## Abstract

This paper reports the experimental wavelet denoising techniques carried out for the first time for a number of modulation schemes for indoor optical wireless communications in the presence of fluorescent light interference. The experimental results are verified using computer simulations, clearly illustrating the advantage of the wavelet denoising technique in comparison to the high pass filtering for all baseband modulation schemes.

© 2013 OSA

## 1. Introduction

Optical wireless communications (OWC) technologies operating in the visible and infrared bands have been extensively studied over the last two decades for indoor and outdoor applications [1–3]. Besides a large license free bandwidth, an inherent security and very high data rates, OWC links do not suffer from multipath induced fading due to relatively short carrier wavelengths and photodetectors with surface areas that are orders of magnitude greater than the transmit optical wavelength. OWC systems using the near-infrared wavelengths in the range of 600-900 nm are popular in indoor applications due to availability of cheap optical components including light emitting diodes (LEDs) and photodiodes. Recently, we have seen a growing interest in visible light communications (VLC) using semiconductor and organic based white LED for indoor applications as white LEDs offer a dual functionality of illumination and data communications [4]. However, there are still a number of challenges in VLC systems including the low bandwidth of the white LED and the light dimming [5].

Depending on applications and requirements, the line of sight (LOS) and the diffuse link configurations can be adopted for OWC. In comparison to the directed LOS link configurations, the diffuse link has a higher path loss, but is more resilient to blocking and shadowing. However, the transmission rate in a diffuse link is limited to few megabits per second (Mbps) due to the multipath induced intersymbol interference (ISI). To reduce the ISI and therefore increase the data rate, a number of equalization techniques including the artificial neural network (ANN) have been proposed [6, 7]. In addition to ISI, the other key challenge in indoor OWC systems is the florescent light interference (FLI) with harmonics extending up to 0.5MHz. A number of mitigation techniques have been proposed to reduce the effect of FLI including high pass filtering (HPF), differential receivers, polarizers and wavelet denoising [8–11]. The filtering technique is the simplest and cheapest of all as it does not require an additional receiver. The comparative study carried out using computer simulation [2, 6] has established that the wavelet denoising outperforms the HPF maximum filter with a significant reduction in system complexity. For example, the order for wavelet denoising is 60 in comparison to a HPF filter order of 2148 at a data rate of 200 Mbps [2]. In [6], it was demonstrated that the wavelet denoising can be implemented using the DSP board with a limited capability and without performance penalty. The first experimental results of wavelet denoising in a room environment for a link length of 1m was reported in [11] that used the on and off keying non-return-to-zero (OOK-NRZ) modulation scheme. It was shown that the optical signal-to-noise ratio (OSNR) improved from ~3 dB for HPF to ~6 dB using the wavelet denoising at 25 Mbps. In this paper, we have further extended the experimental study by incorporating the wavelet denoising technique to other baseband modulation techniques including pulse position modulation (PPM) and digital pulse interval modulation (DPIM). This is the first time that wavelet denoising is experimentally demonstrated for PPM and DPIM and results are compared with HPF. The experimental results are also verified using computer simulation carried out based on the measured impulse response and interference.

## 2. Experimental set-up

In this section we describe the experimental set-up adopted to evaluate the effect of FLI and the wavelet denoising as outlined in Fig. 1. The transmitter consists of a data source, a data encoder for generating different modulation schemes and a pulse shaping transmitter filter. A programmable arbitrary waveform generator (AWG) is used to generate a pseudo random binary sequence (PRBS) of length 2^{10}-1 and encoded into the desired modulation formats, followed by the rectangular pulse shaping filter, see Fig. 1. The output of the filter directly modulates the intensity of a laser diode operating at a wavelength of 830 nm with a maximum optical output power of 10 mW. The laser has a beam divergence angle of < 0.3° and hence a light shaping diffuser (LSD) with a 10° divergence angle is incorporated to increase the optical coverage area. The receiver front-end consists of a concentration lens (a focal length of 5 cm and a radius of 2.5 cm), and a silicon PIN photodiode (Centronic OSD15-5T) with a responsivity of 0.45 A/W at 830 nm, followed by a transimpedance amplifier (TIA) (Analog device AD8015) with the noise characteristics of 3.0pA/√Hz at 100 MHz. The receiver is located at 2 m from the ceiling and 1 m from the transmitter; pointing towards the ceiling. The alignment is adjusted such that FLI photocurrent is at its maximum value. The output of the TIA is sampled at 10 times the slot rates and stored using a real time digital oscilloscope. Further signal processing and performance evaluations are all carried out in the MATLAB environment.

