LED non-linearity mitigation in a NOMA-OFDM VLC system using a union of precoder and companding

The power domain non-orthogonal multiple access (NOMA) has been considered as an outstanding candidate for 5G visible light communication networks. Due to the various salient features like robustness to multi-path fading, low latency, high compatibility with multiple input multiple output systems, etc. orthogonal frequency division multiplexing access (OFDM) is foreseen to exist in 5G systems. NOMA-based optical OFDM (O-OFDM) is expected to be a promising candidate for supporting high rate internet connectivity, especially for green indoor mobile networks. The OFDM waveform suffers from high PAPR issue. The high PAPR degrades the BER and also enhances the non-linearity in an O-OFDM system. In this paper, a hybrid technique using a blend of precoder with compander is implemented to reduce the PAPR of NOMA based DC-biased O-OFDM (DCO-OFDM) system. The proposed NOMA DCO-OFDM system exhibits a low PAPR of only 4.3 dB. Also, for a reference bit error rate of 10-4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-4}$$\end{document}, the proposed technique displays an error vector magnitude of 13.2 dB.


Introduction
An unprecedented proliferation in the usage of high-speed indoor data communication networks for different services like work from home (WFH), online education, internet of things (IoT), cloud storage etc., and the omnipresent internet connectivity in the past 2 years has resulted in a massive surge in the global data traffic. To deal with it, the current radio frequency (RF) bandwidth scheme has a significant problem coping with the required spectrum. The availability of vast unregulated visible spectrum demands a paradigm shift in the existing wireless system moving to mobile internet connectivity utilizing the lighting infrastructure. With the exception of serving illumination, visible light communication (VLC) makes use of LEDs' luminescence for high transmission capacity especially in indoor wireless networks (Rehman et al. 2019). Owing to the huge unlicensed spectrum, robust security, low cost, low latency, immunity to electromagnetic interference (EMI) etc., the VLC supports the green aspect of next-generation 5G/6G wireless networks with energy-efficient data transmission (Rehman et al. 2019). LED-based VLC systems have recently been employed to provide extended radio services, as well as medical applications, in addition to providing low-cost illumination (Chaudhary et al. 2019(Chaudhary et al. , 2020. In an optical wireless system, the low 3-dB bandwidth ( ∽ 20 MHz) of LEDs used as the transmitter restricts to achieve the practicable system capacity. Due to its numerous advantages, orthogonal frequency division multiplexing (OFDM) modulation has been the state-of-theart for improving system capacity during the last decade. OFDM is projected to play a crucial role in developing 5G communication networks owing to its scalability with multiple input multiple output (MIMO) technologies (Sanchis-Borrás et al. 2017).
Non-orthogonal multiple access (NOMA) is a feasible approach for enhancing system capacity in the forthcoming fifth-generation (5G) VLC network due to its reduced latency and higher spectrum efficiency (Marshoud et al. 2016). In contrast to orthogonal frequency division multiplexing access (OFDMA), users in NOMA have simultaneous access to both frequency and time, and are differentiated by their power domains (Dai et al. 2015). NOMA in association with OFDM modulation format is anticipated to support low latency, improved spectral efficiency, and wider cell coverage (Baig 2017). To boost the capacity of the NOMA VLC system, several efforts have been undertaken to implement OFDM schemes (Lin et al. 2017;Valluri et al. 2020). The DCO-OFDM method is used to improve the user holding range in a NOMA VLC system in Lin et al. (2017) and Valluri et al. (2020).
During the inverse fast Fourier transform (IFFT), however, the accumulation of highly coherent data symbols frequently raises the peak magnitude of the output signal. To measure this phenomenon, the peak-to-average power ratio (PAPR) is used. A high PAPR OFDM signal is undesirable in an optical communication system due to the nonlinear voltage-current (V-I) relationship of LED employed as a transmitter. Nonlinear distortion and poor bit error rate (BER) are the major detrimental effects of a high PAPR system. In order to compensate for nonlinear distortion, the power amplifier's quiescent point in the linear zone must be backed off. It lowers the signal-to-noise ratio (SNR) at the receiver and reduces the efficiency of the amplifier. Nonetheless, using a power amplifier with a large dynamic range increases the overall system cost.
The majority of recent research contributions pertaining to the implementation of a precoder exist for radio frequency (RF) based NOMA systems (Baig 2017;Baig et al. 2017Baig et al. , 2018Yu 2021;Singh et al. 2018;Huang and Su 2018;Fathy et al. 2020). In this paper, the precoder proposed by Slimane (2007) is chosen in conjunction with μ-law compander due to its several advantages, including low complexity, downward compatibility, and ease of symbol detection at the receiver, among others, to reduce the PAPR and nonlinear characteristics in NOMA-based OFDM-VLC systems for 5G applications. To maintain the symbol detectability property, the precoding matrix must be orthogonal and meet the symbol separability condition given by Eqs. (21) and (23) in Slimane (2007). The orthogonality property of the precoding matrix used in Slimane (2007) has been verified while also maintaining the symbol detectability condition. Previously, we used the orthogonal multiplexing access (OMA) scheme to successfully implement the approach for PAPR reduction and non-linearity mitigation in DCO-OFDM and ADO-OFDM systems Ghorai 2020, 2021). The paper presents the extension of our work in Sharan and Ghorai (2020). The NOMA has been applied to multiplex two users with a single base station. The DCO-OFDM, a most commonly used method for obtaining non-negative signal in visible light communication has been used for uni-polar signal transmission (Armstrong 2009). However, it is widely acknowledged that DCO-OFDM fails to provide the full LED dimming range for illumination and energy savings. In Elgala and Little (2013) and Wang et al. (2012), approaches such as reverse polarity O-OFDM (RPO-OFDM) and variable M-QAM OFDM have been discussed to keep the effective LED brightness of fast O-OFDM signals in sync with the industry-standard pulse-width modulation (PWM) light dimming technique for reliable message transmission. The main focus of the manuscript, however, is on non-linearity alleviation and improving BER performance. The following are the major contributions of the proposed approach: • The PAPR of a conventional NOMA DCO-OFDM system is 13.3 dB. The proposed scheme reduces the PAPR significantly to 4.3 dB. • The proposed hybrid scheme has an EVM of only 12.3 dB for a reference BER of 10 −4 , compared to 14 dB, 15 dB, and 19 dB for simple NOMA DCO-OFDM, precoded NOMA DCO-OFDM, and combined NOMA DCO-OFDM, respectively. • To mitigate non-linearity in a system, the input back-off (IBO) power of the system must be increased. The increased IBO power reduces the power efficiency of the system. For an IBO of 0-3 dB, the proposed NOMA DCO-OFDM system has the lowest EVM (%) in comparison to the precoded and companded NOMA DCO-OFDM systems.

