Peak-to-average Power Ratio Reduction Research Articles

Exploring and Analyzing a Hybrid PAPR Reduction Method for OFDM Optimization

Orthogonal Frequency Division Multiplexing (OFDM) is a effective modulation technique widely used in modern communication systems, including 5G and wireless networks because of its high spectral efficiency and robustness towards multipath fading. However, OFDM signals are characterized by a high Peak-to-Average Power Ratio (PAPR), which can severely impact the power efficiency and operational cost of these systems. This research investigates and analyse effectiveness of two conventional PAPR reduction methods that is Selective Mapping (SLM), and Partial Transmit Sequence (PTS) with incorporating their approach of PAPR reduction to develop a hybrid variant: SLM-PTS. This study utilized MATLAB simulations to implement and test each PAPR reduction technique on a standard OFDM system model. Parameters such as the number of subcarriers, oversampling factor, and modulation types were systematically varied to analyze the impact on PAPR, BER, and computational complexity. The effectiveness of each technique was measured using the Complementary Cumulative Distribution Function (CCDF) of PAPR values and BER performance under different channel conditions. Key findings reveal that hybrid techniques, particularly SLM & PTS, offer significant improvements in PAPR reduction compared to traditional methods alone, without a corresponding increase in BER or computational overhead. The research underscores the potential of hybrid PAPR reduction techniques to significantly enhance the efficiency and reliability of OFDM systems. These findings have important implications for the design and optimization of next-generation wireless communication systems, suggesting that hybrid approaches can provide a balanced solution to the longstanding issue of PAPR in OFDM transmissions. This study contributes valuable insights into the practical application of combined PAPR reduction strategies, offering a pathway toward more power-efficient and robust OFDM technologies. Keywords : OFDM, PAPR, CCDF, SLM and PTS

High-security multidimensional data protection system based on the Hartley algorithm-driven chaotic scheme

This paper proposes a high-security multidimensional data protection system based on the Hartley algorithm-driven chaotic scheme. We utilize the fast Hartley algorithm instead of the fast fourier computation, and we employ chaotic sequences generated by the multi-winged chaotic system to achieve chaos-driven 3D constellation mapping, effectively integrating the chaotic system with the stochastic amplitude modulator. We reduce the signal’s peak-to-average power ratio (PAPR) by deploying a random amplitude modulator. Simultaneously, this approach enhances the security of the physical layer of the signal. The PAPR reduction can reach up to 2.6 dB, while the most robust and stable modulator scheme can gain 2 dB. Finally, in the Hartley frequency domain, the signal's frequency is disrupted, providing the entire system with a key space of 10131 to resist violent cracking and thus improving the system's overall security. To validate the feasibility of our scheme in comparison to conventional IFFT-based encrypted 3D orthogonal frequency division multiplexing, We achieved a transmission rate of 27.94 Gb/s over a 2 km multicore fiber. Experimental results show that since the random amplitude generator effectively reduces PAPR, our proposed encryption scheme increases the forward error correction threshold range by 1.1 dB, verifying that our proposed scheme has highly reliable security performance.

Dynamic thresholding logarithmic companding for PAPR reduction in MIMO-OFDM systems for 5G wireless communication

In order to advance 5G wireless communication technology, this paper presents a novel method for lowering the Peak-to-Average Power Ratio (PAPR) in Multiple-Input Multiple-Output Orthogonal Frequency-Division Multiplexing (MIMO-OFDM) systems. It is called the Dynamic Thresholding-based μ-law (DT-μ-law) logarithmic companding technique, and it greatly improves the performance of the system by effectively broadcasting data streams on a single frequency across multiple channels. This technique's ability lies in compressing the amplitude of the transmitting signal beyond a specific threshold value before the parallel-to-serial conversion block in the MIMO-OFDM system. It employs the direct insertion of an offset value into the guard bits, rather than using a step function for the amplitude reduction process, which can reduce additional system complexity and data loss during signal expansion at the receiver end. This technique is more adequately suited for dynamic data rate shifting and interference within a limited threshold value. The dynamic thresholding value (α) is determined by calculating the median and standard deviation of the μ-law companding. This ensures the effective compression of higher amplitude signals at the transmitter, using μ-law log companding. To streamline the decompanding process at the receiver, an offset is introduced, facilitating a smoother transition and reducing complexity. The results demonstrate that the proposed DT- μ-law companding technique significantly improves PAPR reduction while maintaining low Bit Error Rates (BER) and high average spectral power efficiency. This efficiency is optimal when the μ value is maintained within the range of 4–4.5. Furthermore, it was observed that an increase in the μ value corresponds to a decrease in both PAPR value and BER. Specifically, at a signal-to-noise ratio of 15.2 dB, the BER stabilizes at 10−1. Compared to existing methods like the Max-Min Decomp-SLM approach, this technique offers lower Signal-to-Noise Ratio (SNR) values, thereby enhancing spectral efficiency and maximizing data capacity.