As in typical communication systems, the received signal is first pass through a low pass filter (LPF) to limit the noise and then down-sampled to obtain one sample per slot. In order to avoid ambiguities in the text, the terminology ‘slot’ is used for all modulation schemes. Midpoint sampling is used for the maximum SNR. The signal is then denoised using either a HPF or a discrete wavelet transform (DWT) to reduce the effect of FLI. The denoising techniques are further discussed in Section 3.

In order to show the effectiveness of the wavelet denoising, three baseband modulation schemes namely OOK-NRZ, PPM and DPIM are selected. The selection is primarily based on the spectral contents near the DC region and the baseline wander (BLW) effect. PPM and OOK-NRZ have null and high spectral contents at the DC region, respectively while the spectral contents of DPIM at low frequencies falls between OOK and PPM. The detailed studies of modulation schemes in terms of the spectral properties, error probability and capacity have been reported the literature and hence are not replicated. A brief survey of the modulation schemes under the study is provided here for completeness.

For OOK, PPM and DPIM the transmitted data sequence can be represented as:

*p*(

*t*) is the pulse shape,

*c*is a random variable, which represents the presence or absence of a pulse in the

_{k}*k*

^{th}time slot and

*P*is the received peak optical power.

_{r}To achieve the same data throughput as OOK-NRZ, the slot durations of PPM and DPIM are kept shorter than that of OOK and are given by:

where*T*= 1/

_{b}*R*,

_{b}*R*is the bit rate,

_{b}*M*is a bit resolution and

*L*= 2

*.*

^{M}For the threshold detection schemes, with threshold level set midway between expected one and zero levels, the slot error probability is given by [6]:

where*Q*(.) is the Marcum’s Q-function,

*N*/2 is the double-sided power spectral density (PSD) of noise, and

_{o}*E*is the symbol energy.

The average energy per bit *E _{b}* is related to the symbol energy as follows:

*R*is the photodetector responsivity.

## 3. Results and discussion

The experiment is carried out in the presence of florescent lamp (manufactured by Philips) with the average illuminance at the table height of ~350 lux. To quantify the link performance, we use *Q*-factor given by:

*v*&

_{H}*v*are the mean received voltages and

_{L}*σ*&

_{H}*σ*are the standard deviations for the ‘high’ and ‘low’ level signals, respectively. Since FLI is not a white Gaussian noise, the

_{L}*Q*-factor does not provide an accurate picture of the link error performance and hence the SER is also estimated by comparing the transmitted data with the recover data.

Figure 2 illustrates that FLI waveform is a distorted sinusoidal signal with a fundamental frequency of 50 kHz and harmonic frequencies extending up to 0.5 MHz [11]. The effect of FLI is reduced at the receiver by using a 1st order digital Butterworth HPF with a cut-on frequency *f _{c}* of 0.5 MHz

*The selection of*

_{.}*f*depends on the harmonics of the FLI. Alternatively, DWT with a suitable denoising algorithm can be used.

_{c}DWT can be realized using successive application of low pass *g*(*n*) and high pass *f*(*n*) filters to the signal *y*(*n*) and down-sampling by 2. The filter coefficients *g*(*n*) and *f*(*n*) depends on the wavelet family and can be found in [12]. The first level decomposition gives the approximation and detail coefficients *y*_{1}* _{l}* and

*y*

_{1}

*; respectively as:*

_{h}The approximation coefficient *y*_{1}* _{l}* can be further decomposed into the second level of approximation and detail coefficients

*y*

_{2}

*and*

_{l}*y*

_{2}

*, respectively and so on. The wavelet denoising, in our case, relies on the spectral separation of the FLI and modulating signals by using different levels of wavelet decomposition. In order to illustrate the concept, the difference in DWT coefficients using Daubechies 8 wavelet for the received OOK-NRZ signal at 10 Mbps with and without FLI is given in Fig. 2 (b-c). The number of decomposition level is 4. Note that there is a significant difference in the approximation coefficient; however differences in the detail coefficients are insignificant. Hence, the wavelet denoising is carried out by setting the approximation coefficients to a null value. The number of wavelet decomposition levels is determined using:*

_{h}*f*= 1/

_{s}*T*,

_{s}*T*is the slot duration. The value of

_{s}*f*is selected as 0.3 MHz as it offers the optimum denoising [6].

