Nonlinear Power Amplifier Research Articles

Gibbs-Phenomenon-Reduced Digital PWM for Power Amplifiers Using Pulse Modulation

The pulse-modulated polar transmitter (PMPT) uses radio-frequency (RF) phase modulated signal with pulse-width modulated envelope to drive a power amplifier (PA) as a switch to achieve high linearity and high efficiency. However, as the signal bandwidth increases, various non-idealities limit the performance of the PMPT architecture. In this paper, a Gibbs-phenomenon reduction filter is proposed with a partial Fourier series of digital pulse-width modulation (PWM) such that the pulsed signal is more immune to the distortion in nonlinear high-efficiency RF PAs. For validation, a prototype transmitter was tested with a 20-MHz bandwidth 256-QAM 5G new radio (NR) signal at 2.14 GHz. The proposed method achieved a drain efficiency of 28.3%, error vector magnitude (EVM) of 1.67%, and adjacent channel leakage ratio (ACLR) of -45.4 dBc at an output power of 18 dBm using the prototype transmitter. Linearity requirements for base stations were met without the use of any digital predistortion methods.

Linearization of power amplifiers with mismatched output impedance using on-line digital pre-distortion structure

This letter introduces a novel on-line digital pre-distortion structure for linearizing RF power amplifier under the output impedance mismatch conditions. Unlike traditional off-line structures, the proposed structure updates its weight parameters adaptively synchronizing with the power amplifier load impedance. Furthermore, this letter analyses with a MOSFET model and proves that the output conductance of MOSFET are relevant to nonlinearity of power amplifier with variable load impedance. To verify this structure and the analysis, a simulation on MATLAB Simulink was built using a N-channel MOSFET based on Shichman-Hodges model. Proposed on-line Digital Pre-Distortion structure significantly acquired better linearity performance with variable load impedance than conventional off-line structures.

An Orthogonal Polynomial-Based Analytical Expression of Nonlinear Power Amplifier for FBMC Systems

A filter bank multicarrier modulation (FBMC) is a strong promising solution for the fifth generation (5G) and beyond in broadband wireless communications. Nonetheless, one of the main disadvantages of the multicarrier techniques-based communication systems is the high peak-to-average power ratio (PAPR) of transmitting signals resulting in a nonlinear distortion of the signals, which is caused by a high power amplifier (HPA). Many kinds of research related to the nonlinear distortions induced by HPA have been proposed. However, there are solely limited studies on the analytical derivation of the nonlinear HPA characteristic. In this paper, an orthogonal polynomial based-analytical expression of a nonlinear power amplifier for baseband uniform, exponential, and Rayleigh input distribution of FBMC systems is proposed. The probability of error performances (BER) comparison between the proposed orthogonal polynomial method and the conventional polynomial method is determined. In addition, a theoretical performance analysis of the proposed method is derived to evaluate the BER performances in the frequency-selective Rayleigh fading channel. In the simulation, the BER performance of a nonlinearly amplified FBMC systems is investigated at a different IBO. The simulation results indicate that the proposed orthogonal polynomial method significantly outperforms the conventional polynomial method in terms of a normalized mean squared error (NMSE) and BER performance. Moreover, the theoretical error probability is compared with the simulation results and it could be found that the theoretical BER performance is relatively close to the simulated result.

Low-Complexity Equalisers for Offset Constellations in Massive MIMO Schemes

Massive multi-input-multi-output (m-MIMO) schemes require low-complexity implementations at both the transmitter and the receiver side, especially for systems operation at millimeter wave (mmWave) bands. In this paper, we consider the use of offset constellations in m-MIMO systems operating at mmWave frequencies. These signals are designed to have either an almost constant envelope or be decomposed as the sum of constant-envelope signals, making them compatible with strongly nonlinear power amplifiers, which can have low-implementation complexity and high amplification efficient, making them particularly interesting for mmWave communications. We design and evaluate low-complexity frequency-domain receivers for offset signals. It is shown that the proposed receivers can have excellent performance/complexity trade-offs in m-MIMO scenarios, making them particularly interesting for future wireless systems operating at mmWave bands.