Enhancing PAPR reduction efficiency in MIMO-OFDM systems via selective mapping and metaheuristic algorithms

The relentless evolution of communication systems, driven by the demands of 5G and the impending 6G networks, necessitates heightened data rates and spectral efficiency. orthogonal frequency division multiplexing (OFDM), a form of multicarrier modulation employed in multi-input multi-output (MIMO) systems, stands as a pivotal technology. Yet, OFDM grapples with challenges, notably the peak-to-average power ratio (PAPR) issue. Selective mapping (SLM) has been a favored technique for mitigating PAPR in OFDM, albeit challenged by computational complexities in its pursuit of discovering optimal phase factors. This paper pioneers a transformative approach by integrating metaheuristic algorithms genetic algorithm (GA), particle swarm optimization (PSO), and the innovative fireworks algorithm (FWA) into SLM for PAPR reduction while minimizing computational complexity. Simulation results not only affirm the efficacy of SLM-based techniques but also spotlight the potential of metaheuristic algorithms in addressing PAPR challenges in modern communication systems. The study transcends single-antenna systems, extending to MIMO-OFDM systems based on WiMAX standards, validating the efficacy of these techniques in multi-antenna configurations. Crucially, the FWA, proposed for the first time in this paper, emerges as a robust candidate, striking an enviable balance between computational efficiency and performance, achieving a notable PAPR reduction with a favorable search number.

Reducing peak‐to‐average power ratio of filtered non‐orthogonal multiple access and new radio 5g waveforms using hybrid partial transmit sequence‐companding technique

AbstractFor fifth‐generation (5G) and beyond 5G communications, filtered nonorthogonal multiple access (F‐NOMA) can be used as a waveform contender. Filtering‐based waveform frameworks provide suppression of out‐of‐band emission (OOBE) and asynchronous transmission. For new types of waveforms, a high peak‐to‐average power ratio (PAPR) remains a challenge. A high PAPR in multicarrier systems can be efficiently mitigated by applying partial transmit sequence (PTS). Combining PAPR reduction techniques can improve the transmission efficiency by nonlinearly scaling the signal amplitudes before transmission and inversely scaling them at the receiver. We propose a hybrid technique that combines PTS and companding to reduce the PAPR in an F‐NOMA system. Conventional nonorthogonal multiple access (NOMA) is compared with F‐NOMA, and systems with and without the hybrid technique are examined regarding metrics including the power spectral density, bit error rate (BER), and computational complexity. Compared with NOMA, simulation results show that F‐NOMA using the proposed technique improves the PAPR and OOBE while preserving the BER performance of F‐NOMA.

Papr reduction through Gaussian pre-coding in DCO-OFDM systems

Visible light communication (VLC) utilizes commercially available light-emitting diodes (LEDs) for short-distance wireless data transmission, aligning with lighting standards for indoor wireless access. The inherent challenge of achieving high data rates in VLC due to the limited spectral bandwidth of white LEDs has led to the adoption of orthogonal frequency division multiplexing (OFDM). However, conventional OFDM presents issues with peak-to-average power ratio (PAPR), pushing LEDs into a nonlinear zone, resulting in energy inefficiencies and signal distortion that degrades the bit error rate (BER). The study focuses on pre-coding within DC-biased optical OFDM (DCO-OFDM) using a Gaussian matrix (GM) for PAPR reduction. The proposed Gaussian pre-coding method demonstrates superior PAPR performance compared to conventional discrete cosine transform (DCT) pre-coding method, especially when integrated with μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu$$\\end{document}-Law companding. Simulation results indicate that increasing the number of candidate GMs enhances PAPR performance, albeit with increased system complexity. The combination of DCT and Gauss pre-coding with μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu$$\\end{document}-Law companding exhibits a 2 dB improvement in PAPR, though at the expense of BER performance.

