Abatement of PAPR for ACO-OFDM deployed in VLC systems by frequency modulation of the baseband signal forming a constant envelope

Optics Communications 393 (2017) 258–266

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Optics Communications journal homepage: www.elsevier.com/locate/optcom

Abatement of PAPR for ACO-OFDM deployed in VLC systems by frequency modulation of the baseband signal forming a constant envelope ⁎,1

Vinay Kumar Singha, a

MARK

, U.D. Dalala

Sardar Vallabhbhai National Institute of Technology, Surat, Gujarat, India

A R T I C L E I N F O

A BS T RAC T

Keywords: PAPR reduction Optical OFDM Constant envelope LED Visible light communication

To inhibit the effect of non-linearity of the LEDs leading to a significant increase in the peak to average power ratio (PAPR) of the OFDM signals in the Visible light communication (VLC) we propose a frequency modulated constant envelope OFDM (FM CE-OFDM) technique. The abrupt amplitude variations in the OFDM signal are frequency modulated before being applied to the LED for electro-optical conversion resulting in a constant envelope signal. The LED is maintained in the linear region of operation by this constant envelope signal at sufficient DC bias. The proposed technique reduces the PAPR to the least possible value ≈0 dB. We theoretically analyze and perform numerical simulations to assess the enhancement of the proposed system. The optimal modulation index is found to be 0.3. The metrics pertaining to the evaluation of the phase discontinuity is derived and is found to be lesser for the FM CE-OFDM as compared to the phase modulated (PM) CE-OFDM. The receiver sensitivity is improved by 1.6 dB for a transmission distance of 2 m for the FM CE-OFDM as compared to the PM CE-OFDM at the FEC threshold. We compare the BER performance of the ideal OFDM (without the non linearity of LED), power back-off OFDM, PM CE-OFDM and FM CE-OFDM in an optical wireless channel (OWC) scenario. The FM CE-OFDM has an improvement of 2.1 dB SNR at the FEC threshold as compared to the PM CE-OFDM. It also shows an improvement of 11 dB when compared with the power back-off technique used in the VLC systems for 10 dB power back-off.

1. Introduction The adaptation of the multicarrier communication in the Visible light communication (VLC) technology has intrigued the research to progress in a direction to not only attain higher data rate [1] but also to achieve more robustness to the non-linearity's of the so developed system [2–4]. The uniqueness of this system is that it caters need for the indoor lighting and the data accessibility simultaneously [5]. The driving factor towards the advancement of the VLC is the simplicity of implementation of the system for high speed indoor applications. IEEE 802.15 WPAN TG 7 completed a PHY and MAC standard in 2011. The state of the art in the solid state lightening provides modern day light emitting diodes (LEDs) that are not only energy efficient but also have modulation bandwidths that are claimed to be tens of GHz [6]. The indoor lighting is already being replaced with these energy efficient LEDs. The other notable advantages of the VLC over the RF indoor communication system include unlimited bandwidth, no restriction on the transmission power considering the health regulations, no eavesdropping on the data as the signal is confined within the indoors by the opaque walls.

⁎

1

A typical optical orthogonal frequency division multiplexed signal (O-OFDM) for the VLC is obtained by intensity modulation and direct detection (IM-DD) by the LED and the photodetector, respectively. The information contained in the amplitude of the electrical signal gets converted in to the equivalent intensity of the optical signal proportional to the luminous efficacy of the employed LED [7]. At the receiver the photodetector converts back the received optical signal falling on its surface to its responsivity times, corresponding electrical signal which is processed further. To ensure faithful intensity modulation at the LED the OFDM (electrical) signal is required to be real and positive throughout. For this the Hermitian symmetry is imposed on the data symbols to be fed before the OFDM block. The two techniques of generating the real and unipolar OFDM signals for optical communication are described in detail in [8]. In the Asymmetrically Clipped Optical OFDM (ACO-OFDM) the data is modulated only on the alternate subcarriers. In the Direct Current biased Optical OFDM (DCO-OFDM) a sufficient bias is given to the OFDM signal to make it unipolar. The former is reported to have achieved a gain of 3 dB over the latter for electrical power requirement. However, the power

Corresponding author. E-mail addresses: [email protected] (V. Kumar Singh), [email protected] (U.D. Dalal). Postal address: Electronics Department, Sardar Vallabhbhai National Institute of Technology, Surat, Gujarat - 395007, India.

http://dx.doi.org/10.1016/j.optcom.2017.02.065 Received 24 January 2017; Received in revised form 25 February 2017; Accepted 26 February 2017 Available online 03 March 2017 0030-4018/ © 2017 Elsevier B.V. All rights reserved.

