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Abstract
In this work, we propose a novel visible light communication (VLC) scheme utilizing multiple different red green and blue triplets each with a different emission spectrum of red, green and blue for mitigating the effect of interference due to different colors using spatial multiplexing. On-off keying modulation is considered and its effect on light emission in terms of flickering, dimming and color rendering is discussed so as to demonstrate how metameric properties have been considered. At the receiver, multiple photodiodes with color filter-tuned on each transmit light emitting diode (LED) are employed. Three different detection mechanisms of color zero forcing, minimum mean square error estimation and minimum mean square error equalization are then proposed. The system performance of the proposed scheme is evaluated both with computer simulations and tests with an Arduino board implementation.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction and goals
Due to the proliferation of personal mobile devices connected to the Internet, the need of exchanging a large amount of data at very high speed has considerably increased during the last years, and this trend will continue in the future. Addressing this issue, visible light communication (VLC) can be a very effective complementary technology to existing radio frequency (RF). VLC systems do not suffer from RF interference and they can be adopted in places like airplanes and hospitals where the use of RF technology is partially or totally limited. Besides, light emitting diodes (LEDs) are more power efficient devices than incandescent lamps, and they also provide data transmission while illuminating. Stating this twofold application, VLC system meets the requirements for reducing the global electromagnetic pollution and is currently a viable and promising technology both for providing data communications [1–3] and localization [4–6].
Due to its simple implementation, on-off keying (OOK) is the simplest used intensity modulation/direct detection (IM/DD) scheme with VLC technology. It is possible to achieve very high data rates even adopting OOK not-return to zero (NRZ) modulation, as demonstrated by Fujimoto et al. [7], where a system including a single commercially available red, green and blue (RGB) visible LED, a low-cost PIN-PD and pre-emphasis and post-equalizing blocks is presented. High-speed VLC systems employing different modulation schemes, such as OOK, applied to RGB LED light sources are investigated experimentally at Heinrich Hertz Institute [8]. Depending on modulation format, link distance and receiver sensitivity, communication data rates up to 800 Mb/s have been demonstrated using off-the-shelf optical components. More, as white LED consists of red, green and blue chips (i.e. RGB LEDs), the employment of wavelength division multiplexing (WDM) is introduced to increase the data transmission rate. The chance of simultaneously sending an independent data stream on different color components according to WDM is tackled in a recent research [9]. Specifically, it is shown that a rate adaptive scheme used in a LED-based communication can lead to an aggregate data rate beyond 10 Gb/s. Also in this case channel knowledge at the transmitter is required. Moreover, the cross-talk interference, that is the interference generated by different colors, at the receiver is neglected by the use of dichroic mirrors. This is a viable solution even though it fails to work if multiple red, blue or green light are used, that is, when an array of LEDs is adopted. In fact, using multiple LEDs increases the spectral efficiency of the system. Recently, some works have been done in consideration of multiuser scheme for VLC system employing RGB-LEDs at the transmitter. A multiuser multiple-input-single-output (MISO)-VLC system that employs multi-chip LEDs with different colors at the transmitter is proposed [10]. At the receiver, each user is equipped with a PD that utilizes an optical filter to concentrate on a corresponding monochromatic light of a specific LED chip. That work aims also at maximizing the multiuser sum rate by proposing an electrical and optical power allocation scheme with constraints on illumination. A joint transceiver and offset design method are proposed and analyzed for both the single user point-to-point and the multiuser MISO uplink and downlink systems in [11] where the transmitter consists of two triplets of RGB-LEDs and the receiver equipped with six photodiode (PD) detectors, each with red, green and blue filters. Input-dependent shot noise is taken into consideration when evaluating the performance of such system. That system aims at using precoding by assuming perfect channel knowledge at the transmitter and receiver by assuming also some specific channel configurations without taking into account LED and photodiode characteristics, nor implementation. However, the iterative algorithm requires complexity of the order to seconds to work that is not of practical implementation.