Proposed NOMA DCO-OFDM model
Multiplexing of two users on a single base station is considered in this study. Practically, two users are considered in the NOMA application to lower both the detection delay and computational complexity at the receiver (Ding et al. 2016). Figure 1 depicts the implementation of the proposed NOMA O-OFDM system. As illustrated in the figure, the modulated data of users 1 (U 1 ) and 2 (U 2 ) are individually pre-processed in the transmitter section of the proposed hybrid NOMA scheme using a precoding matrix (PM). The precoded information of both users is transmitted simultaneously using the superposition coding (SC) technique, and power allocation (PA) is Fig. 1 Transceiver of the proposed NOMA DCO-OFDM system performed based on the channel state information (CSI) of U 1 and U 2 (Islam et al. 2017). The Hermitian symmetry (HS) operation is performed before the inverse fast Fourier transform (IFFT) to obtain a real valued time-domain signal. Direct current (DC) bias clipping is applied to the output of the IFFT to produce a non-negative real signal. The μ-law compander is applied to the time domain signal before it is passed through the OSRAM SFH 4230, a high power LED used for message broadcast.
The photodiode (PD) used as the receiver converts the optical signal to an electrical signal through the process of photodetection. The received electrical signal is de-precoded after passing through the inverse μ-law compander. To separate the information of individual users, the principle of successive interference cancellation (SIC) is applied to the composite signal. Ultimately, the demodulator is used to recover the transmitted data from U 1 and U 2 .

