Abstract

Color-shift keying (CSK) is a modulation scheme in RGB-LED based visible light communication (VLC) where each symbol is mapped into a color of the visible spectrum. According to the IEEE 802.15.7 standard, nine valid combinations of symbols exist to construct 4, 8 or 16-CSK constellations. However, to the best of our knowledge, no formal rules are specified to determine which design performs better among the nine proposed. In this work, we presented a heuristic, machine learning-based approach to determine the best performing 8-CSK constellation and the most suitable algorithm to classify received 8-CSK modulated signals in terms of classification accuracy and bit-error rate (BER). The constellation built on the triangle with vertices at {429, 509, 564} nm scored a BER at 14 dB of 2.3E-3, 3.1E-4, 4.9E-5 and 1.6E-4 for each of the proposed algorithms that are several dBs lower than the worst performing constellations designed on the triangles {429, 564, 753} nm, {429, 564, 703} nm and {429, 564, 656} nm, demonstrating that indeed there exists a difference among the proposed designs independently of the adopted decision strategy and consequently room for improvement for the existing CSK standard.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

It is expected that more than 50 billion devices will be connected to the Internet by 2020 [1]. As a consequence, the urgency of high-speed connectivity and broader spectrum for these devices has paved the way to the development of visible light communication (VLC) technology, whose range of frequency is larger and unlicensed compared to radio frequency communication [24]. In particular, the growth in light-emitting diodes (LEDs) lightning has catalyzed the progresses in the field. Many investigations on the modulation format of VLC system have been reported such as pulse amplitude modulation (PAM), pulse width modulation (PWM) or discrete multi-tone modulation (DMT) [58]. While VLC could work also with other standard modulation formats, color shift keying (CSK) modulation format has been proposed by IEEE for RGB-LED VLC communication system and standardized as 802.15.7 [910]. Rather than relying on the in-phase/quadrature representation, CSK constellation is built on the two-dimensional international commission on illumination (CIE) color space of 1931: each binary symbol is associated to (x, y) coordinates representing a color. In IEEE 802.15.7, seven of these coordinates are picked to characterize the seven color bands in which the spectrum is divided along with a binary code and central wavelength as shown in Fig. 1. The same standard proposes nine different arrangements of triplets I – J – K among these coordinates to constitute the three vertices on which constellations are built such that their reciprocal distance is maximized as reported in Table 1 and depicted in Fig. 2 [11]. IEEE standard, however, does not present an optimal design methodology. In fact, there have been several attempts to optimize the standardized procedure of constructing CSK constellations. In Ref. [1216], for example, maximum likelihood estimation is used as a criterion for detection. Bai et al. designed the constellation map under specific lighting conditions [13]. In Ref. [14], an interior point algorithm is proposed to find locally optical symbol sets; Aziz et al. derived a formula for the best minimum distance between symbols as a function of the modulation order M and the preset chromaticity displacement (x ˜ y ˜) [15], while in Ref. [16] the design has been modelled as disk-packing problem and solved through a billiard ball algorithm. A different approach is through Quad-LEDs (QLEDs), in which an additional band v for a total of four, corresponding to blue, cyan, yellow and red bands, is introduced and the square constellation with higher SNR allows better transmission performances compared with the triangular constellation [17].

 figure: Fig. 1.

Fig. 1. The seven color bands of the visible light spectrum.

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 figure: Fig. 2.

Fig. 2. Vertices of the valid CSK combinations represented on the 1931 CIE diagram.

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Tables Icon

Table 1. Valid CSK color band combinations.

In this paper, a heuristic methodology based on four machine learning algorithms implemented at the receiver side is devised for a RGB-LED based visible light communication system. This approach does not introduce a new constellation design or deviate from the IEEE 802.15.7 original standard. In addition, it keeps the problem of constellation design as simple and general as possible, without introducing system-specific variables or considerations as it is done for optimization problems as treated in Ref. [18]. Finally, it explores the feasibility of learning theory, adaptive receivers and determines the most suitable algorithm among those proposed for classifying CSK-modulated signals. With a minimum BER of 4.9E-5 at 14 dB via K-Nearest Neighbors (KNN), combination #9 is at least 1 dB lower than combination #8, 2 dB lower than combination #5 and several dBs lower for #1 and #3 for each of the proposed algorithms.

2. System model

The adopted channel model is given in Fig. 3. For each of the nine combinations, a sequence of N = 30000 bits has been mapped to the corresponding color for a total of eight symbols described as pairs (xp yp). Since CSK modulated signal is transmitted through three i – j – k bands, it is needed to convert the xy color coordinates into a three-dimensional intensity vector as

$${p_m} = {[{{P_{i,m}} {P_{j,m}} {P_{k,m}}} ]^T}$$
where the subscript m indicates the m-th symbol. The vector pm has been obtained by solving the linear system with Eqs. (2)–(4) for Pi, Pj and Pk as
$${x_p} = {P_i}{x_i} + {P_j}{x_j} + {P_k}{x_k}$$
$${y_p} = {P_i}{y_i} + {P_j}{y_j} + {P_k}{y_k}$$
and
$${P_i} + {P_j} + {P_k} = 1 $$
in which (xi yi), (xj yj) and (xk yk) are the color coordinates of the three light sources, while Eq. (4) guarantees uniform average intensity so that no flickering is perceived. The channel propagation matrix is represented as a 3 × 3 matrix, i.e. three intensity-modulation/direct-detection (IM/DD) channels in the form of
$$\textbf{H} = \left[ \begin{array}{ccc} {{h_{ii}}}&{{h_{ij}}}&{{h_{ik}}}\\ {{h_{ji}}}&{{h_{j\dot{j}}}}&{{h_{jk}}}\\ {{h_{ki}}}&{{h_{kj}}}&{{h_{kk}}} \end{array} \right] $$

 figure: Fig. 3.