After the literature review, it appears that multiple-input-multiple-output (MIMO) schemes including the use of multiple colors (more than the simple single red, green and blue configuration) as a viable road for improving spectral efficiency with the goal of obtaining white light as illumination service has not been tackled both from theoretical and experimental point of view. In this context, we propose and demonstrate the possibility of using multiple RGB-LEDs (multiple triplets) for spatial multiplexing. Specifically, each RGB-LED is assumed to have slightly different emission spectra so that the red LED of the first RGB-LED is different (from the spectral point of view) from the red LED of other RGB-LED and similarly for green and blue LEDs. Doing this allows us to multiplex independent information on each LED and the effect of color interference, that is color cross-talk, is investigated.
Furthermore, we design the proposed system with constraint on illumination by taking into account color-rendering, flickering and discussing about dimming. Besides, three different type of detection mechanisms are then applied and analyzed. Those are color zero forcing (CZF), minimum mean square error (MMSE) without channel estimation and minimum mean square error (MMSE) with channel equalization. The scheme presents the transmission of pilot symbols that can be used for channel estimation due to its possible variability caused by the receiver mobility in a room. The performance is evaluated both with computer simulations and tests with an Arduino board implementation.
About paper organization, in Sect. 2 we detail the system model while in Sect. 3 we present both zero forcing and minimum mean square error equalization methods applied to the proposed scheme. Furthermore, we present the performance of the proposed architecture in Sect. 4 and we compare it with the literature in Sect. 4.1. The implementation on a Arduino board is described and tests reported in Sect. 5 while in Sect. 6 we draw conclusion.
2. System model
Let us consider the presence of Nt LED triplets, so having 3Nt LEDs at the transmitter. Each triplet is characterized by red green and blue colors and the red of the first triplet is different, from a spectral point of view, from the red of the second triplet and so forth, and the same is also for green and blue. In Fig. 1 we show the system architecture including the presence of multiple LEDs. The transmitted signal during the signaling interval Tp by the i-th LED triplet is given by:
where ci belongs to the set that collects the three colors emitted by the i-th triplet. The term is a binary value and represents the OOK symbol emitted by the c color of the i-th triplet. Moreover, is the shape of radiation representing the light emitted by the ci-th color LED of the i-th triplet. It is important to note that when we consider two different colors, namely ci and cl, we have . Hence, the whole transmitted signal is given byIn order to avoid ambiguity, we name the emission in the signalling time of a single pulse (or its absence) as OOK symbol, while we indicate the triplet of OOK symbols emitted during Tp with RGB-OOK symbol and we call the 3Nt-ple of OOK symbols emitted by all the available LEDs in the signaling interval Tp as MIMO-RGB-OOK symbol.
Regarding Eq. (1), the presence of the term implicitly leads the transmitter to emit different light intensities over the time since each LED (R, G and B) can be in the on or off state. Hence, before proceeding, we go in depth with some possible issues related to light and color perception. Even though we turn on and off the light, Bloch’s law [12, Chapt.3] ensures that flickering effects are avoided if OOK symbol transmission rate is kept above 50-100 Hz.
About dimming, we can recognize that the proposed system has a limited support. In fact, while OOK itself presents a 50% dimming with respect to full illumination, we can define dimming as the full illumination (no modulation) when we use 3Nt LEDs. If we choose, due to possible system requirements, to use a lower number of LEDs with the respect to the maximum allowed (let us say 3Mt), we achieve a dimming level given by (Mt/Nt)·50%.
Furthermore, since the light radiation is able to excite the retina [12][Chapt.2], the second Bloch’s law still allows us to state that the eye is unable to follow the on-off transitions. In fact, when the light beam impacts on the retina, the sensation is hold for approximately 20ms that is the integration time of the visual system and after the light will impress a new image (this is also the effect on the basis of television). About color rendering some insight should be given. By resorting to the CIE 1931 diagram reported in Fig. 2, we show how choosing one triplet of primary colors can allow the representation of each color in the area defined by the triangle whose vertexes are identified by the primaries. and the lines connecting the vertexes represent the bounds of the region collecting all the colors that can be obtained. Hence, we show in Fig. 2 the colors that can be represented with a first triplet (RGB1) and with a second triplet (RGB2). Both the triplets are able to obtain white light. However, since the light emitted is tied to the MIMO-RGB-OOK symbol that the transmitter is emitting, it is possible that, for example, red and blue are on while green is off (so generating a magenta hue). Moreover, we must note that the whole human vision system works on the basis of the above mentioned integration time, that is, 20ms. This implies that the sensation is the time average measured on that interval. This implicitly corresponds to say that the eye sees the short time Fourier transform that, in this case, is characterized by essentially Nt different whites whose combination still falls in the white area of the CIE 1931 diagram. This consideration is based on the principle of metamerism [12][Chapt.2] and justifies the choice of the wavelength of the signals emitted by the triplets.