Optics Communications 393 (2017) 258–266

V. Kumar Singh, U.D. Dalal

most advantage of the phase modulation transformation is that one can achieve the lowest possible PAPR=0 dB. This PAPR reduced revamped signal can be amplified (in RF)/electro-optical converted (in optical) with least power back-off thereby increasing the range of the system as more power is transmitted into the channel and maximizing the efficiency of the employed non linear device. Effectively the OFDM signal modulates the phase of the carrier. The envelope of such a modulated signal essentially remains constant. In [22] the phase of the carrier is modulated by the OFDM signals for the RF transmission and the author names it as the CE-OFDM. It is reported that the CE-OFDM is suited for non-linear and efficient amplification. The studies conducted by [23] on the performance of CE-OFDM in an ideal AWGN and frequency selective channel revealed that the phase detector at the receiver end achieves optimum performance for small modulation indices and low power efficiency. It was concluded that the CE-OFDM signal is more useful for power constrained systems. The research work presented in [24] proposes a linear receiver for the PMOFDM system. It is claimed that the receiver model is computationally less complex as compared to the conventional angle detection technique and also is immune to the threshold effect. A CE-M-ary time orthogonal (CE-MTO) was shown to have comparable performance to CE-OFDM in [25]. This approach is easier in implementation and is based on orthogonal waveforms in time domain. In the case of fiber transmission [26] proposed the CE-OFDM as a technique of mitigating the non linearity of the transmission media in Optical Direct-Detection (DD) systems. Significant tolerance to fiber non linearity is reported with BER improvement by a factor of 1000 as compared to DD-OFDM system. In this work we propose a PAPR reduction technique based on the Frequency Modulation of the ACO-OFDM to form a CE signal for the LEDs in the VLC system. We theoretically analyze and perform numerical simulations to assess the performance of the system. The technique of frequency modulation proves to be robust to the phase discontinuities which demodulating at the receiver as compared to the CE signal generated by the phase modulation. Since the PAPR is practically nil there is no more a requirement of the power back-off on the system to keep the non linearity of the LED under check. However to keep the LED in its linear region of operation we chose the bias point optimally so that the CE-OFDM signal never drives it into saturation. The transformation of the signal into a CE makes this technique a distortionless one thereby making it a better choice over the non distortionless techniques of PAPR reduction. The system is simple to implement and needs slight modification of the O-OFDM system in VLC by incorporating the frequency modulation block. The interleaving and coding technique become computational burdening as compared to the FM-CE OFDM. The simulation results are in good agreement with the numerical analysis presented in this paper. At the FEC threshold the receiver sensitivity is improved by 1.6 dB for the FM CE-OFDM as compared to the PM CE-OFDM at a transmission distance of 2 m. We compare the BER performance of the ideal OFDM (without the non linearity of LED), power back-off OFDM, PM CE-OFDM and FM CE-OFDM in an optical wireless channel (OWC) scenario. The FM CE-OFDM shows an improvement of 2.1 dB SNR at the FEC threshold in comparison to the PM CEOFDM. It also shows an improvement of 11 dB when compared with the power back-off technique used in the VLC systems for 10 dB power back-off. The rest of this paper is as follows: In Section 2 the system description of the FM CE-OFDM is given. The effect of applying the power back-off to maintain the LED in its linear region of operation is shown detail in Section 3. We also show the effect of power back-off on the LED based on the error vector magnitude (EVM) performance for back-to-back system at 0 dB and 2 dB in the same section. The EVM vs power back-off ratio and the metric for total degradation are also given in the same section. The FM CE-OFDM system metrics is developed in Section 4. The effect of modulation index is also shown here. The

