## 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 [2–4]. 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) [5–8]. 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. [12–16], 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].

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 (*x _{p} y_{p}*). 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

*m*indicates the m-

*th*symbol. The vector p

*has been obtained by solving the linear system with Eqs. (2)–(4) for*

_{m}*P*,

_{i}*P*and

_{j}*P*as and in which (

_{k}*x*), (

_{i}y_{i}*x*) and (

_{j}y_{j}*x*) 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

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

where**r**= [

*R*]

_{i}R_{j}R_{k}^{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’

*as in Eq. (7):*

_{m}*x’*). The resulting constellation diagrams constitute the data processed by the learning decision block.

_{p}y’_{p}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.

## 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.

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.

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.

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.

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.

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