On the study of the relation between linear / nonlinear PAPR reduction and transmission performance for OFDM-based VLC systems

The relation between the peak-to-average-power-ratio (PAPR) reduction schemes and the transmission performance of the orthogonal frequency division multiplexing (OFDM) based visible light communication (VLC) system is experimentally investigated. The linear selective mapping (SLM) scheme and the nonlinear logarithmic companding scheme are optimized by considering both PAPR reduction and bit error rate (BER) performance. It is demonstrated that the logarithmic companding scheme, albeit providing larger PAPR reduction when compared to the SLM scheme, may result in worse BER performance due to the additional noise induced in its expanding process. Both numerical and experimental investigations show that, at the expense of increased complexity and reduced efficiency, the VLC system using the linear SLM scheme exhibits better BER performance compared to the system using the nonlinear logarithmic companding scheme. We show that for a 400-Mb/s transmission at a distance of 1 m, the BER can be reduced from 2.02 × 10 to 2.51 × 10 by using logarithmic companding scheme. By using the linear SLM scheme, the BER can be further reduced to 1.77 × 10. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement OCIS codes: (060.2605) Free-space optical communication, (060.4510) Optical communications. References and links 1. A. Jovicic, J. Li, and T. Richardson, “Visible light communication: opportunities, challenges and the path to market,” IEEE Commun. Mag. 51(12), 26–32 (2013). 2. L. Grobe, P. Anagnostis, H. Jonas, S. Dominic, L. Friedrich, H. Florian, K. Christoph, J. Volker, and L. KlausDieter, “High-speed visible light communication systems,” IEEE Commun. Mag. 51(12), 60–66 (2013). 3. T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50(1), 100–107 (2004). 4. H. Elgala, R. 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Introduction
Recently, visible light communication (VLC) is emerging as a competitive technology for both indoor and outdoor wireless communication and has attracted increasing attention [1][2][3].With the gradual replacement of traditional lighting sources, high-brightness light-emitting diodes (LEDs) and laser diodes (LDs) have been envisioned as the light sources to provide high-speed VLC transmission.One of the main concerns for the lighting source used in VLC is the nonlinearity.A theoretical model for LED nonlinearity was proposed in [4].In [5], the nonlinearity of LED in the VLC system was experimentally characterized.Generally, the nonlinear transfer functions of LEDs or LDs (the output light signal versus the input electrical signal) leads to the degradation of transmission performance.In prior works, orthogonal frequency division multiplexing (OFDM) has been demonstrated to be a preferable solution to improve the spectral efficiency of VLC systems [6,7].However, the effect of system's nonlinearity can be aggravated in the VLC system using OFDM technique due to the high peak to average power ratio (PAPR) of the time-domain signal [8,9].This is because part of the OFDM signal (the peaks) are clipped or distorted by the LED/LD, due to the high PAPR issue.The clipping/distortion imposes inevitable BER performance degradation to the system.PAPR is regarded as an important metric for the OFDM-based communication system when evaluating its performance.
Effective PAPR reduction schemes to suppress nonlinearity effect in radio frequency (RF) communication have been studied in prior works [10][11][12].In [13,14], PAPR reduction methods have also been introduced to quadrature amplitude modulation (QAM) OFDM based VLC systems.In the literature, various approaches have been proposed, including clipping [15,16], companding transforms [17][18][19][20][21][22], and precoding schemes [23][24][25][26][27] to reduce the PAPR of OFDM signals.The clipping method introduces both in-band distortion and out-ofband radiation on OFDM signals, and thus results in system performance degradation when the clipping ratio exceeds a certain threshold [28].The tone reservation method was proposed in [29,30], which can effectively suppress the clipping noise, at the expense of channel resource and algorithm complexity.However, most of the prior works mainly focused on the theoretical analysis of PAPR reduction schemes in VLC system performance, with an emphasis on the improvement of PAPR reduction.The relation between PAPR reduction and transmission performance has not been studied.Generally, the nonlinear companding and linear precoding methods are more favorable for OFDM-based communication systems due to their efficient PAPR reduction performances and low algorithm complexity.However, PAPR reduction may not necessarily lead to better performance.Therefore, it is desirable to investigate the relation between PAPR reduction and transmission performance of OFDM-VLC system.
