## Abstract

We propose a scheme to improve the SNR distribution as well as the spectral efficiency of M-QAM OFDM signal for indoor visible light communication by tilting the receiver plane. Newton method is employed for the photo-detector to receive maximum power by finding the optimal tilting angle. This method is a fast algorithm that only three searching steps are needed. The simulation results show that in the case of one LED source, the maximum spectral efficiency improvement is 0.44bit/s/Hz when the launching power of LED source is 12W; while in the case of four LED sources, the maximum spectral efficiency improvement is 0.21bit/s/Hz when the total launching power of the four LED sources is 12W.

© 2011 OSA

## 1. Introduction

Recently, indoor visible light communication (VLC) using light-emitting diode (LED) has aroused many researchers’ interests, from modulation format to channel modeling [1–3]. LED has been applied more frequently as the light source for illumination, due to its high efficiency and energy conservation properties compared with incandescent and fluorescent lamp [1]. The light from LED is a natural carrier for high speed communication. Report shows that the data rate for VLC by LED can reach more than 100Mbit/s [4]. In VLC system, the receiver collects light from two parts: (i) line of sight (LOS) (from LED sources directly), (ii) non-LOS (due to the reflection of the floor, ceiling and walls). The results in [1] reveal that the proportion of LOS is higher than 95%, while the reflection (non-LOS) part only holds less 5% proportion. So in this paper, we assume that the floor and walls’ absorption is so high that only the LOS portion of the received light is considered. The NLOS effect will be discussed extensively in the following work.

When there are several LEDs on the ceiling as the light sources, the receiver collects light from multi-path, which causes inter-symbol interference (ISI) [5], deteriorating the system performance. It has been demonstrated that orthogonal frequency division multiplexing (OFDM) which is also known as discrete multi-tone (DMT) is a promising solution to fight against ISI in VLC [5] and other communication systems [6].

In VLC system, receivers may locate at some places far away from LED source, where the signal to noise ratio (SNR) is much smaller than other areas. Such low SNR degrades the system performances by lowering the spectral efficiency - a significant factor in the design of adaptive optical communication system [6,7] - hence making the system unavailable in these areas of the room. The low SNR in these areas is caused on the one hand by its longer distance away from LEDs and on the other hand by the incident angle.

In this paper, we propose and demonstrate a scheme to improve the SNR distribution in a whole room as well as the spectral efficiency of multi-level quadrature amplitude modulation (M-QAM) OFDM signal by tilting the receiver plane in order to collect maximum optical power. Newton method is employed to search the optimum tilting angle within three searching steps. The rest of this paper is organized as follows. The principle of tilting receiver plane to collect maximum light is described in Section 2. Section 3 shows the improvement of spectral efficiency of M-QAM OFDM signal in two cases: one LED source and four LED sources. The conclusions are given in Section 4.

## 2. Principle of tilting receiver plane

The setup of indoor visible light communication using one LED source is shown in Fig. 1
, where the LED source locates on the ceiling and the receiver locates on a desk. The parameters of the system setup are listed in Table 1
. Let *φ* be the angle of irradiance from the LED. As in [8,9], the generalized Lambertian radiation pattern in Eq. (1) is used to model LED radiant irradiance:

*m*is the order of Lambertian emission which is defined by the transmitter’s semi-angle at half power

*φ*,

_{1/2}*m*= ln(1/2)/ln(cos(

*φ*)).The channel direct current (DC) gain is given as [1,8]

_{1/2}*d*is the distance between the source and the receiver,

*A*is the physical area of photo-detector, and

*θ*is the angle of incidence. Angles

*φ*and

*θ*are associated with the positions of both source and receiver. Let [

*X*,

_{S}*Y*,

_{S}*Z*] and [

_{S}*X*,

_{R}*Y*,

_{R}*Z*] be the locations of source and receiver respectively, then

_{R}*X*. Equation (3) indicates that the irradiance angle

*φ*is constant for a particular source and receiver. However the situation of the angle of incidence

*θ*is different. The value of

*θ*is determined not only by the locations of source and receiver, but also by the dihedral angle between the receiver plane and desk where the receiver locates. Let

**and**

*V*_{RS}**be the vector from the receiver to the source and the vector of receiver respectively, then**

