Single Carrier Modulation Research Articles

60 GHz RF module with beam-steering optimization algorithm for high data rate access and backhaul communications

This paper presents an 802.11ad-based radio frequency module for high data rate fixed wireless access and backhaul communications. The transceiver chip is manufactured in SiGe BiCMOS technology covering 57–71 GHz, providing 16 RX and 16 TX paths with combined output power of more than 20 dBm. The chip is packaged using embedded wafer-level BGA technology of the size 12.6times 12.6times 0.8~{text{ mm }}^3 and employs advanced dielectric materials with 2 metallic redistribution layers. The package integrates the transceiver chip with RX and TX high gain PCB antenna arrays, allowing effective isotropic radiated power (EIRP) of more than 40 dBm. Beam steering is achieved in ± 50^{circ } by the transceiver through providing appropriate weights to the antenna arrays. The paper presents generation of beamforming lookup table along with optimization of the power distribution to the array. This optimization results in flattening of the EIRP over the whole beam-steering range and frequency bandwidth. The module allows for data rates up to 10 Gbps by employing full-channel 128 QAM and half-channel 256 QAM single-carrier modulation.

Photonic Sub-Terahertz IM Links: Comparison Between Double and Single Carrier Modulation

Two different modulation schemes have been employed in photonic sub-THz systems to transmit intensity modulated signals: the dual-carrier (D-C) and single-carrier (S-C) schemes. Although it has been stated in the literature that D-C modulation performs better than S-C modulation, no demonstration of such claim has been provided so far. In this letter, we show that the superiority of one scheme or the other depends on the normalization factor that is used for comparison. Through mathematical analysis we show that, when 2-pulse amplitude modulation (2-PAM) signals are considered and the average photocurrent is taken as the normalization factor, the D-C scheme exhibits a 3-dB gain over the S-C scheme in the peak voltage of the recovered signal. However, the analysis also reveals that equal performance should be obtained when these schemes are compared in terms of transmitted sub-THz energy and that the S-C scheme should achieve better results when the comparison is made in terms of the output power of the lasers. We also run simulations to examine the impact of the non-linear transfer curve of a Mach-Zehnder modulator (MZM) on higher-order IM formats such as 4- and 8-PAM. The results of these simulations show that the penalty of the S-C scheme under photocurrent normalization progressively vanishes as the modulation order increases, and for 8-PAM signals, the S-C achieve better results than the D-C scheme. We attribute the deterioration of the D-C scheme with higher modulation orders to the signal-signal beat interference (SSBI).

HW/SW Platform for Measurement and Evaluation of Ultrasonic Underwater Communications.

The purpose of this work is to present a flexible system that supports the study of wideband underwater acoustic communications (UAC). It has been developed both to measure channels and to test transmission techniques under realistic conditions in the ultrasonic band. This platform consists of a hardware (HW) part that includes multiple hydrophones, projectors, analog front-ends, acquisition boards, and computers, and a software (SW) part for the generation, reception, and management of acoustic sounding signals and noise. UAC channels are among the most hostile ones and exhibit an important attenuation and distortion, essentially due to both multipath propagation, which results in a very long channel impulse response, and time-varying behavior, which produces a notable Doppler spread. To cope with this challenging medium, sophisticated transmission techniques must be employed. In this sense, adequate signal processing algorithms have been designed aiming not only at the analysis and characterization of underwater communication channels but also at the evaluation of diverse modulation, detection, and coding schemes, from Orthogonal Frequency Division Multiplexing (OFDM) to single-carrier digital modulations with a single-input multiple-output (SIMO) configuration that takes advantage of diversity techniques. Wideband sounding signals, to be injected into the sea from the transmitter side, are created with patterns that allow multiple tests on a batch. With offline processing of the captured data at the receiver side, different trials can be carried out in a very flexible manner. The different aspects of the platform are described in detail: the HW equipment used, the SW interface to control acquisition boards, and the signal processing algorithms to estimate the UAC channel response. The platform allows the analysis and design of new proposals for underwater communications systems that improve the performance of the current ones.

