Compensation Of Nonlinear Distortion Research Articles

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.

Experimental results on nonlinear distortion compensation using photonic reservoir computing with a single set of weights for different wavelengths

Photonics-based computing approaches in combination with wavelength division multiplexing offer a potential solution to modern data and bandwidth needs. This paper experimentally takes an important step towards wavelength division multiplexing in an integrated waveguide-based photonic reservoir computing platform by using a single set of readout weights for up to at least 3 ITU-T channels to efficiently scale the data bandwidth when processing a nonlinear signal equalization task on a 28 Gbps modulated on-off keying signal. Using multiple-wavelength training, we obtain bit error rates well below that of the 1.5×10-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1.5 \ imes \\,10^{-2}$$\\end{document} forward error correction limit at high fiber input powers of 18 dBm, which result in high nonlinear distortion. The results of the reservoir chip are compared to a tapped delay line filter and clearly show that the system performs nonlinear equalization. This was achieved using only limited post processing which in future work can be implemented in optical hardware as well.

Deep photonic reservoir computer based on frequency multiplexing with fully analog connection between layers

Reservoir computers (RCs) are randomized recurrent neural networks well adapted to process time series, performing tasks such as nonlinear distortion compensation or prediction of chaotic dynamics. Deep reservoir computers (deep-RCs), in which the output of one reservoir is used as the input for another one, can lead to improved performance because, as in other deep artificial neural networks, the successive layers represent the data in more and more abstract ways. We present a fiber-based photonic implementation of a two-layer deep-RC based on frequency multiplexing. The two RC layers are encoded in two frequency combs propagating in the same experimental setup. The connection between the layers is fully analog and does not require any digital processing. We find that the deep-RC outperforms a traditional RC by up to two orders of magnitude on two benchmark tasks. This work paves the way towards using fully analog photonic neuromorphic computing for complex processing of time series, while avoiding costly analog-to-digital and digital-to-analog conversions.

Enhanced Pre/Post Compensation of Fiber Link Nonlinear Distortion by a Stepwise Parameter Profiled Fiber and Phase Conjugation Module

Compensation of nonlinear distortion in long distance communication links from the power induced Kerr effect is demonstrated at the transmitter or receiver by the combination of optical phase conjugation (OPC) and propagation in a stepwise parameter profiled fiber (SPF). The SPF tailored with an increasing nonlinearity and decreasing dispersion parameter on average with distance as well as Raman gain induces a distortion more closely matching that of the link to improve propagation symmetry for enhancing overall distortion cancellation by OPC. Measurements show for a module inserted at the transmitter or receiver with a 60 km long SPF comprising of three different fibers, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q²</i> -factor is improved by 2.3 and 1.7 dB, respectively, compared to without for transmitting 5 channel WDM dual polarization 12 Gbaud 16-QAM signals in 2×160 km fiber spans that both include dispersion compensation. Similarly, recirculating loop transmission of the same signal over 18×80 km (1440 km) shows improved <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q²</i> -factors of 1.9 and 1.3 dB, respectively. This corresponds to extending the transmission reach by 125 and 80%, respectively, for matched performance at equal launch power, highlighting the greater nonlinear distortion tolerance achievable with advanced OPC designs.

Enhanced Compensation of Nonlinear Signal Distortion by Optical Phase Conjugation in Step-Parameter Profiled Fiber Links

