Cross-modulation Distortion Research Articles

Digital cancellation of multi-band passive inter-modulation based on Wiener-Hammerstein model

Utilizing multi-band and multi-carrier techniques enhances throughput and capacity in Long-Term Evolution (LTE)-Advanced and 5G New Radio (NR) mobile networks. However, these techniques introduce Passive Inter-Modulation (PIM) interference in Frequency-Division Duplexing (FDD) systems. In this paper, a novel multi-band Wiener-Hammerstein model is presented to digitally reconstruct PIM interference signals, thereby achieving effective PIM Cancellation (PIMC) in multi-band scenarios. In the model, transmitted signals are independently processed to simulate Inter-Modulation Distortions (IMDs) and Cross-Modulation Distortions (CMDs). Furthermore, the Finite Impulse Response (FIR) filter, basis function generation, and B-spline function are applied for precise PIM product estimation and generation in multi-band scenarios. Simulations involving 4 carrier components from diverse NR frequency bands at varying transmitting powers validate the feasibility of the model for multi-band PIMC, achieving up to 19 dB in PIMC performance. Compared to other models, this approach offers superior PIMC performance, exceeding them by more than 5 dB in high transmitting power scenarios. Additionally, its lower sampling rate requirement reduces the hardware complexity associated with implementing multi-band PIMC.

High-Efficiency Mitigation of Nonlinear Distortion in Microwave Photonics Link Assisted by Artificial Neural Network

A microwave photonics radio over fiber link can deliver the radio frequency (RF) signal to realize the antenna remote. When the signal is a broadband and multicarrier RF signal, there are some linear distortions in the link, such as the crossmodulation distortion (XMD) and third-order intermodulation distortion (IMD3). It will destroy the wide-bandwidth performance of the link. Traditional postdigital compensation methods for XMD and IMD3 mitigation extract the baseband signal and reconstruct the compensation signal with calculated compensation factor. Here, a kind of artificial neural network genetic algorithm (ANN-GA) distortion compensation technique is proposed to seek the compensation factor instead of calculations. The neural network algorithm is used to fit the mapping function between the compensation factor and the distortion and give a set of predicted data as the original individual fitness value for the genetic algorithm. Based on the original value, the minimal distortion, the corresponding optimal compensation factors γ and α are found with optimization iterations. Taking advantage of the optimal compensation factors, based on the traditional postdigital compensation method, the distortion is mitigated with a suppression ratio of -84.4 dB. In our paper, the mitigation technology of the XMD and IMD3 can be applied for any kinds of link instead of mathematically modelling the link and calculating the compensation factor. The technology can improve the intelligence and flexibility of microwave photonic link linearization design.

A Tunable Multimode Quadrature Balanced N-Path Diplexer With Nonlinear Cross-Modulation Distortion Correction

A tunable active diplexer based on quadrature balanced N-path mixers for single-antenna frequency-division duplex (FDD), half-duplex (HD), and carrier aggregation (CA) wireless is proposed. The balanced structure provides wideband TX noise cancellation in the RX band and low sensitivity to antenna VSWR variations, while sharp filtering between adjacent channels is achieved by the highly frequency-dependent input matching of the N-Path mixers. The diplexer's performance is enhanced by nonlinear digital algorithms accounting for cross-modulation distortion between the two channels and maintaining optimal performance at high TX power levels.

Augmented Convolutional Neural Network for Behavioral Modeling and Digital Predistortion of Concurrent Multiband Power Amplifiers

Neural network (NN)-based models are perceived as being accurate models for power amplifier (PA) behavioral modeling and digital predistortion (DPD) applications. However, the complexity of NN’s models in terms of the number of coefficients increases with the memory depth, nonlinearity order, signal bandwidth, and the number of carriers. In this article, a novel augmented convolutional neural network (ACNN)-based DPD is proposed to linearize the concurrent multiband PAs. In the ACNN model, the convolution layer with a fully connected layer serves to model the intermodulation distortion (IMD), cross-modulation distortion (CMD), and nonlinearities of the concurrent multiband PA. The pooling layer in the ACNN reduces the model’s complexity. The measurement results show that the proposed DPD requires significantly fewer coefficients and floating-point operations (FLOPs) than the state-of-the-art DPDs. This model’s complexity reduction arises with the number of carriers in the multiband aggregated signal. The measurement results also show that the proposed DPD has a better linearization performance in terms of metrics, such as normalized mean square error (NMSE), adjacent channel power ratio (ACPR), and error vector magnitude (EVM).

