Nonlinear High Power Amplifier Research Articles

S-curve bias optimization of navigation signals based on a pre-distortion method

Abstract Nonideal radio-frequency (RF) emission channels directly affect the quality of navigation signals. In particular, the deviation in the pseudo-range, caused by differences among the RF channels of multiple satellites, can decrease user positioning accuracy. Previous studies have primarily focused on designing pre-distortion filters to improve the performance of non-ideal RF channels in navigation signal generators. However, this study shows that using a pre-distortion filter alone limits the improvement of the S-curve bias because the constant-envelope character is compromised, and the nonlinearity of the high-power amplifier (HPA) becomes more pronounced. Applications that require better accuracy require require a smaller S-curve bias. This study proposes a method to compensate for the nonideal RF channel by using pre-distortion that considers both the nonlinear HPA and nonideal filter characteristics. The proposed method is validated through numerical analysis and simulations. The results show that the proposed method can reduce the S-curve bias across different receiver configurations. This study is a useful reference for improving the quality of navigation signals, particularly in terms of correcting the S-curve bias.

Performance Analysis of Uplink Code Division Multiplexing for LEO Satellite Constellations Under Nonlinear Power Amplifiers.

This paper studies the performance of the communication link between a ground station and the satellites of a LEO constellation, employing code division multiplexing and a non-linear high-power amplifier. The analysis shows that the input power selection at the high-power amplifier of the ground station has a significant impact on overall system performance. The results concerning output power, the challenge of adjusting the back-off with a continuously changing number of satellites, and improved energy efficiency suggest operating in saturation. In this scenario, we can choose to transmit directly the sign of the sum of the signals directed to individual satellites. Analytical exact and simplified results are derived, enabling the estimation of performance as a function of the number of satellites being served when the amplifier operates at saturation. These analytic results are further validated through simulations. A formula to compute the loss across different numbers of satellites is also presented. The performance under saturated amplifier conditions is evaluated, compared, and discussed, providing valuable insights for simplifying the design and operation of satellite uplink communication systems under power amplifier constraints.

The Joint Channel Coding and Pre-Distortion Technique on the USRP-Based MIMO-OFDM System

Modern wireless communication systems use orthogonal frequency division multiplexing (OFDM), a multi-carrier modulation method that resists multipath channels and provides bandwidth efficiency. OFDM is generally used with a Multiple-Input Multiple-Output (MIMO) system to boost diversity gain and channel capacity. MIMO-OFDM has several advantages, but its high PAPR value is a drawback. A non-linear high-power amplifier (HPA) can distort signals with high PAPR values. This issue can be resolved by employing predistortion, which compensates for nonlinear HPA. In addition to PD, channel coding can be used to improve the quality of systems with high PAPR values by adding redundant bits to the bits to be sent. In this paper, we report the experimental evaluations of the joint channel coding and pre-distortion (PD) technique on a 2x2 MIMO OFDM system using USRP hardware. The experiments are conducted in two scenarios: line-of-sight (LOS) and nonline-of-sight (NLOS) scenarios. The channel coding used in this scenario is convolutional code with code rates of 1/2, 2/3, and 3/4. From the results of the experiment, it can be seen that the system that uses PD combined with the convolution code produces better performance in the LOS and NLOS scenarios compared to the system without PD. In the LOS scenario, the use of PD can improve the SNR value of code rates 1/2, 2/3, and 3/4 by approximately 58.74%, 75.97%, and 96.20%. In the NLOS scenario, the use of PD can improve the SNR value of code rates 1/2, 2/3, and 3/4 by about 60.71%, 73.59%, and 71.84%. The measurement of the LOS scenario gives a better SNR value than the NLOS scenario, with a maximum SNR value of 30.86 dB, while the maximum SNR value of the NLOS scenario is 30.23 dB. This happened because the LOS scenario suffered minimal multipath fading compared to the NLOS scenario

Some power allocation algorithms for cognitive uplink satellite systems

Cognitive satellite communication (SatCom) is rapidly emerging as a promising technology to overcome the scarcity of the exclusive licensed band model in order to fulfill the increasing demand for high data rate services. The paper addresses power allocation methods for multi-operator multi-beam uplink satellite communication systems co-existing with a Ka-band terrestrial network, using cognitive radio paradigm. Such a scenario is especially challenging because of (i) the coexisting multiple SatCom operators over the cognitive band need to coordinate the use of their resources under limited inter-operator information exchange, and (ii) nonlinear onboard high power amplifier (HPA) which leads to nonlinear interference between users and beams. In order to tackle the first challenge, we propose distributed power allocation algorithms including the standard Alternate Direction Multiplier Method (ADMM); Regarding the HPA nonlinear impairment, we propose nonlinear-aware power allocation based on Signomial Programming. The proposed solutions outperform state-of-the-art in both cases.