Eigendecomposition-Precoded Faster-Than-Nyquist Signaling With Index Modulation

In this paper, we propose a precoded faster-than-Nyquist (FTN) signaling technique for time-domain single-carrier index-modulated symbol transmission. More precisely, eigenvalue decomposition (EVD) precoding is adopted for the FTN transmission of data bits modulated by single-carrier time-domain index modulation (IM). While the FTN scheme increases the spectral efficiency and data rate by increasing the density of transmit symbols, the time-domain IM works towards the same objective while maintaining symbol sparsity. We analytically derive the constrained capacity of the proposed system. Our simulation results show that the proposed scheme has better bit error ratio (BER) performance than the conventional FTN-IM scheme, particularly for the scenario of a higher packing ratio. With the proposed scheme, a 2.5 dB performance gain is observed at the BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−4</sup> , where the packing ratio is 0.7 and the roll-off factor is 0.5 in the channel-uncoded scenario. We further analyze our scheme’s performance by characterizing its minimum Euclidean distance and inter-symbol interference. Furthermore, we present a three-stage serially concatenated iterative detection architecture for the proposed EVD-FTN-IM signaling scheme. It is demonstrated in our simulations that a near-capacity BER performance is achievable in the proposed turbo-coded FTN-IM scheme.

Adaptive Single Carrier Modulation scheme based MLI supported TDVC for Voltage Quality enhancement

Abstract In this article, An Adaptive Single Carrier Modulation (ASCM) scheme based Multilevel Inverter (MLI) is proposed for the Transformerless Dynamic Voltage Compensator (ASCM-MLITDVC) to enhance the load Voltage Quality (VQ). The enhancement of VQ includes voltage sag, swell, unbalance and reducing Total Harmonic Distortion (THD). The Pulse Generation Unit (PGU) require more Carrier Waves (CW) for higher levels of MLI with respect to the number of switches used. This made the PGU complex, hence a carrier wave modulation scheme is proposed which can use it for n number of levels. The Position of CW is altered automatically with respect to the amplitude of Reference Staircase Waveform (RSW). The RSW is created by utilizing the Half Height Method and optimized NLM scheme which makes the least possible output THD is achieved. This scheme is implemented utilizing a real-time simulator OP4500. The results are obtained by conducting Power Hardware in Loop (P-HIL) test method to prove ASCM-MLITDVC can enhance load VQ with reduced THD.

Deep Learning-Enabled Inverse Design of 30–94 GHz Psat,3dB SiGe PA Supporting Concurrent Multiband Operation at Multi-Gb/s

Deep learning and artificial intelligence, in general, is advancing scientific discovery and technological inventions through its ability to extract inherently hidden features and map it to output in a highly complex multi-dimensional space. Synthesis of electromagnetic (EM) structures with nearly arbitrary with desired functional properties is such an example of a high dimensional optimization space. In this article, we employ deep convolutional neural network (CNN) to allow robust and rapid prediction of scattering properties of nearly arbitrary planar electromagnetic structures on chip. Utilizing this, the work reports an mm-wave PA in 90-nm SiGe with a novel deep learning-enabled inverse design of low-loss, broadband output matching network that achieves a PAE of 16%–24.7%, a saturation power of 16.7–19.5 dBm across P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sat, 3 dB</sub> bandwidth of 30–94 GHz (103.2%), while supporting both single-carrier high-speed modulation and concurrent multiband multi-Gb/s non-constant amplitude modulation. The P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sat, 3 dB</sub> bandwidth covers from 5G band up to W-band and is higher than all reported mm-wave silicon PAs which have peak PAE > 20% and demonstrates for the first time concurrent multiband (triple-band) transmission with superior performance at multi-Gb/s.

Frequency Domain Detection and Precoding for Massive MIMO With Single Carrier Modulation

Single carrier modulation (SCM) schemes are attractive for uplink (UL) transmissions due to improved power efficiency at the user equipment (UE) transmitter compared with multi-carrier modulation schemes. In a massive MIMO scenario with SCM, the UL detection must mitigate the effects of inter-symbol interference and multi-user interference. This processing is effectively performed in the frequency domain (FD) using a minimum mean squared error (MMSE) detector when the transmission is framed with a cyclic prefix. This paper analyzes an MMSE-based detector compatible with distributed processing in a time-division duplex (TDD) system. The matrix inverses computed for the UL detection are then reused to perform multi-user precoding for the downlink (DL). We find that this scheme yields tremendous savings in computational complexity compared to commonly used zero-forcing (ZF) precoding without sacrificing any performance. Since MMSE processing introduces a bias to the estimates, we derive the scalar coefficients necessary to cancel the MMSE bias. The impact of channel estimation errors is analyzed for both the UL and DL cases in conjunction with a power-efficient approach to SCM channel estimation. Moreover, extensive simulations are performed to confirm our theoretical findings.