Fig. 3. The channel model of RGB-LED based visible light communication.

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The discrete-time received signal is given by Ref. [17], assuming additive white Gaussian noise (AWGN) introduced as

$$\boldsymbol{r} = \boldsymbol{H} \cdot {p_m} + \boldsymbol{n}$$
where r = [ Ri Rj Rk] T and n are the received signal intensity and AWGN vectors, respectively. With a suitable channel estimation sequence such as OOK-modulated Walsh codes is possible to reconstruct the channel matrix H. For the sake of simplicity, we assumed an ideal scenario case in which it is known a priori. At the receiver side, the RGB compensation module multiplies the received signal vector with the inverse of the channel response (i.e. ignoring the noise component) to obtain an estimated intensity vector p’m as in Eq. (7):
$${p^{\prime}_{m}} = [{P^{\prime}_{i,m}} {P^{\prime}_{j,m}} {P^{\prime}_{k,m}}]^{T} = \boldsymbol{H}^{- 1} \cdot {p_m}$$
The inverse procedure of Eqs. (2)–(3) is then performed in order to obtain the corresponding estimated color symbols (x’p y’p). The resulting constellation diagrams constitute the data processed by the learning decision block.

After separating the received data into training and testing sets of features (2-dimensional color coordinates) and labels (8 possible symbols), the received pairs have been classified through four supervised learning algorithms and their accuracy has been evaluated.

2.1 Algorithms

The four algorithms selected represent the most widespread tools used for classification problems, and they are briefly introduced in this section.

A support-vector machine (SVM) is a supervised learning model popular for classification and regression tasks [18]. Mathematically, it corresponds to the classification of data points in a K-dimensional space through a (K-1)-dimensional hyperplane such that the distance between data points belonging to different classes is maximized. For the 8-CSK problem presented in this paper, there are a total of 8 classes in a two-dimensional color space, for which the hyperplane corresponds to a line between clusters of data.

Logistic regression is a statistical tool in which independent input values are linearly combined to predict through the logistic (or sigmoid) function the probability of the mentioned input to belong to each of the classes [19]. Differently from SVMs, logistic regression is an example of probabilistic algorithm. Multinomial logistic regression, in particular, is used in the case of three or more unordered classes, for which the output will be a M dimensional vector of probabilities.

K-Nearest Neighbors (KNN) is a non-parametric algorithm which can be adopted when little or no probability distribution of the data is available [20]. It is based on the Euclidean distance between training and testing samples, then from a set S of the K smallest distances evaluated is returned the most recurrent label. For the task proposed in the paper is has been chosen as K = 5 after trial-and-error tuning.

A neural network (NN) is a machine learning structure inspired by a simplified functioning of neuronal cells in the brain [21,22]. It is represented through a multi-layered structure of nodes or “neurons” connected between each other. In general input, output and a series of hidden layers are distinguished. Mathematically, it is able to model non-linear, virtually very complex mapping between input features and output labels depending on the activation function (function at the output of each layer), the weights of each neuronal link and a function of the input feature. The structure of the NN adopted for the proposed task is summarized in Table 2.

Tables Icon

Table 2. The adopted neural network structure

3. Results and discussions

Evaluations have been first carried out with a signal-to-noise ratio (SNR) of 10 dB, since it was the lowest SNR level at which a clear constellation diagrams could be distinguished at receiver side. The highest classification accuracies have been reached for combinations #9, #2 and #8, peaking at 99.6% through SVM and KNN, 99.6% through NN and 99.4% through NN, respectively. Consequently, the BER resulted to be the lowest for the three constellations are 4E-3, 4E-3 and 6E-3 respectively, all of the same order of the forward error correction (FEC) threshold of 3.8E-3. Note that the BER has been evaluated in the worst-case scenario for which BER = SER. The signal modulated according to combination #6 has also been classified with an error as low as 1.3% through NN. Combinations #4 and #5, instead, did not reach accuracies above 83% (BER = 0.17) and 80% (BER = 0.203) respectively, implying a highly unreliable transmission close to pure randomly classified symbols (i.e. BER = 0.5). In five out of nine combinations (#1, #2, #3, #6, #8) the algorithm that classified the 8-CSK symbols more accurately resulted to be the three-layer neural network, followed by the support vector machine, that resulted the most accurate algorithm in three out of nine combinations (#5, #7, #9). Only in one case, KNN (for arrangement #9, ex-aequo with SVM) and Logistic Regression (for #4) have been the classifiers with the lowest error. The overall accuracies scored by each of the four decision algorithms are summarized in Fig. 4, while the corresponding minimum BER evaluated is given in Fig. 5.

 figure: Fig. 4.

Fig. 4. Classification accuracies for the nine 8-CSK combinations at SNR = 10 dB.

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 figure: Fig. 5.

Fig. 5. Minimum BER ordered for the nine 8-CSK combinations at SNR = 10 dB.

