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- Open Access

# Modeling and analysis of variable PPM for visible light communications

- Jong-Ho Yoo
^{1}and - Sung-Yoon Jung
^{1}Email author

**2013**:134

https://doi.org/10.1186/1687-1499-2013-134

© Yoo and Jung; licensee Springer. 2013

**Received:**26 March 2012**Accepted:**8 May 2013**Published:**24 May 2013

## Abstract

Variable pulse position modulation (VPPM) is a new modulation scheme that supports simultaneously illumination with dimming control and communication. In this paper, the transmitter, optical wireless channel, and receiver structure of VPPM were modeled mathematically, and their error performance for examining the communication performance according to dimming level and data rate was analyzed. The results highlight the need for careful consideration of the tradeoff between the dimming flexibility and communication performance according to the channel condition in VPPM.

## Keywords

- Channel Condition
- Error Performance
- Communication Performance
- Visible Light Communication
- Optical Rate

## 1. Introduction

Recently, light-emitting diode (LED) research has focused on the emerging lighting infrastructure due to Green IT technical innovations. LED lighting is superior to existing incandescent and fluorescent lighting in terms of the long life expectancy, high tolerance to humidity, minimal heat generation, and low power consumption. Another important benefit of LEDs is that it is a controllable digital device. Therefore, many attempts have been made to merge LEDs with information technology (IT). Among them, visible light communication (VLC), which uses LED as a communicating device, has emerged as a new Green IT convergence technology [1–3]. Generally, VLC uses intensity modulation with a direct detection (IM/DD) scheme, which utilizes the amplitude (or intensity) of light to transmit data. Human eyes recognize only the mean intensity when light changes faster than the maximum flickering time period, which is defined as 5 ms. Therefore, both lighting and communication can be implemented simultaneously. In IEEE, the corresponding VLC standardization was recently published by the IEEE Standards Association [4].

This paper proposes the transmit-receive (TX-RX) modem structure, which is a mathematical model of VPPM and an optical wireless channel. The error performance of the model was then analyzed with regard to the dimming level for the illumination and channel condition. Based on the analytical and simulated results, this paper provides a guideline for the VPPM operation to satisfy both lighting and communication abilities for a given environmental condition.

## 2. System description

*b*∈ {0, 1} are transmitted, the VPPM modulated signal

*s*(

*t*) is generated considering the target dimming level as follows:

*d*≤ 100).

*φ*

_{ i }(

*t*)(

*i*= 0, 1) is the basis function that changed according to dimming level. Section 3 provides details of the basis function. After passing through a VPPM pulse-shaping filter, the transmitted signal has the following form:

*T*

_{d}is the total time duration required to transmit each data block,

*T*

_{d}=

*T*

_{s}+

*T*

_{g}, where

*T*

_{s}is the symbol duration and

*T*

_{g}is the guard time to avoid inter-symbol interference caused by channel dispersion. The LED is driven by the current signal controlled by

*x*(

*t*). The LED emits the light signal

*X*(

*t*), which has the mean optical power, ${P}_{t}=\frac{1}{T}{\displaystyle {\int}_{0}^{{T}_{\mathrm{d}}}X\left(t\right)\phantom{\rule{0.25em}{0ex}}\mathit{dt}}$. After passing through the optical channel

*h*

_{o}(

*t*), the optical signal

*y*(

*t*) received is given as follows:

*n*

_{o}(

*t*) is the optical noise source.

*y*(

*t*) is converged to an electric signal through a photodiode (PD) to produce the signal

*r*(

*t*) as follows:

where *R* is the PD conversion responsivity (A/W), *H*(0) means the path loss gain of the signal, *h*(*t*) denotes the electrical impulse response of the optical wireless channel, and *n*(*t*) is the electrical additive white Gaussian noise.

where *C* is the number of channel cluster, *G*_{
i
} is the channel gain of the *i* th cluster, *τ*_{
i
} is the time constant of the *i* th cluster, and *t*_{
d,i
} is the time delay of the *i* th cluster.

*r*(

*t*) is received, the receiver will generate the received vector

*r*= [

*r*

_{0},

*r*

_{1}] through a matched filtering process as follows:

where *q*_{
i
}(*t*) = *φ*_{
i
}(*t*) ∗ *h*(*t*) (*i* = 0, 1) denotes the template pulse dispersed by the channel.