Channel Characterization and SC-FDM Modulation for PLC in High-Voltage Power Lines

Digital communication over power lines is an active field of research and most studies in this field focus on low-voltage (LV) and medium-voltage (MV) power systems. Nevertheless, as power companies are starting to provide communication services and as smart-grid technologies are being incorporated into power networks, high-voltage (HV) power-line communication has become attractive. The main constraint of conventional HV power-line carrier (PLC) systems is their unfeasibility for being migrated to wideband channels, even with a high signal-to-noise ratio (SNR). In this scenario, none of the current linear/non-linear equalizers used in single carrier schemes achieve the complete compensation of the highly dispersive conditions, which limits their operation to 4 kHz channels. In this paper, a new PLC-channel model is introduced for transmission lines incorporating the effects of the coupling equipment. In addition, the use of the single-carrier frequency-division modulation (SC-FDM) is proposed as a solution to operate PLC systems in a wide bandwidth, achieving transmission speeds above those of the conventional PLC system. The results presented in this paper demonstrate the superior performance of the SC-FDM-PLC over conventional PLC systems, obtaining a higher transmission capacity in 10 to 30 times.

Design of a Robust Orthogonal Frequency Division Multiplexing (OFDM) Transceiver for a Cognitive Radio Testbed

Primarily, a Cognitive Radio (CR) resolves the problem of spectrum scarcity and underutilization. However, it should also attain a good throughput and Quality of Service (QoS) as its objectives. These requirements are solely dependent on the modulation used. Though single carrier modulations such as Gaussian Minimum Shift Keying (GMSK) are highly spectral efficient, they are not robust to frequency selective fading. An implementation of multicarrier modulation supports high spectral efficiency and resistance to multipath fading. Therefore, in this paper, there is a comprehensive how-to-guide of the design of Orthogonal Frequency Division Multiplexing (OFDM) in cognitive radio using GNU Radio (GR) 3.8 that interfaces with Universal Software Radio Peripheral (USRP) B210s for video transmission. The implementation achieved allows for the choice of any modulation schemes out of four commonly used ones for communication of the payloads thus offering dynamism for use in a cognitive radio system. The effective implementation of the proposed methods in this paper is verified by the successful transmission and reception of a 4 minute 37 seconds MP4 video across the different choices of modulation schemes. It was observed that the error performance of the payloads degraded with higher constellation points however, the throughput was increased. Hence, the trade-off between error probability and throughput in the cognitive radio is based on the radio-scene metrics about the signal-to-noise ratio (SNR) of the available channels.

Orthogonal Time Sequency Multiplexing Modulation: Analysis and Low-Complexity Receiver Design

This paper proposes orthogonal time sequency multiplexing (OTSM), a novel single carrier modulation scheme that places information symbols in the delay-sequency domain followed by a cascade of time-division multiplexing (TDM) and Walsh-Hadamard sequence multiplexing. Thanks to the Walsh Hadamard transform (WHT), the modulation and demodulation do not require complex domain multiplications. For the proposed OTSM, we first derive the input-output relation in the delay-sequency domain and present a low complexity detection method taking advantage of zero-padding. We demonstrate via simulations that OTSM offers high performance gains over orthogonal frequency division multiplexing (OFDM) and similar performance to orthogonal time frequency space (OTFS), but at lower complexity owing to WHT. Then we propose a low complexity time-domain channel estimation method. Finally, we show how to include an outer error control code and a turbo decoder to improve error performance of the coded system.

Time-domain dual component computation diversity based on generalized hybrid carrier

In this paper, the concept of computation diversity is proposed by employing generalized hybrid carrier (GHC) system. The signal is backed up by transform-domain computation to enhance the anti-fading capability. Theoretical analysis is presented to demonstrate the superiority of the proposed method. Numerical simulations in doubly-selective fading channels are provided to verify the results. The bit error rate (BER) performance is guaranteed with a small computational complexity increment. The proposed method not only extends the new diversity dimension, but also improves the diversity gain of the system without occupying additional wireless resources. Moreover, the proposed method shows good adaptability with single carrier modulation and improves diversity performance. As the simulation results shown, time-domain dual component computation diversity (TDC-CD) has 1dB BER gain and 0.1 diversity gain at high signal-to-noise ratio, and single carrier system with TDC-CD achieves 2dB BER gain at 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−4</sup> .