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In Fig. 6, the nine plots of the classified 8-CSK received signal according to their corresponding best performing algorithm have been grouped together, showing the resulting learning-based decision regions. It can be seen how the best performing combinations correspond to constellations with received symbols more widely spaced among each other (as shown in Fig. 6) such as #2, #6 and #9, while sharper, polygonal Voronoi regions are associated to higher classification uncertainty, as for #3, #4 and #5.

 figure: Fig. 6.

Fig. 6. Classified 8-CSK received signal according to their corresponding best performing algorithm for the nine combinations at SNR = 10 dB. White squares represent the original color coordinate of each symbol, the colored dots the received clustered coordinate representing a same symbol.

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Subsequently, SNR has been varied from 1 dB to 16 dB and the BER deriving from the learning-based decision has been evaluated both by algorithm and by combination to verify the consistency of the previous claims. The threshold of 16 dB has been picked since by increasing the SNR above 16 dB the algorithms scored an accuracy of 100%, that is unfeasible in real physical systems, and for this reason has been omitted. The best performing 8-CSK constellation resulted to be the one built according to combination #9 for each of the four algorithms. At 14 dB, BER of 2.3E-3, 3.1E-4, 4.9E-5 and 1.6E-4 were recorded for SVM, LR, KNN and NN classified signals, respectively. Next best performing combinations, compared by FEC level, were: #4 at 13.9 dB, #6 at 14.1 dB and # 2 at 14.3 dB for SVM; #4 at 14.3 dB, #2 at 14.8 dB and #8 at 15.1 dB for LR; #4 at 14.1 dB #6 at 14.2 dB and #2 at 14.4 dB for KNN; #4 at 13.9 dB, #6 at 14.1 dB and #2 at 14.4 dB for ANN. Findings are summarized in Table 3.

Tables Icon

Table 3. Top four combinations ordered by SNR at which the FEC level is reached.

The results are almost identical and accordance with what reported in Fig. 4 and with the only exception of combination #4, for which outlier points have been registered at 10 dB with significantly higher BER than average (see Fig. 8). Similarly, combination #1, #3 and #5 have been recorded to be the worst performing, with a BER at 16 dB always of the order of 1E-2 for combination #1 and #3, while the aforementioned combinations all scored a BER below the forward error correction (FEC) threshold of 3.8E-3 already at 14 dB or slightly below, as in Table 3 and Fig. 7. Moreover, it has been observed again that for all of the nine combinations the algorithms scoring the lowest BER for a fixed power level resulted to the SVM and the three-layer NN, while Logistic Regression and KNN algorithms generally lagged behind as can be seen in Fig. 8. This is particularly evident when the power level is above 12 dB, after which the difference between the BER curves can be better appreciated. The only exceptions to this claim are found for combination #1 and #9, in which KNN outperforms the other algorithms for higher SNR levels.

 figure: Fig. 7.

Fig. 7. BER curves of the nine combinations with SNR ranging between 1-16 dB for each of the four classification algorithms.

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 figure: Fig. 8.

Fig. 8. Measured and fitted BER curves of the four classification algorithms with SNR ranging between 1-16 dB for each of the nine combinations.

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With respect to real CSK-based signal transmission, however, some further considerations have to be done to guarantee more reliable results. Firstly, at the receiver side a color calibration block should be present to compensate coordinate errors and attenuate the crosstalk among different color bands [17]. The received noisy constellation of the system presented, instead, did not take into account the boundaries of the color diagram i.e. included coordinates outside the visible spectrum and hence not representable. This implies that the presented results might deviate from a real-case scenario. Secondly the color Gamut, i.e. the range of colors that a device can display, reproduce or capture is generally a much more limited subset with respect to the whole visible spectrum in the CIE 1931 diagram [23]. A camera with smaller Gamut as a receiver, for example, will necessarily need more compressed constellations (as combination #4 or #5), reason for which the means proposed cannot assure the absolute superiority of combinations #9, #2, #4 and #8 with respect to others based solely on the proposed means. Lastly the color accuracy has also to be considered, since different devices might not be able to distinguish or to reproduce colors too close to each other according to MacAdam ellipses theory [24].

4. Conclusions

A heuristic, machine learning approach to determine (i) the best performing constellations among the nine valid design combinations suggested by the IEEE standard and (ii) the most suitable algorithm for classifying 8-CSK modulated signal has been proposed. It has been demonstrated how the 802.15.7 combinations #9, #4, #6 and #2 reached a same BER level with several dBs of difference with respect others regardless of the adopted decision strategy and that therefore it does exist a difference that allows to further specify the CSK modulation standard. In addition, it has been shown and that the neural network and support vector machine classified 8-CSK modulated signal with the highest accuracy reaching the FEC threshold at an SNR below 14 dB and regardless of the combination to which they have been applied to, opening to machine learning-based cognitive transceivers for visible light communication.

Funding

Shenzhen Science and Technology Innovation Commission (JCYJ20180507183815699, JCYJ20170818094001391, KQJSCX20170727163424873); Tsinghua-Berkeley Shenzhen Institute (TBSI) Faculty Start-up Fund; Shenzhen Data Science and Information Technology Engineering Laboratory.

Disclosures

The authors declare no conflicts of interest.