Information Energy Capacity Region for SWIPT Systems Over Rayleigh-Fading Channels

In this paper, we study the fundamental limits of simultaneous information and power transfer over a Rayleigh-fading channel, where the channel input is constrained to peak-power (PP) constraints that vary in each channel use by taking into account high-power amplifier (HPA) nonlinearities. In particular, a three-party communication system is considered, where a transmitter aims simultaneously conveying information to an information receiver and delivering energy to an energy harvesting receiver. For the special case of static PP constraints, we study the information-energy capacity region and the associated input distribution under: a) average-power and PP constraints at the transmitter, b) an HPA nonlinearity at the transmitter, and c) nonlinearity of the energy harvesting circuit at the energy receiver. By extending Smith’s mathematical framework, we show that the optimal input distribution under those constraints is discrete with a finite number of mass points. We show that HPA significantly reduces the information energy capacity region. In addition, we derive a closed-form expression of the capacity-achieving distribution for the low PP regime, where there is no trade-off between information and energy transfer. For the case with time-varying PP constraints, we characterize the optimal input distribution of this channel by using Shannon’s coding scheme. Specifically, we numerically study a particular scenario for the time-varing PP constraints, where the PP constraint probabilistically is either zero or equal to a non-zero constant.

Low-complexity selective mapping technique for PAPR reduction in downlink power domain OFDM-NOMA

To support ultra-massive connectivity, non-orthogonal multiple access (NOMA) techniques are expected to be used in 6G instead of conventional orthogonal multiple access (OMA) techniques. Furthermore, given that orthogonal frequency division multiplexing (OFDM) was used by 4G and 5G, NOMA is expected to be combined with OFDM to mitigate frequency selectivity in multipath channels. However, after passing through nonlinear high power amplifiers (HPAs), OFDM-NOMA has reportedly suffered from nonlinear distortion due to the high peak-to-average power ratio (PAPR) problem, thus reducing users’ achievable data rates, sum rate capacity, and users’ bit error rate after going through nonlinear HPAs. Many PAPR reduction techniques have been introduced in the literature; however, high PAPR reduction gain comes at the expense of computational complexity. In this paper, a novel selective mapping (SLM) scheme for PAPR reduction in OFDM-NOMA systems is proposed. By utilizing the structure of the OFDM-NOMA transmitter, the proposed SLM scheme achieves the same performance as that of the conventional SLM scheme while requiring less computational complexity.

Waveform Design for Wireless Power Transfer With Power Amplifier and Energy Harvester Non-Linearities

Waveform optimization has shown its great potential to boost the performance of far-field wireless power transfer (WPT). Current research has optimized transmit waveform, adaptive to channel state information, to maximize the harvested power in WPT while accounting for the energy harvester (EH)'s non-linearity. However, the existing transmit waveform design disregards the non-linear high power amplifiers (HPA) at the transmitter. Driven by this, this paper optimizes a multi-carrier waveform at the input of HPA to maximize the harvested DC power considering both HPA's and EH's non-linearities. Two optimization models are formulated based on whether the frequencies of the input waveform are concentrated within the transmit pass band or not. Analysis and simulations show that, while EH's non-linearity boosts the power harvesting performance, HPA's non-linearity degrades the harvested power. Hence, the optimal waveform shifts from multi-carrier that exploits EH's non-linearity to single-carrier that reduces HPA's detrimental non-linear distortion as the operational regime of WPT becomes more sensitive to HPA's non-linearity and less sensitive to EH's non-linearity (and inversely). Simultaneously, operating towards HPA's non-linear regime by increasing the input signal power benefits the harvested power since HPA's DC power supply is better exploited, whereas the end-to-end power transfer efficiency might decrease because of HPA's increasing non-linear degradation. Throughout the simulations, the proposed waveforms show significant gain over those not accounting for HPA's non-linearity, especially in frequency-flat channels. We also compare the two proposed waveforms and show that the severity of HPA's non-linearity dictates which of the two proposed waveforms is more beneficial.