efficient system is prone to the effect of DC offset arising from the interference at low frequency and additive channel noise [9]. The efficiency of the DCO-OFDM is less as compared to the ACO-OFDM for smaller constellation in terms of the average optical power. Although the OFDM modulated waveform has multitude of advantages in both the RF and optical domain, its predominant drawback is that the signal profile has intermittent peaks that occur throughout the length of the OFDM signal contributing immensely to the peak-toaverage power ratio (PAPR) [10]. The unreasonable amount of PAPR begets the OFDM sensitive to non-linear distortion caused by the transmitter's power amplifier (PA) in the RF domain and the clipping and LED non-linearity in the optical domain. The non linearity of the LED is due to the non-radiative recombination taking place inside the depletion region. This recombination of holes and electrons is a temperature dependent phenomenon which amplifies as the driving current is increased. Thus higher the surges of current being fed to the LED the higher the intensity of the non linearity. This would limit the signal amplitude and degrade the OFDM system performance. To avert such a short coming of the precedent OFDM signal power back off is employed [11]. The system would suffer from generation of intermodulation components, leading to an up rise in the unwanted spectral components that broaden the same thereby contributing significantly to degrade the performance of the system. However in the RF domain such an increase in the power back off is reported to have an adverse effect on the PA at the front end. In optical domain this power back off leads to deteriorate the optical signals intensity which inherently contributes to the degradation in the signal to noise ratio (SNR) of the system. Techniques to confront the PAPR are basically classified into two categories: (a) distortionless that includes tone reservation (TR) and coding schemes, (b) non-distortionless schemes such as filtering, clipping windowing [10]. Other literature [12] suggests predistortion schemes and [13] in detail explain algorithms about receiver correction based on iterative decoding. In optical domain also numerous techniques have been reported to counter the PAPR. [14] presents the reduction of PAPR based on the trellis coding to reduce the average optical power and block coding based on mapping technique at the expense of the transmission bandwidth increase. The selective mapping (SLM) technique reduces the peak signal amplitude to lower the ratio. In [15] the peak signals were reduced up on insertion of pilot symbol (PS) phase rotation in the OFDM signal. By increasing the sampling rate to up to six times on the most distorted subcarriers [16] showed that the PAPR could be reduced. Discrete Fourier Transform precoding in combination with a clipping scheme was studied and analyzed experimentally in [17] for an improvement of 4.5 dB for QPSK OFDM compared to conventional DFT precoded system. Based on the spreading technique, [18] proposes a combination of DFT spreading technique with clipping for PAPR reduction in ACO-OFDM systems for clipping ratio of 2.2. In [19] the authors propose a Toeplitz matrix based Gaussian blur method at the transmitter and orthogonal matching pursuit algorithm at the receiver for the reduction of PAPR in ACO-OFDM for VLC. In terms of the complementary cumulative distribution function (CCDF) the blur technique shows an improvement of 6 dB when compared to original ACO-OFDM signal. Implementation of a non-conventional transformthe Discrete Hartley Transform (DHT) along with the CE modulation based on the phase of the carrier signal is proposed in [20] showing improvement in terms of the BER and PAPR compared to the conventional O-OFDM. The detailed analysis is performed based on the phase modulation index of the system. A possible perspective of the alleviation of the PAPR is transforming the OFDM signal itself. This approach is applicable to the signal by transforming it before its amplification (in RF)/electro-optical conversion (in optical) at the transmitter and applying a reverse transformation before the demodulation at the receiver. A companding technique is described by the authors of the [21]. A similar technique but based on the phase modulation transform is emphasized in [22]. The fore259

Optics Communications 393 (2017) 258–266

V. Kumar Singh, U.D. Dalal

Fig. 1. Setup for generation of FM CE-OFDM in VLC system.

signal is bipolar which is clipped at zero to obtain the unipolar and real ACO-OFDM signal. To reduce the PAPR of this signal we put it across a frequency modulator whose sampling frequency ( fsamp) > > twice the carrier frequency (2fcarrier ). This converges the abrupt time varying amplitude peaks after the IFFT into almost constant amplitude signal. Hence the PAPR is reduced here. The frequency modulated CE is generated at this stage. The cyclic prefix (CP) addition follows this stage. Finally the frequency modulated CE O-OFDM is fed to the LED via the biasing network. At the receiver the intensity modulated signal reaching the photodetector along with the channel noise added is detected and converted to the electrical domain followed by the removal of the CP. The electrical signal is then demodulated by the FM demodulation at the same fsamp to recover back the OFDM signal. The original transmitted bits are derived by applying the FFT followed by the m-QAM demapping. The received constellation at a signal to noise ratio (SNR) of 15 dB for the first 100 OFDM symbols is shown in Fig. 2(b). Fig. 3 shows the time domain plot of the ACO-OFDM generated before the frequency modulation block (Table 1).

numerical results for the complete system analysis are shown in Section 5. An emphasis on the phase discontinuity for the comparison of the FM CE-OFDM with the PM CE-OFDM is shown in the first part of this section. The total degradation for varied modulation indices is shown next. The complete BER analysis for the ideal OFDM, power back-off OFDM, PM CE-OFDM and FM CE-OFDM is presented in the third part of this section. The paper concludes with Section 6. 2. System description The setup for the generation of the FM CE-OFDM is shown in Fig. 1. The serial input bit sequence from the source after being parallel converted is mapped to the m-QAM (Quadrature amplitude modulation) constellation points. We take m=4 as shown in Fig. 2(a). These constellation points are then appended with their complex conjugates to ensure the hermitian symmetry. For the generation of the ACOOFDM signal we apply the IFFT (inverse fast fourier transform) on this array of constellation symbols by setting the data on the alternate sub carriers while the others are set to zero. We chose 512 FFT points for the transformation and 256 sub carriers. In time domain the resulting

Fig. 2. (a) 4-QAM constellation at the input of the IFFT block (b) Constellation at the output of the FFT block in the receiver.