References

1. L. Ericsson, “More than 50 billion connected devices,” White Paper14(1) (2011).

2. L. E. M. Matheus, A. B. Vieira, L. F. Vieira, M. A. Vieira, and O. Gnawali, “Visible Light Communication: Concepts, Applications and Challenges,” IEEE Commun. Surv. Tutorials 21(4), 3204–3237 (2019). [CrossRef]  

3. M. Akanegawa, Y. Tanaka, and M. Nakagawa, “M. Basic study on traffic information system using LED traffic lights,” IEEE Trans. Intell. Transp. Syst. 2(4), 197–203 (2001). [CrossRef]  

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

5. G. Ntogari, T. Kamalakis, J. W. Walewski, and T. Sphicopoulos, “Combining illumination dimming based on pulse-width modulation with visible-light communications based on discrete multitone,” J. Opt. Commun. Netw. 3(1), 56–65 (2011). [CrossRef]  

6. F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, H. T. Huang, and C. H. Ho, “1.1-Gb/s white-LED-based visible light communication employing carrier-less amplitude and phase modulation,” IEEE Photonics Technol. Lett. 24(19), 1730–1732 (2012). [CrossRef]  

7. I. Neokosmidis, T. Kamalakis, J. W. 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]  

8. K. Lee and H. Park, “Modulations for visible light communications with dimming control,” IEEE Photonics Technol. Lett. 23(16), 1136–1138 (2011). [CrossRef]  

9. IEEE Standard for Local and Metropolitan area networks - Part 15.7: “Short-Range Wireless Optical Communication Using Visible Light”, (2011).

10. S. Rajagopal, R. D. Roberts, and S. K. Lim, “IEEE 802.15. 7 visible light communication: modulation schemes and dimming support,” IEEE Commun. Mag. 50(3), 72–82 (2012). [CrossRef]  

11. A. Yokoi, J. Son, and T. Bae, “More description about CSK constellation,” IEEE802(7), 3–46 (2010).

12. G. Cossu, A. M. Khalid, P. Choudhury, R. Corsini, and E. Ciaramella, “Long distance indoor high speed visible light communication system based on RGB LEDs,” Proceedings of the Asia Commun. Photon. Conf, 1–3 (2012).

13. B. Bai, Q. He, Z. Xu, and Y. Fan, “The color shift key modulation with non-uniform signaling for visible light communication,” IEEE Intern. Conf. on Comm. in China Workshops, 37–42, (2012).

14. E. Monteiro and S. Hranilovic, “Constellation design for color-shift keying using interior point methods,” IEEE Globecom Workshops, (2012).

15. A. E. Aziz, K. T. Wong, and J. C. Chen, “Color-shift keying—How its largest obtainable “minimum distance” depends on its preset operating chromaticity and constellation size,” J. Lightwave Technol. 35(13), 2724–2733 (2017). [CrossRef]  

16. R. J. Drost and B. M. Sadler, “Constellation design for color-shift keying using billiards algorithms,” IEEE Globecom Workshops, (2010).

17. Z. Wang, Q. Wang, W. Huang, and Z. Xu, “Visible Light Communications,” IEEE Press, Wiley (2017).

18. E. Monteiro and S. Hranilovic, “Design and Implementation of Color-Shift Keying for Visible Light Communications,” J. Lightwave Technol. 32(10), 2053–2060 (2014). [CrossRef]  

19. C. Cortes and V. Vapnik, “Support-vector networks,” Int. J. Mach. Learn. Cybern. 20(3), 273–297 (1995). [CrossRef]  

20. R. E. Wright, “Logistic regression.” (1995).

21. T. Cover and P. Hart, “Nearest neighbor pattern classification,” IEEE Trans. Inf. Theory 13(1), 21–27 (1967). [CrossRef]  

22. L. K. Hansen and S. Peter, “Neural network ensembles,” IEEE Trans. Pattern Anal. Mach. Intell. 12(10), 993–1001 (1990). [CrossRef]  

23. J. Morovič, “Color gamut mapping,” Vol. 10. John Wiley & Sons (2008).

24. M. Wood “MacAdam ellipses,” Out of the Wood, Mike Wood Consulting LLC. (retrieved on Jun. 8, 2011). Retrieved from the internet: URL: http://www.mikewoodconsulting.com/articles/Protocol%20Fall202010 (2010).