Fig. 2 CIE 1931 diagram with primaries and regions of affordable colors with two triplets of primaries.
Moving on the signal that is received by the j-th photodiode, with , related to the emission of a single MIMO-RGB-OOK symbol we have that
where ∗ is the convolution operator, is the whole channel impulse response from LED emitting the ci color to the photodiode tuned on the cj one, while describes the noise. Before proceeding it is mandatory to explain the role played by and the different features that compose the channel impulse response. The term can be exploded as follows where is the effect of free space propagation that can be modeled according to geometrical parameters. More insight about this can be found in [13] where the propagation features of the channel have been detailed. Summarizing, we can affirm that we resort to Lambertian model (see [14]) and the propagation environment is non-directed line-of-sight (LOS) thus meaning that we are in the presence of a main component (LOS) and some reflective paths. Recently additional insights have been considered in the Literature by showing how delay spread is around tens of nanoseconds [15,16]. Moreover, fL(t) in Eq. (4) models the effect of the lens (if present) used to focus the light beam as depicted in Fig. 1 and its modeling can follow the work presented in [17]. Furthermore, fcj(t) in Eq. (4) is the impulse response of the OAF represented by the above mentioned colored transparent stripes whose modeling is relatively simple if, with a spectrum analyzer, a white light is used in order to test the wavelength response. Last, fPD(t) in Eq. (4) is the impulse response of the photodiode. It is worth providing an example about the role played by OAF. In fact, while it is reasonable to expect that the OAF of a red tuned photodiode is able to reduce the effect of blue light, it is not the same for the red emitted by another triplet. Let us say that the best approach that one can pursue is having the light spectrum of same color emitted by different triplets separated in the wavelength domain. As it will result clearer in the following this is not so simple with LEDs while in principle it can be affordable with lasers.3. Detection mechanisms
We need to preliminary sample the received signal after each photodiode so to have yj(nTs), Ts being the sample time. This operation is performed by the analog to digital converter (ADC) as depicted in Fig. 1. In this way, by extending this mechanism to all the RGB components we obtain, by assuming Ts = Tp, the following analytical description:
where S is a (M × 3Nt) matrix collecting the M MIMO-RGB-OOK symbols emitted by the 3Nt LEDs during the coherence time Tcoh of the channel with M = ⌊Tcoh/Tp⌋ while W gathers the (M × 3Nt) noise samples. Since we deal with OOK symbols the generic element of S is a zero or the light intensity associated to the on signal. We remark that the OOK stream on one LED is independent from the other ones. We additionally define as , the set collecting all the possible combinations of matrices S. Furthermore, H collects the 3Nt × 3Nt channel impulse responses as given in Eq. (4) in which each component is assumed to be sufficiently short in time to be modeled as a coefficient. Before proceeding, some analysis on the assumption made on H are mandatory. By observing the modeling provided in the previous section for what concerns transmitter and channel, we can argue that if the transmission speed is not so high with respect to photodiode bandwidth, this latter is able to follow the speed of LED. Otherwise we need time (or frequency)-based equalization. Here we focus on the first case even though we discuss about this issue in the numerical results.We compare here two different detection mechanisms, namely, spatial Zero-Forcing, that in this case means Color Zero Forcing (CZF) and Minimum Mean Square Error (MMSE) by implementing this latter in two different ways.