Filtered Ofdm System Model for Papr Reduction in the Growth Of 5g

A proposed waveform for fifth generation (5G) communications is the filtered orthogonal frequency division multiplexing (F-OFDM) system. Filtering-based waveform frameworks distinguish themselves by suppressing out-of-band emission and asynchronous transmission. Meanwhile, the high Peak-To-Average Power Ratio (PAPR) remains a barrier to new waveform possibilities. Partials transmit sequence (PTS) is a successful strategy for reducing high PAPR in multicarrier networks. This work presents a multicarrier in OFDM and UFMC based on the Filter Bank Multicarrier (FBMC) waveform for communication systems. Furthermore, FBMC waveforms have limited orthogonality between subcarriers, which can mitigate Doppler and multipath effects. This FBMC approach uses the cosine law to filter the traffic signal, and the Welch algorithm is offered for segmentation, which lowers noise in estimated power spectra. As a result, a hybrid Selective Mapping (SLM) with Cuckoo Search and Ant Lion Optimization (CS-ALO) algorithms is suggested using the FBMC framework to reduce PAPR in the OFDM system. The proposed work is implemented, and detailed experimental research is carried out to show the increased performance in 5G networks. Based on a fair comparison, the F-OFDM scheme outperforms previous approaches in terms of BER and multicarrier system capacity. Simulation results show that the proposed waveform design and processing method outperform standard OFDM and F-OFDM methods in PAPR reduction and communication integrated systems.

Two-stage collaborative information interaction reliability improvement for the distribution grid

The impulse noise generated by a large volume of power electronics devices imposes a hazardous impact on information interaction reliability in low-voltage distribution grids. In this paper, we propose a two-stage collaborative information interaction reliability improvement algorithm to minimize the bit error rate (BER) of the information interaction under impulse noise. In the first stage, the transmission-side peak-to-average power ratio (PAPR) is reduced based on the adaptive particle swarm optimization (PSO)-enabled partial transmit sequence (PTS). In the second stage, the reception-side dual-signal blanking is proposed based on the transmission-side PAPR and reception-side useful signal power estimation and peak median ratio. The transmission–reception collaborative information interaction reliability improvement is realized through two aspects. First, transmission-side PAPR reduction improves the performance of reception-side signal blanking by making it easier to distinguish useful signals from impulse noise. Second, the transmission-side PAPR is utilized to improve the estimation accuracy of both coarse and precise thresholds in dual-signal blanking. Simulation results show that the proposed algorithm outperforms existing algorithms in both PAPR reduction and BER performances to achieve information interaction reliability improvement effectively.

A Survey of PAPR Techniques Based on Machine Learning.

Orthogonal Frequency Division Multiplexing (OFDM) is the modulation technology used in Fourth Generation (4G) and Fifth Generation (5G) wireless communication systems, and it will likely be essential to Sixth Generation (6G) wireless communication systems. However, OFDM introduces a high Peak to Average Power Ratio (PAPR) in the time domain due to constructive interference among multiple subcarriers, increasing the complexity and cost of the amplifiers and, consequently, the cost and complexity of 6G networks. Therefore, the development of new solutions to reduce the PAPR in OFDM systems is crucial to 6G networks. The application of Machine Learning (ML) has emerged as a promising avenue for tackling PAPR issues. Along this line, this paper presents a comprehensive review of PAPR optimization techniques with a focus on ML approaches. From this survey, it becomes clear that ML solutions offer customized optimization, effective search space navigation, and real-time adaptability. In light of the demands of evolving 6G networks, integration of ML is a necessity to propel advancements and meet increasing prerequisites. This integration not only presents possibilities for PAPR reduction but also calls for continued exploration to harness its potential and ensure efficient and reliable communication within 6G networks.

