Low Peak-to-average Power Ratio Research Articles

OFDM-based 2D generalized optical quadrature spatial modulation for MIMO-OWC systems

An innovative scheme, named orthogonal frequency division multiplexing (OFDM)-based two-dimensional (2D) generalized optical quadrature spatial modulation (GOQSM), is proposed for bandlimited multiple-input multiple-output optical wireless communication (MIMO-OWC) systems. In this scheme, by way of combining two consecutive time slots into one time block, 2D GOQSM mapping can be executed in spatial domain and time domain. Therefore, more spatial bits can be transmitted, resulting in the increase of system spectral efficiency. Furthermore, discrete Fourier transform (DFT) spreading is further introduced in OFDM-based 2D GOQSM systems, so as to substantially reduce the peak-to-average power ratio (PAPR) of the transmitted signals. To evaluate and compare the performance of OFDM-based 2D GOQSM systems with other traditional systems, numerical simulations are conducted under various spectral efficiencies. The obtained simulation results prove that the proposed OFDM-based 2D GOQSM scheme with DFT spreading can achieve better bit error rate performance and lower PAPR than other benchmark schemes.

Multipath Analysis of Pruned DFT-Spread FBMC-OQAM in Underwater Acoustic Channels

During modulation, when each phase of subcarriers is the same or similar, the superimposed signal will be modulated by the same initial phase, resulting in a large instantaneous power peak, namely the higher peak-to-average power ratio (PAPR). After signals propagate through different paths, the interference is caused by the superposition of each component according to their respective phases, which distorts original signals or produces errors. To reduce the PAPR and resist the influence of long-time delays, we propose to employ the discrete Fourier transform spread filter bank multicarrier (DFT-spread FBMC) to achieve it. Different from general FBMC technologies, it adds a precoding matrix before the offset quadrature amplitude modulation (OQAM). By comparing with orthogonal frequency division multiplexing technology, this letter explores its PAPR performance under different delays. The results show that the pruned DFT-spread FBMC-OQAM has a lower PAPR and better performance in long-time delays underwater channels.

Variation Approach-Based Nonlinear Companding Scheme for PAPR Reduction in OFDM Systems

Orthogonal frequency division multiplexing (OFDM) continues to find vast deployment in current and next generation wireless communication systems. However, high peak-to-average power ratio (PAPR) is one of the major drawbacks in the OFDM system. In this paper, we develop a variation approach based nonlinear companding (VANC) scheme to reduce the PAPR in OFDM systems. It aims to find the probability density function (PDF) for OFDM signal amplitudes with low PAPR and low distortion compared with their original Rayleigh distribution. The target PDF is found by solving a variation optimization problem model, which is built to find the lowest PDF distortion with both average signal power and probability conservation constraint. To the best of our knowledge, it is the first time that the variation method is used to find companding function to address the high PAPR problem. We then propose an algorithm with companding operation based on quantized levels. Simulation results validate the performance superiorities of the proposed scheme to that of other typical companding schemes.

Interference optimized dual-functional radar-communication waveform design with low PAPR and range sidelobe

Dual-functional radar-communication system integrates the radar and communication functions into one system with a shared dual-functional waveform. In this paper, we focus on the problem of dual-functional waveform design under the peak-to-average power ratio (PAPR) constraint and low range sidelobe requirement. When the conventional schemes aim to minimize the multi-user interference (MUI) energy and maximize the similarity to the reference radar waveform, in our proposed method, a weighted summation objective function incorporated with the PAPR constraint and optimized MUI is constructed for the waveform design. Specifically, MUI is classified into destructive interference and constructive interference, while the latter is exploited as a free power for communication and is constrained to guarantee the communication quality-of-service (QoS). To tackle the resulting high order nonconvex problem, we develop an iteration algorithm based on the alternating direction method of multipliers (ADMM) procedure, which involves two quadratic programming subproblems in each iteration and is easy to solve with the current solver. Moreover, by taking the imperfect channel state information (CSI) into consideration, we further investigate the robust dual-functional waveform design problem with the bounded uncertainty of the CSI. Numerical simulations validate the effectiveness of the proposed method.

Robust Adaptive Transmit Beamforming under the Constraint of Low Peak-to-Average Ratio.