References

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  • |
  • |
  • |

  1. L. Ericsson, “More than 50 billion connected devices,” White Paper14(1) (2011).
  2. L. E. M. Matheus, A. B. Vieira, L. F. Vieira, M. A. Vieira, and O. Gnawali, “Visible Light Communication: Concepts, Applications and Challenges,” IEEE Commun. Surv. Tutorials 21(4), 3204–3237 (2019).
    [Crossref]
  3. M. Akanegawa, Y. Tanaka, and M. Nakagawa, “M. Basic study on traffic information system using LED traffic lights,” IEEE Trans. Intell. Transp. Syst. 2(4), 197–203 (2001).
    [Crossref]
  4. T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Broadcast Telev. Receivers 50(1), 100–107 (2004).
    [Crossref]
  5. G. Ntogari, T. Kamalakis, J. W. Walewski, and T. Sphicopoulos, “Combining illumination dimming based on pulse-width modulation with visible-light communications based on discrete multitone,” J. Opt. Commun. Netw. 3(1), 56–65 (2011).
    [Crossref]
  6. F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, H. T. Huang, and C. H. Ho, “1.1-Gb/s white-LED-based visible light communication employing carrier-less amplitude and phase modulation,” IEEE Photonics Technol. Lett. 24(19), 1730–1732 (2012).
    [Crossref]
  7. I. Neokosmidis, T. Kamalakis, J. W. 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]
  8. K. Lee and H. Park, “Modulations for visible light communications with dimming control,” IEEE Photonics Technol. Lett. 23(16), 1136–1138 (2011).
    [Crossref]
  9. IEEE Standard for Local and Metropolitan area networks - Part 15.7: “Short-Range Wireless Optical Communication Using Visible Light”, (2011).
  10. S. Rajagopal, R. D. Roberts, and S. K. Lim, “IEEE 802.15. 7 visible light communication: modulation schemes and dimming support,” IEEE Commun. Mag. 50(3), 72–82 (2012).
    [Crossref]
  11. A. Yokoi, J. Son, and T. Bae, “More description about CSK constellation,” IEEE802(7), 3–46 (2010).
  12. G. Cossu, A. M. Khalid, P. Choudhury, R. Corsini, and E. Ciaramella, “Long distance indoor high speed visible light communication system based on RGB LEDs,” Proceedings of the Asia Commun. Photon. Conf, 1–3 (2012).
  13. B. Bai, Q. He, Z. Xu, and Y. Fan, “The color shift key modulation with non-uniform signaling for visible light communication,” IEEE Intern. Conf. on Comm. in China Workshops, 37–42, (2012).
  14. E. Monteiro and S. Hranilovic, “Constellation design for color-shift keying using interior point methods,” IEEE Globecom Workshops, (2012).
  15. A. E. Aziz, K. T. Wong, and J. C. Chen, “Color-shift keying—How its largest obtainable “minimum distance” depends on its preset operating chromaticity and constellation size,” J. Lightwave Technol. 35(13), 2724–2733 (2017).
    [Crossref]
  16. R. J. Drost and B. M. Sadler, “Constellation design for color-shift keying using billiards algorithms,” IEEE Globecom Workshops, (2010).
  17. Z. Wang, Q. Wang, W. Huang, and Z. Xu, “Visible Light Communications,” IEEE Press, Wiley (2017).
  18. E. Monteiro and S. Hranilovic, “Design and Implementation of Color-Shift Keying for Visible Light Communications,” J. Lightwave Technol. 32(10), 2053–2060 (2014).
    [Crossref]
  19. C. Cortes and V. Vapnik, “Support-vector networks,” Int. J. Mach. Learn. Cybern. 20(3), 273–297 (1995).
    [Crossref]
  20. R. E. Wright, “Logistic regression.” (1995).
  21. T. Cover and P. Hart, “Nearest neighbor pattern classification,” IEEE Trans. Inf. Theory 13(1), 21–27 (1967).
    [Crossref]
  22. L. K. Hansen and S. Peter, “Neural network ensembles,” IEEE Trans. Pattern Anal. Mach. Intell. 12(10), 993–1001 (1990).
    [Crossref]
  23. J. Morovič, “Color gamut mapping,” Vol. 10. John Wiley & Sons (2008).
  24. M. Wood “MacAdam ellipses,” Out of the Wood, Mike Wood Consulting LLC. (retrieved on Jun. 8, 2011). Retrieved from the internet: URL: http://www.mikewoodconsulting.com/articles/Protocol%20Fall202010 (2010).

2019 (1)

L. E. M. Matheus, A. B. Vieira, L. F. Vieira, M. A. Vieira, and O. Gnawali, “Visible Light Communication: Concepts, Applications and Challenges,” IEEE Commun. Surv. Tutorials 21(4), 3204–3237 (2019).
[Crossref]

2017 (1)

2014 (1)

2012 (2)

F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, H. T. Huang, and C. H. Ho, “1.1-Gb/s white-LED-based visible light communication employing carrier-less amplitude and phase modulation,” IEEE Photonics Technol. Lett. 24(19), 1730–1732 (2012).
[Crossref]

S. Rajagopal, R. D. Roberts, and S. K. Lim, “IEEE 802.15. 7 visible light communication: modulation schemes and dimming support,” IEEE Commun. Mag. 50(3), 72–82 (2012).
[Crossref]

2011 (2)

2009 (1)

2004 (1)

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

2001 (1)

M. Akanegawa, Y. Tanaka, and M. Nakagawa, “M. Basic study on traffic information system using LED traffic lights,” IEEE Trans. Intell. Transp. Syst. 2(4), 197–203 (2001).
[Crossref]

1995 (1)

C. Cortes and V. Vapnik, “Support-vector networks,” Int. J. Mach. Learn. Cybern. 20(3), 273–297 (1995).
[Crossref]

1990 (1)

L. K. Hansen and S. Peter, “Neural network ensembles,” IEEE Trans. Pattern Anal. Mach. Intell. 12(10), 993–1001 (1990).
[Crossref]

1967 (1)

T. Cover and P. Hart, “Nearest neighbor pattern classification,” IEEE Trans. Inf. Theory 13(1), 21–27 (1967).
[Crossref]

Akanegawa, M.

M. Akanegawa, Y. Tanaka, and M. Nakagawa, “M. Basic study on traffic information system using LED traffic lights,” IEEE Trans. Intell. Transp. Syst. 2(4), 197–203 (2001).
[Crossref]

Aziz, A. E.

Bae, T.

A. Yokoi, J. Son, and T. Bae, “More description about CSK constellation,” IEEE802(7), 3–46 (2010).

Bai, B.

B. Bai, Q. He, Z. Xu, and Y. Fan, “The color shift key modulation with non-uniform signaling for visible light communication,” IEEE Intern. Conf. on Comm. in China Workshops, 37–42, (2012).