PAPR reduction using model‐driven hybrid algorithms in the 6G NOMA waveform

AbstractIn the evolving landscape of sixth‐generation (6G) network technologies, Non‐Orthogonal Multiple Access (NOMA) systems are pivotal for achieving enhanced spectral efficiency and network capacity. However, a significant challenge in NOMA systems is the high Peak‐to‐Average Power Ratio (PAPR), which undermines system efficiency by necessitating high‐power amplifiers (HPAs) to operate in their less efficient, non‐linear range. Addressing this, we introduce a novel hybrid approach, the Selective Mapping‐Circular Transformation Method (SLM‐CTM), which ingeniously amalgamates the strengths of Selective Mapping (SLM) and the Circular Transformation Method (CTM) to mitigate PAPR issues. SLM is renowned for its peak power reduction capabilities without adding to system complexity, whereas CTM is valued for its simplicity and controlled signal distortion. The proposed SLM‐CTM strategy employs a blend of linear and nonlinear techniques to effectively lower PAPR in non‐orthogonal NOMA configurations, thereby reducing high‐power peaks while simultaneously enhancing signal quality. This paper delineates the application of the SLM‐CTM algorithm to evaluate critical NOMA parameters such as Power Spectral Density (PSD), Bit Error Rate (BER), and PAPR. Simulation results highlight the efficacy of SLM‐CTM over conventional SLM, demonstrating a significant throughput improvement of 3.2 dB and a PAPR reduction of 4.6 dB, underscoring the potential of SLM‐CTM in elevating the performance of NOMA systems within 6G network.

Modified Error Function Companding for reduction of PAPR in GFDM signals

Generalized Frequency Division Multiplexing (GFDM) is a multicarrier modulation technique, nevertheless, it provides high peak to average power ratio (PAPR) which affects the power amplifier (PA) efficiency. In this work, the modified error function companding is proposed for reducing PAPR in GFDM signals. The power scaling parameter (η) and companding parameter (a) are used to reduce the peak power. The average power is not altered in the proposed method, so there is no need to adjust the dynamic gain of PA. The theoretical expressions for the transform gain, achievable PAPR reduction and closed form expression of attenuation factor are derived. Moreover, the transform gain, attenuation factor, power spectral density, PAPR and bit error rate (BER) performance of the proposed method is analysed for different values of companding parameter. The results ensure that the proposed mEFC method at a=1 provides significant PAPR reduction than existing companding methods.

A Novel Alternating μ-Law Companding Algorithm for PAPR Reduction in OFDM Systems

Orthogonal frequency division multiplexing (OFDM) inherits multi-carrier systems’ inevitable high peak-to-average power ratio (PAPR) problem. In this paper, a novel alternating companding technique is proposed to combat the harassment of high PAPR. The sequential μ-law companding (SULC) and a tone with a lower PAPR result in only partial tones needing companding. The SULC scheme’s PAPR and bit error rate (BER) performance has been balanced and improved. However, the computational complexity is still too high to be implemented. Therefore, this study sorted the transmission signals according to their amplitudes. Then, all the tones are divided into two groups by estimating the rough companding amount (around 54% of the subcarriers), using traditional parallel companding for the first group and the other group only by partial μ-law companding. This alternating μ-law companding (AULC) is proposed to improve the PAPR performance and simultaneously reduce complexity. Simulation results show that the proposed AULC method appreciably reduces the PAPR by about 5 dB (around 45%) compared with the original μ-law at complementary cumulative distribution function (CCDF) equal to 10−4. Moreover, it only requires a moderate complexity to outperform the other companding schemes without sacrificing the BER performance in the OFDM systems.

A novel piecewise nonlinear companding scaling scheme for FBMC PAPR reduction

The performance of offset quadrature amplitude modulation filter bank multi carrier (OQAM-FBMC) has been noticed to be affected by a high peak-to-average power ratio (PAPR). High PAPR causes the transmit power amplifier to become saturated, improving the bit error rate (BER) and causing out of band (OOB) distortions. In this paper, the PAPR of FBMC systems can be reduced by using shifting and scaling the trigonometric companding technique associated with a reduced BER performance and the power spectral density (PSD) with low OOB distortions. The characteristics of low peak signals are not changed by this companding scheme, while the characteristics of high peak signals are transformed into scaling piecewise nonlinear trigonometric functions. By tuning the parameters the suggested technique maintains the average signal power level unchanged. The theoretical analysis of the proposed scheme is also studied and also compared with the simulation results. The performance of the trigonometric companding scheme is also analysed with the μ-law and A-law existing companding methods and the suggested method obtaining 3 dB and 3.2 dB PAPR improvement respectively. The proposed technique determined to be better in terms of BER performance and spectrum efficiency.