Nonlinear Three-Port Representation of PAs for Embedded Self-Calibration of Envelope-Dependent Dynamic Biasing Implementations

This paper proposes a three-port power amplifier (PA) representation based on distinct sets of nonlinear complex polynomials that describe a combiner, a nonlinear baseband-to-RF converter and a nonlinear RF amplifying function, for processing the PA's input modulated signal and any envelope-dependent dynamic biasing signal. This novel representation of PA nonlinearities simplifies computation and renders possible analytical formulations to describe a 3-port PA system. It allows accurate prediction of the PA's output distortion components as a function of an input multi-tone excitation and a multi-tone dynamic biasing signal. The representation is intended for a context proposed, to the best of the authors' knowledge for the first time, and envisioned as promising for future mobile communication equipment - the automatic optimization of linearity performance in Radio Frequency Integrated Circuit (RFIC) PAs under any modulated excitation and employing envelope-dependent biasing, through implementation of embedded self-calibration within the transmitter front-ends. In this context, the representation introduced here compares favorably in terms of accuracy with respect to Volterra-based approaches and allows a simpler characterization, while the literature often points to the complexity inherent to Volterra-based approaches. The proposed representation allows the optimization of the PA's dynamic biasing for linearity improvement from one mobile unit to another through embedded self-calibration starting from quasi-static measurements alone of the PA's input/output power. Its applicability is highlighted through benchmarking against experimental results demonstrating accurate PA characterization for multiple PA platforms under different dynamic biasing techniques. In one implementation using an industry-designed GaAs PA, it accurately predicts the dynamic biasing adjustments to achieve more than 4dB reduction in the output intermodulation distortion (IMD3). In another implementation using the recently introduced positive envelope feedback linearization scheme, the proposed representation allows, for the first time, analytically predicting the condition of closed-loop stability and the requirements for the feedback components with experimental verification.

Energy-Reliability Aware Link Optimization for Battery-Powered IoT Devices With Nonideal Power Amplifiers

In this paper, we study cross-layer optimization of low-power wireless links for reliability-aware applications while considering both the constraints and the nonideal characteristics of the hardware in Internet-of-Things (IoT) devices. Specifically, we define an energy consumption (EC) model that captures the energy cost—of transceiver circuitry, power amplifier (PA), packet error statistics, packet overhead, etc.—in delivering a useful data bit. We derive the EC models for an ideal and two realistic nonlinear PA models. To incorporate packet error statistics, we develop a simple, in the form of elementary functions, and accurate closed-form packet error rate approximation in Rayleigh block-fading. Using the EC models, we derive energy-optimal yet reliability and hardware compliant conditions for limiting unconstrained optimal signal-to-noise ratio (SNR), and payload size. Together with these conditions, we develop a semi-analytic algorithm for resource-constrained IoT devices to jointly optimize parameters on physical (modulation size, SNR) and medium access control (payload size and the number of retransmissions) layers in relation to link distance. Our results show that despite reliability constraints, the common notion—higher-order ${M}$ -ary modulations are energy optimal for short-range communication—prevails, and can provide up to 180% lifetime extension as compared to often used OQPSK modulation in IoT devices. However, the reliability constraints reduce both their range and the energy efficiency, while nonideal traditional PA reduces the range further by 50% and diminishes the energy gains unless a better PA is used.

Energy and Spectrally Efficient Modulation Scheme for IoT Applications.

Due to the Internet of Things (IoT) requirements for a high-density network with low-cost and low-power physical (PHY) layer design, the low-power budget transceiver systems have drawn momentous attention lately owing to their superior performance enhancement in both energy efficiency and hardware complexity reduction. As the power budget of the classical transceivers is envisioned by using inefficient linear power amplifiers (PAs) at the transmitter (TX) side and by applying high-resolution analog to digital converters (ADCs) at the receiver (RX) side, the transceiver architectures with low-cost PHY layer design (i.e., nonlinear PA at the TX and one-bit ADC at the RX) are mandated to cope with the vast IoT applications. Therefore, in this paper, we propose the orthogonal shaping pulses minimum shift keying (OSP-MSK) as a multiple-input multiple-output (MIMO) modulation/demodulation scheme in order to design the low-cost transceiver architectures associated with the IoT devices. The OSP-MSK fulfills a low-power budget by using constant envelope modulation (CEM) techniques at the TX side, and by applying a low-resolution one-bit ADC at the RX side. Furthermore, the OSP-MSK provides a higher spectral efficiency compared to the recently introduced MIMO-CEM with the one-bit ADC. In this context, the orthogonality between the in-phase and quadrature-phase components of the OSP are exploited to increase the number of transmitted bits per symbol (bps) without the need for extra bandwidth. The performance of the proposed scheme is investigated analytically and via Monte Carlo simulations. For the mathematical analysis, we derive closed-form expressions for assessing the average bit error rate (ABER) performance of the OSP-MSK modulation in conjunction with Rayleigh and Nakagami-m fading channels. Moreover, a closed-form expression for evaluating the power spectral density (PSD) of the proposed scheme is obtained as well. The simulation results corroborate the potency of the conducted analysis by revealing a high consistency with the obtained analytical formulas.