Chen, C. W.

F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, H. T. Huang, and C. H. Ho, “1.1-Gb/s white-LED-based visible light communication employing carrier-less amplitude and phase modulation,” IEEE Photonics Technol. Lett. 24(19), 1730–1732 (2012).
[Crossref]

Chen, J. C.

Choudhury, P.

G. Cossu, A. M. Khalid, P. Choudhury, R. Corsini, and E. Ciaramella, “Long distance indoor high speed visible light communication system based on RGB LEDs,” Proceedings of the Asia Commun. Photon. Conf, 1–3 (2012).

Ciaramella, E.

G. Cossu, A. M. Khalid, P. Choudhury, R. Corsini, and E. Ciaramella, “Long distance indoor high speed visible light communication system based on RGB LEDs,” Proceedings of the Asia Commun. Photon. Conf, 1–3 (2012).

Corsini, R.

G. Cossu, A. M. Khalid, P. Choudhury, R. Corsini, and E. Ciaramella, “Long distance indoor high speed visible light communication system based on RGB LEDs,” Proceedings of the Asia Commun. Photon. Conf, 1–3 (2012).

Cortes, C.

C. Cortes and V. Vapnik, “Support-vector networks,” Int. J. Mach. Learn. Cybern. 20(3), 273–297 (1995).
[Crossref]

Cossu, G.

G. Cossu, A. M. Khalid, P. Choudhury, R. Corsini, and E. Ciaramella, “Long distance indoor high speed visible light communication system based on RGB LEDs,” Proceedings of the Asia Commun. Photon. Conf, 1–3 (2012).

Cover, T.

T. Cover and P. Hart, “Nearest neighbor pattern classification,” IEEE Trans. Inf. Theory 13(1), 21–27 (1967).
[Crossref]

Drost, R. J.

R. J. Drost and B. M. Sadler, “Constellation design for color-shift keying using billiards algorithms,” IEEE Globecom Workshops, (2010).

Ericsson, L.

L. Ericsson, “More than 50 billion connected devices,” White Paper14(1) (2011).

Fan, Y.

B. Bai, Q. He, Z. Xu, and Y. Fan, “The color shift key modulation with non-uniform signaling for visible light communication,” IEEE Intern. Conf. on Comm. in China Workshops, 37–42, (2012).

Gnawali, O.

L. E. M. Matheus, A. B. Vieira, L. F. Vieira, M. A. Vieira, and O. Gnawali, “Visible Light Communication: Concepts, Applications and Challenges,” IEEE Commun. Surv. Tutorials 21(4), 3204–3237 (2019).
[Crossref]

Hansen, L. K.

L. K. Hansen and S. Peter, “Neural network ensembles,” IEEE Trans. Pattern Anal. Mach. Intell. 12(10), 993–1001 (1990).
[Crossref]

Hart, P.

T. Cover and P. Hart, “Nearest neighbor pattern classification,” IEEE Trans. Inf. Theory 13(1), 21–27 (1967).
[Crossref]

He, Q.

B. Bai, Q. He, Z. Xu, and Y. Fan, “The color shift key modulation with non-uniform signaling for visible light communication,” IEEE Intern. Conf. on Comm. in China Workshops, 37–42, (2012).

Ho, C. H.

F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, H. T. Huang, and C. H. Ho, “1.1-Gb/s white-LED-based visible light communication employing carrier-less amplitude and phase modulation,” IEEE Photonics Technol. Lett. 24(19), 1730–1732 (2012).
[Crossref]

Hranilovic, S.

E. Monteiro and S. Hranilovic, “Design and Implementation of Color-Shift Keying for Visible Light Communications,” J. Lightwave Technol. 32(10), 2053–2060 (2014).
[Crossref]

E. Monteiro and S. Hranilovic, “Constellation design for color-shift keying using interior point methods,” IEEE Globecom Workshops, (2012).

Huang, H. T.

F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, H. T. Huang, and C. H. Ho, “1.1-Gb/s white-LED-based visible light communication employing carrier-less amplitude and phase modulation,” IEEE Photonics Technol. Lett. 24(19), 1730–1732 (2012).
[Crossref]

Huang, W.

Z. Wang, Q. Wang, W. Huang, and Z. Xu, “Visible Light Communications,” IEEE Press, Wiley (2017).

Inan, B.

Kamalakis, T.

Khalid, A. M.

G. Cossu, A. M. Khalid, P. Choudhury, R. Corsini, and E. Ciaramella, “Long distance indoor high speed visible light communication system based on RGB LEDs,” Proceedings of the Asia Commun. Photon. Conf, 1–3 (2012).

Komine, T.

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

Lee, K.

K. Lee and H. Park, “Modulations for visible light communications with dimming control,” IEEE Photonics Technol. Lett. 23(16), 1136–1138 (2011).
[Crossref]

Lim, S. K.

S. Rajagopal, R. D. Roberts, and S. K. Lim, “IEEE 802.15. 7 visible light communication: modulation schemes and dimming support,” IEEE Commun. Mag. 50(3), 72–82 (2012).
[Crossref]

Lin, C. T.

F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, H. T. Huang, and C. H. Ho, “1.1-Gb/s white-LED-based visible light communication employing carrier-less amplitude and phase modulation,” IEEE Photonics Technol. Lett. 24(19), 1730–1732 (2012).
[Crossref]

Matheus, L. E. M.

