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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 14 — Jul. 4, 2011
  • pp: 13418–13427
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Performance improvement by tilting receiver plane in M-QAM OFDM visible light communications

Zixiong Wang, Changyuan Yu, Wen-De Zhong, and Jian Chen  »View Author Affiliations


Optics Express, Vol. 19, Issue 14, pp. 13418-13427 (2011)
http://dx.doi.org/10.1364/OE.19.013418


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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

1. T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50(1), 100–107 (2004). [CrossRef]

3

3. M. Zhang, Y. Zhang, X. Yuan, and J. Zhang, “Mathematic models for a ray tracing method and its applications in wireless optical communications,” Opt. Express 18(17), 18431–18437 (2010). [CrossRef] [PubMed]

]. 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

1. T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50(1), 100–107 (2004). [CrossRef]

]. 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

4. J. Vucic, C. Kottke, K. Habel, and K.-D. Langer, “803Mbit/s visible light WDM link based on DMT modulation of a single RGB LED luminary,” in Proc. OFC, Los Angeles, CA, OWB6 (2011).

]. 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

1. T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50(1), 100–107 (2004). [CrossRef]

] 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

5. S. K. Hashemi, Z. Ghassemlooy, L. Chao, and D. Benhaddou, “Orthogonal frequency division multiplexing for indoor optical wireless communications using visible light LEDs,” in International Symposium on Communication Systems, Networks and Digital Signal Processing, 174–178 (2008).

], 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

5. S. K. Hashemi, Z. Ghassemlooy, L. Chao, and D. Benhaddou, “Orthogonal frequency division multiplexing for indoor optical wireless communications using visible light LEDs,” in International Symposium on Communication Systems, Networks and Digital Signal Processing, 174–178 (2008).

] and other communication systems [6

6. J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol. 27(3), 189–204 (2009). [CrossRef]

].

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

6. J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol. 27(3), 189–204 (2009). [CrossRef]

,7

7. A. Svensson, “An introduction to adaptive QAM modulation schemes for known and predicted channels,” Proc. IEEE 95(12), 2322–2336 (2007). [CrossRef]

] - 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.

2. Principle of tilting receiver plane

The setup of indoor visible light communication using one LED source is shown in Fig. 1
Fig. 1 Illustration of source and receiver in visible light communication.
, 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

Table 1. Parameters of VLC System Setup

table-icon
View This Table
| View All Tables
. Let φ be the angle of irradiance from the LED. As in [8

8. J. R. Barry, Wireless Infrared Communications (Kluwer Academic Publishers, 2006).

,9

9. L. Zeng, D. O’Brien, H. Le-Minh, K. Lee, D. Jung, and Y. Oh, “Improvement of data rate by using equalization in an indoor visible light communication system,” in International Conference on Circuits and Systems for Communications, 678–682 (2008).

], the generalized Lambertian radiation pattern in Eq. (1) is used to model LED radiant irradiance:
R(φ)=(m+1)cosm(φ)2π,
(1)
where m is the order of Lambertian emission which is defined by the transmitter’s semi-angle at half power φ1/2, m = ln(1/2)/ln(cos(φ1/2)).The channel direct current (DC) gain is given as [1

1. T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50(1), 100–107 (2004). [CrossRef]

,8

8. J. R. Barry, Wireless Infrared Communications (Kluwer Academic Publishers, 2006).

]
H(0)=R(φ)Ad2cos(θ)=(m+1)cosm(φ)A2πd2cos(θ),
(2)
where 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 [XS, YS, ZS] and [XR, YR, ZR] be the locations of source and receiver respectively, then
cos(φ)=ZSZR[XS,YS,ZS][XR,YR,ZR],
(3)
where Xis the norm of 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 VRS and VR be the vector from the receiver to the source and the vector of receiver respectively, then
cosθ=(vR,vRS)vRvRS,
(4)
where (VRS , VR) is the inner product of VRS and VR. So the channel DC gain in Eq. (2) becomes
H(0)=(m+1)A2πd2cosm(φ)(vR,vRS)vRvRS
(5)
The recovered electrical signal after photo-detection is denoted as s(t) = R* Prx (1 + MI*f(t)), where the average received power Prx = H(0)*Ptx; Ptx is the launching power of LED; R is responsivity of photo-detector; MI is the modulation index [10