Joint Carrier-Phase Estimation for Digital Subcarrier Multiplexing Systems With Symbol-Rate Optimization

Digital subcarrier multiplexing (SCM) has recently emerged as a promising solution for next-generation ultra-high-baudrate coherent optical communication systems. Among its distinctive advantages over traditional single-carrier modulation, SCM enables the exploitation of symbol-rate optimization (SRO), which has been shown to enable the passive mitigation of the nonlinear interference noise (NLIN) that is generated during propagation over dispersion-unmanaged optical fiber systems. However, the full exploitation of SRO-based NLIN mitigation is severely hindered by the uncompensated distortion caused by laser phase noise (LPN) and non-linear phase noise (NLPN), whose impact is magnified by the use of low-baudrate subcarriers. Resorting to low-complexity carrier phase estimation (CPE) algorithms, in this paper we experimentally demonstrate that it is possible to overcome the hurdles posed by LPN and NLPN in SCM systems, provided that adequate joint-subcarrier CPE processing is employed. A dual-stage joint-processing approach composed of a pilot-based CPE optionally followed by a blind phase search (BPS)-based estimator is implemented and experimentally assessed, enabling to effectively optimize the symbol-rate per subcarrier down to 3 GBaud, in accordance with the theoretical SRO predictions for the system under test. In addition, we demonstrate that signal-to-noise ratio (SNR) gains of more than 1 dB can be achieved through joint-subcarrier CPE processing in shorter-reach links, while this gain tends to progressively reduce with increasing propagation distance, down to about 0.5 dB gain after 3000 km propagation.

Влияние нестационарных помех в анализе информационных моделей с модуляцией с одной и несколькими несущими

The aim of the study is to try to analyze the most common mechanisms of impulse noise impact on data transmitted in the symbols of single-carrier and multi-carrier modulation systems. The paper solves the problem of a qualitative analysis of the destructive effect of impulse noise on the possibility of restoring symbols of digital modulation systems operating on the basis of a copper cable infrastructure. The performed analysis uses induction as research methods, which allows extending isolated special cases of symbol distortion to the generalized procedures for degrading the transmitted information quality; an analogy involving the consideration of similar mechanisms for modifying data in a stream of modulated signals with one carrier and multiple ones. The novelty of the findings obtained consists in generalizing the process of decoding errors due to noise bursts to the systems with one carrier and several ones, as well as in differentiating the influence of the noise pulse duration and power on the transmitted symbols. As the main findings of the work, we can note the identification of the impact ambiguity of impulse noise on the transmission systems of digital subscriber lines, expressed in the necessity to take into account while analyzing both the parameters of the noise itself and the type of modulation, and the energy and time relationships between the useful signal and noise. Thus, the work shows that the destructiveness degree of the impulse noise impact on the transmission system of a digital subscriber line is determined by several characteristics that should be taken into account when developing mechanisms for the protection against interference, or, conversely, to justify the inappropriateness of their use.

A Janus compatible software-defined underwater acoustic multiple-input multiple-output modem

This article describes the implementation of a multiple-input multiple-output acoustic communication link in shallow water conditions to enable a software-defined acoustic modem with a maximum transmission rate of 20 kbps in a 5-kHz bandwidth. The reliability improvement of a low-complexity Alamouti space–time block code is evaluated to improve the diversity in a high-rate transmission mode using single carrier modulation, as well as in a low-rate transmission mode relying on continuous-phase frequency-shift keying. Using measurements in realistic subsea conditions, the effect of the spatial channel correlation is demonstrated. It is found that for the space–time block code/continuous-phase frequency-shift keying, the spatial diversity is significantly degraded due to the high spatial correlation. In contrast, for the high-mode transmission rate, space–time block code with single carrier modulation offers a bit error rate improvement by a factor over hundred, in comparison to a single transmit element, demonstrating that the multiple-input multiple-output optimal code depends on the software-defined acoustic modem transmission mode.