Improving the efficacy of optical phase conjugation (OPC) for compensating nonlinear signal distortion in long distance optical fiber links from the Kerr effect is demonstrated. This is based on tailoring the link spans as step-parameter profiled fiber (SPF) for progressively increasing nonlinearity and decreasing dispersion with distance to mitigate the impact of propagation loss on unbalancing the phase distortion induced before and after OPC. With addition of a dispersion element after OPC, the SPF design also targets compensation in a shorter subsection of spans where induced nonlinear distortion is strongest. This enables performance benefit with less required parameter change in spans comprising just two or three segments of different regular fibers as 2-SPF and 3-SPF, respectively. Numerical simulations of 5 channel WDM dual polarization (DP) 32 Gbaud 64-QAM signals in a 12 × 130 km fiber link shows use of OPC and a 58 km 3-SPF in spans achieves 2.1 dB higher <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q²</i> -factor at 5 dB higher launch power than without. Similarly, measurements of 5 channel WDM DP 12 Gbaud 16-QAM signals in a 2 × 155 km link shows use of OPC and a 41 km 2-SPF in spans achieves 1.2 dB higher <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q²</i> -factor at 6 dB higher launch power and with low bit error rate compared to without. The improvements highlight the OPC advancements achievable by link design with regular fibers.

LED communications with linear complexity compensation of dynamic nonlinear distortion.

An in-depth study of the second order Volterra kernel of light emitting diodes (LEDs) is provided, with a special focus on compensation of dynamic nonlinear distortion generated by the LED when used as a communications signal transmitter. It is shown that from the factorization of the kernel in the frequency domain follows a simplified time-domain model for LED nonlinearity, consisting of three operations: two linear filtrations and squaring. Next, using the pth inverse theory, the corresponding block structures of nonlinear pre- and postdistorters are derived. As it turns out, they exhibit linear computational complexity. It is shown that the model coefficients defining the kernel may be estimated up to the Nyquist frequency. Numerical results indicate that pre- and postdistortion achieve the same performance with respect to receiver signal to noise power ratio (SNR) and have a considerable advantage over linear equalizers. However, in a practical scenario, the predistortion increases the peak to average power ratio of the transmitted signal (unless it is not high already), possibly leading to performance inferior to postdistortion. Finally, it is shown that the simplified equalizer based on the LED model has roughly identical performance to the regular, quadratic Volterra equalizer.

Efficient Realization for Third-Order Volterra Filter Based on Singular Value Decomposition

Nonlinear distortion in loudspeaker systems degrades sound quality and must be properly compensated for by linearization techniques. One technique to reduce nonlinear distortion is to use a Volterra Filter, which approximates the nonlinearity of the target loudspeaker using the Volterra series expansion. In general, the Volterra Filter is computationally very expensive, and the amount of computation needs to be reduced for real-time processing. In this paper, we propose an efficient implementation of the third-order Volterra filter based on singular value decomposition. The proposed method determines the necessary coefficients based on the symmetry of the third-order Volterra filter and applies singular value decomposition to them. In the filter structure consisting of singular values and their corresponding singular vector, the computational complexity of the third-order Volterra filter can be reduced by eliminating the part of the filter with small singular values. By focusing on the magnitude of the singular values, the proposed method can improve the computational efficiency of the third-order Volterra filter without decreasing its approximation accuracy. Simulation results show that the proposed method can improve the computational efficiency by 60% while maintaining the nonlinear distortion compensation performance of the micro-speaker for smartphones by about 8 dB.

R-LIO: Rotating Lidar Inertial Odometry and Mapping

In this paper, we propose a novel simultaneous localization and mapping algorithm, R-LIO, which combines rotating multi-line lidar and inertial measurement unit. R-LIO can achieve real-time and high-precision pose estimation and map-building. R-LIO is mainly composed of four sequential modules, namely nonlinear motion distortion compensation module, frame-to-frame point cloud matching module based on normal distribution transformation by self-adaptive grid, frame-to-submap point cloud matching module based on line and surface feature, and loop closure detection module based on submap-to-submap point cloud matching. R-LIO is tested on public datasets and private datasets, and it is compared quantitatively and qualitatively to the four well-known methods. The test results show that R-LIO has a comparable localization accuracy to well-known algorithms as LIO-SAM, FAST-LIO2, and Faster-LIO in non-rotating lidar data. The standard algorithms cannot function normally with rotating lidar data. Compared with non-rotating lidar data, R-LIO can improve localization and mapping accuracy in rotating lidar data.