Linearized wideband and multi-carrier link based on TL-ANN

The analog photonics link (APL) is widely used in microwave photonics. However, in wideband and multi-carrier systems, the third inter-modulation distortion (IMD3) and cross-modulation distortion (XMD) will jointly limit the spurious-free dynamic range (SFDR) of links. In this paper, we experimentally present a linearized wideband and multi-carrier APL, in which the IMD3 and XMD are mitigated simultaneously by using artificial neural networks with transfer learning (TL-ANN). In this experiment, with different artificial neural networks, which are trained with the knowledge obtained from the two- or three-sub-carrier system, the IMD3 and XMD are suppressed by 21.71 dB and 11.11 dB or 22.38 dB and 16.73 dB, and the SFDR is improved by 13.4 dB or 14.3 dB, respectively. Meanwhile, compared with previous studies, this method could reduce the training time and training epochs to 16% and 25%.

A Multimode 5–6 GHz FD/HD/FDD Quadrature Balanced CMOS Front End With Transmit–Receive Cross-Modulation Distortion Correction

We introduce a multimode and wideband quadrature balanced CMOS RF front end (RFFE) supporting full-duplex (FD), half-duplex (HD), and frequency-division duplex (FDD) operation at the 5-6 GHz band. The proposed RFFE is enhanced by nonlinear digital algorithms that maintain optimal performance at high transmit (Tx) power levels. A theoretical model of the transmit-receive (TR) cross-modulation (CM) distortion mechanism stemming from instantaneous variations in the power amplifiers (PAs) output impedance is laid out and verified in simulation and measurement. A 2-D digital postdistortion (2-D DPoD) algorithm that utilizes the known baseband Tx signal and the downconverted distorted Rx signal is proposed to linearize the CM-distorted Rx signal, in conjunction with wideband digital RF and baseband cancellation of the Tx self-interference at the receiver input and 1-D digital predistortion to linearize the Tx signal. The system was characterized in simultaneous TR operation using 802.11ac VHT Wi-Fi signals at 10 dBm average Tx power. In the FD mode using 20 MHz signals, TR isolation of 66 dB was achieved, and the 2-D DPoD corrected Rx error vector magnitude (EVM) by 11 dB to a value of -33 dB. In the FDD mode with 800 MHz frequency separation, 14 dB improvement was demonstrated in Rx EVM with 2-D DPoD to the levels of -35 and -31 dB for 20 and 160 MHz signals, respectively. Similar EVM values were measured in the HD Rx mode at -40 dBm average Rx power, along with Rx insertion loss lower than 1 dB without using a TR switch.

Wideband Linearization of a Carrier Aggregation Transmitter Using Analog Signal Injection and 2-D Digital Predistortion

We introduce a transmitter (TX) architecture and a linearization technique for concurrent transmission of two intraband noncontiguous carrier aggregation signals in the 5 GHz frequency band. The technique is based on low-power and narrowband analog signal injection to compensate for out-of-band (OOB) third-order intermodulation distortions (IMD3), together with 2-D digital predistortion to address error vector magnitude (EVM) degradation caused by in-band intermodulation and cross-modulation distortions. The hybrid analog-digital design enables wideband linearization over the entire third-order distortion bandwidth (BW) using practical sampling rate requirements from the digital-to-analog converter (DAC) and analog-to-digital converter (ADC). The system’s performance was evaluated using a class AB power amplifier implemented in the 180 nm CMOS technology and two VHT 802.11ac Wi-Fi signals with a 20 MHz modulation BW. The linearization technique achieves 7–12 dB cancellation of OOB IMD3 products along with 6–9 dB of in-band EVM correction at 8 dBm average output power over a BW of up to 1.2 GHz, with only 60 MHz BW requirement from the DACs and ADCs.

Nonlinear Distortions Compensation Based on Artificial Neural Networks in Wideband and Multi-Carrier Systems

Three-order inter-modulation distortions (IMD3) is a tough problem which appears in analog photonics links (APL). In multi-carrier systems, out-band signals will also lead to nonlinear distortion which is referred as cross-modulation distortion (XMD). The two kinds of distortion will jointly limit dynamic range. In this paper, we propose to adopt an artificial neural network (ANN) as the processing approach which could mitigate IMD3 and XMD simultaneously. The IMD3 and XMD are suppressed by 29.76 dB and 22.18 dB respectively in the experiment. Compared with traditional approaches, the proposed method shows better performance and generalization ability.