Power Line Communications for Automotive High Voltage Battery Systems: Channel Modeling and Coexistence Study with Battery Monitoring

As electric vehicles are gaining increasing worldwide interest, advances in driving range and safety become critical. Modern automotive battery management systems (BMS) compete with challenging performance and safety requirements and need to monitor a large amount of battery parameters. In this paper, we propose power line communications (PLC) for high voltage (HV) traction batteries to reduce the BMS wiring effort. By modeling a small-scale battery pack for frequencies up to 300 MHz, we predict the PLC channel transfer characteristics and validate the results using a PLC hardware demonstrator employing a narrowband single-carrier modulation. The results demonstrate that battery PLC is a demanding task due to low access impedances and cell coupling effects, yet transfer characteristics can be improved by optimal impedance matching. PLC for HV BMS not only saves weight and cost, but also improves flexibility in BMS design. PLC enables single-cell monitoring techniques such as online electrochemical impedance spectroscopy (EIS) without additional wiring. Online EIS can be used for in-situ state and temperature estimation saving extra sensors. This work unveils possible coexistence issues between PLC and battery monitoring. In particular, we demonstrate that certain PLC data or packet rates have to be avoided not to interfere with EIS measurements.

Quad-Mode VCSEL Optical Carrier for Long-Reach Ka-Band Millimeter-Wave Over Fiber Link

A quad-mode optical carrier generated by mode-deviated injection-locking a vertical-cavity surface-emitting laser (VCSEL) at a beating frequency of 40 GHz is demonstrated for establishing a long-reach millimeter-wave over fiber (MMWoF) link, in which only one mode of the quad-mode optical carriers is modulated by the 16-quadrature amplitude modulation (16-QAM) orthogonal frequency division multiplexing (OFDM) data stream to achieve an optical single-carrier modulation (OSCM). Such an OSCM operation reduces the long-reach single-mode-fiber (SMF) transmission induced RF power fading effect to significantly suppress the frequency notch in the modulated spectrum of the delivered QAM-OFDM data after remotely heterodyne detection. With destructively interfered beating the quad-mode optical carrier at the remote node, the peak power of the optically heterodyned MMW central carrier can be attenuated by 38.3 dB, which saves the gain of the photodetector and electrical amplifier to efficiently boost the carried QAM-OFDM data. This architecture ensures sufficient power of the 16-QAM OFDM data after optoelectrical conversion and facilitates the quad-mode optical carrier based MMWoF link to achieve 50-km wired SMF and 10-m wireless MMW transmissions with the error vector magnitude of 17.2%, signal-to-noise ratio of 15.28 dB, and bit error rate of 3.5×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> at a data rate of 12 Gbps.

An Adaptive Multi-Mode Underwater Acoustic Communication System Using OSDM and Direct Sequence Spread Spectrum Modulation

Dynamic underwater acoustic network is a research hotspot. Due to the complexity and time-varying of underwater acoustic channel, the performance of single-mode underwater acoustic communication system is often limited by the worst channel situation. Orthogonal signal division multiplexing (OSDM) is a new signal modulation technology, which can be regarded as a bridge between single carrier modulation and orthogonal frequency division multiplexing (OFDM) modulation. In order to improve the channel adaptive ability of underwater acoustic communication system and obtain a unified architecture of different carrier modulation, an adaptive multi-mode underwater acoustic communication system based on OSDM and direct sequence spread spectrum modulation (AMMUAC/OS) is proposed in this paper. Combined with spread spectrum modulation, the system can realize single carrier time domain spread spectrum (SC-TDSS), single carrier system with cyclic prefix (SC-CP), OSDM, multicarrier frequency domain spread spectrum (MC-FDSS), and OFDM communication system by adjusting the vector length M of OSDM. The addition of a variety of digital mapping methods enables the system to achieve multi-mode communication with a unified architecture. Based on the relationship between the OSDM vector length M and the underwater acoustic channel delay, a joint adaptive decision criterion based on the maximum channel delay and the channel signal-to-noise ratio (SNR) is proposed. Firstly, the OSDM vector length M is determined according to the maximum channel delay, and then the system communication mode is selected according to the channel SNR. Orthogonal matching pursuit (OMP) channel estimation algorithm is used to obtain channel information and minimum mean square error (MMSE) channel equalization algorithm is used for channel compensation. An adaptive multi-mode data frame structure is designed for the interaction between the sender and the receiver. The simulation results show that the proposed AMMUAC/OS can adapt to underwater acoustic channels with different channel delay and SNR.