A hybrid approach based on companding and PTS methods for PAPR reduction of 5G waveforms

ABSTRACT As a crucial enabler for the fifth-generation air interface, the filter bank multicarrier with offset quadrature amplitude modulation (FBMC/OQAM) is being investigated by several researchers. This article suggests using partial transmit sequence (PTS) and companding to create a hybrid peak-to-average power ratio (PAPR) reduction strategy for FBMC/OQAM signals. In the novel PTS Companding scheme, there are several segments to the data block signal, and the overlapping factor determines the number of data blocks in each segment. To obtain the lowest signal power in each segment, we choose the best data block to broadcast and examine the next overlapping data block concurrently. After that, the segment FBMC/OQAM signal peaks are compressed using companding. Based on simulation results and analysis, the proposed hybrid PTS Companding method in FBMC/OQAM systems may reduce PAPR more effectively than conventional PTS and Companding schemes. According to simulation results, the hybrid process can achieve around 5 dB greater PAPR performance than the conventional PTS and companding schemes.

Deep learning based asymmetrical autoencoder for PAPR reduction of CP-OFDM systems

Adoption of Orthogonal Frequency Division Multiplexing (OFDM) in 5th Generation New Radio (5G NR) as a multicarrier modulation technique allows high data rate transmission with lower complexity. However, problem such as peak to average power ratio (PAPR) has decreased the transmitter efficiency. Recently, several attempts have been made to reduce the high PAPR in OFDM utilizing deep learning (DL) based on autoencoder architecture. However, the proposed autoencoder using symmetrical autoencoder (SAE) is followed by high computational complexity at both transmitter and receiver as well as BER performance degradation. Since 5G NR focuses on massive 5G internet of things eco-system, a flexible carrier spacing is used to support diverse spectrum bands which is afterward named as Cyclic Prefix OFDM (CP-OFDM). In this study, we aimed to contribute to this growing area of research by exploring the potential of our proposed asymmetrical autoencoder (AAE) to reduce high PAPR in the CP-OFDM system. Four AAE models have been developed in this study and the performance of the models were evaluated based on comprehensive conditions such as data training at different corruption levels, cyclic prefix length, upsampling factors and loss function levels. The investigation of AAE in 5G CP-OFDM system has shown superior performance using a 5×1 AAE model that can reduce a substantial amount of PAPR, BER degradation and computational complexity compared to conventional SAE. This study lays the groundwork for future research into the asymmetrical approach of autoencoder especially in 5G and beyond networks.

Enhanced PAPR reduction in DCO-OFDM using multi-point constellations and DPSO optimization

DC-biased optical OFDM (DCO-OFDM) is a commonly used method of OFDM in visible light communication (VLC). Unfortunately, VLC systems that use OFDM often experience a high peak-to-average power ratio (PAPR). To address this issue, this study proposes a novel method called the multi-point constellation method (MPC) to reduce PAPR in DCO-OFDM. The MPC method involves adding extra alternative constellation points around the existing points and using the discrete particle swarm optimization (DPSO) algorithm to select the constellation points with the lowest PAPR. The proposed MPC method is also combined with selective mapping (SLM), a well-known PAPR reduction technique in the literature. Simulation results show that the proposed MPC method outperforms the SLM method in reducing PAPR in 4-QAM and 16-QAM modulations when used in combination with SLM. Furthermore, increasing the number of iterations and particles in the DPSO algorithm improves the PAPR reduction performance of the proposed method even further.

Performance enhancement and PAPR reduction for MIMO based QAM-FBMC systems.