In radar detection, in order to make the beam have variable directivity, a Capon beamformer is usually used. Although this traditional beamformer enjoys both high resolution and good interference suppression, it usually leads to high sidelobe and is sensitive to array steering vector (ASV) mismatch. To overcome such problems, this study devises a novel, robust adaptive beamformer that is robust to ASV mismatch under the constraint where the sidelobe is oriented to the ground. Moreover, to make full use of the transmit power, the constraint of a low peak-to-average power ratio (PAPR) is also taken into consideration. Accordingly, this robust adaptive beamformer is developed by optimizing a transmitting beamformer constrained by ASV mismatch and low PAPR. This optimization problem is transformed into a second-order cone programming (SOCP) problem which can be efficiently and exactly solved. The proposed transmit beamformer possesses not only adaptive interference rejection ability and robustness against ASV mismatch, but also direct sidelobe control and a low PAPR. Simulation results are presented to demonstrate the superiority of the proposed approach. The proposed method can make the peak sidelobe level (PSL) level on the ground side below −30 dB.

Relation between spectra of Narain CFTs and properties of associated boolean functions

Recently, the construction of Narain CFT from a certain class of quantum error correcting codes has been discovered. In particular, the spectral gap of Narain CFT corresponds to the binary distance of the code, not the genuine Hamming distance. In this paper, we show that the binary distance is identical to the so-called EPC distance of the boolean function uniquely associated with the quantum code. Therefore, seeking Narain CFT with large spectral gap can be addressed by getting a boolean function with high EPC distance. Furthermore, this problem can be undertaken by finding lower Peak-to-Average Power ratio (PAR) with respect to the binary truth table of the boolean function. Though this is neither sufficient nor necessary condition for high EPC distance, we construct some examples of relatively high EPC distances referring to the constructions for lower PAR. We also see that codes with high distance are related to induced graphs with low independence numbers.

PAPR Reduction of OFDM Waveform in Integrated Passive Radar and Communication Systems

For the dual-function radar and communication (DFRC) system based on the orthogonal frequency division multiplexing (OFDM) signal, low peak-to-average power ratio (PAPR) design of the waveform is very important to improve the transmitting efficiency and overall performance. In this paper we consider this problem in the context of the integrated passive radar and communication (IPRC) system in which the channel state information (CSI) and transmitting waveform are unknown to the passive radar. In this context, the traditional constellation extension method is applicable but the effect of PAPR reduction is limited by the constellation size. To solve this problem, we propose a low PAPR waveform design method suitable for a large constellation size. The new method makes two improvements to significantly reduce the PAPR by increasing the constellation point participating in the extension and expanding the extension regions, which is independent of the CSI. Specifically, we adjust the extension regions by the scaling factor to obtain different PAPR, while remaining the pilot data unchanged. Furthermore, the communication performance is semi-analytically analyzed, and the consistency of semi-analytical results and simulation results verifies the effectiveness of the proposed method. Analysis and numerical results demonstrate that the proposed method can achieve good comprehensive performance of communication and passive radar detection compared with other methods in the case of large constellation size.

A Novel Modulation Technique with Low PAPR for 5G-IoT Systems

For existing orthogonal frequency division multiplexing (OFDM) in 5G internet of things (5G-IoT) systems, one of the critical problems is the high peak to average power ratio (PAPR), which seriously degrades the energy efficiency. To this end, we propose a novel modulation technique with low PAPR for IoT systems, which preserves the advantage of low implementation complexity and ability to fight against multipath channels. The key methodology is the employment of symbol repetition in the frequency domain. Hence, by designing the appropriate phase factors on the repeated symbols, the PAPR of transmitted signals is equivalent to that of an OFDM signal with a reduced size of discrete Fourier transform (DFT). It is demonstrated that, even if there exists repetitive symbols, the proposed method can still maintain an unreduced spectral efficiency performance. Moreover, to evaluate the proposed method, the Monte-Carlo simulations are conducted for the complementary cumulative distribution function (CCDF) and the bit error rate under multipath fading channels. The simulations show that, as CCDF = 10 − 3 , the proposed method can achieve 2.5 dB gains about the PAPR compared with the original OFDM signal.