Algorithms for distributing DSSS codes in industrial WSNs with real transmitters and narrow-band interference

The versatility of simple electronic nodes and debugging of communication protocols in unlicensed frequency bands constitute the main reasons for the adoption of industrial wireless sensor networks (IWSNs). However, the industrial environments, in which IWSNs function, are characterized by a harsh impact of physical and electromagnetic factors that destabilize the operation of equipment and worsen the noise immunity of channels. To consider the effect of these two groups of factors on communication quality, we develop a novel model of an IWSN channel as the dependence of bit error probability (BEP) on signal distortions and interference impact. We found that direct sequence spread spectrum (DSSS) codes of a signal have different effects on the compensation of nonlinear signal distortions and external interference. Further, we propose an algorithm for the distribution of DSSS codes among real transmitters by BEP values in channels with known additive and multiplicative interference. Here, the distribution of codes is based on the minimax criterion. Finally, for cases when a signal is characterized by a-priori uncertainties of fading, we suggest an alternative algorithm for selecting a DSSS code based on Pareto bicriteria optimization.

Compensation of nonlinear distortion in hybrid beamforming MIMO transmitters

Compensation of nonlinear distortion in hybrid beamforming MIMO transmitters is an open and challenging field of research. The goal of the study is to find an efficient method for linearization of power amplifiers in fully connected hybrid beamforming MIMO transmitters, which would not additionally increase the complexity of the system too much. In this paper, the polynomial-based compensation method of nonlinear distortion in hybrid beamforming MIMO transmitters is presented. The method is verified through comprehensive Matlab simulations. A 64x64 fully connected hybrid beamforming MIMO system with 2 RF branches on the transmitting side and 2 RF branches on the receiving side was considered. The proposed memory polynomial digital predistortion model is based on direct transmit-end feedback. Simulations were performed for different parameters of the memory polynomial model and analyzed. The obtained results are presented in graphical form, using Power Spectrum Density, and in numerical form, using metrics in time and frequency domain, such as Normalized Mean-Squared Error and Error Vector Magnitude. It is shown that the proposed memory polynomial digital predistortion model can very well compensate nonlinear distortion in fully connected hybrid beamforming MIMO transmitter. It has been also demonstrated that with increasing model complexity, ie with increasing memory depth and nonlinearity order of memory polynomial model, better compensation of nonlinear distortion in hybrid beamforming MIMO transmitters can be achieved.

Predistortion Approaches Using Coefficient Approximation and Bidirectional LSTM for Nonlinearity Compensation in Visible Light Communication

A Light-Emitting Diode (LED) has a nonlinear characteristic, and it contains fundamental limitations for the performance of Visible Light Communication (VLC) systems in indoor environments when using intensity modulation with Orthogonal Frequency Division Multiplexing (OFDM). In this paper, we investigate this nonlinear characteristic with analysis and proposal. At first, we identified the LED nonlinear characteristics in terms of bit-error performances. After analysis, we propose initial predistortion schemes to mitigate the nonlinearity matters. In the predistortion schemes, the nonlinear distortion compensation model contains predistortion features with the LED inverse characteristics. Considering a Direct-Current-biased Optical OFDM (DCO-OFDM) system, we compared the Bit-Error Rate (BER) performances with and without compensation via simulations. The performance on the LED with the compensation showed LED nonlinearity could significantly improve the bit-error performance. In addition, with consideration that the predistortion model is insufficient to represent LED distortion, we investigated possible opportunities of distortion correction using Bidirectional Long Short-Term Memory (BLSTM), one of the leading deep learning approaches. Its result showed promising improvement of the distortion compensation as well.