L. E. M. Matheus, A. B. Vieira, L. F. Vieira, M. A. Vieira, and O. Gnawali, “Visible Light Communication: Concepts, Applications and Challenges,” IEEE Commun. Surv. Tutorials 21(4), 3204–3237 (2019).
[Crossref]

Monteiro, E.

E. Monteiro and S. Hranilovic, “Design and Implementation of Color-Shift Keying for Visible Light Communications,” J. Lightwave Technol. 32(10), 2053–2060 (2014).
[Crossref]

E. Monteiro and S. Hranilovic, “Constellation design for color-shift keying using interior point methods,” IEEE Globecom Workshops, (2012).

Morovic, J.

J. Morovič, “Color gamut mapping,” Vol. 10. John Wiley & Sons (2008).

Nakagawa, M.

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

M. Akanegawa, Y. Tanaka, and M. Nakagawa, “M. Basic study on traffic information system using LED traffic lights,” IEEE Trans. Intell. Transp. Syst. 2(4), 197–203 (2001).
[Crossref]

Neokosmidis, I.

Ntogari, G.

Park, H.

K. Lee and H. Park, “Modulations for visible light communications with dimming control,” IEEE Photonics Technol. Lett. 23(16), 1136–1138 (2011).
[Crossref]

Peter, S.

L. K. Hansen and S. Peter, “Neural network ensembles,” IEEE Trans. Pattern Anal. Mach. Intell. 12(10), 993–1001 (1990).
[Crossref]

Rajagopal, S.

S. Rajagopal, R. D. Roberts, and S. K. Lim, “IEEE 802.15. 7 visible light communication: modulation schemes and dimming support,” IEEE Commun. Mag. 50(3), 72–82 (2012).
[Crossref]

Roberts, R. D.

S. Rajagopal, R. D. Roberts, and S. K. Lim, “IEEE 802.15. 7 visible light communication: modulation schemes and dimming support,” IEEE Commun. Mag. 50(3), 72–82 (2012).
[Crossref]

Sadler, B. M.

R. J. Drost and B. M. Sadler, “Constellation design for color-shift keying using billiards algorithms,” IEEE Globecom Workshops, (2010).

Son, J.

A. Yokoi, J. Son, and T. Bae, “More description about CSK constellation,” IEEE802(7), 3–46 (2010).

Sphicopoulos, T.

Tanaka, Y.

M. Akanegawa, Y. Tanaka, and M. Nakagawa, “M. Basic study on traffic information system using LED traffic lights,” IEEE Trans. Intell. Transp. Syst. 2(4), 197–203 (2001).
[Crossref]

Vapnik, V.

C. Cortes and V. Vapnik, “Support-vector networks,” Int. J. Mach. Learn. Cybern. 20(3), 273–297 (1995).
[Crossref]

Vieira, A. B.

L. E. M. Matheus, A. B. Vieira, L. F. Vieira, M. A. Vieira, and O. Gnawali, “Visible Light Communication: Concepts, Applications and Challenges,” IEEE Commun. Surv. Tutorials 21(4), 3204–3237 (2019).
[Crossref]

Vieira, L. F.

L. E. M. Matheus, A. B. Vieira, L. F. Vieira, M. A. Vieira, and O. Gnawali, “Visible Light Communication: Concepts, Applications and Challenges,” IEEE Commun. Surv. Tutorials 21(4), 3204–3237 (2019).
[Crossref]

Vieira, M. A.

L. E. M. Matheus, A. B. Vieira, L. F. Vieira, M. A. Vieira, and O. Gnawali, “Visible Light Communication: Concepts, Applications and Challenges,” IEEE Commun. Surv. Tutorials 21(4), 3204–3237 (2019).
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Wang, Q.

Z. Wang, Q. Wang, W. Huang, and Z. Xu, “Visible Light Communications,” IEEE Press, Wiley (2017).

Wang, Z.

Z. Wang, Q. Wang, W. Huang, and Z. Xu, “Visible Light Communications,” IEEE Press, Wiley (2017).

Wei, C. C.

F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, H. T. Huang, and C. H. Ho, “1.1-Gb/s white-LED-based visible light communication employing carrier-less amplitude and phase modulation,” IEEE Photonics Technol. Lett. 24(19), 1730–1732 (2012).
[Crossref]

Wong, K. T.

Wood, M.

M. Wood “MacAdam ellipses,” Out of the Wood, Mike Wood Consulting LLC. (retrieved on Jun. 8, 2011). Retrieved from the internet: URL: http://www.mikewoodconsulting.com/articles/Protocol%20Fall202010 (2010).

Wright, R. E.

R. E. Wright, “Logistic regression.” (1995).

Wu, F. M.

F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, H. T. Huang, and C. H. Ho, “1.1-Gb/s white-LED-based visible light communication employing carrier-less amplitude and phase modulation,” IEEE Photonics Technol. Lett. 24(19), 1730–1732 (2012).
[Crossref]

Xu, Z.

Z. Wang, Q. Wang, W. Huang, and Z. Xu, “Visible Light Communications,” IEEE Press, Wiley (2017).

B. Bai, Q. He, Z. Xu, and Y. Fan, “The color shift key modulation with non-uniform signaling for visible light communication,” IEEE Intern. Conf. on Comm. in China Workshops, 37–42, (2012).

Yokoi, A.