Performance evaluation of MIMO DFT-Spread WR-OFDM system for spectrum efficiency and power efficiency

ABSTRACT It is important to design a spectrum-efficient and power-efficient wireless communication system, which is the main design target in cellular and wireless communication engineering. Basically, to make it, the desired system must have a low peak-to-average power ratio (PAPR), low-level of out-of-band (OOB) power emission and can provide a high throughput. In this paper, we propose a high-throughput cellular communication system, namely Discrete Fourier Transform-Spread Windowing and Restructuring Orthogonal Frequency Division Multiplexing (DFT-Spread WR-OFDM), which has considerably low PAPR and low OOB power emission for upcoming next-generation beyond 5G (B5G) and 6G cellular communication systems. High PAPR is still one of the challenging issues for the MIMO-OFDM system. The proposed system is an effective arrangement of DFT-Spreading and windowing techniques to reduce PAPR and OOB power emission, respectively. Multiuser diversity is obtained using localized subcarrier mapping. We take advantages of spatial multiplexing to enhance the data throughput significantly. Additionally, frequency-domain equalization (FDE)-minimum mean squared error (MMSE) is used to combat the inter-symbol interference (ISI) effect. Simulation results verify that the suggested system considerably lowers PAPR and OOB power emission compared to the conventional systems. Furthermore, the proposed scheme shows better bit error rate (BER) performance over the MIMO Rayleigh fading channel environment. Simulation results also confirmed that the channel capacity of our suggested system is better than the conventional multi-carrier systems.

Filtered-orthogonal wavelet division multiplexing (F-OWDM) technique for 5G and beyond communication systems.

Filtered-orthogonal frequency division multiplexing (F-OFDM) is one of the most protruding multicarrier modulation (MCM) techniques for fifth-generation and beyond wireless communication. However, it possesses a high peak-to-average power ratio (PAPR), which results in its poor performance. Thus, a novel wavelet based MCM technique, namely filtered orthogonal wavelet division multiplexing (F-OWDM), is proposed as an efficient alternative to conventional F-OFDM (C-F-OFDM) to reduce the PAPR. In this model, the traditional Fourier transforms (FT) as used in C-F-OFDM was replaced with Wavelet Transforms. The proposed F-OWDM system does not require a cyclic prefix because of the overlapping sub-carriers in the time and frequency domains. Thus, the F-OWDM system exhibits higher bandwidth efficiency. In this paper, the performance of the F-OWDM system with various wavelets from different wavelet families under an additive white Gaussian noise and flat fading channel is investigated. The PAPR and bit error rate (BER) of the F-OWDM system using Haar, discrete Meyer, bi-orthogonal, symlet, and Daubechies wavelets are analyzed. A comparative study between F-OWDM and C-F-OFDM is also presented. From the results, it is able to prove that F-OWDM has the advantage of lower PAPR and lower bit error rate than the C-F-OFDM system.

Numerical Simulation and Implementation of FBMC System with Low PAPR for Efficient 5G Applications

Recently, FBMC (Filter Bank Multi-Transporter) has emerged as an alternative to orthogonal frequencies Division Multiplexing (OFDM) (OFDM). As part of the FBMC strategy, wider ranges of frequencies are now within reach, as well as lower out-of-band (OOB) outflows. Comparatively speaking, The Peak-to-average Power Ratio (PAPR) in OFDM frameworks is still high for FBMC, so this isn't surprising. The FBMC framework has been given some OFDM-based PAPR reduction innovation.. PAPR advancements are reduced in this paper OFDM frameworks employ phase modification (PR) and modified PR (MPR) algorithms as a foundation for their proposed FBMC framework. Simply integrate DFT (Discrete Fourier Transform) Spread range and FBMC-OQAM (Filter Bank Multi-Transporter) into SC-FDMA (Single Bearer Recurrence Division Multiple Entrance). As long as you keep the quadrature sufficiency tweak in check, PAPR (peak normal power proportion), which was formerly negligible, is now much less. Taking advantage of DFT's single-bearer impact, unique approaches can be taken. There should be no problems with the quadrature phase channel in terms of the IQ coefficients for each subcarrier. We use FBMC waveforms to generate DFT augmentation and ITSM conditions, and then select the one with the lowest pinnacle power as a means of further increasing the amount decreased PAPR. Regardless of the number of candidates, the basic count portion, for example, DFT Share with IDFT, only executes once, unlike the typical SI (side data) based PAPR reduction Programs.