Simulation Analysis of Low PAPR FFT-based OFDM Through Nakagami Channel

In response to the inefficiency of power amplifier in conventional Orthogonal Frequency Division Multiplexing (OFDM) system, a low Peak-to-Average Power Ratio (PAPR) scenario can be obtained by implementing several PAPR reduction techniques. Partial Transmit Sequence (PTS) is a well-known instance to provide zero distortion for the system, while clipping is one of the simplest methods but it is sacrificing the error rate performance. In this work, Authors focused on analyzing the implementation of PTS and Palm Date Leaf clipping technique on OFDM system with 16-, 64-, 256-, and 1024-QAM under various Nakagami channel. In addition, the High-Power Amplifier (HPA) was also considered by using Solid State Power Amplifier (SSPA) model. It was found that linear HPA serves as the lower boundary for non-linear HPA, and system under high saturation level performs similarly. In physical properties, high saturation level is equivalent to higher power consumption in amplifier. Thus, optimal level was obtained by considering taking the one with moderate BER performance. After the system’s PAPR was reduced, the optimum saturation level of HPA was found to be 5 dB, 8 dB, 9 dB, and 11 dB for each Quadrature Amplitude Modulation (QAM) under Nakagami channel with m value of 1.5. However, this value was found to be ample for lower m value such as 1 or 0.7. In this case, the system required lower saturation level on the HPA for Nakagami channel with lower m value.

Autoencoder‐based deep learning for massive multiple‐input multiple‐output uplink under high‐power amplifier non‐linearities

In this paper, the authors study the compensation of high-power amplifier (HPA) non-linear distortion in the multi-user (MU) massive multiple-input multiple-output (MIMO) systems and focus on uplink transmission, where the base station (BS) uses a large antenna array. First, the authors present a non-linear distortion iterative cancellation (NDIC) algorithm-based MMSE and approximate message passing (AMP) at the receiver level, in order to estimate and mitigate jointly a non-linear distortion and the channel noise. Second, the authors propose a novel distortion cancellation technique based on deep learning. At this level, the authors first introduce a multilayer neural network, trained in the Levenberg–Marquardt algorithm by eliminating HPA non-linearities on the ‘Pre distortion’ transmitter and ‘Post distortion’ receiver side. Next, the authors developed a novel end-to-end (E2E) learning approach for the joint transmitter and non-coherent receiver in the Rayleigh fading channel. The basic idea lies in the use of deep neural networks (DNNs), auto encoder (AE) for unknown channels, where DNNs are applied to perform several functions and modules existing in the transmission chain. The simulation results demonstrate the strong potential of the proposed approach E2E in terms of improving the link quality and symbol error rate (SER) compared to other compensation techniques presented in this work.

Multi-Tone Harmonic Balance Optimization for High-Power Amplifiers through Coarse and Fine Models Based on X-Parameters.

In this study, we focus on automated optimization design methodologies to concurrently trade off between power gain, output power, efficiency, and linearity specifications in radio frequency (RF) high-power amplifiers (HPAs) through deep neural networks (DNNs). The RF HPAs are highly nonlinear circuits where characterizing an accurate and desired amplitude and phase responses to improve the overall performance is not a straightforward process. For this case, we propose a coarse and fine modeling approach based on firstly modeling the involved transistor and then selecting the best configuration of HAP along with optimizing the involved input and output termination networks through DNNs. In the fine phase, we firstly construct the equivalent modeling of the GaN HEMT transistor by using X-parameters. Then in the coarse phase, we utilize hidden layers of the modeled transistor and replace the HPA’s DNN to model the behavior of the selected HPA by using S-parameters. If the suitable accuracy of HPA modeling is not achieved, the hyperparameters of the fine model are improved and re-evaluated in the HPA model. We call the optimization process coarse and fine modeling since the evaluation process is performed from S-parameters to X-parameters. This stage of optimization can ensure modeling the nonlinear HPA design that includes a high number of parameters in an effective way. Furthermore, for accelerating the optimization process, we use the classification DNN for selecting the best topology of HPA for modeling the most suitable configuration at the coarse phase. The proposed modeling strategy results in relatively highly accurate HPA designs that generate post-layouts automatically, where multi-tone harmonic balance specifications are optimized once together without any human interruptions. To validate the modeling approach and optimization process, a 10 W HPA is simulated and measured in the operational frequency band of 1.8 GHz to 2.2 GHz, i.e., the L-band. The measurement results demonstrate a drain efficiency higher than 54% and linear gain performance more than 12.5 dB, with better than 50 dBc adjacent channel power ratio (ACPR) after DPD.