PAPR computation
Let X 1 and X 2 represent the modulated symbols of user-1 (U 1 ) and user-2 (U 2 ) respectively. The modulated data are pre-processed in the frequency domain using a predetermined matrix P M of the order R × Q given by (Slimane 2007) where R is N+N P , Q is the number of base-band modulated data sub-carriers, N P are nulls carriers used with 0 ≤ N P < N . The precoded output signals are obtained as The unit element of precoder matrix is defined as (Slimane 2007) where p m,0 is given by Assuming that channel state information of U 1 is superior to U 2 , a fixed power NOMA approach is employed without loosing generality. The precoded NOMA signal S[k] PNOMA obtained as a result of superposition coding is expressed as (Yang et al. 2018) (1) where is the power allocation factor and P tot is the total power of Y 1 and Y 2 . The Hermitian symmetry (HS) yields an output vector that is double the length of original input sequence (Sharan and Ghorai 2020) and S 2N−K = S * K is the complex conjugate of the vector S K . The result of the inverse fast Fourier transform (IFFT) followed by DC bias clipping produces a real-valued time-domain precoded NOMA-DCO signal, shown as (Sharan and Ghorai 2020) The time-domain precoded NOMA signal is subjected to the μ-law companding. As a result of the compander output, the recommended transmitted signal is given by where denotes the compression control factor which extends from 0 to 255, v is the greatest amplitude and sgn indicates the signum function. The proposed transmitted time domain signal's PAPR is defined as the signal's maximum power divided by its mean power. Mathematically, it is computed as where |S(n) Proposed,max | 2 denotes the maximum power and E |S(n) Proposed | 2 represents the mean power of the transmitted signal.

Proposed receiver
At the receiver of the NOMA network, the base station (BS) receives the signal transmitted by each mobile user. With the assumption of reciprocal nature of the transmitter and receiver, the received signal is expressed as L defines the overall number of users. h k relates to the kth user's channel coefficient. P tot indicates total common usage power. n is the normally distributed AWGN with 0 mean and standard deviation : As shown in Fig. 1, the inverse μ-law is applied to the received user signal followed by the FFT operation and de-precoding of the signal. The signal obtained as the result of the inverse μ-law operation is expressed as

Theoretical evaluation of the proposed NOMA DCO-OFDM system
The high PAPR in the NOMA DCO-OFDM system causes clipping distortion which degrades the net throughput of the system. In order to improve its transmission performance, the proposed scheme employs a precoder in conjunction with a μ-law compander. In precoding matrix (PM) approach, a predetermined matrix is used to pre-process the modulated data of each user in the frequency domain. In precoding matrix (PM) approach, the modulated data of each user is multiplied by a preset matrix P M as indicated in Eqs. (2) and (3). The use of PM pre-processes data in the frequency domain by generating a cyclic shifted copy of the subcarrier waveforms. The variation in the shape of the sub-carriers reduces the degree of autocorrelation among sub-carriers. So, this leads to the drop in the PAPR of the system due to the combination of low number of similar phase sub-carriers. The application of μ-law compander to the precoded signal raises the average power of the signal. The increase in average power lowers the overall PAPR of the system. The use of precoder decreases the clipping distortion which leads to improvement in the BER of the system. The uniform SNR distribution among data carriers degrades the BER. The SNR of ith sub-carrier in a conventional OFDM is computed as (Jiang et al. 2018) where |X(i)| 2 is the power of ith signal, 2 i represents clipping distortion power, and h −1 i 2 i is the channel noise power. The SNR of ith precoded signal is given by The use of precoder in presence of nulls modifies the 1 , the precoder lowers the SNR and BER of the system degrades. However, for ith carrier if , the precoder enhances the SNR to improve the BER of the system. So, the use of precoder with overhead (10% nulls) redistributes the SNR among different sub-carriers. As a consequence, each data carrier attains an average value. The overall improvement is obtained in presence of PM if the average SNR is sufficient for 16-QAM demodulator.