Ciphered BCH Codes for PAPR Reduction in the OFDM in Underwater Acoustic Channels

We propose an effective, low complexity and multifaceted scheme for peak-to-average power ratio (PAPR) reduction in the orthogonal frequency division multiplexing (OFDM) system for underwater acoustic (UWA) channels. In UWA OFDM systems, PAPR reduction is a challenging task due to low bandwidth availability along with computational and power limitations. The proposed scheme takes advantage of XOR ciphering and generates ciphered Bose–Chaudhuri–Hocquenghem (BCH) codes that have low PAPR. This scheme is based upon an algorithm that computes several keys offline, such that when the BCH codes are XOR-ciphered with these keys, it lowers the PAPR of BCH-encoded signals. The subsequent low PAPR modified BCH codes produced using the chosen keys are used in transmission. This technique is ideal for UWA systems as it does not require additional computational power at the transceiver during live transmission. The advantage of the proposed scheme is threefold. First, it reduces the PAPR; second, since it uses BCH codes, the bit error rate (BER) of the system improves; and third, a level of encryption is introduced via XOR ciphering, enabling secure communication. Simulations were performed in a realistic UWA channel, and the results demonstrated that the proposed scheme could indeed achieve all three objectives with minimum computational power.

Single- Versus Multicarrier Terahertz-Band Communications: A Comparative Study

The prospects of utilizing single-carrier (SC) and multi-carrier (MC) waveforms in future terahertz (THz)-band communication systems remain unresolved. On the one hand, the limited multi-path components at high frequencies result in frequency-flat channels that favor low-complexity wideband SC systems. On the other hand, frequency-dependent molecular absorption and transceiver characteristics and the existence of multi-path components in indoor sub-THz systems can still result in frequency-selective channels, favoring off-the-shelf MC schemes such as orthogonal frequency-division multiplexing (OFDM). Variations of SC/MC designs result in different THz spectrum utilization, but spectral efficiency is not the primary concern with substantial available bandwidths; baseband complexity, power efficiency, and hardware impairment constraints are predominant. This paper presents a comprehensive study of SC/MC waveforms for THz communications, utilizing an accurate wideband THz channel model and highlighting the various performance and complexity trade-offs of the candidate schemes. Simulations demonstrate that discrete-Fourier-transform spread orthogonal time-frequency space (DFT-s-OTFS) achieves a lower peak-to-average power ratio (PAPR) than OFDM and OTFS and enhances immunity to THz impairments and Doppler spreads, but at an increased complexity cost. Moreover, DFT-s-OFDM is a promising candidate that increases robustness to THz impairments and phase noise (PHN) at a low PAPR and overall complexity.

Phase Noise Resilient Three-Level Continuous-Phase Modulation for DFT-Spread OFDM

In this paper, a novel waveform with low peak-to-average power ratio (PAPR) and high robustness against phase noise (PN) is presented. It follows the discrete Fourier transform spread orthogonal frequency division multiplexing (DFT-s-OFDM) signal model. This scheme, called 3MSK, is inspired by continuous-phase frequency shift keying (CPFSK), but it uses three frequencies in the baseband model – specifically, 0 and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pm f_{symbol}/4$ </tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{symbol}$ </tex-math></inline-formula> is the symbol rate – which effectively constrains the phase transitions between consecutive symbols to 0 and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pm \pi /2$ </tex-math></inline-formula> rad. Motivated by the phase controlled model of modulation, different degrees of phase continuity can be achieved, allowing to reduce the out-of-band (OOB) emissions of the transmitted signal, while supporting receiver processing with low complexity. Furthermore, the signal characteristics are improved by generating an initial time-domain constant envelope signal at higher than the symbol rate. This helps to reach smooth phase transitions between 3MSK symbols, while the information is encoded in the phase transitions. Also the possibility of using excess bandwidth is investigated by transmitting additional non-zero frequency bins outside the active frequency bins of the basic DFT-s-OFDM model, which provides the capability to greatly reduce the PAPR. The most critical tradeoffs of the oversampled schemes are that improved PAPR is achieved with the cost of somewhat reduced link performance and, in case of excess band, also the spectrum efficiency is reduced. Due to the fact that the information is encoded in the phase transitions, a receiver model that tracks the phase variations without needing reference signals is developed. To this end, it is shown that this new modulation is well-suited for non-coherent receivers, even under strong phase noise (PN) conditions, thus allowing to reduce the overhead of reference signals. Evaluations of this physical-layer modulation and waveform scheme are performed in terms of transmitter metrics such as PAPR, OOB emissions and achievable output power after the power amplifier (PA), using a practical PA model. Finally, coded radio link evaluations are also provided, demonstrating that 3MSK has a similar bit error rate (BER) performance as that of traditional quadrature phase-shift keying (QPSK), but with significantly lower PAPR, higher achievable output power, and the possibility of using non-coherent receivers.