3.1. Color zero forcing
The CZF method aims at inverting the channel by using the inverse matrix of H, that is, a spatial filter Z = H−1 so as to obtain
Two important elements must be underlined. First, in order to proceed with this approach, knowledge about the channel is required at the receiver. This can be inferred by transmitting periodically a training sequence characterized by so as to have
and we consider the estimated channel . Hence the matrix inversion will be operated on the basis of the estimated one so Eq. (6) should be rewritten as follows Second, another issue to be tackled is about the inversion of the channel matrix. Spatially speaking it is possible, especially in line of sight propagation, that some paths present spatial correlation, that is, the channel matrix has not full rank. We can observe that in order to avoid this situation we can space LEDs and photodiodes. Moreover, since the channel matrix considers also the effect of OAF the channel H can be interpreted as the Hadamard product of two matrices representing different terms of the whole channel, where the first one, H1 takes into account the propagation , photodiode fPD(t) and lens fL(t) effects, while the second one H2 only models the OAF behavior. Hence, we can write H = H1 ○ H2.About the decision mechanism, this latter can be described by the following expression that comes from the application of the maximum likelihood criterion by assuming that noise presents white Gaussian statistics:
At a first glance, Eq. (9) appears to be costly to be solved since finding the above minimum should imply to check among matrices. Just to give a quick example, if Nt = 4 and M = 10, the number of comparisons to perform is 2120 that is not viable in real systems. However, we must highlight that we deal with OOK and the symbol detection requires a threshold mechanism. This implies that we can detect the 3Nt signals present in the 3Nt photodiode branches as shown in Fig. 1 in parallel, every Tp seconds.3.2. Minimum mean square error
In this section differently from the above cited CZF mechanism we will discuss about the possible implementation of MMSE criterion. We follow two different approaches to arrive at the detection phase. The first one does not require to directly estimate the channel and it aims at estimating S while the second one requires channel estimation in order to perform equalization. To handle this, we resort to the Orthogonal Projection Lemma (OPL) due to the Gaussianity of the problem. Hence, we have that the observation should be orthogonal to the error when deriving the MMSE filter. This means that we have
and we can derive G as follows by using the OPL E (.) the expected value operator, and with very simple algebra we can write where RYY is the autocorrelation related to the received matrix and RYS is the crosscorrelation between the input (transmitted) and output (received). As for CZF case, while RYY is based on what has been received, RYS should require to know what has been transmitted. However, handling RYS means to acquire, during a training phase, information about the above correlation. This implies that the estimated version of RYS can be obtained via the following mechanism where the term Sk represents the k-th matrix emitted as training that should be known by the receiver and Yk is the k-th matrix received. We name this approach as MMSE estimation (MMSE-es) since we proceed to estimate S. The other MMSE approach is the spatial equalization of the received matrix. This approach requires to estimate the channel H with a training sequence known at the receiver also including what has been described for CZF. Basing on the this latter and, more, by considering that representing the noise power that can be estimated through a sufficiently long observation when the communication is not active, we can obtain the following expression by resorting to the equalization theory [18] We name this approach as MMSE equalization (MMSE-eq). Also in the two MMSE mechanisms we can apply the maximum likelihood criterion so as to arrive at the following minimization The discussion after Eq. (8) is still valid here since the number of matrices comparison is huge. However, we newly highlight that basing on the fact that we have independent symbols we can perform detection according to threshold detectors and in particular, 3Nt parallel detectors detecting the symbol every Tp seconds, that is, at each row of .4. Numerical results and implementation
We first evaluate the performance of the proposed system by performing computer simulations. These are performed by resorting to the channel model provided in [19] which takes into account the propagation in terms of reflections and direct path loss. Moreover, we use the parameters in line with the contribution in [20] with the exception of LEDs that in our contribution are RGB and not white. For what concerns LEDs, we refer to the Luxeon Star Rebel Red, Green and Blue whose features can be found in [21]. We use those LEDs for the implementation and summarize their key features in Table 1.