Minimization of PAPR for DFT-Spread OFDM With BPSK Symbols

In this paper, the problem of reducing the peak-to-average power ratio (PAPR) of a discrete Fourier transform spread orthogonal frequency-division multiplexing signal is considered for the transmission of BPSK symbols. In particular, a joint optimization of the constellation-rotation angle and the pulse-shaping vector is conducted with or without the allocation of additional sub-carriers. To avoid the exponential complexity required to evaluate the PAPR, a computationally efficient upper bound on the worst-case PAPR is derived and adopted as the objective function. Unlike conventional upper bounds, the proposed upper bound exploits the structure in the relative phase among symbol waveforms and incorporates the constellation-rotation effect. The signal-to-interference-plus-noise ratio (SINR) at the output of a constellation-derotating matched filter is also derived along with a generalized Nyquist criterion and adopted as the inequality constraint function. Then, joint optimizations are conducted through numerical search for various signal parameters and target SINRs. Surprisingly, the optimal rotation angle is neither 0 nor $\pi /2$ . It is shown that the proposed combinations significantly outperform the existing combinations of the rotation angle and the shaping vector when the signal is amplified by a nonlinear power amplifier.

New technique combining the Tone Reservation method with Clipping technique to reduce the Peak-to-Average Power Ratio

Nonlinear distortions and impairments appear in multicarrier signal with high fluctuations when amplified by a Radio Frequency Power Amplifier (RF PA). Clipping (CL) technique offers a simple way to reduce these fluctuations in Orthogonal Frequency Division Multiplexing (OFDM) Technique, but may degrade seriously the transmission quality. This is why the new mobile standards propose other methods, like the Tone Reservation (TR) technique in the Digital Video Broadcasting-Terrestrial (DVB-T), that reduce the Peak-to-Average Power Ratio (PAPR) without reaching optimal performances. This paper deals with how we can use the TR technique, which exploits null sub-carriers for generating corrective signal, in combining to CL technique in order to improve PAPR reduction without data loss. Also, we show some comparison results on the PAPR reduction obtained with proposed scheme and other techniques. Experiments using a simulated example on a complete WiMax 802.16e transmitter have been made in order to investigate the PAPR reduction performances on presence of the non-linear Power Amplifier model based on gain compression response and phase distortion.

Wide band digital predistortion using iterative feedback decomposition

This paper presents a new digital predistortion (DPD) technique for wide band applications. Digital predistortion is the most useful linearization technique to reduce power amplifier (PA) nonlinearity effects due to its high flexibility and low complexity. However, this technique requires high performances ADC to digitize the feedback signal whose bandwidth is equal to several times the original bandwidth due to spectral regrowth generated by the PA nonlinearity. This point represents one of the main bottlenecks for the deployment of the wideband LTE-A standard. The method proposed in this paper calculates the DPD coefficients iteratively using an ADC with a fixed bandwidth equal to the original bandwidth. The proposed method has been simulated and compared with other methods using Matlab. Simulation results show that the proposed method has almost the same performance as the other methods with an ACPR of − 60 dB. Moreover, it reduces considerably the constraints on the ADC and the power calculation resources.

Subnominal Operation of Class-E Nonlinear Shunt Capacitance Power Amplifier at Any Duty Ratio and Grading Coefficient

This paper presents an analytical model to design a class-E power amplifier under only zero-voltage-switching (ZVS) term with the MOSFET nonlinear drain–source shunt parasitic capacitance that is named as the subnominal operation. The presented analysis is performed under any grading coefficient m of MOSFET body junction diode and any duty ratio D . The grading coefficient m along with the switching duty ratio D are implemented as tuning variables to satisfy design specifications and ZVS term simultaneously. The restriction of selecting the value of m and D for the subnominal operation has a major effect on simultaneously satisfying of load-resistance, operating frequency, and junction capacitance, which is the main result from this study. The obtained laboratory experiment from the fabricated typical circuit under the required output power 6.2 W with the satisfied duty ratio D = 0.4 is used to show the validity of the theoretical predicted expressions.

