ASCO-OFDM based VLC system throughput improvement using PAPR precoding reduction techniques

The huge bandwidth and immunity to electromagnetic interference make visible light communication (VLC) systems the preferred technique for many applications. Unfortunately, the superposition of multiple subcarriers in VLC orthogonal frequency division multiplexing systems leads to a high peak-to-average power ratio (PAPR). So, in this study, we aim to reduce PAPR in VLC systems and improve the system performance by proposing non-distorting PAPR reduction techniques like precoding techniques as it doesn’t affect the system data rate because they do not require any obligatory transmission of side information. Moreover, it has a very good ability to reduce the PAPR without affecting the system BER performance. So, different precoding reduction techniques are proposed like discrete cosine transform (DCT), discrete sine transform (DST), discrete Hatley transform (DHT), and Vandermonde like matrix (VLM), to address the high PAPR and light-emitting diode-restricted linear range problems in VLC systems. The proposed technique using DHT, DCT, DST, and VLM provided a significant advantage in reducing the PAPR by 1.35 dB, 1.46 dB, 2.12 dB, and 2.17 dB, respectively. So the proposed technique is based on using the VLM precoding technique to achieve maximum reachable PAPR reduction value. Also, a comparison of the presented work and related literature reviews for PAPR reduction techniques are held to ensure the validity and effectiveness of the proposed scheme.


Introduction
Visible light communication (VLC) has recently taken the interest of the research community, industry, and academia owing to its legendary notability of simultaneously ensuring lighting and high data rate communication by using cost-effective optoelectronic devices such as light emitting diodes (LED) to transmit data, and photodetector (PD) to receive optical signals and convert them to electrical signals (Hameed et al. 2022). VLC has become the most advanced method of transmitting light via optics. It is an enhanced form of free-space optical communication, particularly for indoor areas. Several optoelectronic/photonic devices/platforms, including Mach Zehnder interferometers, Fiber Bragg gratings, and semiconductor optical amplifiers, started to concentrate and move some of their applications to keep up with the visible broad use of VLC technology, particularly in indoor optical communication settings (Mohammed et al. 2021). Moreover, several studies show the widespread use of many applications using VLC that need high data demands such as high-speed video streaming, localization, high bit rate data broadcasting in interior structures, the development of the physical layer for 5G, and underwater VLC. It is also favored in electromagnetic interference-sensitive applications, such as airplanes and hospitals (Ahmad et al. 2020;Li et al. 2020;Mohammed et al. 2021;Valluri et al. 2020). This aggressive data demand depletes the available radio frequency (RF) spectrum, causing it to become overcrowded. The rapid development of LED promotes the use of VLC as a solution to the problem of insufficient bandwidth (Sharan et al. 2022). Due to the benefits of license-free available spectrum, low power consumption, and safety, as VLC uses light as a medium to convey data, and light signals cannot pass through barriers, a high level of secure communication may be assured (Valluri et al. 2020). So, VLC is seen as a viable complement to radio frequency communications (Wang and Ren 2020). Moreover, due to LED non-coherent emission properties, VLC depends on intensity modulation (IM) forms at the transmitter end and direct detection (DD) at the receiver end. Also, due to LED restricted modulation bandwidth, VLC must rely on multicarrier modulation techniques such as orthogonal frequency division multiplexing (OFDM). OFDM was incorporated for VLC because of its inherent nature of being resistive to multipath fading scenarios and overcoming inter-symbol interference (ISI) (Vappangi et al. 2018). But the OFDM method used in RF cannot be used directly in VLC, since IM/DD systems are a big rudimentary work that requires much effort as it can't work with the bipolar and complex OFDM signal as in RF. Thus, the time domain signal must be both unipolar, and real to be applicable in VLC systems. Moreover, the input to the Inverse Fast Fourier Transform (IFFT) must meet Hermitian symmetry conditions to produce a real-valued signal. Even if the aforementioned limits result in a real generated signal, it is still in a bipolar form. So, to convert this bipolar signal to a unipolar signal, different optical OFDM (OOFDM) modulation techniques should be used as suggested in the literature (Ahmad et al. 2020;Alrakah et al. 2021;Farid et al. 2022a, b;Wu et al. 2015). Some of these optical modulation techniques are direct current biased optical OFDM (DCO-OFDM) , asymmetrically clipped optical OFDM (ACO-OFDM) (Ahmad et al. 2020), asymmetrically and symmetrically clipping optical OFDM (ASCO OFDM) (Wu et al. 2015), enhanced ASCO OFDM (E-ASCO OFDM) (Farid et al. 2022a, b), pulse amplitude modulated discrete multitone modulation (PAM-DMT) (Alrakah et al. 2021), unipolar OFDM (U-OFDM) and various additional hybrid types like asymmetrically clipped DC-biased optical OFDM (ADO-OFDM) (Hameed et al. 2021). Despite the VLC numerous benefits, a VLC-OFDM-based system has some difficulties that must be resolved. Peak to average power ratio (PAPR) is the most harmful problem, resulting from the superposition of a large number of subcarriers, whose constructive combination may result in high peak values in the time domain. In addition, the restricted dynamic range of LED demands addressing the PAPR problem in VLC. For an LED with a restricted dynamic range, that is, with a very small linear region in its current-voltage (I-V) characteristics, a low PAPR signal is required. Because, if the PAPR signal is large, the peaks that lie beyond the linear region will be clipped and more distortion will be applied to the signal. LED is the primary source of nonlinearity in VLC (Abd Elkarim et al. 2020). So, to reduce LED-induced nonlinear distortions, it is necessary to either linearize the nonlinear transfer characteristics of LED or emphasize PAPR reduction approaches. Much significant research dealing with the linearization of LED transfer characteristics uses digital pre-distortion techniques to compensate for the nonlinear LED features (Abd Elkarim et al. 2020;Elgala et al. 2009);; . In this research, PAPR reduction methods are used to accommodate the restricted dynamic range of LED. So, to achieve optimal system performance with increased spectral efficiency and high power efficiency, as well as effective use of the available optical spectrum, the PAPR issue in VLC must be solved.