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Fig. 3. Time domain plot of the ACO-OFDM Signal before the frequency modulation. Fig. 4. EVM vs Bias voltage for LED at no power back-off.

Table 1 System parameters for generation of FM CE-OFDM.

To restrict the distortions incurring due to the PAPR a typical scaling of the average power of the signal intended for transmission has to be incorporated which is defined as the power back-off [11] given by

Parameters

Value

m-QAM, m OFDM bandwidth N-point IFFT/FFT, N Number of sub carriers OFDM symbol duration Cyclic prefix Carrier frequency, fcarrier Sampling frequency, fsamp

4 10 MHz 512 256 25.6 μs 25% 1.2 MHz 6 MHz

Linear region of LED Optical efficiency of LED OWC length Photodetector responsivity, 9

2.0–2.3 V 43 lm/W Up to 2 m 0.4 A/W

PBO =

To determine the impact of the PAPR on the system performance we first define the model of the LED (LRTBG6S6) [27]used in this analytical approach. The LED is the non linear device in the VLC link. The electro-optical conversion is governed by the voltage current relationship as [7] (1)

where the instantaneous current flowing through the LED is i (t ), Io denotes the reverse leakage current, V is the applied potential across the LED, q is the electronic charge=1.60217662×10–19 C, K is the Boltzmann constant and T is the absolute temperature in °K. The equivalent optical power corresponding to the instantaneous current flowing through the LED would then be,

Po =

ηext hν Io (eVq / KT −1), q

(3)

In Fig. 4 we can see that at no power back-off for various bias voltages within the linear region of the LED [27] the EVM for the first 100 OFDM modulated signal yields maximum of 35% with a floor value=17%. The most linear region of the LED is described with 2.1– 2.3 V. Beyond this the EVM would again rise due to the saturation and non linear effect of the LED. When we apply a power back-off=2 dB the EVM performance of the system is enhanced. This is shown in Fig. 5. It may be noted that the EVM floor for the first instance of bias voltage reduces by 3%. This explains that if the OFDM signal could be modified before being applied to the LED by some means that could inherently bring in power back-off, the system EVM performance would be escalated. Fig. 6 shows the plot between EVM and power back off for all the four points of bias voltage for the LED up to 10 dB. A gradual decrease of the EVM for all the bias voltages is seen as the power backoff applied is gradually increased. High level of power back-off shows favorable reduction in the EVM as the case is analyzed for back-to-back operation. The effect of diminishing the input signal strength at the LED would lead to a drastic reduction of the illumination requirement. Specifically for VLC systems the set bias point and the power back-off applied should be such that the minimal level of brightness which is

3. Power back off in LED for linear operation

i (t ) = Io (eVq / KT −1),

Psat . Pin

(2)

where Po is the optical output power, ηext is the external quantum efficiency and hν is the photon energy. It becomes evident that the current power relationship of the LED's non linearity can be mapped back to the electron hole recombination. The release of phonons which do not contribute to the output optical power causes this non linearity. Moreover non linear harmonics of the input signal are also generated. However we do not take into account of the harmonics in the work here. Thus the impact of nonlinearity can be sensed when the device is deployed for signal transmission with the input signal (with power=Pin ) varying between the turn-on voltage and the saturation value(with power=Psat ). Near the saturation the non-linearity is more pronounced. This enforces to limit the signal amplitude within an identified linear region of operation of the LED.

Fig. 5. EVM vs Bias voltage for LED at 2 dB power back-off.

261

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V. Kumar Singh, U.D. Dalal t

θ (t ) =

∫ 0

dθ = dt

t

∫

t

2πk f ZB (τ ) dτ = 2πk f

0

∫

ZB (τ ) dτ. (7)

0

Considering a carrier with a frequency of fcarrier and amplitude Acarrier the FM modulated constant envelope signal would be

x (t ) = Acarrier cos (2πfcarrier t +θ (t )) t ⎞ ⎛ ZB (τ ) dτ ⎟ . = Acarrier cos ⎜2πfcarrier t +2πk f ⎟ ⎜ ⎠ ⎝ 0

∫

(8)

We introduce the term modulation index β related to k f by the ratio of the amplitude of the OFDM signal A ZB to the frequency of the OFDM signal fZB , yielding the FM modulated constant envelope signal as

⎛ fZ x (t ) = Acarrier cos ⎜2πfcarrier t +2πβ B ⎜ A ZB ⎝

t

∫ 0

⎞ ZB (τ ) dτ ⎟ . ⎟ ⎠

(9)

Fig. 6. EVM vs Power back-off for back-to-back operation of LED in linear region.