10. I. Neokosmidis, T. Kamalakis, J. Walewski, B. Inan, and T. Sphicopoulos, “Impact of nonlinear LED transfer function on discrete multitone modulation: analytical approach,” J. Lightwave Technol. 27(22), 4970–4978 (2009). [CrossRef]

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

8. J. R. Barry, Wireless Infrared Communications (Kluwer Academic Publishers, 2006).

],
SNR=(RH(0)PtxMIf(t))2σshot2+σthermal2
(6)
where DC component of the recovered electrical signal is blocked, the parameters to determine shot noise and thermal noise are the same as those in [1

1. T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50(1), 100–107 (2004). [CrossRef]

]. We also assume that the power of modulating OFDM signal is unity, i.e. |fOFDM|2=1. The SNR distribution of receiver locates on the desk plane (z = 0.85m) is shown in Fig. 2(a)
Fig. 2 SNR (dB) distribution of VLC with one LED source on the ceiling, (a) before, and (b) after tilting receiver plane. Launching power of LED: 12W.
, 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 VR and VRS. Note that the vector VR is always perpendicular to the receiver plane. The vector VRS is also constant for a particular source and receiver. It is easy to find that the value of cosθ in Eq. (4) is maximized when the two vectors (VRS, VR) 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 cosθ. After tilting the receiver plane towards the source in order to make the two vectors (VRS, VR) parallel, the value of 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 VRS in Eq. (4) could be expressed as VRS = [a, b, c] = [XR, YR, ZR] - [XS, YS, ZS], 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 VR 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 VR becomes [sinβ·cosα, sinβ·sinα, cosβ], where β is the inclination angle [12

12. C. H. Edwards and D. E. Penney, Calculus (Prentice Hall, 2002).

] which is the same as the tilting angle, as shown in Fig. 3
Fig. 3 Principle of tilting the receiver plane to collect optimum optical power.
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
Fig. 4 Source projection locates in the first quadrant of receiver.
, which takes the first quadrant for example.
α={arctan(|(YSYR)/(XSXR)|)source projection in the 1st quadrantπarctan(|(YSYR)/(XSXR)|)source projection in the 2nd quadrantπ+arctan(|(YSYR)/(XSXR)|)source projection in the 3rd quadrant2πarctan(|(YSYR)/(XSXR)|)source projection in the 4th quadrant
(7)
Thus, the value of cosθ in Eq. (4) becomes
cosθ=(vR,vRS)vRvRS=asinβcosα+bsinβsinα+ccosβa2+b2+c2.
(8)
The channel DC gain after tilting is denoted as f (β),
f(β)=(m+1)cosm(φ)A2πd2a2+b2+c2(asinβcosα+bsinβsinα+ccosβ)
(9)
The initial inclination angle 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 VR and VRS tend to be parallel to each other. More and more optical power is collected. The electrical machinery will not stop changing the tilting angle 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

13. M. T. Heath, Scientific Computing—An Introductory Survey (McGraw-Hill, 2002).

]-which is defined as
βn+1=βnf(1)(βn)f(2)(βn),
(10)
where f(1)(β) and f(2)(β) are the first and second order derivative of 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
H(0)=i=14R(φi)Adi2cos(θi)=i=14(m+1)cosm(φi)A2πdi2cos(θi).
(11)
The launching power of each LED is 3W, which guarantees that the total launching power is 12W the same as the situation of only one LED source on the ceiling. The SNR distribution for four LED sources is depicted in Fig. 5 (a)
Fig. 5 SNR (dB) distribution of VLC for four LED sources on the ceiling, (a) before, and (b) after tilting receiver plane. Total launching power of four LEDs: 12W.
. We see that the maximum SNR value is 30.29dB while the minimum SNR value is 16.55dB. The peak-to-valley SNR value is 13.74dB due to the location and properties of four LED sources listed in Table 1. In addition, in the areas inside the projections of LEDs on the desk plane as described in Fig. 6
Fig. 6 Projections of LEDs on the desk plane.
, the SNR distribution is flat and almost constant, so there is no need to adjust the SNR distribution in this area. For the place which is outside projections of LEDs on the desk plane, again we improve the SNR distribution by tilting the receiver plane. When the receiver is not equidistance to any of two LEDs, it faces to the nearest LED of the four, determining the value of azimuth angle 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.

f(β)=i=14fi(β)=i=14m+12πcosm(φ)Acos(θi)di2=i=14(m+1)cosm(φ)A2π([sinβcosαi,sinβsinαi,cosβ],[ai,bi,ci])di2ai2+bi2+ci2
(12)

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

5. S. K. Hashemi, Z. Ghassemlooy, L. Chao, and D. Benhaddou, “Orthogonal frequency division multiplexing for indoor optical wireless communications using visible light LEDs,” in International Symposium on Communication Systems, Networks and Digital Signal Processing, 174–178 (2008).