Related work
In the literature, different PAPR reduction methods (Anwar et al. 2022) for OOFDM have been researched, which may be generally grouped into the following categories: • Signal distortion approaches (SDA): These techniques change the OOFDM signal before it is sent, to reduce the PAPR. Some of these SDA are companding (Zhang et al. 2016), peak windowing (Abed et al. 2015), and clipping and filtering (Wang and Chen 2014;Xu et al. 2014); ; . In companding techniques, the OFDM signal is changed in a way that is not linear to lower the PAPR values. But this nonlinearity operation breaks the orthogonality of OFDM, which means that the system performance is degraded. The clipping and filtering technique is based on the idea that high signal peaks don't happen very often, so these peaks can be clipped, which distorts the signal. These techniques are easy to use, but on the other side, they cause clipping distortion, which degrades the system BER performance. • Multiple signaling and probabilistic approaches (MSP): These approaches create multiple alternative signals with identical information, and the signal with the lowest PAPR is chosen for transmission. The most common probabilistic approaches are partial transmit sequences (PTS) (Niwareeba et al. 2022), selected mapping (SLM) (Niwareeba et al. 2022;Li et al. 2020); ; , and tone-reservation (TR) (Arvola et al. 2022).
Most of these approaches lead to data rate loss as they need extra side information and degrade bandwidth efficiency. • Precoding approaches (PA): it is one of the most basic strategies for reducing PAPR.
However, these approaches need more bandwidth and add complexity overhead but the inverse precoding approach (IPA) overcomes this issue. In Abdulwali et al.