Simultaneous Suppression of Even-Order and Third-Order Distortions in Directly Modulated Analog Photonic Links

A high-linearity directly-modulated analog photonic link (APL) with simultaneous suppression of the even-order intermodulation distortion, third-order intermodulation distortion (IMD3), and cross-modulation distortion (XMD) is proposed and experimentally demonstrated by the corporation of push–pull structure and an adaptive compensation algorithm. In the proposed directly-modulated APL system, the push–pull structure is introduced to effectively eliminate all the even-order nonlinear distortions, including the second-order intermodulation distortion and the second-order harmonic distortions. To further simultaneously suppress the IMD3 and XMD, an adaptive compensation algorithm is designed and adopted at the receiver. The experimental results show that the second-order spurious-free dynamic range and the third-order spurious-free dynamic range is improved by 19.8 and 12.4 dB, respectively, corresponding to 7.15% error vector magnitude performance improvement for a 120 Mb/s 64QAM-OFDM RF signal transmission when the input RF power is 13 dBm.

Harmonic, Intermodulation and Cross-Modulation Distortion in Directly Modulated Quantum Cascade Lasers

Using a simplified rate equation model, expressions for harmonic, intermodulation and cross-modulation distortion for a directly modulated quantum cascade laser can be derived. This paper shows how such derivations can be done and discusses some implications for quantum cascade lasers. It is important to understand such distortion, especially for applcations in communication systems.

Elimination of cross-modulation distortion in a radio frequency–amplified intensity-modulation direct-detection analog photonic link

By cascading two standard Mach–Zehnder modulators (MZMs), we propose and demonstrate a scheme to effectively eliminate the cross-modulation distortion (XMD), which results from the out-of-band interference in multicarrier intensity-modulation direct-detection (IMDD) analog photonic links. When the bias angle of the cascaded modulator is specifically designed, the XMDs, both from the photonic link itself and from the nonlinear electrical amplifiers, are well suppressed. Our proposal is theoretically analyzed, and the performance of the cascading system is experimentally demonstrated. A suppression ratio of more than 30 dB is achieved by the cascading scheme. By using the high-performance pre- and postamplifiers, the measured link gain and noise figure are improved by 62 and 32 dB, respectively.

Digital linearization for broadband multicarrier analog photonic link incorporating downconversion

The multicarrier analog photonic links suffer from both the traditional third-order intermodulation distortions (IMD3) and the cross-modulation distortions (XMDs), severely limiting the dynamic range of the links. This paper proposes and demonstrates an effective technique based on a single modulator and photodetector to simultaneously realize the downconversion and receiving of multiple radio frequency signals, as well as suppress the nonlinearities, including the IMD3 and XMD. In the scheme, the nonlinear compensation information is directly obtained from hardware then the distortion compensation is carried out in the digital domain. Experimental results show that the XMD and IMD3 distortions are suppressed with 36.6 and 25.8 dB, respectively, and the link dynamic range is improved by 25 dB, preventing the degradation of the dynamic range of the link. Moreover, the structure of our scheme can eliminate the stringent requirement for hardware.

Digital suppression of both cross and inter-modulation distortion in multi-carrier RF photonic link with down-conversion.

We propose and demonstrate a novel scheme to effectively suppress the cross modulation distortion (XMD) and the third-order inter-modulation distortion (IMD3) which exist in wide-band, multi-carrier analog photonic link (APL) system. Such nonlinearities, which are caused by the out-of-band and in-band signals, respectively, constrain the link's performance severely. Instead of building an extra nonlinear path in hardware, the XMD and IMD3 compensation information is extracted from the received distorted signal, and both distortions are then suppressed by digitally multiplying the distorted signal with the compensation information. After compensation in the digital domain, the down-converted XMD and IMD3 distortions are experimentally suppressed with 33 dB and 25 dB, respectively, resulting in an improved upper limit for the SFDR.

Generalization of Linear Rosenstark Method of Feedback Amplifier Analysis to Nonlinear One

Abstract This paper deals with an extension of the Rosenstark’s linear model of an amplifier to a nonlinear one for the purpose of performing nonlinear distortion analysis. Contrary to an approach using phasors, our method uses the Volterra series. Relying upon the linear model mentioned above, we define first a set of the so-called amplifier’s constitutive equations in an operator form. Then, we expand operators using the Volterra series truncated to the first three components. This leads to getting two representations in the time domain, called in-network and inputoutput type descriptions of an amplifier. Afterwards, both of these representations are transferred into the multi-frequency domains. Their usefulness in calculations of any nonlinear distortion measure as, for example, harmonic, intermodulation, and/or cross-modulation distortion is demonstrated. Moreover, we show that they allow a simple calculation of the so-called nonlinear transfer functions in any topology as, for example, of cascade and feedback structures and their combinations occurring in single-, two-, and three-stage amplifiers. Examples of such calculations are given. Finally in this paper, we comment on usage of such notions as nonlinear signals, intermodulation nonlinearity, and on identification of transfer function poles and zeros lying on the frequency axis with related real-valued frequencies.