B-Spline Neural Network Assisted Space-Time Equalization for Single-Carrier Multiuser Nonlinear Frequency-Selective MIMO Uplink

This paper designs a nonlinear space-time equalizer based on B-spline neural network (BSNN) for the singlecarrier high-throughput multiuser frequency-selective multipleinput multiple-output (MIMO) nonlinear uplink. Specifically, based on a BSNN parametrization of the nonlinear high power amplifiers (NHPAs) at mobile terminals’ transmitters, a novel nonlinear identification scheme is developed to estimate the nonlinear dispersive MIMO uplink channel, which includes the BSNN models for the NHPAs at transmitters as well as the frequency-selective MIMO channel impulse response (CIR) matrix. Furthermore, the BSNN inverse models of the NHPAs are also estimated in closed-form. This allows the base station to implement nonlinear multiuser detection effectively using the space-time equalization (STE) based on the estimated frequencyselective MIMO CIR matrix and followed by compensating for the nonlinear distortion of the transmitters’ NHPAs based on the estimated BSNN inverse models. Simulation results are utilized to demonstrate the superior bit error rate performance of our nonlinear STE approach for single-carrier highthroughput multiuser nonlinear frequency-selective MIMO uplink.

A Survey on Robust Modulation Requirements for the Next Generation Personal Satellite Communications

The unrelenting technological advancement in the generation of wireless networks in recent years has awakened the motion concerning the inclusion of satellites in personal communications. Leveraging their ability to provide wide coverage, uniform services, wide bandwidth, and so forth, Satellite systems will be expected to co-exist with the current state-of-the-art infrastructure of terrestrial networks. Herein, we present a comparative study on the representative digital modulation techniques for use in personal satellite communications. We discuss the advantages and limitations of different modulation techniques, such as phase shift keying, continuous phase modulation, amplitude phase shift keying, and quadrature amplitude modulation. We also perform evaluations based on spectral efficiency, power efficiency, modulation error ratio, error vector magnitude, and peak-to-average power ratio in the presence of high power amplifier nonlinearities and Doppler effects. Comparisons in the form of tables, illustrations, and curves are also presented. In correspondence to the comparisons made basing on the aforementioned metrics, we conclude that continuous phase modulation is the best candidate modulation scheme for personal satellite communications since it outperforms other schemes by compromising the trade-off between power efficiency, bandwidth efficiency, and immunity to errors. We further present open issues that would reinforce personal satellite communications in terms of reliability, throughput and latency, other than power and spectral efficiency, if combined with appropriate modulation schemes.

Impact of HPA nonlinearity on the performance of power domain OFDM-NOMA system

Non-orthogonal multiple access (NOMA) is expected to be used in beyond fifth-generation (B5G) and sixth-generation (6G) mobile networks to support ultra-massive connectivity. Since the two preceding mobile networks generations used orthogonal frequency division multiplexing (OFDM), NOMA is expected to be combined with OFDM. Unfortunately, the OFDM signal suffers from a high peak to average power ratio (PAPR) that limits its performance as it passes through the nonlinear high power amplifier (HPA). In literature, few works have studied the effect of nonlinear distortion on OFDM-NOMA. Furthermore, the HPA models used in previous works to describe the impact of nonlinear distortion on OFDM-NOMA in downlink (DL) were impractical or inaccurate. In contrast, this work uses the well-known soft limiter (SL) model with input back-off (IBO) as a practical controlling parameter. Also, instead of investigating the effect of nonlinear distortion on OFDM-NOMA in DL only, this work investigated this effect in both DL and uplink (UL). In particular, during this work, the performance of the OFDM-NOMA system in the presence of nonlinear distortion in both UL and DL is investigated in terms of users’ achievable data rate, sum rate capacity, system fairness, and the bit error rate (BER) of each user. Results showed that, in DL, the NU is the most affected by the nonlinear distortion, while, in UL, the nonlinear distortion caused by the NU’s HPA is more severe than the nonlinear distortion caused by other users.