Research main contributions
In this research, according to the best author's knowledge on reducing the PAPR for VLC systems, this is the first time a PAPR reduction technique is introduced to the E-ASCO OFDM system. The distinctive feature behind E-ASCO OFDM is it has a high spectrally efficient, high data rate, and power-efficient system with good system BER performance compared to other existing optical modulation techniques ); Ahmad et al. 2020). But, unfortunately, the E-ASCO OFDM system has a PAPR problem. So, in this research, a new modified system named precoding E-ASCO OFDM (PE-ASCO OFDM) system is investigated to overcome such PAPR problem. PE-ASCO OFDM is based on introducing different PA such as DHT, DST, DCT, and VLM to the conventional E-ASCO OFDM system to overcome the PAPR problem and taking into consideration their effects on the system BER performance since there is a tradeoff between reducing the PAPR and improving the system BER performance. The main contributions of this paper are as follows: • The PE-ASCO OFDM has been proposed which consists of different PA such as DHT, DST, DCT, and VLM, this approach has resulted in lower PAPR and high spectral efficiency over earlier explored alternatives without any degradation in the system BER performance. • The difference between the main contribution of the manuscript and the previously published work is that the previously published work is focusing on the PAPR over the RF OFDM systems. Whereas the concurrent research is focusing on the OFDM over the VLC as a new carrier or new technology that may be the most promising technique in 6G networks. As in 6G, the data rate becomes hundreds of megabits per second so, the PAPR problem must be tackled by taking into consideration the VLC constraints. The other PAPR reduction techniques are studied and investigated the effect of bipolar data on the system whereas, in our system we have to modify the data stream in a unipolar shape to follow the VLC data transmission constraints, so the PAPR will be more degraded because the system will have only one-sided (positive) pulses so we will suffer a huge effect of high PAPR so we have to think about how could we deal with such performance degradation and the challenge that comes from the characteristics of VLC transmission environment. In addition, there is a required high data rate transmission so the authors proposed the PE-ASCO OFDM that is based on E-ASCO OFDM system which has a high data rate with good system BER performance compared to other published systems as will be illustrated in the manuscript. Moreover the proposed PE-ASCO OFDM compromise between such a high data rate and good system BER performance. • This work provides a comprehensive performance analysis for the proposed PE-ASCO OFDM in terms of PAPR and BER. • The analytical expression for PAPR and simulation results for the proposed PE-ASCO are explained and analyzed.
Page 5 of 23 410 The rest of the paper is organized as follows, Sect. 2, describes the conventional E-ASCO OFDM system, and the mathematical description for the PAPR and different PRT in OOFDM are introduced in Sect. 3. Section 4 describes the proposed PE-ASCO OFDM system model and parameters. Finally, the results of the simulation and the comparison between the proposed plans are discussed in Sect. 5.

Conventional E-ASCO system model
The E-ASCO and the ASCO OFDM systems have the same transmitter but differ in the receiver as explained in detail in Farid et al. (2022a, b), and since the PAPR is measured at the transmitter side so, the PAPR is the same for ASCO and E-ASCO OFDM systems. But in this work, the aim behind studying the PRT in E-ASCO OFDM rather than ASCO OFDM is that the E-ASCO OFDM has more features as low receiver complexity by O ( Nlog 2 N ) with better overall system BER performance than the ASCO OFDM (Farid et al. (2022a, b). The ASCO OFDM system was to boost a high data rate while maintaining an acceptable BER performance. The E-ASCO OFDM system increases the data rate by using (3N∕4) subcarriers containing data, where (N) is the FFT size. However, since the samples are split into two frames during transmission, the data rate spectrum efficiency ratio is reduced to 37.5% (Wu et al. 2015). ASCO OFDM system is a mixture system whereas odd subcarriers carried an asymmetric time domain signal as ACO-OFDM (Mohammed et al. 2021), and symmetric time domain signal for even subcarriers (Wu et al. 2015). Figure 1 shows the E-ASCO OFDM transmitter and receiver block diagram. The input data is modulated by M-ary quadrature amplitude modulation (M-QAM) at the transmitter, and the generated modulated symbols have complex values. The modulated symbols are then translated from serial-to-parallel (S/P) form, and Hermitian symmetry is applied to obtain the real signal. In addition, the output of Hermitian symmetry is applied to an Inverse fast Fourier transform (IFFT) block that provides a real bipolar signal. Then, a clipping technique is taken to acquire a suitable signal for transmission through the VLC system. The data is then applied to a parallel to serial (P/S) block to convert it into a serial data bit stream, and a cyclic prefix (CP) is appended to the start of each time-domain OFDM signal. Moreover, a detailed analysis and description of the E-ASCO receiver were introduced by Farid et al. (2022a, b).

