amplifier pre-distortion is proposed. For the first scheme, fractional order terms are included in the conventional memory polynomial containing the odd and even order polynomial terms, which is called Scheme One. The second scheme, called Scheme Two, simply replaces even order polynomial terms with fractional order polynomial terms to improve the linear performance of power amplifiers. The mathematical expressions for these two schemes are derived. The computer simulations and numerical analysis show that, compared with the conventional pre-distortion methods, 11dB and 8.5dB more out-of-band suppression gain can be obtained by Scheme One and Scheme Two, respectively. Corresponding FPGA realization shows that the two schemes are cost-effective in terms of hardware resources.

A Compact Envelope-Memory Polynomial for RF Transmitters Modeling With Application to Baseband and RF-Digital Predistortion

In this letter, a compact envelope-memory polynomial based model, suitable for forward and reverse modeling of weakly nonlinear wireless transmitters and power amplifiers (PAs) exhibiting electrical memory effects, is presented. This model is implemented in a complex gain based architecture and takes advantage of the dependency of PA nonlinearity on the magnitude of the input signal. Contrary to conventional memory polynomials, the proposed model can be implemented in baseband, as well as in radio frequency, digital predistorters. A 100-W average power transmitter is used for experimental validation of the forward and reverse models. Both forward and reverse modeling results obtained with the proposed model are comparable to that of the conventional memory polynomial.

A Data-Based Nested LUT Model for RF Power Amplifiers Exhibiting Memory Effects

In this letter, a new model is proposed for radio frequency power amplifiers exhibiting memory effects. The model is based on nested look-up tables that compute the estimated amplifier output signal, based on the current input sample and the preceding ones. The model is validated experimentally, using input and output waveforms of a high-power LDMOS based amplifier driven by a multicarrier WCDMA signal. It is shown that the performance of the proposed model is comparable to that of the conventional memory polynomial model. However, the nested look-up table based model significantly reduces the complexity of the identification of the model's parameters, as well as the computational complexity in calculating the estimated output signal.