In this work, the transmission performance of DC-biased OFDM (DCO-OFDM) VLC system with linear/nonlinear PAPR reduction processing is extensively investigated via both numerical simulations and experimental verification.The nonlinear companding and linear precoding for PAPR reduction are evaluated using the logarithmic companding scheme and the selective mapping (SLM) precoding scheme, respectively.We characterize the relation between linear/nonlinear PAPR reduction and the corresponding transmission performance.It is demonstrated that for the nonlinear logarithmic companding scheme, excessive PAPR reduction may induce severe noise expansion, resulting in bit error rate (BER) performance degradation.In contrast, for the linear SLM scheme, a larger PAPR reduction consistently offers a better BER performance.Experimental results show that for a ~400-Mb/s VLC transmission over 1 m, the BER can be reduced from 2.02 × 10 −3 to 2.51 × 10 −4 and 1.77 × 10 −6 for the logarithmic companding and SLM scheme, respectively.

Principles and experimental setup
Firstly, the transmission performance of the QAM-OFDM VLC system using PAPR reduction schemes is theoretically analyzed.Note that the processing of the transmitted signal and the received signal in the simulation is the same as that in the experimental verifications.In the following, unless otherwise noted, the block size of fast Fourier transform (FFT) is 256, the length of the cyclic prefix (CP) is 1/32 of one OFDM symbol, and 127 out of 256 subcarriers are modulated with 16 QAM signal.The optical wireless channel model used in this work is where y(t) represents the received signal current, x(t) represents the transmitted optical signal, h(t) is the system impulse response, the symbol ⊗ denotes the convolution operation, γ is the detector responsivity, and n(t) is the additive white Gaussian noise (AWGN).The characteristics of the light source are included in the total channel impulse response.The output signal contains a Gaussian noise having a total variance N, which is defined as where shot noise and thermal noise contributions are taken into account when modeling the channel noise, q is the electronic charge; r P represents the average power of the signal before DC blocking; B is equivalent noise bandwidth.C bl , C fr and C ch are the parameters related to background light current noise, feedback-resistor noise, and FET channel noise, respectively.The noise component that is proportional to the received signal optical power is represented by the signal current induced noise N s , whereas the remaining components that depend on the background light and receiving circuits are expressed as the background noise N bg .Therefore, the system SNR can be derived as ( ) where r S denotes the average power of the signal after DC blocking.For the OFDM signals having higher PAPR, the output electrical power from the signal generator will be lower, assuming peak-to-peak output voltage is fixed.This results in lower SNR at the receiver.In the following, the impacts of different factors on the relation between PAPR reduction and transmission performance will be extensively investigated for the OFDM based VLC system.The factors include the parameter of PAPR reduction schemes, FFT block size, QAM modulation order and AWG's sampling rate that are closely related to signal power or background noise.
In this work, two widely used PAPR reduction schemes, i.e., logarithmic companding and SLM with different parameter value are investigated.For the logarithmic companding scheme, the signal is compressed at the transmitter and is reconstructed by the corresponding expanding processing at the receiver.The compressing is given by ( ) where x and y are the time-domain signals before and after companding at the transmitter, respectively.A is the maximum value of x and μ is an adjustable companding parameter, which is related to the level of PAPR reduction for OFDM signals.The system performance of the OFDM VLC system using logarithmic companding with different μ values will be investigated via both simulations and experiments in Section 3.
In contrast, the main idea of the SLM precoding is to generate a set of different candidate data blocks by multiplexing the original signal with different phase sequences.Then, the phase sequence exhibiting the lowest PAPR is selected for precoding [10].Amusing P* is the selected phase sequence, the signal before CP insertion at the transmitter can be obtained as where , U is the number of phases and N is the length of phase sequence that equals to the FFT block size.Generally, the phase elements in the candidate phase sequences are selected from the unit vector set {e i2πk/U , 0≤k<U} in the SLM scheme, such as { ± 1} for U = 2 and { ± 1, ± i} for U = 4.The received signal can be recovered by the corresponding decoding processing, i.e., dividing the corresponding phase sequence.
In the experiments, the performance of the OFDM VLC system using SLM with different phase number U will be investigated for different system configurations.In addition, the performance of the combination of logarithmic companding and SLM, which offers more efficient PAPR reduction, will also be studied for extensive performance evaluation.The experimental setup of a DCO-OFDM VLC system with PAPR reduction is shown in Fig. 1.