The PAPR of the above formed FM modulated OFDM time varying signal is

required for illumination for indoors according to the lighting standards is maintained. To reduce the nonlinear distortion in the optical signal, the power back-off is hence compulsory. If the input fed to the LED is taken to be the OFDM signal the consequences of PAPR worsen the system performance under no power back-off applied. The abrupt amplitude peaks in the OFDM signal would end up in either getting clipped (if the LED goes in to saturation) or contribute to the generation on the non linear harmonic terms (for non linear region of operation). The signal propagating further down the link still gets degraded in the channel. It becomes impetus to not arbitrarily apply the power back without considering the channel effects. A measure of the power back-off can be well understood by evaluating the overall degradation of the system when the channel is introduced. The reduction in the input power reduces the signal to noise ratio of the signal to be transmitted. This has an impact on the degradation at the receiver. Besides this the added channel attenuation and noise addition also distorts the received signal thereby degrading the signal further. The total degradation is then computed as,

TD PBO = SNR LED PBO −SNRchannel +PBO

(dB )

max x (t )FFT PAPRFFT

ZB

⎪

t ∈[0, T )

⎛ ⎧ M −1 ⎫⎞ x (t )FFT = Acarrier cos ⎜⎜2πfcarrier t +2πk f R ⎨ ∑ *me j 2πfm t ⎬ ⎟⎟ ⎩ m =0 ⎭⎠ ⎝ ⎪

⎪

⎪

⎛ ⎧ M −1 ⎫⎞ x (t )FFT = Ac cos ⎜⎜2πfc t +2πk f R ⎨ ∑ *me j 2πfm t ⎬ ⎟⎟ +CP. ⎩ m =0 ⎭⎠ ⎝

(11)

⎪

⎪

⎪

⎪

(12)

Assuming that the LED is sufficiently biased in the linear region of operation by the DC bias, the conversion of the electrical signal to optical intensity by the LED based on Eq. (2) can be modeled as below,

Po = (5)

⎧ ⎫ ⎛ ⎧ M −1 ⎫⎞ ⎪ ηext hν ⎪ ⎨Ac cos ⎜⎜2πfc t +2πk f R ⎨ ∑ *me j 2πfm t ⎬ ⎟⎟ +CP ⎬. ⎪ q ⎪ ⎩ m =0 ⎭⎠ ⎝ ⎩ ⎭ ⎪

⎪

⎪

⎪

(13)

This optical signal traverses the OWC modeled by the equation [7]

where *m is the mth data from the data vector of J = [*0*1*2…*k] modulated by the mth subcarrier with a frequency of fm . Let the rate of change of frequency of the carrier which is to be frequency modulated by the OFDM signal be, θ wrt to the instantaneous amplitude of the OFDM baseband signal denoted by

dθ (t ) = 2πk f ZB (t ) dt

⎪

The prefixing of the cyclic prefix is followed which leads to the formation of the complete OFDM signal in the electrical domain, intended for transmission into the channel,

(4)

⎪

⎪

(10)

The complete passband FM modulated signal is then given by the metric,

After imposing the hermitian symmetry to obtain the real and unipolar OFDM signals we get the instantaneous amplitude, ⎪

,

with TZB being the OFDM symbol duration. It is noticeable that the numerator in the PAPR metric is now a constant as the maximum that can be attained is the amplitude of the carrier signal itself. Unlike the previous case where the instantaneous amplitude of the OFDM signal was abruptly varying within each OFDM symbol block. Thus the ratio attains a value no more than max x (t )FFT .

4. Generation of the frequency modulated CE-OFDM

⎧ M −1 ⎫ = R ⎨ ∑ *me j 2πfm t ⎬ ⎭ ⎩ m =0

2

∫ x (t )FFT 2

where the term SNRchannel is the signal to noise ratio required to achieve a specific BER, SNR LED PBO is the required SNR when considering the nonlinear LED at a particular power back-off.

FFT (t )

=

t ∈[0, T ) TZB 1 TZB 0

h (t ) =

Ar (ml +1) ml cos (ϕ) g (ψ )cos(ψ ) δ (t −λ ), 2πd 2

(14)

where Ar denotes the aperture area of the detector, d is the channel length, ml is Lamberts mode number (=1) that expresses the directivity of the source beam, the angle of transmission from the normal at the emitting surface is denoted by ϕ ,ψ is the incidence angle of the radiation, g (ψ ) is the gain of the associated receiver optics and λ is the ratio of the channel length and the velocity of light in vacuum. The received optical signal at the photodetector surface is then,

(6)

where k f is the frequency deviation sensitivity of the modulator in Hz/V. By integrating the rate of change of frequency we formulate the phase deviation as 262

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V. Kumar Singh, U.D. Dalal

Fig. 7. FM CE- for ACO-OFDM (modulation and demodulation).