,6

6. J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol. 27(3), 189–204 (2009). [CrossRef]

] which is caused by the different arrival time of light from different LED sources [14

14. H. Elgala, R. Mesleh, and H. Haas, “Indoor broadcasting via white LEDs and OFDM,” IEEE Trans. Consum. Electron. 55(3), 1127–1134 (2009). [CrossRef]

]. 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

15. H. Nguyen and E. Shwedyk, A First Course in Digital Communications (Cambridge University Press, 2009).

],

SER1(12Q(3M1ESN0))24Q(3M1ESN0).
(13)

Higher SNR in terms of ES/N0 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

7. A. Svensson, “An introduction to adaptive QAM modulation schemes for known and predicted channels,” Proc. IEEE 95(12), 2322–2336 (2007). [CrossRef]

]. Here we set SER 10−3 as the benchmark SER. As shown in Fig. 8
Fig. 8 Setup for adaptive M-QAM OFDM scheme for visible light communication via IR feedback channel. CP: cyclic prefix, P/S: parallel to serial, S/P: serial to parallel.
, 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

2. M. Z. Afgani, H. Haas, H. Elgala, D. Knipp, and W. Hirt, “Visible light communication using OFDM,” in International Conference on Testbeds and Research Infrastructures for the Development on Networks and Communities, 129–134 (2006).

,6

6. J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol. 27(3), 189–204 (2009). [CrossRef]

]. According to Eq. (13), the SNR thresholds to adjusting M-QAM format are shown in Table 2

Table 2. Thresholds (dB) to Adjusting M-QAM Format

table-icon
View This Table
| View All Tables
.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

16. U. S. Jha and R. Prasad, OFDM towards Fixed and Mobile Broadband Wireless Access (Artech House, 2007).

,17

17. J. Proakis, Digital Communications (McGraw-Hill, 2008).

]
SE=12log2(M)NN+112log2(M),
(14)
where ½ represents the SE reduction caused by Hermitian symmetry. In adaptive M-QAM OFDM scheme, the modulation format in terms of M is varied according to the SNR. The average SE is
SE¯=12i=14log2(Mi)p(Mi),
(15)
where p(Mi) is probability of 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
Fig. 9 Improvement of spectral efficiency by tilting receiver plane, (a) one LED source, (b) four LED sources.
, 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.

References and links

1.

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50(1), 100–107 (2004). [CrossRef]

2.

M. Z. Afgani, H. Haas, H. Elgala, D. Knipp, and W. Hirt, “Visible light communication using OFDM,” in International Conference on Testbeds and Research Infrastructures for the Development on Networks and Communities, 129–134 (2006).

3.

M. Zhang, Y. Zhang, X. Yuan, and J. Zhang, “Mathematic models for a ray tracing method and its applications in wireless optical communications,” Opt. Express 18(17), 18431–18437 (2010). [CrossRef] [PubMed]

4.

J. Vucic, C. Kottke, K. Habel, and K.-D. Langer, “803Mbit/s visible light WDM link based on DMT modulation of a single RGB LED luminary,” in Proc. OFC, Los Angeles, CA, OWB6 (2011).

5.

S. K. Hashemi, Z. Ghassemlooy, L. Chao, and D. Benhaddou, “Orthogonal frequency division multiplexing for indoor optical wireless communications using visible light LEDs,” in International Symposium on Communication Systems, Networks and Digital Signal Processing, 174–178 (2008).

6.

J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol. 27(3), 189–204 (2009). [CrossRef]

7.

A. Svensson, “An introduction to adaptive QAM modulation schemes for known and predicted channels,” Proc. IEEE 95(12), 2322–2336 (2007). [CrossRef]

8.

J. R. Barry, Wireless Infrared Communications (Kluwer Academic Publishers, 2006).

9.

L. Zeng, D. O’Brien, H. Le-Minh, K. Lee, D. Jung, and Y. Oh, “Improvement of data rate by using equalization in an indoor visible light communication system,” in International Conference on Circuits and Systems for Communications, 678–682 (2008).

10.