On the Joint Effects of HPA Nonlinearities and IQ Imbalance on Mixed RF/FSO Cooperative Systems

In this work, we provide a framework analysis of dual-hop hybrid Millimeter Wave Radio Frequency (RF)/Free Space Optical (FSO) MIMO relaying system. The source is equipped with multiple antennas and employs conjugate beamforming while the destination consists of multiple apertures with selection combining. The system also consists of a relay operating at amplify-and-forward mode. The RF channels are subject to Nakagami-m fading while the optical links experience the Málaga distribution. In addition, we introduce the impairments to the relay and receiver. In fact, the relay is impaired by the High Power Amplifier (HPA) nonlinearities while the receiver suffers from the In phase and Quadrature Imbalance. Moreover, we assume two types of HPA nonlinearities impairments called Soft Envelope Limiter (SEL) and Traveling Wave Tube Amplifier (TWTA). Closed-forms of the outage probability, the bit error probability, and the ergodic capacity are derived. Capitalizing on these performances, we derive the high SNR asymptotes to unpack insightful metrics such as the diversity gain. We also address the impacts of some key factors on the system performance such as the impairments, the interferers, the number of antennas and apertures and the pointing errors, etc. Finally, the analytical expressions are confirmed by Monte Carlo simulation.

Particle swarm optimization assisted B-spline neural network based predistorter design to enable transmit precoding for nonlinear MIMO downlink

For the multiple-input multiple-output (MIMO) downlink employing high-order quadrature amplitude modulation signaling and with nonlinear high power amplifiers (HPAs) at base station transmitter, the existing precoding designs relying on the linear MIMO channel can no longer work. We propose an efficient and accurate predistorter design to enable transmit precoding for nonlinear MIMO downlink. Specifically, we obtain the closed-form least squares estimates of the nonlinear HPA’s amplitude and phase response using two B-spline neural networks during training. The estimated HPA’s phase response automatically yields the estimate of the predistorter’s phase response. Based on the B-spline neural network estimate of the HPA’s amplitude response, we construct a B-spline neural network model for the predistorter amplitude response, and we adopt a particle swarm optimization (PSO) algorithm to solve this highly nonlinear optimization problem. Using our accurate predistorter estimate to pre-compensate for the nonlinear distortions of the transmit HPAs, a standard full-digital transmit precoding design can readily be adopted to combat the MIMO channel interference. A simulation study is conducted to demonstrate the effectiveness of our proposed PSO assisted predistorter design.

A novel discrete elephant herding optimization-based PTS scheme to reduce the PAPR of universal filtered multicarrier signal

The recently proposed waveform called universal filtered multicarrier (UFMC) has already managed to get the attention of science world due to its superior features and it has been accepted as one of the foremost fifth generation (5G) waveform contenders. However, due to being a type of multicarrier waveform, the UFMC suffers from the problem of high peak-to-average power ratio (PAPR). In this paper, a new discrete elephant herding optimization-based partial transmit sequence (DEHO-PTS) scheme is suggested to reduce the PAPR of UFMC signals to minimum levels. Due to the fact that the optimization of phase rotation factors multiplied by the sub-blocks in the conventional partial transmit sequence (PTS) technique is a combinatorial optimization problem to be solved in discrete space, in order to integrate the elephant herding optimization (EHO) algorithm into the PTS scheme, we developed its discrete version (DEHO) in this paper. In the simulations, the capability of the suggested DEHO-PTS procedure to minimize the PAPR, suppress the out-of-band emission and decrease the bit error rate of the UFMC signal amplified via a nonlinear high power amplifier was analyzed. Simulation results clearly indicate that our proposed DEHO-PTS procedure can be a serious option for UFMC waveform to minimize the PAPR values of transmission signals due to its significant PAPR reduction, side lobe suppression and bit error rate performances with low computational complexity.