Estimation Techniques for MIMO-OFDM-A Review

In the context of Third-Generation Partnership Project Long-Term Evolution (3GPP LTE), the target data rates are 100 Mb/s in downlink and 50 Mb/s in uplink, and other system features include flexible bandwidths and moderate power consumption of mobile terminals. While the previous 3GPP generations, namely, 3G UMTS and 3.5G HSPA, rely on code-division multiple access (CDMA), LTE adopts orthogonal frequency-division multiple access (OFDMA)-based technologies for its uplink and downlink. Due to high peak-to-average power ratio (PAPR) of OFDMA signals, the single- carrier frequency division multiple access (SC-FDMA), also known as discrete Fourier transform (DFT)-spread OFDMA, has been selected for the uplink transmission in 3GPP LTE systems. SC-FDMA has similar throughput performance as OFDMA but with lower PAPR to increase power efficiency and is less sensitive to frequency synchronization errors, which makes it favorable for mobile terminals.

Discrete W Transform Based Index-Keying M-Ary DCSK for Non-Coherent Chaotic Communications

In this letter, a non-coherent discrete W transform based index-keying M-ary differential chaos shift keying (DWT-IK-MDCSK) system is proposed to tackle the high peak to average power ratio (PAPR) in the code-shifted DCSK systems and meet the demand of high-data-rate transmissions. In such system, multiple chaotic signals and their Hilbert transforms are cooperated closely to convey the M-ary information-bearing signals, and the resultant signals are extended by the index-keying discrete W vectors prior to being added up and transmitted over the channel. Since the index keying technique is used to select the specific discrete W vectors, extra information bits are conveyed by the indices of these vectors, thereby improving the data rate. Then, the analytical bit error rate (BER) expressions of DWT-IK-MDCSK are derived over additive white Gaussian noise (AWGN) and multipath Rayleigh fading channels. Finally, simulation results show the DWT-IK-MDCSK system has a lower PAPR and better BER performance compared to its competitors.

Hybrid scheme of precoder with μ‐law compander for PAPR reduction and nonlinearity improvement in ADO‐OFDM system

SummaryThe application of orthogonal frequency division multiplexing (OFDM) in a visible light communication (VLC) system increases the peak‐to‐average power ratio (PAPR) of the system. Owing to high PAPR, the intrinsic nonlinearity of LED is an important issue in an asymmetrically clipped DC‐biased optical OFDM (ADO‐OFDM) system. In this paper, a hybrid scheme is proposed to reduce the PAPR as well as to mitigate the nonlinearity in an ADO‐OFDM system. The proposed method is a combination of two ADO‐OFDM formats: precoded ADO‐OFDM and μ‐ADO‐OFDM. The preprocessing of the input using a predetermined matrix (PM) in the precoder relieves the need for a handshake at the receiver. The compression of the peak values and enhancement of low amplitudes of the precoded signal in the time domain yield a low PAPR of 2.4 dB only. Besides PAPR reduction, the union of precoder and compander boosts the bit error rate (BER) performance of the traditional ADO‐OFDM system for μ≤128. The combination of precoder with compander decreases the power requirements for high bit rate transmission for a reference BER of 10−3. In this work, nonlinearity is quantified in terms of error vector magnitude (EVM) in percent. The hybrid scheme shows an EVM of 17.23% for 0 dB input backoff power (IBO) much less than 66.4% EVM for a simple ADO‐OFDM system. In addition to low PAPR and mitigation of nonlinearity, the proposed method shows the improvement in power spectral density (PSD) of the system.