*V*_{R}**,**

*V*_{RS}**) is the inner product of**

*V*_{R}**and**

*V*_{RS}**. So the channel DC gain in Eq. (2) becomes**

*V*_{R}*s*(

*t*) =

*R**

*P*(1 +

_{rx}*M**

_{I}*f*(

*t*)), where the average received power

*P*=

_{rx}*H*(0)*

*P*;

_{tx}*P*is the launching power of LED;

_{tx}*R*is responsivity of photo-detector;

*M*is the modulation index [10],

_{I}*f*(

*t*) is the normalized modulating OFDM signal. Hence, the signal to noise ratio (SNR) of a particular receiver position is given by [8],

*z*= 0.85

*m*) is shown in Fig. 2(a) , where the launching power of LED is 12W and the LED locates in the center of the ceiling. From Fig. 2(a) we find that, the maximum SNR is 36.48dB when the receiver is right below the source LED, while the minimum SNR is 13.83dB when the receiver is in the corners of the room. Hence the peak-to-valley value of SNR is 22.65dB, which is caused by the non-normal incidence of the light from LED to the receiver, deteriorating the average system performance in the whole room. Note that 12W-LED is safe for human eyes [11].

The non-normal incidence of the light is caused by the properties of vectors ** V_{R}** and

**. Note that the vector**

*V*_{RS}**is always perpendicular to the receiver plane. The vector**

*V*_{R}**is also constant for a particular source and receiver. It is easy to find that the value of**

*V*_{RS}*cosθ*in Eq. (4) is maximized when the two vectors (

**,**

*V*_{RS}**) are parallel to each other, i.e., the receiver plane faces to the source. In case the receiver does not locate on the desk right below the source on the ceiling, especially when the receiver is in the corners of the room, we cannot get the maximum channel DC gain in terms of**

*V*_{R}*cosθ*. After tilting the receiver plane towards the source in order to make the two vectors (

**,**

*V*_{RS}**) parallel, the value of**

*V*_{R}*cosθ*reaches its maximum-unity, thus maximum channel DC gain of a particular position could be obtained, which is only associated with the transmission distance

*d*.

Vector ** V_{RS}** in Eq. (4) could be expressed as

**= [**

*V*_{RS}*a*,

*b*,

*c*] = [

*X*,

_{R}*Y*,

_{R}*Z*] - [

_{R}*X*,

_{S}*Y*,

_{S}*Z*], which is also constant for a particular source and receiver. Here we assume that tiling the receiver plane will not affect the position of the receiver. In spherical coordinate system, the location of receiver is selected as the origin. Before tilting the receiver plane, the vector

_{S}**is [0, 0, 1], which means that the receiver plane points to the ceiling; after tilting the receiver plane towards the source on the ceiling, the vector**

*V*_{R}**becomes [**

*V*_{R}*sinβ*·

*cosα*,

*sinβ*·

*sinα*,

*cosβ*], where

*β*is the inclination angle [12] which is the same as the tilting angle, as shown in Fig. 3 and the azimuth angle

*α*is determined by the positions of the receiver as well as the source projection on the desk. In the Cartesian coordinate system with receiver as the origin, the value of angle

*α*is expressed in Eq. (7) and also depicted in Fig. 4 , which takes the first quadrant for example.

*cosθ*in Eq. (4) becomes

*f (β)*,

*β*is zero, i.e., the receiver locates on the desk and the angle-tilting is implemented by an electrical machinery. When the inclination angle is increased after tilting the receiver plane, the two vectors

**and**

*V*_{R}**tend to be parallel to each other. More and more optical power is collected. The electrical machinery will not stop changing the tilting angle**

*V*_{RS}*β*until no more optical power could be received. This searching method is known as Newton method-a fast algorithm to find the maximum of

*f (β)*[13]-which is defined as

*f*and

^{(1)}(β)*f*are the first and second order derivative of

^{(2)}(β)*f (β)*. After finding the optimum tilting angle by Newton method, the maximum optical power is obtained in each receiver position. The improved SNR distribution is shown in Fig. 2 (b), where the maximum SNR remains the same 36.48dB while the minimum SNR in the corners of the room increases to 19.51dB. So there is a 5.68dB improvement of peak-to-valley SNR value when there is only one LED source on the ceiling.