⎧ ⎛ ⎧ M −1 ⎫⎞ ηext hν ⎪ ⎨Ac cos ⎜⎜2πfc t +2πk f R ⎨ ∑ *me j 2πfm t ⎬ ⎟⎟ e ⎪ ⎩ m =0 ⎭⎠ ⎝ ⎩

r (t ) =

⎪

⎪

⎪

⎪

⎫ ⎪ A (m +1) +CP ⎬ * r l 2 cos ml (ϕ) g (ψ )cos(ψ ) δ (t −λ )+n (t ), ⎪ 2πd ⎭

Fig. 8. Effect of modulation index on the BER performance of the FM CE-OFDM.

BER reaches ≈10-5. The optimal value of the modulation index is taken to be 0.3. A limitation of the frequency demodulator at the receiver is that at low SNR and for sufficiently large modulation index the demodulation is difficult for signals deeply embedded in noise. Hence an optimum modulation index and sufficiently good amount of SNR is required. For VLC systems the minimum lighting intensity for indoors ensures that the SNR would be appreciably high. This means that the demodulation would only be affected by the choice of modulation index term.

(15)

where the n (t ) is the assumed zero mean additive white Gaussian noise added by the OWC. The equivalent electric current generated in the photodetector with responsivity 9 is

io = 9

⎧ ⎛ ⎧ M −1 ⎫⎞ ηext hν ⎪ ⎨Ac cos ⎜⎜2πfc t +2πk f R ⎨ ∑ *me j 2πfm t ⎬ ⎟⎟ ⎪ e ⎩ ⎩ m =0 ⎭⎠ ⎝ ⎪

⎪

⎪

⎪

⎫ ⎪ A (m +1) +CP ⎬ * r l 2 cos ml (ϕ) g (ψ )cos(ψ ) δ (t −λ )+n (t ). ⎪ 2πd ⎭

5. Simulation results 5.1. Phase discontinuity analysis Upon modulating the frequency of the carrier in accordance with the time varying amplitude of the OFDM signal to obtain a CE-OFDM we observe the appearance of frequency discontinuity in the so formed signal at the demodulation end. This gives a measure of the competency of the proposed solution to the approached problem of PAPR. We derive the metrics for the frequency modulated and phase modulated OFDM signal and compare the two based on the phase discontinuity. We consider the frequency/phase of two consecutive OFDM symbols arbitrarily chosen, spaced in time, at instance of Δt away from each other. The frequency/phase discontinuity would be the difference of these two instances formulated by the definition as below,

(16)

After removing the CP from the signal in Eq. (16) the operation of frequency demodulation is applied by multiplying the signal with a locally generated carrier of the same frequency as that at the transmitter and the frequency deviation. This yields the actual recovered OFDM signal which is processed further as explained in the system description. A typical simulated time frame of an OFDM symbol is shown in Fig. 7. In figure the ACO-OFDM can be seen with abrupt peaks. The FM CE-OFDM is also shown. Notice the conversion of the randomness of the peaks into frequency change instances. The modulated signal swings between the maximum and minimum amplitude as that of the carrier signal. Thus it maintains a constant envelope that can be given to the LED at sufficient bias. This would not drive the LED into its non linear region and hence a proportional amount of optical output power can be achieved. The outcome of demodulation for the ACOOFDM signal can be seen to have small negative peaks that are clipped off. The resemblance of the demodulated signal to the original ACOOFDM is appreciable. The modulation index term introduced in the analysis also has a significant contribution to the system performance. We analyze the effect of varying the modulation index for the FM signal by keeping the LED in the most linear range of operation. Fig. 8 shows the effect on the BER performance of the system by varying the modulation index 2πβ for two different transmit optical powers. The profile of the curve rapidly descends for very low levels of modulation and gradually uplifts itself. Beyond a modulation index of 0.6 the response remains rather unchanged. This behavior is noticed for transmit power=5.2 dBm and 2.3 dBm which are the two extent values for the LED to be kept in linear region of operation. As the optical power is increased from 2.3dBm to 5.2 dBm the response improves as the minimum possible

ϕd = ϕ (iTZB−Δt )−ϕ (iTZB+Δt ),Δt→0

(17)

where the respective phases of the two considered OFDM signals is given by,

ϕ (iTZB−Δt ) = 2πβ ϕ (iTZB+Δt ) = 2πβ

fZB A ZB fZB A ZB

M

∑ *m−1e j2πfm−1 t , m =1 M

∑ *me j2πfm t .