Sparse Kernel Affine Projection-Based Nonlinear Distortion Compensation and Memory Effect Depression Algorithm in VLC Systems

As an emerging wireless application for indoor high-speed wireless access and positioning, visible light communication (VLC) has attracted people’s attentions. However, the nonlinear components employed in VLC systems, especially the light-emitting diodes (LEDs), can cause nonlinear distortion to the transmitted signal, which could severely degrade the system performance. Aiming at the nonlinear characteristics of LED, the sparse kernel affine projection algorithm (SKAPA) is investigated in this paper to eliminate the nonlinear distortion for VLC systems. Based on that, to further remove the bad memory effect of LED, a memory effect depression (MED) scheme is proposed, which is carried out following SKAPA. Simulation results show that SKAPA can compensate for the nonlinear distortions, and the combined SKAPA-MED algorithm has a good performance in dealing with memory LEDs. Compared with Kernel Least-Mean-Square (KLMS), SKAPA exhibits better convergence and bit error rate (BER) performance. Additionally, it is also demonstrated that SKAPA has lower complexity than memory polynomial algorithm, and slightly better detection property can be obtained.

Comparing different nonlinearities in readout systems for optical neuromorphic computing networks

Nonlinear activation is a crucial building block of most machine-learning systems. However, unlike in the digital electrical domain, applying a saturating nonlinear function in a neural network in the analog optical domain is not as easy, especially in integrated systems. In this paper, we first investigate in detail the photodetector nonlinearity in two main readout schemes: electrical readout and optical readout. On a 3-bit-delayed XOR task, we show that optical readout trained with backpropagation gives the best performance. Furthermore, we propose an additional saturating nonlinearity coming from a deliberately non-ideal voltage amplifier after the detector. Compared to an all-optical nonlinearity, these two kinds of nonlinearities are extremely easy to obtain at no additional cost, since photodiodes and voltage amplifiers are present in any system. Moreover, not having to design ideal linear amplifiers could relax their design requirements. We show through simulation that for long-distance nonlinear fiber distortion compensation, using only the photodiode nonlinearity in an optical readout delivers BER improvements over three orders of magnitude. Combined with the amplifier saturation nonlinearity, we obtain another three orders of magnitude improvement of the BER.

An Efficient QAM Detector via Nonlinear Post-Distortion Based on FDE Bank Under PA Impairments

In this paper, we propose a receiver structure for single-carrier uplink transmission with frequency domain equalization (FDE) that is exposed to power amplifier (PA) nonlinearities. A two-stage approach is adopted, in which linear communication channel is equalized at the first stage, and it is followed by post-distortion, where nonlinear distortion is reduced. In the literature, nonlinear processing techniques are proposed, which perform memoryless compensation of nonlinear distortion together with FDE. However, in this study, we show that even if memoryless nonlinearity exists, the received signal is impaired by nonlinear inter-symbol-interference. Therefore, we propose a class of symbol rate post-distortion techniques, which use neighboring received symbols to suppress the nonlinear interference. Three different post-distortion methods, Gaussian process regression (GPR), neural network (NN) and Volterra series (VS) based post-distorters, are considered. Also, a combiner, which intelligently combines the outputs of fractional delayed bank of FDE’s after post-distortion, is proposed to overcome performance degradation of FDE for frequency selective channels under nonlinear distortion. Performances of the proposed techniques are compared with state-of-the-art approaches in terms of bit error rate (BER) and achievable information rate (AIR) metrics. Simulation results demonstrate that post-distortion methods together with bank of FDE outperform state-of-the-art techniques.

Experimental realization of integrated photonic reservoir computing for nonlinear fiber distortion compensation.

Nonlinearity mitigation in optical fiber networks is typically handled by electronic Digital Signal Processing (DSP) chips. Such DSP chips are costly, power-hungry and can introduce high latencies. Therefore, optical techniques are investigated which are more efficient in both power consumption and processing cost. One such a machine learning technique is optical reservoir computing, in which a photonic chip can be trained on certain tasks, with the potential advantages of higher speed, reduced power consumption and lower latency compared to its electronic counterparts. In this paper, experimental results are presented where nonlinear distortions in a 32 GBPS OOK signal are mitigated to below the 0.2 × 10-3 FEC limit using a photonic reservoir. Furthermore, the results of the reservoir chip are compared to a tapped delay line filter to clearly show that the system performs nonlinear equalisation.