## 3. Performance analysis

*φ*

_{ i }(

*t*) and the corresponding template pulse

*q*

_{ i }(

*t*) are normalized to have a unit energy as ${\int}_{0}^{{T}_{\mathrm{s}}}{\phi}_{i}{}^{2}\left(t\right)\mathit{dt}}=1$ and ${\int}_{0}^{{T}_{\mathrm{s}}}{q}_{i}{}^{2}\left(t\right)\mathit{dt}}=1$. Figure 3 shows the signaling structure of the basis function,

*φ*

_{ i }(

*t*), and the template pulse,

*q*

_{ i }(

*t*).

*b*= 0), the signal received is rewritten as follows:

where *γ* = *R* · *H*(0) means the scaling coefficient that contains the effect of the channel path loss gain and PD responsivity.

*n*

_{0},

*n*

_{1}becomes Gaussian random noise with a zero mean and variance

*N*

_{0}/2.

*α*represents the correlation factor, which is defined as follows:

*n*

_{0},

*n*

_{1}) were also correlated due to the correlation factor

*α*as shown below:

Accordingly, it affects the performance of VPPM. Therefore, it is important to consider this correlation factor carefully when operating VPPM.

*z*=

*r*

_{0}-

*r*

_{1}. The conditional mean and variance of

*z*are given as follows:

*b*= 0, can be derived as follows:

*P*

_{e|b = 1}, can be derived as follows:

*a priori*probability of

*b*= 0 and

*b*= 1 is equal to 1/2, the error probability of VPPM can be expressed as

## 4. Simulation result

The VPPM scheme was described, and its error performance was analyzed. This paper presents the analytical and simulated results to test the validity of the analysis and the relationship between the dimming and communication performance in the line-of-sight (LOS) and diffuse channel cases.

**Channel parameters for simulations**

Channel | Parameter | Value |
---|---|---|

LOS |
| |

Diffuse | Number of clusters | 1 |

Channel gain ( | 1 | |

Time delay | 20 ns | |

Time constant | 2.3 × 10 |

_{rx}) by changing the dimming levels in the LOS channel case. The reference SNR

_{rx}denotes the amount of noise power by setting the signal power with a 50% dimming level as the reference signal power. Therefore, the actual SNR

_{rx}will be changed according to the dimming ratio. The figure shows that the analytical curves are well matched with the simulation curves. Therefore, the analytical results provide a good estimation of the performance when the system parameters have been selected. VPPM showed the best performance at the 50% dimming level with the BER degrading symmetrically as the dimming level strays from 50%. A dimming level less than 50% is due to less allocated signal energy. When the dimming level is greater than 50%, the increasing correlation factor degrades the performance faster than the increase in allocated signal energy. Therefore, the dimming levels in VPPM strongly affect the communication performance.

*T*

_{s}) as the optical rate is increasing. This causes a larger correlation factor, which degrades the BER performance.

_{rx}will be determined as a function of the distance, dimming level, optical rate, and environment settings. Figure 6a shows that the distance between TX and RX should be in the range of approximately 2.5 to 3.8 m to achieve a 10

^{-4}BER and 10% to 90% dimming flexibility. In the case of Figure 6b,c, the distance between TX and RX becomes shorter to obtain the same performance (approximately 1.4 ~ 2.2 m at a 3.75-MHz optical rate and 1.5 ~ 1.8 m at a 7.5-MHz optical rate). This is because the noise bandwidth and correlation factor due to a channel dispersion increase with increasing optical rate.

## 5. Conclusion

The error performance of VPPM was analyzed, and the results were confirmed by a simulation under LOS and diffuse channel conditions. An examination of the relationships among the BER curve, dimming level, and optical rate according to the reference SNR_{rx} revealed tradeoffs between the dimming flexibility and communication performance according to the channel condition if the VPPM scheme for VLC is considered. Care should be taken when designing LED illumination infrastructure with a VLC support based on VPPM because the SNR_{rx} in a VLC is related to the LED luminance distribution.

## Declarations

### Acknowledgments

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education, Science and Technology (No. 2010-0021118).

## Authors’ Affiliations

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## Copyright

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.