(18)

m =1

Hence phase discontinuity for PM will be,

ϕd PM = 2πβ =2πβ

fZB A ZB fZB

A ZB

M

∑ *m−1e j2πfm−1 t −2πβ m =1 M

∑ m =1

fZB A ZB

M

∑ *me j2πfm t m =1

(*m −1e j 2πfm −1 t −*me j 2πfm t ).

(19)

The metric in Eq. (19) shows that the discontinuity at the transition from one OFDM symbol to the other for a time duration of Δt depends on the data symbols *m−1 and *m . It also has an effect that is caused due to the change in the subcarrier frequency from fm−1 to fm . At the 263

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V. Kumar Singh, U.D. Dalal

Fig. 9. Phase discontinuity for PM and FM. Fig. 12. BER vs Power back-off for VLC system.

Fig. 13. BER vs Transmitted optical power for PM CE-OFDM and FM CE-OFDM at 2 m distance when the optical power at the receiver is maintained at −5 dBm. Fig. 10. Total degradation vs Power back-off for BER=10-4.

Fig. 14. BER vs Received optical power for PM CE-OFDM and FM CE-OFDM at 2 m distance. Fig. 11. EVM vs Power back-off for VLC system.

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Fig. 15. BER vs SNR+Power back-off for ideal OFDM, Power back-off OFDM, PM CE-OFDM and FM CE-OFDM.

the least attainable value. For the FM CE-OFDM signals, we achieve the least degradation at 3, 2.5 and 2.1 dB for no power back-off with modulation indices set at 0.3, 0.4 and 0.5 respectively. This affirms that limiting the amplitude of the OFDM signal to combat PAPR reduces the total degradation of the system at no extra requirement of the power back-off. This also shows that the modulation index for CE-OFDM can be chosen accordingly for enhancing the system performance. The phase modulated CE-OFDM (not shown here) gives very similar results.

receiver upon the demodulation of this signal to resolve into individual OFDM symbols the effect of such transitions contribute significantly to the distortion even though the PAPR is combated. We now derive the phase discontinuity for the frequency modulated OFDM signal. It should be noted that the frequency modulation of any signal yields the carrier frequency variations within the time span of the modulating signal. Here the change of frequency of the carrier from fm−1 to fm is only within one OFDM symbol formed by the data *m∈J . When this is evaluated at the receiver end, the phase distortion can be written as,

ϕd FM = 2πβ = 2πβ

fZB A ZB fZB A ZB

M

∑ *me j2πfm−1 t −2πβ m =1 M

∑

fZB A ZB

M

∑ *me j2πfm t

5.3. BER analysis

m =1

(*m (e j 2πfm −1 t −e j 2πfm t )).

m =1

The EVM and BER analysis for the power back-off system is shown next. By now it becomes evident that the impact of the non-linearity of the LED contributes significantly to the system performance. The EVM of the system upon deploying the OWC has been shown in Fig. 11. We may deduce that a very large amount of error can be seen for low level of power back-off applied. Upon applying a power back-off =10 dB the system is not capable of retrieving back more than 20% of the bits in total for 4-QAM. If we interpret the BER performance of the system as shown in Fig. 12 the BER=10-3 can be achieved only by applying a power back-off more than 7 dB for 2.2 V and 2.3 V bias and almost 10 dB for 2.1 V and 2.2 V bias. The FM and PM CE-OFDM are compared next based on their BER performances for a modulation index=0.3. The Fig. 13 shows a plot between the transmitted optical power and the BER for a 2 m channel length. Here we vary the gain of the optics involved in the OWC setup as indicated in Eq. (14). The received optical power is set constant at −5 dBm for 2 m distance of the channel. The performance of the system declines gradually as the optical power is increased. This is due to the inherent non-linearity of the LED. The FM CE-OFDM shows a better performance as compared to the PM CE-OFDM due to the significant phase discontinuity within the OFDM symbols and lower SNR of the system. For the FEC threshold of BER=10-3 the FM CEOFDM has ≈1 dB better sensitivity than the PM CE-OFDM. Fig. 14 shows the BER versus received optical power for the PM CEOFDM and FM CE-OFDM at 2 m transmission distance. The FEC limit for the PM CE-OFDM reads −6.8 dB whereas for FM CE-OFDM it is −8.4 dB. This implies an improvement of 1.6 dB for the FM CE-OFDM. This is due to the lesser impact of the phase discontinuity on the latter. The BER decreases as the received power is increased. This is because the effect of the channel introduced attenuation and noise signals diminish in magnitude. Fig. 15 shows the BER versus SNR+ Power back-off performance of the systems described above in detail. To begin with we consider the ideal OFDM case where no non-linear devices are deployed. The profile