Fiber nonlinearity mitigation with a perturbation based Siamese neural network receiver

We simulate nonlinear distortion compensation of single frequency dual polarization signals propagating in single mode optical fibers with a combination of Siamese Neural Networks (SNNs) and a perturbative nonlinearity compensation technique. We find that a 2-branched SNN can enhance the quality factor (Q-factor) of a 3200 km 16-QAM optical system from the 8 dB that is associated with only applying chromatic dispersion compensation (CDC) to 8.9 dB. We then investigate the Q-factor improvement associated with different numbers and widths of SNN branches. We finally demonstrate that the number of inputs to the SNN and hence the computational complexity can be reduced by employing Principal Component Analysis (PCA). This results in a 0.75 dB Q-factor enhancement with 50% fewer inputs than previous designs.

Use of complex fully connected neural networks to compensate for nonlinear effects in fibre-optic communication lines

A scheme is proposed for processing optical signals in a receiver of a communication system, based on complex fully connected neural networks. The influence of the main characteristics of the neural network on the efficiency of nonlinear distortion compensation is studied. A significant advantage of the proposed scheme over real-valued neural networks is demonstrated.

Метод компенсации нелинейных искажений, возникающих при локации маневрирующих целей

В работе предложен метод решения проблемы в области обработки радиолокационных сигналов с линейной частотной модуляцией (ЛЧМ), обеспечивающий компенсацию нелинейных изменений радиальной скорости локационного объекта (ЛО) при его маневрировании. Метод основан на компенсации искажений радиолокационных сигналов, отраженных от ЛО, вызванных нелинейным характером изменения радиальной скорости при маневрировании в предположении линейного изменения скорости за время когерентного накопления (КН). Приведены результаты моделирования обработки сигналов с реализованным методом компенсации. A method for solving the problem in the field of radar signal processing with linear frequency modulation is proposed. The method provides compensation for nonlinear changes in the radial velocity of a aircraft during its maneuvering. The method is based on the compensation of reflected pulses distortions caused by the nonlinear nature of the change in radial velocity of a aircraft during its maneuvering. It is assumed that during the time of doppler process the radial velocity changes linearly. The results of signal processing simulation with the implemented method are presented.

Compensation of SOA-induced nonlinear phase distortions by optical phase conjugation

To answer the question: "Is optical phase conjugation (OPC) capable of compensating nonlinear distortions caused by not only Kerr effect of optical fibre, but also the carrier dynamics of semiconductor optical amplifiers (SOAs)?", we investigate the effectiveness of OPC-based nonlinear compensation for SOAs amplifying a few-channel WDM signal modulated with m-QAM. We use a pair of SOAs with an OPC stage sandwiched between the two so that the combination works as a low-distortion amplifier. Symbol-period longer than the gain recovery time is chosen in our experiments to avoid bit-pattern effects introduced by the SOA. We amplify a 12Gbaud, 16QAM modulated three-channel WDM signal with this technique in the back-to-back configuration which remarkably outperforms a single SOA in the nonlinear regime of operation with an average Q2 improvement better than 4 dB for an output power of 4 dBm. We further demonstrate the practical advantage of the low distortion higher output power capability of the SOA shown in the back-to-back result by carrying out a transmission of the amplified signal through a 160-km fibre, where relatively high launch power is desirable. We also study the case of 64QAM signals and show that approximately a 3 dB Q2 factor improvement can be obtained over single SOA, while without nonlinear phase distortion compensation, the demodulation is nearly impracticable.

Compensation of Nonlinear Distortion in Loudspeakers Considering Nonlinear Viscoelasticity of the Suspension

Compensation of Nonlinear Distortion in Loudspeakers Considering Nonlinear Viscoelasticity of the Suspension