Now we consider the situation when four LED sources locate on the ceiling. The locations of the four LED sources are listed in Table 1. The receiver collects light from all of the four sources. Hence, the channel DC gain in Eq. (2) becomes

*α*. When the receiver is equidistance to two LEDs, it faces to the middle of them. The total channel DC gain is again denoted as

*f (β)*in order to find the optimum tilting angle

*β*.

Applying the same Newton method in Eq. (10), we obtain the improved SNR distribution for four LED sources as shown in Fig. 5(b). The four ridges in the middle of each two of the four LEDs are caused by the receiver’s facing strategy, which is described in last paragraph. We see the maximum SNR is the same-30.29dB, while the minimum SNR value increases to 20.68dB. So 4.13dB-improvement of peak-to-valley SNR value is achieved. Note that Newton method is a fast algorithm to search the optimum tilting angle. Take the receiver position ([4.0 4.0 0.85]) for example. As shown in Fig. 7 , in the two cases-one LED source and four LED sources-only three steps are required to reach the optimum angle, which is fast enough for practical use. Ordinary electrical machinery is competent to this task according to the received optical power.

## 3. Adaptive M-QAM OFDM system setup and discussion

OFDM modulation scheme can fight against inter-carrier interference (ICI) and multipath fading as well as inter-symbol interference (ISI) [5,6] which is caused by the different arrival time of light from different LED sources [14]. Meanwhile, M-QAM modulation format can improve the transmission data rate, comparing with on-off-keying (OOK) and binary phase shift keying (BPSK) modulation formats. The symbol error rate (SER) of M-QAM signal is given by [15],

Higher SNR in terms of E_{S}/N_{0} corresponds to better SER performance. From Fig. 2 and Fig. 5, we find that the distribution of SNR in a particular room is not uniform. Thus, adaptive modulation could be employed to improve the whole system performance [7]. Here we set SER 10^{−3} as the benchmark SER. As shown in Fig. 8
, when the M-QAM OFDM optical signal comes to the photo-detector, its power is detected and sent back to the sources on the ceiling via infrared (IR) feedback channel after tiling the receiver plane. In the places where SNR is low, the small value of *M* is selected to guarantee that 10^{−3} SER could be achieved; while in the places where SNR is high, the modulation format is changed, i.e., advanced M-QAM (large *M*) is applied for high data rate performance. In optical communication, the value of M-QAM OFDM signal should be real by applying Hermitian symmetry which reduces the total spectral efficiency by half [2,6]. According to Eq. (13), the SNR thresholds to adjusting M-QAM format are shown in Table 2
.Suppose that the pulse shape is rectangular and N is the number of subcarriers to implement fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT) in Fig. 8, the spectral efficiency (SE) of a certain M-QAM OFDM signal in unit of bit/s/Hz is expressed as [16,17]

*M*is varied according to the SNR. The average SE is

*p*(

*M*) is probability of

_{i}*M*which is associated with the distribution of SNR in a particular room as described in Fig. 2 and Fig. 5 and Table 2.

From Fig. 9 , we see that the improvement of spectral efficiency brought by tilting the receiver plane is significant. In the case of one LED source, the average improvement is 0.36 bit/s/Hz, and the maximum improvement is 0.44bit/s/Hz when the LED’s launching power is 12W; while in the case of four LED sources, the average improvement is 0.16bit/s/Hz and the maximum improvement is 0.21bit/s/Hz when the LED’s launching power is 12W. We also find that the absolute spectral efficiency after tilting the receiver plane for the case of one LED source is higher than that of four LED sources. So the scheme to improve spectral efficiency by tilting the receiver plane is more effective when there is only on LED source on the ceiling.

## 4. Conclusion

A novel scheme has been proposed to improve the spectral efficiency of adaptive M-QAM OFDM signal in visible light communication by tilting the receiver plane. The optimum tilting angle is searched by Newton method which is a fast algorithm, requiring only three searching steps from the initial state. Simulation results have shown that the improvement of spectral efficiency can reach 0.44bit/s/Hz when the LED’s launching power is 12W for the case of one LED source, while the improvement of spectral efficiency is 0.21bit/s/Hz when the LEDs’ total launching power is 12W for the case of four LED sources.

## Acknowledgment

The authors would like to thank the supports of A*STAR SERC HOME2015 Fund.

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