Results and discussion
The performance of the proposed NOMA DCO-OFDM scheme is evaluated using the simulation results reported in this section. Complementary cumulative distribution function (CCDF), error vector magnitude (EVM) and BER are used to assess the performance of the proposed scheme. In this work, the modulated data is pre-processed using a predetermined matrix before IFFT. The output of IFFT is passed through a μ-law compander. The complete set of simulation parameters are presented in Table 1.
The CCDF is a statistical measure that is used to explain the probability distribution of the PAPR. Figure 2 depicts a CCDF comparison of NOMA DCO, precoded NOMA DCO, companded NOMA DCO, DCO-OFDM with precoder and compander, and the proposed NOMA system. The CCDF of the conventional NOMA DCO-OFDM is the same as obtained in Yang et al. (2018). The result depicts that the PAPR of the proposed hybrid NOMA DCO VLC system is nearly 4.3 dB in comparison to 13.3 dB of the conventional NOMA. The pre-possessing of modulated symbols using a predetermined matrix followed by the μ-law algorithm increases the average power of the signal which results to low PAPR.
The root mean square (r.m.s) of the error vector is defined as the error vector magnitude (EVM), a metric that quantifies non-linearity. The increased BER of the system is indicated by a high EVM. The BER comparison for different NOMA-OFDM systems is shown in Fig. 3. The result illustrates that for a reference BER of 10 −4 the non-linearity of LED is least for the proposed system.
As shown in Fig. 2, implementing the blend of precoder with compander to a conventional DCO-OFDM system gives low PAPR by a very small margin. However, the use of NOMA leads to enhance the capacity by supporting more users. Hence the proposed NOMA based O-OFDM system appears to be a good choice for high burst rate transmission to support the multi users. Figure 4 shows a comparison of EVM performance for NOMA systems. The OSRAM SFH 4230 LED has been used for data transmission. The sixth order curve fitting approach, as outlined in previous works, matches the LED's V-I response curve Ghorai 2020, 2021). The EVM is computed in the presence of an LED for five different bias voltages in the range of 1.6-1.7 V. Figure 4a depicts the EVM performance of various NOMA DCO schemes at 1.6 V with input back-off power ranging from 0 to 8 dB.
The information in Table 2 summarises the performance of each scheme. The μ-NOMA exhibits the highest EVM for all back-off values due to its nonlinear nature. The proposed scheme outperforms traditional NOMA, μ-NOMA, and Precoded NOMA in the range of 0-5 dB back-off power. However, at high back-off power levels of more than 6 dB, the precoded NOMA matches the performance of the proposed schemes. Figure 4c depicts the performance of various schemes at 1.65 V and results are summarised in Table 3. As indicated in the table, the EVM of the suggested scheme drops to 32.49% at 0 dB back-off, indicating a 13% improvement over the same back-off at 1.6 V. In comparison to 1.6 V, the NOMA DCO scheme using the union of precoding and compander offers an improvement of more than 10% for higher back-off values of more than 5 dB. At 1.7 V, the combination of precoder and compander has the lowest EVM of 21.70% at 0 dB, as shown in Table 4, compared to 30.51% and 26.98% for μ-NOMA and traditional NOMA respectively.
In compared to conventional NOMA and Companded NOMA systems, the suggested system reduces non-linearity for 0-5 dB input back-off power, resulting in higher power efficiency.
In a NOMA-based system, successful interference cancellation (SIC) is used at the receiver to decode each user's intended signal. Figure 5 depicts the performance of a SIC receiver as the number of users increases. The figure compares the BER performance of two and three user systems. The results show that User-1 of the U 2 system has a lower BER than User-1 of the U 3 system, and User-2 of the U 2 system has a lower   BER than User-2 of the U 3 system. The increased number of users increases the channel correlation among users. As a result, as the number of users grows, so does the BER for fixed power allocation. So, in order to accommodate a greater number of users without degrading performance, the transmitter power must be increased.

Conclusion
The power domain NOMA is one of the potential multiple access techniques for nextgeneration 5G wireless systems. In this paper, a hybrid approach using a conglomeration of precoder with compander is proposed for PAPR reduction and BER improvement in NOMA based DC-biased optical OFDM system. The proposed method supports the low PAPR and improved non-linearity in a conventional NOMA DCO-OFDM system. The PAPR of the proposed hybrid NOMA DCO VLC system is approximately 4.3 dB, compared to 13.3 dB for the conventional NOMA. The application of NOMA in optical VLC systems manifests improved capacity regions in comparison to the OMA-VLC system. So, the improvement in nonliterary along with low PAPR makes the proposed system to be a good choice for the high-speed 5G indoor mobile data network.
Author contributions All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Availability of data and material Not applicable.

Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.