Advanced OTFS communication system with compact spectrum and power efficiency improvement

SummaryOrthogonal time frequency space (OTFS) modulation technique is one‐step more precoded system of the conventional orthogonal frequency division multiplexing (OFDM) system, i.e., a double precoded system. The OTFS system was suggested especially for the robust and reliable high‐speed vehicle communications and massive multiple‐input multiple‐output (MIMO) systems. Nevertheless, this basic OTFS system has serious problems: high out‐of‐band (OOB) power emission and high peak‐to‐average power ratio (PAPR). This high OOB power spectrum requires a very wide guard band that can produce a great loss of frequency utilization efficiency, and the power efficiency becomes very poor due to this high PAPR problem. Therefore, in this paper, in order to mitigate these drawbacks, an advanced OTFS communication system is proposed to show the compact OOB power spectrum and power efficiency improvement. This system can be designed by discrete Fourier transform (DFT)‐spread windowing and restructuring‐OTFS (DFT‐Spread WR‐OTFS) scheme that can reduce PAPR by 2.1 dB, 0.5 dB, 1.7 dB, and 1.8 dB compared to the conventional OFDM, DFT‐Spread OFDM, basic OTFS and WR‐OTFS schemes, respectively. Consequently, the efficiency of the high power amplifier (HPA) is improved due to the low PAPR of the proposed system. In addition, we comprehensively evaluate the impact of PAPR reduction performance on the OOB power spectrums and bit error rate (BER) performance of each system in HPA linear and nonlinear environments. Simulation results verify that the power spectrums and the BER performance of the proposed system are better than the conventional schemes in HPA nonlinear environments.

CE-OFDM-CDMA Phase Modulation for 5G System

In the present work, we propose a novel modulation scheme for 5G wireless communication system. Our contribution is to combine PM-OFDM (Phase Modulation Orthogonal Frequency Division Multiplexing) and CDMA (Code Division Multiple Access) to exploit their distinctive advantages. On the one hand, PM-OFDM is an effective technique to combat multipath fading effects. On the other hand, CDMA can serve multiple users who are using the same resources of time/frequency. The aim is to make a combination of PM-OFDM and CDMA techniques. In this paper, the OFDM-CDMA scheme and its PAPR (Peak-to-Average Power Ratio) statistics are reviewed. In this paper, the proposed scheme PM-OFDM-CDMA is described and its performances in terms of PAPR, power spectral density, and BER (Bit Error Rate) are analyzed. Moreover, MMSE (Minimum Mean Square Error) equalizer is used to avoid multipath and noise effects simultaneously. The simulation through AWGN (Additive white Gaussian noise) and Rayleigh channels is performed using MATLAB. From the simulation results, we observed that PM-OFDM-CDMA is an efficient technique in terms of energy consumption (PAPR = 0dB). Besides, CE-OFDM-CDMA offers high spectral efficiency with low BER due to its low PAPR. In CE-OFDM-CDMA method, the shape of the spectrum varies according to the value of the modulation index h. The band occupied by the spectrum increases with the value of h. Therefore, CE-OFDM-CDMA could be considered as a suitable technique for 5G applications.

PAPR reduction by combining clipping and piecewise linear companding for OFDM-based VLC systems

A scheme called clipping-piecewise linear companding (C-PLC) was proposed in this paper to address the problem of high clipping noise and peak-to-average power ratio (PAPR) in optical orthogonal frequency division multiplexing (O-OFDM) signal for visible light communication (VLC) systems. The clipping information of the signal could be retained by adding a suffix at its end, which could reduce the clipping noise and PAPR of the VLC system, thus limiting the dynamic range of the signal effectively. In addition, the retained clipping information could be recovered at the receiver, with which the bit error rate (BER) performance could be pronouncedly improved. Furthermore, PLC could map bipolar signals into unipolar signals suitable for VLC and effectively reduce the PAPR of the signals. Simulation results showed that C-PLC system has lower PAPR than that of direct-current biased optical-OFDM and μ-OFDM schemes, and it also demonstrates an improved BER performance. This work will be of good help for the research and development of VLC system.