Table 1. Model Parameters
Regarding receiver, we consider commercial photodiodes, namely Vishay BPW34. Also in this case the key parameters can be found in Table 1 while specifications are reported in [22]. The value for Ts is chosen so as to have 12.5 Mpulses/s on each branch. This choice is justified in order to have a fair performance comparison with the scheme in [20], that is, the same symbol rate emitted by each LED. In all the performed tests/experiments we considered transmitter and receiver perfectly aligned thus meaning that the first LED faces the first photodiode and so forth.
4.1. Computer simulations
We show in Fig. 3 the BER obtained when Nt = 2 and consequently the rate is 75Mb/s when the receiver is located at a distance ranging from 140cm to 300cm. We report the BER for CZF, MMSE-es and MMSE-eq. It is possible to appreciate that the lowest BER values are obtained by MMSE-eq method while the MMSE-es is a bit worse. In fact, MMSE-es achieves BER values that is approximately twice the value of MMSE-eq. On the other hand CZF is a bit far from the above two schemes especially for low distance where its performance is a BER of the order of 10−5 ÷ 10−6. When the distance increases the gap becomes less evident and at high distances CZF results to perform better than the other two even though the values are not acceptable for a communication system.
Fig. 3 BER as a function of distance between transmitter and receiver for the three detection methods when Nt = 2.
In Fig. 4 we compare the three detection methods with the contribution in [20] by assuming 70cm distance between transmitter and receiver. Moreover, we assume imperfect channel estimation at the receiver, that is, using a single pulse per LED. We recall that in [20] a 4×4 system is proposed and white LEDs are used. So, a perfect comparison is not possible since we adopt RGB LEDs. However, in this case, we can consider as comparison the cases characterized by Nt = 1 and Nt = 2. Before proceeding, it is important to specify that the rate values on the horizontal axis are simply obtained for different values of Nt.
Fig. 4 BER as a function of transmission rate. Each marker corresponds to an increment of 3 RGB LEDs (that is Nt). Comparison with [20] is also reported.
It is possible to appreciate that the MMSE-eq is the best performing in terms of BER and for Nt = 1 its BER is below the system in [20]. Moreover, the BER achieved with Nt = 2 is still lower even though the transmission achieves 75Mb/s in place of 50Mb/s. By increasing the number of RGB triplets Nt we have that BER increases. The reason is the inability of the system in separating different components of same colors, for example red of the second triplet on the first red-tuned photodiode. This is due to the crosstalk among colors with very close (overlapping) spectra. In fact, if we neglect its presence, the system is still able to cancel interference
Another way of increasing rate is to reduce signaling time Tp without increasing Nt. This implies that the symbols are much closer in time and possible intersymbol interference (ISI) can occur. In this regard, in Fig. 5 we report for the three detection mechanisms the BER achieved when the rate increases. Differently from Fig. 4 where the signaling time is assigned for each LED and we increase the number of triplets to increase rate, in Fig. 5 we consider Nt = 1 and reduce Tp on each LED from 75ns (40 Mb/s) to 12.5ns (240 Mb/s).
It is possible to appreciate that for low transmission rates the BER values achieved by the three detection methods approach those reported in Fig. 4 for rate equating 37.5 Mb/s. However, when we consider higher transmission rates the delay spread of the channels starts to increase BER since it induces intersymbol interference. Moreover, we can observe that the BER achieved are higher with respect to the case of Fig. 4. This can be justified by observing that the channels delay spread induces performance loss that is higher with respect to the one exhibited in Fig. 4 where the loss is due to the residual unsuppressed color interference. Moreover, increasing transmission rate till to very high values leads to additional ISI due to component limitations like LEDs and PDs. This suggests that, without using an equalizer that should be able also to track channel changes, using multiple RGB elements is preferable to increase rate. In Fig. 6 we report BER values as a function of distance between transmitter and receiver when MMSE-eq is used for detection. We report the BER curves for different number of triplets ranging from 1 to 4, thus meaning that, under the constraint of 12.5 Mpulses on each branch (LED) the total rate is 37.5 Mb/s for Nt = 1, 75 Mb/s for Nt = 2, 112.5 Mb/s for Nt = 3 and 150 Mb/s for Nt = 4.