A Committee Machine Neural Network for Dynamic and its Inverse Modeling of Distortions and Impairments in Wireless Transmitters

The tradeoff between bandwidth efficiency and power efficiency with nonlinear distortion introduced by high power amplifier (HPA) in a modern communication system, at a high bit rate has become a prominent problem. Digital predistortion (DPD), the most cost-effective and yet lesser complex method is a widely used linearization method. In this method, the dynamic nonlinear characteristics of the PA are used to obtain an inverse transfer function to abolish the nonlinearity. The development of a good DPD technique depends on its ability to model an accurate PA behavior and its inverse behavior. Recently, several neural network-based predistortion linearizers had been proposed, and these linearizers are effectively proving their worth, but these methods report inadequate generalization performance in the presence of system imperfections like DC offset, IQ imbalance, and both. The present paper proposes a Mixture of Experts (MOE) based committee machine neural network for modeling the PA/transmitter system transfer function and its inverse transfer function under different system conditions. MOE models encompass a family of modular neural network architectures having several experts network and a single gating network, and targeting to divide a complex problem into simple subtasks. An algorithm based on a maximum likelihood criterion is considered for the MOE network training. The results obtained with the proposed model show good generalization performance with nonlinear HPA and with memory effect in the presence of system imperfections.

A companding approach for PAPR suppression in OFDM based massive MIMO system

Abstract Orthogonal frequency division multiplexing (OFDM) based massive multiuser (MU) multiple input multiple output (MIMO) system is popularly known as high peak-to-average power ratio (PAPR) issue. The OFDM-based massive MIMO system exhibits large number of antennas at Base Station (BS) due to the use of large number of high-power amplifiers (HPA). High PAPR causes HPAs to work in a nonlinear region, and hardware cost of nonlinear HPAs are very high and also power inefficient. Hence, to tackle this problem, this manuscript suggests a novel scheme based on the joint MU precoding and PAPR minimization (PP) expressed as a convex optimization problem solved by steepest gradient descent (GD) with μ-law companding approach. Therefore, we develop a new scheme mentioned to as MU-PP-GDs with μ-law companding to minimize PAPR by compressing and enlarging of massive MIMO OFDM signals simultaneously. At CCDF = 10−3, the proposed scheme (MU-PP-GDs with μ-law companding for Iterations = 100) minimizes the PAPR to 3.70 dB which is better than that of MU-PP-GDs, (iteration = 100) as shown in simulation results.

Advanced SLM scheme based on discrete forest optimization algorithm for PAPR minimization in UFMC waveform

Inherent multicarrier transmission mechanism of the universal filtered multicarrier (UFMC) waveform engenders the problem of high peak-to-average power ratio (PAPR). Since it is impossible for a nonlinear high power amplifier (HPA) to execute a distortionless amplification unless the PAPR of transmission signal is below an acceptable level, eliminating the aforementioned PAPR drawback in UFMC waveform is so critical for smooth communication. With this in mind, we developed a new selective mapping (SLM) scheme based on discrete forest optimization algorithm (DFOA) for the UFMC waveform. The related scheme was created by embedding the DFOA into the conventional SLM with the intention of optimizing the values of phase factors by which the phase rotation process is carried out in frequency domain to reduce the PAPR of eventual time domain signal attained from the SLM output. It is confirmed via the simulations that, remarkable PAPR improvements are achieved through the DFOA-SLM scheme in the UFMC signal thanks to the DFOA-supported search for the optimal sequence of phase factors instead of classical random search strategy inherent in the conventional SLM method.

Bit Error Rate Analysis of NOMA-OFDM in 5G Systems With Non-Linear HPA With Memory

The orthogonal frequency division multiplexing (OFDM) and the non-orthogonal multiple access (NOMA) scheme are presented as promising techniques to meet the requirement of fifth-generation (5G) communication systems. Although much attention has recently been devoted to study these techniques, some scenarios have still been less explored. Considering that a fundamental part of any communication system is the use of power amplifiers, this paper presents an analytical evaluation of the bit error rate (BER) of NOMA-OFDM systems in the presence of a high power amplifier (HPA) with memory. Considering that the non-linear distortions generated by the HPA can be modeled using a polynomial model with memory, new theoretical expressions are developed to obtain the BER of the system. Specifically, exact BER expressions for a downlink NOMA-OFDM system with two users are presented and verified by Monte Carlo simulation results. The obtained numerical results demonstrate that the performance degradation of both users is highly dependent on the non-linear distortions, even when the successive interference cancellation (SIC) technique is performed perfectly.