A Generalized 2-D Linearity Enhancement Architecture for Concurrent Dual-Band Wireless Transmitters

A novel generalized two dimensional (2-D) digital predistortion (DPD) architecture for concurrent dual-band transmitters is presented. The proposed architecture is based on simultaneous injection of in-band intermodulation (IM) and cross-modulation (CM) distortion products. A general fundamental-frequency model for concurrent dual-band transmitter is developed theoretically and proofed experimentally. An individual impact of each IM and CM distortion component is theoretically derived and analyzed. It is clearly proven by theoretical analysis and experiments that the proposed predistorter improves the in-band and out-of-band performances of both signals. The simulation and experimental studies are performed using various signal sets. The proposed predistorter does not depend on frequency separation between bands and has low computational complexity in comparison with concurrent dual-band DPD's state-of-the-art. In addition, it is clearly shown in experiments that when using iterative simultaneous injections, a phenomenon known as distortion compensation limit can be reduced. A presence of memory effects and their mitigation in frequency domain for each band of concurrent dual-band transmitter are also demonstrated in experiments.

Digital joint compensation of IMD3 and XMD in broadband channelized RF photonic link

Based on forward distortion information acquisition and post digital signal processing (DSP), we propose and demonstrate a novel scheme to effectively suppress the third-order intermodulation distortion (IMD3) and cross-modulation distortion (XMD) in a channelized RF photonic link. The simultaneous distortion compensation capacity is studied numerically, and suppression of XMD and IMD3 by about 28 dB and 25 dB, respectively, is achieved experimentally. The scheme principle and the digital compensation procedure are discussed, which shows a simple hardware implementation and algorithm.

Digital compensation of cross-modulation distortion in multimode transceivers

In a multimode transceiver, several communication standards may be active at the same time. Owing to the small size of the transceiver, the transmitter for one standard induces a large interference on the receiver for another one. When this large interference passes through the inherently non-linear receiver front-end (FE), distortion products are generated. Among these products, the cross-modulation (CM) product is the most problematic one, as it always has the same centre frequency as the desired signal. Increasing the FE linearity to lower the CM distortion leads to unacceptable power consumption for a handheld device. Considering the continuous increase of digital computation power governed by Moore's law an attractive alternative approach is to digitally compensate for the CM distortion. An existing solution to compensate for the CM distortion is tailored to single-mode transceivers and requires an auxiliary FE. By using the locally available transmitted interference in the multimode transceiver, the authors propose a CM compensation method which requires no additional analogue hardware. Hence the power consumption and complexity of the multimode transceiver can be reduced significantly. The simulation results demonstrate that the proposed method can lower distortion to a negligible amount at realistic interference levels.

Digital Compensation of Cross-Modulation Distortion in Software-Defined Radios

The wideband RF receiver in a software-defined radio (SDR) system suffers from the nonlinear effects caused by the front-end analog processing. In the presence of strong blocker (interference) signals, such nonlinearities introduce severe cross modulation over the desired signals. This paper investigates how the cross-modulation distortion can be compensated for by using digital signal processing techniques. In the proposed solution, the SDR scans the wide spectrum and locates the desired signal and strong blocker signals. After down-converting these signals separately to the baseband, the baseband processor processes them jointly to mitigate the cross-modulation interferences. As a result, the sensitivity of the wideband RF receiver to the nonlinearity impairment can be significantly lowered, simplifying the RF and analog circuitry design in terms of implementation cost and power consumption. The proposed approach also demonstrates how mixed-signal, i.e., joint analog and digital, processing techniques play a critical role in the emerging SDR and cognitive radio technologies.

Distortion Analysis of Ultra-Wideband OFDM Receiver Front-Ends

This paper presents a comprehensive analysis of the effect of nonlinearities in ultra-wideband orthogonal frequency-division multiplexing receivers. The statistical properties of a quadrature phase-shift keying baseband signal are utilized to derive closed-form expressions for the power spectral density of cross-modulation, intermodulation, and harmonic distortion products of modulated signals, arising from second- and third-order nonlinearities in the receiver. Both narrowband and wideband jammers are considered. The derived expressions are then used to predict the effect of these nonidealities on the link budget of the system

Modeling distortion in multichannel communication systems

A behavioral modeling technique suited to capturing the response of wide-band multifunctional and multichannel amplifiers is introduced. The technique is based on the three-box approximation of the Volterra model and takes into account the dependence of the amplifier characteristics on frequency. The model is coupled with a new nonlinear statistical analysis, which enables accurate estimation of intermodulation and cross-modulation distortions of multiple digitally modulated signals. The model parameters can be obtained using simple measurements.