PAPR and precoding reduction techniques (PRT)
The mathematical description for the PAPR and different PRT in OOFDM are introduced and discussed in this section.

PAPR in OOFDM
PAPR is a critical aspect of the E-ASCO OFDM system's instability. As the nonlinear transfer properties of optical devices, like LED, have a substantial impact on the implementation of optical OFDM. Also, their impact increases as the PAPR increases. So, the PAPR problem should be overcome. The ratio of the maximum instantaneous power to the average power is defined as the PAPR of a discrete E-ASCO OFDM signal x i,jsum (n) as in (1) (Farid et al. 2019).
where x i,jsum (n) is the continuous transmitted time domain signal, and E |.| is the statistical expectation.
When multiple subcarriers have maximum amplitudes at the same time, this leads to a signal's peak power appearing and causes a high PAPR signal. The benefits and drawbacks of a PAPR reduction strategy can be assessed using a complementary cumulative distribution function (CCDF) since PAPR reduction techniques do not provide the same reduction degree for all inputs. CCDF is defined as the probability that the PAPR will exceed a certain value PAPR0 as illustrated in (2). If one scheme is superior to all others in terms of PAPR reduction, its CCDF curve will be to the left of the other. So, a comparison between the CCDF of the proposed precoding techniques will be discussed in the simulation results in Sect. 4.

Precoding reduction techniques (PRT)
This work introduced and explained four precoding techniques which are DHT, DST, DCT, and VLM with their mathematical modeling. Pre-coding matrix k was used in all the mentioned precoding techniques with dimension NxN before the IFFT so we can reduce the PAPR. This process will multiply the input data with the pre-coding matrix k to distribute the energy of data symbols over the subcarriers for reducing the PAPR (Mohammed et al. 2021) as shown in (3). where k is a Precoding Matrix of size NxN.

Discrete hartly transform (DHT)
Any element in the a th row or b th column of the DHT matrix k can be defined as in (4) (Farid et al. 2020;Xu et al. 2022); .

Discrete cosine transform (DCT)
The DCT precoding is based on real conversion that requires the multiplication of data by a cosine equation (Farid et al. 2020;Salama et al. 2011). The DCT matrix can be illustrated as in (5). where k ab is the DCT matrix with a th row and b th column.

Vandermonde like matrix (VLM)
VLM precoding technique is based on reducing the autocorrelation between the data which results in decreasing the PAPR. Moreover, the VLM matrix can be generated in two ways (Mohammed et al. 2021;Sharifi 2019b). Both of them have the same efficiency in reducing the PAPR. So, in this work, the used VLM matrix is illustrated as in (6).
where 0 ≤ a, b ≤ N − 1 and k ab is the VLM matrix with a th row and b th column.
All the previously mentioned PRT (DHT, DCT, VLM, and DST) are invertible transforms, thus we can retrieve the signal at the receiver side.

Discrete sine transform (DST)
DST PRT is also based on reducing the autocorrelation between the data to reduce the signal PAPR. The representation of the time-domain signal x q (n) corresponding to the q th symbol and the frequency domain transform x q (k) as provided by Cinemre et al. (2021), Farid et al. (2022a, b), Vappangi et al. (2022), can be illustrated as in (7).