_{c}The FLI effect is characterized by varying the transmitted optical so that the ratio of the peak modulating photocurrent *I _{m}* to peak FLI current

*I*

_{FLI}

*v*aries at the receiver i.e.:

In order to verify the experimental data, computer simulations are carried out in the Matlab environment using measured experimental parameters. The impulse response of the system was measured by transmitting a narrow pulse of 4 ns. The other measured parameters include the noise density (1.5 nA/√Hz), the average FLI photocurrent (96 μA) and the average modulating signal photocurrent.

The simulated and measured *Q*-factors against the slot rate in the presence of FLI and with and without denoising techniques at μ = 3 is given in Fig. 3. The measurements are closely matched by the simulation results. The constant *Q*-factors are observed in the presence of FLI without denoising irrespective of the modulation schemes. A significant improvement in the *Q*-factor can be observed for all modulation schemes with HPF and DWT based denoising. However, DWT always outperforms HPF for all modulation schemes. The advantage of DWT is clearly manifested in PPM at lower data rates where the *Q*-factors for 4-PPM are ~4 and ~12 with HPF and DWT, respectively. Note that the maximum *Q*-factor is observed between 20 and 30 Mbps for OOK and DPIM, decreasing as the slot rate increases or decreases. This is due to two reasons: a) the *Q*-factor decreases at higher slot rates due to the bandwidth limitation of the system (the 3 dB electrical bandwidth of overall system is ~25 MHz) and also due to the increased noise bandwidth with the slot rate and b) the *Q*-factor is lower at low slot rates due to the BLW effect. The severity of the BLW is the highest in OOK, thus leading to the lowest *Q*-factor at lower slot rates. The effect of the BLW is less apparent at higher slot rates (this work does not aim to achieve higher data rates as the adverse effect of the FLI and BLW is more severe at lower data rates). PPM on the other hand offers the highest *Q*-factor with the maximum value obtained at 10 Mbps as BLW is less pronounced in PPM and a higher cut-off frequency is tolerated. There is a small difference in measured and simulated *Q*-factors for DPIM with DWT denoising. We believe this is due to limited number of DPIM symbols in experimental set-up (500 symbols for 1000 binary data), inadequate to estimate the *Q*-factor correctly in the presence of BLW and the coupling capacitance that was not considered in the simulation.

Figure 4 shows the SER against the slot rate for OOK, 4&8-PPM and 4&8-DPIM in the presence of FLI with and without the system bandwidth constrain (referred to as practical and ideal in the figure). The figure also illustrates the SER performance in an ideal AWGN channel without FLI. For simplicity, the SER floor is set at 10^{−6}, meaning lower SER values are made to be 10^{−6}. With higher values of *µ*, the SER was observed to be less than 10^{−6} . Hence the value of is selected to be 1.5 for a meaningful comparison. The SERs in the presence of FLI without denoising is in the range of 0.1 for all modulation schemes. However, a significant reduction in SER can be observed with denoising techniques. It is clearly demonstrated that DWT outperforms HPF for all cases, offering a clear testimony of the effectiveness of wavelet denoising. For OOK, the minimum achievable SER is ~10^{−5} and ~10^{−3} with DWT and HPF, respectively which are significantly high in comparisons to the ideal AWGN. However, the SER of PPM with DWT matches closely with the ideal AWGN channel performance indicating no power penalty due to FLI with DWT (similar results were derived using simulation in [6]). The SER of the DPIM matches with the ideal AWGN channel for higher slot rates, however a noticeable difference is observed at a slot rate of < 20 Mbps. As expected, the wavelet denoising is most effective for PPM, followed by DPIM and OOK due to progressive reduction of the power contents at low frequencies.

## 4. Conclusion

In this paper, the wavelet denoising technique for indoor optical wireless communications in the presence of the fluorescent light interference was demonstrated experimentally for a number of modulation schemes. The *Q*-factor and the error rate were estimated from the received optical signal with and without the wavelet denoising. The experimental results were also verified using the computer simulation, which clearly demonstrated the effectiveness of the wavelets over high pass filtering for reducing fluorescent light interference.

## Acknowledgments

This work was supported by the EU Cost Action IC 1101.

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