Interleaving Technique Implementation to Reduce PAPR of OFDM Signal in Presence of Nonlinear Amplification with Memory Effects

In OFDM systems, peak-to-average power ratio (PAPR) reduction of the signal is one of the main challenges that need to be overcome in order to use the transmitter in an efficient manner. As one of attractive techniques, interleaving can be used in PAPR reduction for multicarrier signals without spectrum distortion. In this paper, the authors propose to extend the possibilities of interleaving to improve PAPR reduction, to use a new coding of interleaver keys at the transmitter and a robust decoding procedure at the receiver. In order not to degrade the data rate, the use of null subcarriers to transmit side information to the receiver is proposed and evaluated. Simulation results in the context of the WLAN 802.11a standard in the presence of a nonlinear power amplifier model with memory, show a reduction of PAPR of approximately 5.2 dB, and an improvement of bit error rate and error vector magnitude of about 2 decades and 4% respectively, while respecting the spectral mask specification.

Optimum power allocation in OFDM systems under power amplifier nonlinearity

In this paper, the optimum power allocation for subcarriers in orthogonal frequency division multiple system is derived which maximizes the total rate of system under nonlinearity of practical power amplifier. The rate of system by using analytical signal to interference ratio formula is optimized to derive optimal power scales for subcarriers. The problem is nonconvex and a comprehensive learning particle swarm optimization method is designed to solve the problem. The simulation results demonstrate that by considering nonlinearity in power allocation, better rate can be achieved compared to conventional power allocation methods.

Performance evaluation of different precoding matrices for PAPR reduction in OFDM systems

Orthogonal frequency division multiplexing (OFDM) is an attractive technique for wireless communication systems due to its ability to mitigate frequency selectivity. However, OFDM suffers from high peak‐to‐average power ratio (PAPR) problem, which reduces the power amplifier (PA) efficiency or worse it degrades bit error rate (BER) performance and increases out‐of‐band radiation. In literature, there are different PAPR reduction techniques. Among them PAPR reduction by precoding matrices has small computational complexity along with high PAPR reduction gain. In this paper the six precoding matrices found in the literature are compared. Results showed that, all precoding matrices, except the one that based on square‐root raised cosine function (SRC), are not effective in terms of BER performance in presence of nonlinear PA, especially in high modulation order schemes (eg, 16‐QAM and 64‐QAM). However, precoding technique based on SRC matrix requires high data rate loss, to enhance the BER performance in presence of nonlinear PA. So, it can be said that, precoding technique worsens the problem especially in high modulation order schemes, except the SRC matrix‐based precoding technique, which cannot be used without high data rate loss.

Impacts of Crest Factor Reduction and Digital Predistortion on Linearity and Power Efficiency of Power Amplifiers

The linearity and power efficiency are two main factors of power amplifiers (PA), which can hardly be improved together. Digital predistortion (DPD) compensates for nonlinearity and memory effects of PAs in high efficiency zone. However, for advanced communication standards the high peak-to-average power ratio of the modulated signal constrains the PA operating point and thus limits the power efficiency. Crest factor reduction (CFR) techniques are applied to address this problem though they degrade the PA linearity relatively. In this brief, we compare different CFR approaches with respect to their performances in terms of linearity, PA power efficiency, and computational complexity. Classical hard clipping, clip-and-filter as well as joint CFR/DPD methods are considered. To complete the comparison, we propose a modeled CFR identified using indirect learning architecture combined with DPD. The simulation results validate its effectiveness on the trade-off among linearity, PA power efficiency and CFR computational complexity.

Isolator-Less Near-Field RFID Reader for Sub-Cranial Powering/Data Link of Millimeter-Sized Implants

Implants for brain–machine interface (BMI) systems require both wireless powering and data communication to be practical for reliable long-term use. Sub-cranial radio-frequency identification (RFID) readers can receive backscattered data, while providing wireless power to operate the implant. This paper presents a novel reader architecture for an efficient near-field fully integrated RFID reader meant to deliver power to and receive data from BMI implants, where a modified Class-E/Fodd power amplifier (PA) with a current-sense resistor differentially drives a single segmented antenna and acts simultaneously as TX and RX. It operates at 309 MHz and has 54% efficiency. The non-linearity of the switching PA is able to demodulate the backscattered signal to baseband. And the data can be recovered from a current-sense resistor without the need for bulky RF isolators, separate RX/TX antennas, or different frequencies for data/power delivery. The reader, as tested with a proprietary RFID tag through pig-skin and cow-bone, can deliver a maximum of 790 $\mu \text{W}$ to an implant through the skull while consuming 39.4 mW of power. It has a 2-Mb/s data rate with a bit error rate of less than 1e–6.