The QAM-OFDM signals with different PAPR reduction schemes were generated by an arbitrary waveform generator (AWG).The resulting signal, coupled with direct current (DC) bias via a bias-tee, was used to drive a single green LD (Osram PL520).In the experiments, the LD was optimally biased at 6.7 V.The optimal bias voltage was obtained via pilot transmissions.To make fair comparisons, the bias voltage, which directly relates to the distortion induced by LD's nonlinearity, remained unchanged for all the experiments.At the receiver, the signal was detected by a photodiode (PD) and then amplified by a transimpedance amplifier (TIA).Subsequently, the signal was recorded by a digital storage oscilloscope (DSO) for further offline signal processing.The sampling rate of DSO was 1.25 GS/s, while the sampling rate of AWG varied from 100 MS/s to 300 MS/s to investigate the performance under different system bandwidth.All the experiments were conducted under normal ambient illumination (∼400 lx).

Results and discussion
The PAPR reduction performance can be characterized by the complementary cumulative distribution function (CCDF) of PAPR distribution for the time-domain OFDM signals.Figure 2(a) shows the CCDF results of the 16QAM-OFDM signals (FFT block size equals to 256) using logarithmic companding and SLM precoding schemes with different parameter values.For the linear SLM scheme, when phase number U is increased from 4 to 16, nearly identical PAPR performance can be achieved, indicating that only minor PAPR reduction can be obtained when the U value is greater than 4. In contrast, for the nonlinear logarithmic companding scheme, more efficient PAPR reduction can be achieved by increasing the value of companding parameter μ, which aligns with Eq. ( 4).When μ value equals to 3, the PAPR performance of the signal using logarithmic companding is similar to that of the signal using the SLM scheme.The time-domain OFDM signals, with and without the aforementioned schemes, are also shown in Figs.2(b)-2(e).For the OFDM signals with a lower PAPR, a larger output electrical power can be obtained when the signals are fed into AWG, resulting in a higher SNR if the additional noise impact is not taken into account.However, as mentioned above, the corresponding post-processing at receiver for the companding PAPR reduction schemes may also introduce nonlinear expanded noise.Hence it is desirable to investigate the impact of PAPR reduction schemes on the transmission performance, especially for the frequency-selective fading VLC systems.
Before conducting further investigations, the performance optimization of the SLM scheme or the logarithmic scheme in the VLC system is firstly performed.Figure 3 gives the BER performance of the OFDM-based VLC system using logarithmic companding and the SLM scheme with different parameter values.As is revealed from Fig. 3(a), the BER performance of VLC system using logarithmic companding scheme does not vary monotonically with the value of parameter μ.The system has the best BER performance when the μ value is around 1.2.As μ is increased to near 4, the system performance is worse than that in the scenario without PAPR reduction.This depicts an interesting result that a larger The exper using the SLM better BER pe improvement the SLM sch processing, th addition, whe very small, w result, the lin logarithmic co by using the l Fig. 3 with d tion may not g heme.The sim h well with the nent N bg is con l power.The B better PAPR r can be attribute optimal μ valu improvement scheme as sho APR reduction dered.R performance ase numbers a the increase in s a monotonic ).This is beca ng noise will b n 4, the improv R reduction per better BER per better PAPR re h a larger μ valu based VLC system g SLM scheme wit performance fo en in Fig. 3  We furthe OFDM VLC block size and the following the optimal v Figure 4(a) gi without PAPR shown that th due to more s have similar P using SLM sc reduction as s better BER pe more efficient reduction offe The BER companding a Figs.4(b) and used, the BER block size.In OFDM VLC noise induced block size ha reduction per performance companding f Fs of QAM-OF ction, with log in Fig. 5(a).T s, the improve nd companding than that of th = 0.01).Insets: the two parameter PR reduction sc hich are closel ns, the μ value number U is 4 ignal with diffe mic compandin a higher PAPR n that all the O garithmic com th smaller FFT ore, since a sm r PAPR reduct d by using the panding.QAM-OFDM V emes for differ wn in Fig. 4(b    system can be hods.We hav nce for the OFD ic companding value of 0.

Conclusio
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Fig. 1 .
Fig. 1.Experimental setup of the OFDM-based VLC system using PAPR reduction.
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