(20)

If we look closer and compare the Eqs. (19) and (20) we find that the frequency modulation technique yields less distortion as it only depends on the frequency change from fm−1 to fm . This is plotted graphically for normalized time of the OFDM symbol duration in Fig. 9. The abrupt phase discontinuities are prominent in the phase modulated OFDM signal as compared to the frequency modulation technique. The FM signal has discontinuities of very meager amplitude. Thus we adopt the frequency modulation technique of generating the CEOFDM signal. 5.2. Analysis of the total degradation in the system In Section 3 we described the effect of power back-off on the non linearity of the LED. It was shown that without applying the power back-off it is difficult to obtain a faithful conversion of the electrical signal applied to the LED into its proportional amount of output in the form of optical intensity. But if the frequency modulated OFDM signal is considered then the instantaneous nonlinearity results in constant amplitude. Therefore the LED's non linearity has no impact on the CEOFDM performance and no power back-off is needed. The total degradation for CE-OFDM is defined as

TD = SNRFM −SNRchannel

(dB )

(21)

where and SNRFM is the required SNR for the frequency modulated CEOFDM system and SNRchannel is the required SNR for the subcarrier modulation. Fig. 10 shows the effect of the power back-off on the ideal OFDM (with an assumed linear electro-optical converter), 4/16-QAM and FM CE-OFDM at a target BER=10-4. The subcarriers are set to 256. The least degradation for 16-QAM at 3 dB power back-off is 5.1 dB. The total degradation for 4-QAM at 2 dB power back-off is 3.2 dB which is 265

Optics Communications 393 (2017) 258–266

V. Kumar Singh, U.D. Dalal

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of the curve reveals that the BER is solely dependent on the channel conditions and is only linearly improving with the SNR. The FEC threshold is obtained at an SNR of 25 dB. The contributions to the distortion in the signals are the channel attenuation and the white Gaussian noise. The next set of system that we analyze is the power back-off signals. The power back-off is varied between 0 dB and 10dB. For no power back-off the OFDM signal shows an irreducible error floor which is way above the FEC threshold. The implication is that non linearity of the LED sets the signal more prone to distortions. This reduces as the power back-off is applied and the signal is brought within the linear region of operation. When the power back-off is set to 10 dB the performance improves drastically but only at very high SNRs. The PM CE-OFDM signal at low SNR gives performance very similar to the power back-off cases. But as the SNR increases the effect of the constant amplitude that mitigates the non linearity of the LED surfaces. This enhances the performance and the FEC threshold is reached within 17 dB of SNR. For the FM CE-OFDM the performance still becomes better due to the reduction in the phase discontinuity of the modulated signal. The FM CE-OFDM shows an improvement of 2.1 dB over the PM CE-OFDM. It also has an improvement of 11 dB over the power back-off OFDM signal at 10 dB. 6. Conclusion The effect of non-linearity of the LEDs leading to a significant increase in the peak to average power ratio (PAPR) of the OFDM signals in the Visible light communication (VLC) is mitigated by the proposed frequency modulated constant envelope OFDM (FM CEOFDM) technique. Before the electrical OFDM signal gets converted into its equivalent optical intensity, the baseband signal is frequency modulated. We achieve the least possible value of the PAPR ≈0 dB.The optimal modulation index for frequency modulation is found to be 0.3 in the work here for FM CE-OFDM. The phase discontinuity parameter is quiet low for the FM CE-OFDM as compared to the PM CE-OFDM. The receiver sensitivity improves by 1.6 dB at FEC threshold for FM CE-OFDM as compared to PM CE-OFDM when the transmission distance is 2 m. A comparison of ideal OFDM (without non linearity of LED), power back-off OFDM, PM CE-OFDM and FM CE-OFDM is performed based on the BER performance in the OWC scenario. The FM CE-OFDM shows an improvement of 2.1 dB SNR at the FEC threshold as compared to the PM CE-OFDM. Its performance is better by 11 dB when compared with the power back-off technique used in the VLC systems for 10 dB power back-off. Acknowledgements The authors are thankful to Media Lab Asia, Department of Electronics and Information Technology (DEITY) (PhD-MLA/4(11)/ 2014), for sponsoring this research work under the Visvesvaraya PhD scheme of DEITY, 2014. References [1] Yu-Chieh Chi, et al., 450-nm GaN laser diode enables high-speed visible light communication with 9-Gbps QAM-OFDM, Opt. Express 23 (10) (2015) 13051–13059.

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