The proposed precoding E-ASCO (PE-ASCO) OFDM system
The proposed PE-ASCO OFDM incorporates different PAPR precoding reduction techniques such as DCT, DST, DHT, and VLM for reducing the PAPR of the PE-ASCO OFDM system to enhance the system power efficiency and reduce LED-induced nonlinear distortions. Figure 2 represents the block diagram for the transmitter and the receiver of the PE-ASCO OFDM. The proposed PE-ASCO differs from the conventional E-ASCO OFDM represented in Fig. 1 in inserting a precoding block and inverse precoding block after the (S∕P) block at the transmitter, and before the (P∕S) block at the receiver respectively as marked by red rectangles in Fig. 2. Also, Figs. 3 and 4 show a flowchart to summarize the PE-ASCO OFDM transmitter and receiver processes respectively.
The transmitted data bit stream is applied to a mapper followed by a S/P block that generates parallel data symbols which are applied to one of the previously mentioned proposed precoding techniques that are mathematically represented in Sect. 3. The output data symbols from the precoder X(k) is represented in (8).
The X(k) symbols are separated into three components X L (k), X M (k), X N (k) as represented in (9), and (10).
where k is the symbol index that ranges as, Then, X L (k), X M (k), andX N (k) data symbols are applied to Hermitian symmetry and data arrangement block (Farid et al. 2022a, b) as shown in Fig. 5 and following (11). where 1 ≤ k ≤ N 4 , and X(0) = 0. The Hermitian symmetry outputs are X oddi (k), X oddj (k) , and X even (k) corresponding to X L (k), X M (k), andX N (k) data symbols respectively, where, X oddi (k), and X oddj (k) are two data vectors with only odd-indexed data symbols from the original data stream, i.e., both vectors have zeros at all even indices as represented in (11) and (12). Also, X even (k) is a data vector with only even-indexed data symbols from the original data stream i.e., the even data vector has zeros at all odd indices, as represented in (13).   Table 1 illustrates the data symbol structure in PE-ASCO OFDM with N =16 subcarriers as an example. Then, the data vectors X oddi (k), X oddj (k) , and X even (k) are applied to the IFFT block to get a real bipolar time domain signal. The arrangement of the data symbols carried on odd, and even subcarrier positions lead to an asymmetric signal around (n= N 2 ) at the output of the IFFT block as shown in Fig. 6 and represented in (14) and a symmetric signal around (n = N 2 ) at the output of the IFFT block as shown in Fig. 7 and represented in (15) respectively (Farid et al. (2022a, b). Moreover, this arrangement helps in recovering the clipped part of the signal at the receiver after the clipping process is applied to the transmitted signal at the transmitter to make the signal positive to be valid for transmission through a VLC channel as illustrated by Wu et al. (2015).
In Fig. 2 two IFFT blocks at the transmitter generate three frames. The first two framesx oddi (n),x oddj (n) are created from the first IFFT block. The transmitted bipolar asymmetric samples are then converted into positive samples by using a negative clipper block which outputs x oddi (n), andx oddj (n) signals as represented in (16), (17), and (18). The second IFFT block generates the last frame x even (n).
Then, x even (n) is separated into two equal parts each of ( N ) samples x evenPC (n) , and x evenNC (n) . The x evenPC (n) part is the absolute value of the negative frame resulting from applying positive clipping to x even (n) signal, and x evenNC (n) is the negative clipping  (Farid et al. 2022a, b) version of x even (n) as illustrated in (19) and (20) respectively. Then, the two transmitted OFDM symbols are x isum (n) and x jsum (n) as in (21) and (22).
At the receiver, the received signal y(n) is separated into two parts y A (n) and y B (n) to make a special process on them to extract the data carried on the odd subcarriers. Then, by subtracting the odd signal y i,jodd (n) from the total received signal y(n) , the data carried on the even subcarriers can be extracted. A detailed mathematical expression and description for these processes are illustrated in Farid et al. (2022a, b). Then, y i,jodd (n) and y even NC, PC (n) signals are applied to the FFT block to convert them into Y i,jodd (k) and Y even (k) signals which are represented in the time domain. Finally, the extracted data symbols Y i,jodd (k) , and Y even (k) are applied to a data symbol arrangement then the inverse precoding reduction technique (IPRT) to make the inverse of the precoding process occur at the transmitter side to get the actual transmitted data without any distortion. Also, the output from IPRT is applied to a de-mapper block that output the original data.