АНАЛИЗ И РАЗРАБОТКА ПОЛЯ ОЦЕНКИ КАНАЛА ДЛЯ МОДУЛЯЦИИ С ОДНОЙ НЕСУЩЕЙ В IEEE 802.11AY

This paper describes structure of a channel estimation field for the single carrier (SC) modulation based on the IEEE 802.11ad standard supporting transmission of radio signals between devices with multiple antennas for transmission and reception (MIMO – Multiple Input Multiple Output). Channel estimation field design uses a developed set of reference sequences based on complementary Golay pairs having similar statistical characteristics. All sequences are orthogonal to each other and each complementary pair has a pair in the set with zero cross-correlation property between them. Usage of this property allows to cancel out interstream interference during channel estimation procedure. A key property of the developed set is a common hardware architecture for a generator and correlator. Proposed structure of the channel estimation field is flexible and can be extended to arbitrary number of spatial streams for transmission. To analyze influence of the proposed channel estimation field on system performance, dependence of packet error rate on signal to noise ratio (SNR) was simulated for MIMO configuration with two transmit and two receive antennas for real and ideal channel estimations. System performance is analyzed in two channel models: the line of sight channel and the Rayleigh channel corresponding to the best and worst case of the signal propagation. It was shown that degradation of the SNR operating points depending on a modulation-coding scheme is in range 0.6-1.1 dB for the line of sight channel model and 0.7-1.5 dB for the Rayleigh channel model. This solution is already adopted by the IEEE 802.11ay standardization group.

Deep Learning-Based Automatic Modulation Classification With Blind OFDM Parameter Estimation

Automatic modulation classification (AMC) is an essential factor in dynamic spectrum access to fulfill the spectrum demand of 5G wireless communications for achieving high data rate and low latency. Many deep learning (DL)-based AMC methods have achieved improved accuracy for classifying analog modulation schemes, single-carrier-based modulation schemes, and multi-carrier signals using several DL architectures such as the convolutional neural network (CNN) and long-short term memory (LSTM). However, most conventional DL-based AMC methods have confused the orthogonal frequency multiplexing division (OFDM)-based signals with different OFDM useful symbol lengths. To resolve the issue, we propose a CNN model operating on the fast Fourier transformation window bank (FWB) to extract the useful symbol length in OFDM, which represents the identification of each OFDM-based wireless communication technology. After extracting the OFDM useful symbol length, we propose a DL-based AMC system combined with FWB and in-phase and quadrature-phase signals to classify the OFDM symbol length and single-carrier modulation schemes simultaneously. Furthermore, we explore the constraints of the FWB parameters according to the length and the fast Fourier transformation (FFT) size of the OFDM signal to achieve good classification accuracy through the experiment. We constructed a dataset by generating OFDM signals of different lengths while changing the FFT size in a fixed bandwidth and selecting only quadrature amplitude modulation (QAM) schemes from RadioML2016.10a. Experimental results show the improved classification accuracy by about 30% over conventional classifiers in additive white Gaussian noise, synchronization impairments, and fading environments.

Reliability and Performance Improvement of PUC Converter Using a New Single-Carrier Sensor-Less PWM Method With Pseudo Reference Functions

A new single-carrier sensor-less pulsewidth modulation (PWM) method using suggested pseudo reference functions is proposed for packed U-cell (PUC) converter to improve performance and reliability of the PUC converter. It is composed of one PWM carrier signal and two suggested pseudo reference functions. By employing the proposed modulation method, the PUC dc capacitor voltage ripple is substantially decreased, and faster sensor-less capacitor voltage balancing is obtained. Moreover, the power losses are evenly distributed among all power switches. Consequently, notable reduction of the PUC dc capacitor voltage ripple and even distribution of the power loss among switches enhance the PUC converter's reliability and lifetime. In addition, odd multiples of the switching harmonic clusters are eliminated from the output voltage; thus, the values of output passive filter components are halved. Hence, applying the proposed single-carrier sensor-less PWM method remarkably improves the performance, power density, reliability, and lifetime of the PUC converter and notably simplifies implementation of the switching pattern. Provided experimental results and comparisons as well as reliability analysis verify the viability and effectiveness of the proposed PWM method.