Filter Bank Multi-Carrier (FBMC) is attracting significant interest as a multi-carrier modulation (MCM) approach for future communication systems. It offers numerous advantages in contrast to Orthogonal Frequency Division Multiplexing (OFDM). Nonetheless, similar to many other MCM techniques, FBMC encounters a significant challenge with a high Peak-to-Average Power Ratio (PAPR). Additionally, incorporating Multiple-Input and Multiple-Output (MIMO) into FBMC presents heightened difficulties due to the presence of complex interference and increased computational complexity. In this paper, we first study the performance analysis of MIMO based Quadrature Amplitude Modulation (QAM)-FBMC systems considering the system complexity and interference. To enhance coverage effectively using beamforming with multiple antennas, it is essential to reduce PAPR to minimize the input backoff (IBO) required by nonlinear power amplifiers. Therefore, we propose new PAPR reduction method for MIMO based QAM-FBMC systems leveraging the null space within the MIMO channel using clipping and filtering (CF) technique. The PAPR reduction signals generated in this process are then mapped to the null space of the overall MIMO channel for each frequency block. Through computer simulations using a nonlinear power amplifier model, we illustrate that the proposed method substantially enhances both PAPR and throughput of MIMO based FBMC systems compared to conventional methods.

Spread spectrum OFDM-IM with X-transform

This paper proposes a developed index modulated spread spectrum orthogonal frequency division multiplexing (OFDM) that is based on X-transform (IM-XOFDM-SS). The presented OFDM sends information not only by M-ary data symbols but also by indexes bits that used to select the spreading code from a known set, and applies the X-transform for baseband processing. A theoretical analysis for upper bound bit-error rate (BER) over Rayleigh fading channels is derived for the proposed scheme. Simulations results show that our proposed scheme outperforms the competitive benchmark systems in terms of BER, peak-to-average power ratio (PAPR) and computational complexity. It achieves, at 10−4 BER, about 22 dB and 21 dB SNR gain when spectral efficiency is SE=1 bps/Hz. Additionally, it gains about 5.5 dB PAPR reduction in comparison to IM-OFDM-SS scheme that is based on FFT for baseband processing.

Evaluation of OFDM system in terms of PAPR and BER using PAPR Reduction Techniques : Windowing and Clipping

The issue of transferring signals in a non-intrusive and efficient manner is highly intriguing. Consequently, the utilisation of the Orthogonal Frequency Division Multiplexing (OFDM) transmission technology is employed due to its enhanced resilience against multipath fading and its ability to achieve better efficiency compared to alternative wireless communication methods. Although the PAPR issue offers certain benefits, it poses undesirable consequences for OFDM, leading to a significant decrease in data transmission rate. Consequently, the mitigation of peak-to-average power ratio (PAPR) issues leads to an improvement in the quality of service. The reduction of PAPR can be achieved by the implementation of clipping and windowing techniques. These approaches arrange the signal into discrete levels of similar magnitude and apply clipping to minimise the bit error rate (BER), resulting in a drop in PAPR. The proposed approach is implemented using the MATLAB software.

Analysis of PAPR reduction of optical-OTFS for 256-QAM using companding and clipping–filtering algorithms

Abstract The article presents an investigation into Peak-to-Average Power Ratio (PAPR) reduction techniques in Optical Orthogonal Time Frequency Space (O-OTFS) modulation. Focusing on clipping and filtering as well as companding methods, the study explores their efficacy in mitigating PAPR challenges inherent in O-OTFS waveforms. The research evaluates the impact of these techniques on signal quality, particularly in the context of a Rician channel. Clipping and filtering (C&F) are examined for their ability to control amplitude peaks, while companding is analyzed for its role in optimizing dynamic range. The study conducts a comprehensive analysis of Bit Error Rate (BER) and power spectrum density (PSD) under varying conditions, shedding light on how these methods influence the reliability and robustness of OTFS communication. The investigation considers the interplay of these PAPR reduction methods with the unique characteristics of the Rician and Rayleigh channel, which includes a dominant line-of-sight component. The findings contribute valuable insights into designing efficient OTFS modulation systems for real-world scenarios. Ultimately, this research aims to provide a deeper understanding of PAPR reduction strategies in OTFS, offering guidance for optimizing signal processing techniques in communication systems where mitigating PAPR is crucial for achieving high performance and reliable data transmission. It is noted that the proposed C&F and companding algorithms outperform the conventional methods and achieved a PAPR gain of 1–3 dB and BER gain of 10.6–2 dB.