Numerical results and analysis
The numerical results of the PAPR and BER system performance corresponding to the proposed PE-ASCO OFDM using different PRT (e.g., DCT, DHT, DST, and VLM), and the conventional E-ASCO OFDM system are compared and simulated using MATLAB.  Farid et al. (2022a, b) to analyze the effect of changing the modulation order on the PAPR and BER system performance. Moreover, the simulated channel is additive white Gaussian noise (AWGN) channel. This work is also associated with a high IFFT size (N = 1024) (i.e., extensive processing data). Table 2  The PAPR reduction effectiveness is measured by the PAPR CCDF (Mohammed et al. 2021). the values of PAPR o is calculated at CCDF= 10 −3 same as in the literature. where, PAPR o is the instantaneous PAPR value at CCDF = 10 −3 . In addition, the two parameters PAPR gain and E b ∕N odiff are introduced in this work for comparison purposes. At which PAPR gain is defined as the amount of reduction in PAPR o of the proposed technique compared to the conventional E-ASCO PAPR o which is mathematically calculated by subtracting the PAPR o of the proposed PE-ASCO OFDM from the E-ASCO OFDM PAPR o at CCDF = 10 −3 . The greater the PAPR gain , the more efficient the used PAPR reduction technique. while E b ∕N odiff is defined as the difference between the conventional E-ASCO OFDM system E b ∕N o and the required E b ∕N o after applying the PAPR reduction technique as represented in (24). E b ∕N odiff is mathematically calculated by subtracting the E b ∕N o of the proposed PE-ASCO technique from the E-ASCO E b ∕N o value at BER = 10 −4 . It is worth mentioning that, there are three instances for the E b ∕N odiff value: • If Eb∕No diff = 0, there is no degradation in the system BER performance.
• If Eb∕No diff > 0, the system BER performance improves because less energy is required to accomplish the same BER. • If Eb∕No diff < 0, the system BER performance degrades because more energy is required to achieve the same BER.

PAPR results
A comparison between the PAPR for the proposed PE-ASCO OFDM system using different PRT techniques is introduced in this section to identify the most suitable technique for reducing the PAPR taking into consideration the system BER performance for PE-ASCO OFDM. Figure 8 shows the evaluation of the PAPR for the conventional E-ASCO OFDM system that was previously represented in Fig. 1 and the PAPR for the proposed PE-ASCO based VLC system represented in Fig. 2 with different proposed PRT (DCT, DHT, DST, and VLM) using 16-QAM modulation technique. Figure 8 shows that at CCDF = 10 −3 , the value of PAPR o for the E-ASCO OFDM is equal to 15.5 dB, and the PAPR o for PE-ASCO OFDM using DHT, DCT, DST, and VLM PRT is 14.15 dB, 14.04 dB, 13.38 dB, and 13.33 dB, respectively. This means that the proposed PE-ASCO system using different PRT causes a reduction in the PAPR compared to the conventional ASCO-OFDM system. Since the PAPR reduction value varies from using one PRT to another, so the PAPR gain when applying DHT, DCT, DST, and VLM PRT in the PE-ASCO OFDM system are 1.35 dB, 1.46 dB, 2.12 dB, and 2.17 dB, respectively as summarized in Table 3. Table 3 shows comparison results according to PAPR at CCDF=10 −3 for the proposed PE-ASCO OFDM system using different PRT.
Also, Fig. 9 shows the evaluation of the PAPR for the conventional E-ASCO OFDM system, and the proposed PE-ASCO OFDM system, with different proposed PRT (DCT, DHT, DST, and VLM) using different modulation schemes order (M) at CCDF = 10 −3 . At which the best reduction technique is the one with minimum PAPR o overall different constellation sizes (4, 16, 64, 256, 1024, and 4096-QAM). Figure 9 shows that generally for all the represented curves at a constant CCDF = 10 −3 , as the constellation size increases the PAPR o increases. Also, we can notice that both PE-ASCO using DST, and VLM curves are almost concatenated so, they have almost the same PAPR o response overall constellation sizes. Also, PE-ASCO using DST or VLM PRT is having the minimum PAPR o values compared to other existing PRT and conventional ASCO OFDM systems. On the other hand, the PE-ASCO OFDM system using DCT or DHT has comparable PAPR o system performance which is also better than the E-ASCO OFDM PAPR o response.
So, all the proposed PRT (DHT, DCT, DST, and VLM) in the PE-ASCO OFDM system have lower PAPR than the conventional E-ASCO OFDM system. But, the proposed PE-ASCO OFDM system using DCT or DHT has less impact on reducing the PAPR than the proposed PE-ASCO using DST or VLM.