In this case it is possible to appreciate that when the number of triplets is only one, the BER is the smallest. This can be justified by observing that no interference among the same color of different triplets occurs. When the number of triplets increases the rate achieved is higher even though interference is present. However, it is interesting to note that for Nt = 2 the BER is twice (approximately) of that achieved with a single triplet. So, for example at 170cm the BER obtained with Nt = 2 is 1.1·10−6 while with Nt = 1 is 5.7·10−7.
5. Arduino implementation
Moving on the description of the implementation, we used an Arduino-Due board that presents a clock at 84Mhz. It is important to note that we aim at having the symbol rate on each branch of the order of the one [20] we generate a stream at 84Mb/s that is identically divided in 6 sub-streams (Nt = 2) so we have on each branch a rate of 14Mb/s.
This is possible by properly check the clock of the board and sending breaking messages to generate pulses that are in line, from the symbol time point of view, with the clock. Since we use the same LEDs for all reds, greens and blues, we distinguish the red of the first triplet by the red of the second one by using OAF also at the transmitter side. In this regard, Fig. 7 shows in the upper part the effect of generating different colors by using filters.
Fig. 7 Picture of the implementation of two triplets and effects of filtering with OAFs tuned on red, green and blue respectively of the first triplet.
In Fig. 7 we report also the effect of using OAFs at the receiver without taking the picture with the lens for sake of clarity of the image. Hence, the second picture of Fig. 7 reports how the photodiode tuned on the red of first triplet sees the six LEDs. Analogously the third picture of Fig. 7 reports the effect of filtering the six light sources with a first triplet green OAF. The fourth picture of Fig. 7 reports the effect of the first triplet blue OAF. It is interesting to note that the red OAF almost totally reduces the effect of blue LEDs and considerably attenuates the effect of green. The green OAF does not neglect the effect of red and blue due to its bandwidth. However it is able to reduce in magnitude their effect. Moreover, the blue OAF is able to suppress the red component and reduce the green one. We can affirm that, if we look at the sub-matrix modeling the channel from the two transmitting triplets to the first triplet of photodiodes, it presents very low coefficients for green and blue detected by red, sufficiently small components for red and blue detected by green and zero coefficients for reds toward blue.
In Fig. 8 we report the comparison between the simulations and the implemented case. It is worth noting that the case Nt = 1 differs from Nt = 2 since the former works with a transmission rate of 42 Mb/s while the latter transmits with a transmission rate of 84 Mb/s. In line with the results obtained in Fig. 6 we note that transmitting at a lower speed allows to preserve reliability since a lower BER is achieved and this is true at any distance between transmitter and receiver. On the other hand, the distance between the curves is very small and this allows to conclude that the model used for simulation is highly close to the reality.
Fig. 8 BER as a function of transmission distance when different number of triplets is used. Comparison between computer simulation and implementation is reported.
Last, but not least, since we discuss earlier about color rendering features of the scheme, we do not analyze it from a quantitative point of view. Hence, in order to check how much the light obtained is likelihood to the target light, we resort to the evaluation of the color rendering index [23] that, starting from the reference illuminant D65 defined by CIE 1931, and by taking into account the emission of the LEDs, we achieve a value of 86. We recall that the value goes from 0 to 100 where 100 means perfect color match and very high precision white light LEDs (used only for illumination) can achieve a value of 95.
6. Conclusion
In this work we proposed MIMO-OOK scheme using multiple triplets characterized by different RGB emissions. The spectral efficiency of the system is 3Nt times the one achieved by single LED OOK. The scheme utilizes a preliminary optical analog filtering in order to reduce the effect of color interference and a subsequent processing is able to reduce the interference of a color on the same color, i.e. red of one triplet on the red-tuned photodiode of a different triplet. This allows also to separate channels and obtaining uncorrelated channels from the spatial diversity perspective so allowing the use of the proposed color/spatial equalization methods. Moreover, using different RGB triplets and achieving also good white illumination levels as measured by CRI. We compared the proposed scheme with the literature when white LEDs are used and we achieve the same BER with higher rate and also the implementation supports the effectiveness of the proposed system.
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