5G: performance and evaluation of FS‐FBMC against OFDM for high data rate applications at 60 GHz

This study presents a frequency spreading filter bank multi-carrier (FS-FBMC) waveform as a potential candidate for the fifth generation (5G) network applications at millimetre-waves (mmWaves). The proposed model is developed based on the orthogonal frequency division multiplexing (OFDM) waveform standardised by IEEE 802.15.3c for 60 GHz high data-rate applications. The effects of non-linearities of power amplifiers (PAs) at 60 GHz for both OFDM and FS-FBMC are presented and compared using a realistic PA model. In particular, the sensitivity of both transmission schemes to the non-linear effects is investigated and its impact on the performance degradation in terms of output-power-backoff, is characterised over typical indoor line-of-sight, kiosk and residential, 60 GHz IEEE channel models. The assessment metrics considered are bit error rate and out-of-band emissions. This study concludes radio access schemes for future communication generations, i.e. 5G may employ OFDM for up-link and FS-FBMC for down-link due to the sensitivity to PA non-linearities of both waveforms.

Waveform comparison and PA nonlinearity effects on CP‐OFDM and 5G FBMC wireless systems

AbstractIn this article, a waveform comparison and power amplifier nonlinearity effects on cyclic prefix orthogonal frequency‐division multiplexing (CP‐OFDM) and 5G filter bank multicarrier (FBMC) wireless systems are presented. The 5 MHz CP‐OFDM and 5G FBMC signals are used in Matlab simulations, while 1.4 and 3 MHz of both signals are used in experiment. It is noted that 1.4 and 3 MHz CP‐OFDM signals have larger side‐lobes in comparison with 5G FBMC signals. The 5G FBMC signals have stepper slope at the edges and very low out‐of‐band leakage.

Orthogonal Scalar Feedback Digital Pre-Distortion Linearization

Digital pre-distortion (DPD) systems are employed to reduce intermodulation at the output of intrinsic non-linear RF power amplifiers. Typical DPD algorithms use time-domain linear regression to calculate the model coefficients used to compensate the amplifier’s distortion. This solution has high complexity and limited performance. This paper presents an innovative DPD system where the feedback information is a scalar measurement taken from the feedback signal. Different feedback information can be obtained from the distorted signal, e.g., the adjacent channel leakage rejection or the spectral mask margin. The DPD model coefficients estimation becomes a generic numerical optimization problem and is conducted iteratively in a coefficient-by-coefficient basis. A new coefficient orthogonalization algorithm removes the interaction between orders, resulting in a faster convergence time and lower output power variation across the iterations. The numerical optimization problem is simplified, since the nonlinear model becomes orthogonal in the intermodulation domain, i.e., the adjustment of given coefficient does not affect the others. Simulations and experimental results show that the proposed algorithm can effectively and efficiently compensate the nonlinear distortion and reduce the spectral regrowth.

Compensation of the Nonlinear Power Amplifier by Using SCPWL Predistorter with Genetic Algorithm in OFDM technique

The High Power Amplifiers (HPAs), which are used in wireless communication, are distinctly characterized by nonlinear properties. The linearity of the HPA can be accomplished by retreating an HPA to put it in a linear region on account of power performance loss. Meanwhile the Orthogonal Frequency Division Multiplex signal is very rough. Therefore, it will be required a large undo to the linear action area that leads to a vital loss in power efficiency. Thereby, back-off is not a positive solution. A Simplicial Canonical Piecewise-Linear (SCPWL) model based digital predistorters are widely employed to compensating the nonlinear distortion that introduced by a HPA component in OFDM technology. In this paper, the genetic algorithm has been used to optimized the SCPWL coefficients by using Matlab 2015b, and then the Bit Error Rate (BER) performance has been evaluated for OFDM signal with 16-QAM and 64-QAM modulations in three cases, with nonlinear effects, without nonlinear effects (ideal case), with SCPWL and with nonlinear effects (compensated case)). The simulation results showed that the predistorter that adjusted by the genetic algorithm accomplishes huge execution change by successfully compensating the nonlinearity and reducing the input and output back-off (IBO, OBO) of the HPA.