A. Yokoi, J. Son, and T. Bae, “More description about CSK constellation,” IEEE802(7), 3–46 (2010).

IEEE Commun. Mag. (1)

S. Rajagopal, R. D. Roberts, and S. K. Lim, “IEEE 802.15. 7 visible light communication: modulation schemes and dimming support,” IEEE Commun. Mag. 50(3), 72–82 (2012).
[Crossref]

IEEE Commun. Surv. Tutorials (1)

L. E. M. Matheus, A. B. Vieira, L. F. Vieira, M. A. Vieira, and O. Gnawali, “Visible Light Communication: Concepts, Applications and Challenges,” IEEE Commun. Surv. Tutorials 21(4), 3204–3237 (2019).
[Crossref]

IEEE Photonics Technol. Lett. (2)

F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, H. T. Huang, and C. H. Ho, “1.1-Gb/s white-LED-based visible light communication employing carrier-less amplitude and phase modulation,” IEEE Photonics Technol. Lett. 24(19), 1730–1732 (2012).
[Crossref]

K. Lee and H. Park, “Modulations for visible light communications with dimming control,” IEEE Photonics Technol. Lett. 23(16), 1136–1138 (2011).
[Crossref]

IEEE Trans. Broadcast Telev. Receivers (1)

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

IEEE Trans. Inf. Theory (1)

T. Cover and P. Hart, “Nearest neighbor pattern classification,” IEEE Trans. Inf. Theory 13(1), 21–27 (1967).
[Crossref]

IEEE Trans. Intell. Transp. Syst. (1)

M. Akanegawa, Y. Tanaka, and M. Nakagawa, “M. Basic study on traffic information system using LED traffic lights,” IEEE Trans. Intell. Transp. Syst. 2(4), 197–203 (2001).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

L. K. Hansen and S. Peter, “Neural network ensembles,” IEEE Trans. Pattern Anal. Mach. Intell. 12(10), 993–1001 (1990).
[Crossref]

Int. J. Mach. Learn. Cybern. (1)

C. Cortes and V. Vapnik, “Support-vector networks,” Int. J. Mach. Learn. Cybern. 20(3), 273–297 (1995).
[Crossref]

J. Lightwave Technol. (3)

J. Opt. Commun. Netw. (1)

Other (11)

IEEE Standard for Local and Metropolitan area networks - Part 15.7: “Short-Range Wireless Optical Communication Using Visible Light”, (2011).

L. Ericsson, “More than 50 billion connected devices,” White Paper14(1) (2011).

R. J. Drost and B. M. Sadler, “Constellation design for color-shift keying using billiards algorithms,” IEEE Globecom Workshops, (2010).

Z. Wang, Q. Wang, W. Huang, and Z. Xu, “Visible Light Communications,” IEEE Press, Wiley (2017).

A. Yokoi, J. Son, and T. Bae, “More description about CSK constellation,” IEEE802(7), 3–46 (2010).

G. Cossu, A. M. Khalid, P. Choudhury, R. Corsini, and E. Ciaramella, “Long distance indoor high speed visible light communication system based on RGB LEDs,” Proceedings of the Asia Commun. Photon. Conf, 1–3 (2012).

B. Bai, Q. He, Z. Xu, and Y. Fan, “The color shift key modulation with non-uniform signaling for visible light communication,” IEEE Intern. Conf. on Comm. in China Workshops, 37–42, (2012).

E. Monteiro and S. Hranilovic, “Constellation design for color-shift keying using interior point methods,” IEEE Globecom Workshops, (2012).

R. E. Wright, “Logistic regression.” (1995).

J. Morovič, “Color gamut mapping,” Vol. 10. John Wiley & Sons (2008).

M. Wood “MacAdam ellipses,” Out of the Wood, Mike Wood Consulting LLC. (retrieved on Jun. 8, 2011). Retrieved from the internet: URL: http://www.mikewoodconsulting.com/articles/Protocol%20Fall202010 (2010).

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Figures (8)

Fig. 1.
Fig. 1. The seven color bands of the visible light spectrum.
Fig. 2.
Fig. 2. Vertices of the valid CSK combinations represented on the 1931 CIE diagram.
Fig. 3.
Fig. 3. The channel model of RGB-LED based visible light communication.
Fig. 4.
Fig. 4. Classification accuracies for the nine 8-CSK combinations at SNR = 10 dB.
Fig. 5.
Fig. 5. Minimum BER ordered for the nine 8-CSK combinations at SNR = 10 dB.
Fig. 6.
Fig. 6. Classified 8-CSK received signal according to their corresponding best performing algorithm for the nine combinations at SNR = 10 dB. White squares represent the original color coordinate of each symbol, the colored dots the received clustered coordinate representing a same symbol.
Fig. 7.
Fig. 7. BER curves of the nine combinations with SNR ranging between 1-16 dB for each of the four classification algorithms.
Fig. 8.
Fig. 8. Measured and fitted BER curves of the four classification algorithms with SNR ranging between 1-16 dB for each of the nine combinations.

Tables (3)

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Table 1. Valid CSK color band combinations.

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Table 2. The adopted neural network structure

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Table 3. Top four combinations ordered by SNR at which the FEC level is reached.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

pm=[Pi,mPj,mPk,m]T
xp=Pixi+Pjxj+Pkxk
yp=Piyi+Pjyj+Pkyk
Pi+Pj+Pk=1
H=[hiihijhikhjihjj˙hjkhkihkjhkk]
r=Hpm+n
pm=[Pi,mPj,mPk,m]T=H1pm

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