BER results
Since there is always a tradeoff between decreasing the PAPR and the system BER performance, in this section, the BER curves for the PE-ASCO OFDM system using different PRT are illustrated and compared to the conventional E-ASCO OFDM system.
The BER curves represented in Fig. 10, for PE-ASCO OFDM using different PRT show a very close BER performance for the different proposed PRT in PE-ASCO OFDM since at the transmitter there is a precoding matrix applied to the data symbols and at the receiver, the inverse of this precoding matrix is applied to the received data so, this is the procedure that is used to reduce the PAPR in these techniques. Figure 11 shows the relation between the required Eb∕No with different modulation orders to achieve a BER of 10 −4 for the Conventional E-ASCO OFDM, and PE-ASCO OFDM using DHT, DCT, DST, and VLM PRT. Figure 11 shows that the proposed PE-ASCO OFDM system Eb∕No curves using different PRT and the conventional E-ASCO OFDM system Eb∕No curve are overlapping with minor differences at some points. So, they are all almost having the same response after varying the modulation order (e.g., M = 4, 16, 64, 1024, 4096 QAM). Also, it has the same response as the conventional E-ASCO OFDM BER system performance which is one of  its merits as it has a significant effect on reducing the PAPR as explained previously and shown in Fig. 8 without affecting the system BER performance even at high modulation orders. Table 4 shows a comparison results according to the required Eb∕No at BER=10 −4 for the proposed PE-ASCO OFDM system using different PRT.
From the results in Table 4, we can notice that any of the proposed PRT in the PE-ASCO OFDM system can achieve a PAPR gain with different values of reduction without any degradation in BER system performance. But, Since the PAPR is the main interest of the current work, so, we can consider that the PE-ASCO OFDM system using VLM PRT is the optimal technique which has the highest PAPR reduction without any degradation in the BER system performance compared to the conventional E-ASCO OFDM.

Comparison with other published works
This section compares the specifications of the proposed work in this thesis to those of comparable works in the literature. However, this is the first time studying the PAPR concept in the E-ASCO OFDM systems. So, the comparison with the literature is limited to various optical modulation-based VLC systems such as ACO-OFDM, and DCO OFDM by comparing the amount of PAPR gain and Eb∕No diff for each system as shown in Table 5. The definition of main judgment factors is defined previously at the beginning of this section. So, the best technique is the one with the greatest amount of PAPR gain while causing no degradation in system BER performance (i.e., Eb∕N0 diff = 0). Table 5 demonstrates that this proposed technique provided a significant advantage in reaching high calculated PAPR gain without BER system degradation. This is done when applying VLM PRT in the PE-ASCO OFDM system.

Conclusions
In this paper different precoding techniques are proposed for the PE-ASCO OFDM VLC system for reducing the PAPR to get power efficient VLC system. The proposed PRT are evaluated and compared with each other in addition to the conventional E-ASCO OFDM system according to PAPR reduction capability and system BER performance to get the optimal PRT in reducing PAPR while keeping the system BER performance without degradation for the PE-ASCO OFDM system. Simulation results indicate that the proposed VLM pre-coding scheme outperforms the DHT, DCT, and DST pre-coding schemes by 0.82 dB, 0.71 dB, and 0.05 dB respectively, in the PE-ASCO OFDM system as it reduces the high PAPR of the PE-ASCO OFDM system by 2.7 dB without any degradation in system BER performance. This research increases the compatibility of the E-ASCO OFDM system with practical applications. A comparison with related literature is performed to validate and assure the innovation and performance of the suggested methods. permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.