I. Neokosmidis, T. Kamalakis, J. Walewski, B. Inan, and T. Sphicopoulos, “Impact of nonlinear LED transfer function on discrete multitone modulation: analytical approach,” J. Lightwave Technol. 27(22), 4970–4978 (2009). [CrossRef]

11.

http://www.effled.com/15W-high-power-led-p-58.html

12.

C. H. Edwards and D. E. Penney, Calculus (Prentice Hall, 2002).

13.

M. T. Heath, Scientific Computing—An Introductory Survey (McGraw-Hill, 2002).

14.

H. Elgala, R. Mesleh, and H. Haas, “Indoor broadcasting via white LEDs and OFDM,” IEEE Trans. Consum. Electron. 55(3), 1127–1134 (2009). [CrossRef]

15.

H. Nguyen and E. Shwedyk, A First Course in Digital Communications (Cambridge University Press, 2009).

16.

U. S. Jha and R. Prasad, OFDM towards Fixed and Mobile Broadband Wireless Access (Artech House, 2007).

17.

J. Proakis, Digital Communications (McGraw-Hill, 2008).

OCIS Codes
(060.4080) Fiber optics and optical communications : Modulation
(060.4230) Fiber optics and optical communications : Multiplexing
(060.4510) Fiber optics and optical communications : Optical communications
(230.3670) Optical devices : Light-emitting diodes

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: March 29, 2011
Revised Manuscript: June 2, 2011
Manuscript Accepted: June 4, 2011
Published: June 27, 2011

Citation
Zixiong Wang, Changyuan Yu, Wen-De Zhong, and Jian Chen, "Performance improvement by tilting receiver plane in M-QAM OFDM visible light communications," Opt. Express 19, 13418-13427 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-14-13418


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References

  1. T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50(1), 100–107 (2004). [CrossRef]
  2. M. Z. Afgani, H. Haas, H. Elgala, D. Knipp, and W. Hirt, “Visible light communication using OFDM,” in International Conference on Testbeds and Research Infrastructures for the Development on Networks and Communities, 129–134 (2006).
  3. M. Zhang, Y. Zhang, X. Yuan, and J. Zhang, “Mathematic models for a ray tracing method and its applications in wireless optical communications,” Opt. Express 18(17), 18431–18437 (2010). [CrossRef] [PubMed]
  4. J. Vucic, C. Kottke, K. Habel, and K.-D. Langer, “803Mbit/s visible light WDM link based on DMT modulation of a single RGB LED luminary,” in Proc. OFC, Los Angeles, CA, OWB6 (2011).
  5. S. K. Hashemi, Z. Ghassemlooy, L. Chao, and D. Benhaddou, “Orthogonal frequency division multiplexing for indoor optical wireless communications using visible light LEDs,” in International Symposium on Communication Systems, Networks and Digital Signal Processing, 174–178 (2008).
  6. J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol. 27(3), 189–204 (2009). [CrossRef]
  7. A. Svensson, “An introduction to adaptive QAM modulation schemes for known and predicted channels,” Proc. IEEE 95(12), 2322–2336 (2007). [CrossRef]
  8. J. R. Barry, Wireless Infrared Communications (Kluwer Academic Publishers, 2006).
  9. L. Zeng, D. O’Brien, H. Le-Minh, K. Lee, D. Jung, and Y. Oh, “Improvement of data rate by using equalization in an indoor visible light communication system,” in International Conference on Circuits and Systems for Communications, 678–682 (2008).
  10. I. Neokosmidis, T. Kamalakis, J. Walewski, B. Inan, and T. Sphicopoulos, “Impact of nonlinear LED transfer function on discrete multitone modulation: analytical approach,” J. Lightwave Technol. 27(22), 4970–4978 (2009). [CrossRef]
  11. http://www.effled.com/15W-high-power-led-p-58.html
  12. C. H. Edwards and D. E. Penney, Calculus (Prentice Hall, 2002).
  13. M. T. Heath, Scientific Computing—An Introductory Survey (McGraw-Hill, 2002).
  14. H. Elgala, R. Mesleh, and H. Haas, “Indoor broadcasting via white LEDs and OFDM,” IEEE Trans. Consum. Electron. 55(3), 1127–1134 (2009). [CrossRef]
  15. H. Nguyen and E. Shwedyk, A First Course in Digital Communications (Cambridge University Press, 2009).
  16. U. S. Jha and R. Prasad, OFDM towards Fixed and Mobile Broadband Wireless Access (Artech House, 2007).
  17. J. Proakis, Digital Communications (McGraw-Hill, 2008).

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