1. Introduction

The next generations of telecommunication networks must be prepared for an increase in the demand for higher bit rates, especially for video streaming, online gaming, real-time communications and other data-intensive applications, which leads to a significant enlargement of the required transmission bandwidth [1]. Interestingly, this demand is usually associated with indoor applications, corresponding to about 80% of data traffic [2]. Furthermore, the current development of a new generation (6G) of mobile communications is also triggered by the need to introduce new services and applications that can improve cost, energy, spectral and operational efficiency [3]. In order to support this new scenario, it is important to introduce novel high-capacity communication technologies to complement the RF wireless networks, since even with efficient frequency and spatial reuse, the RF spectrum is becoming heavily congested [4].

Following this challenge, visible light communication (VLC) has recently started to attract more interest since it offers illumination and wireless communications in the visible band (430-790 THz) with hundreds of terahertz of unlicensed bandwidth [5]. VLC can complement the RF wireless network by offering high-capacity mobile communication. First, it has the advantage that the light does not penetrate opaque objects and then can provide secure wireless communications using small cells with no inter-cell interference [4], [6]. Furthermore, these systems can reuse the implemented lighting infrastructure for communication purposes, thus being able to potentially reduce installation and operational costs. Finally, VLC presents even better propagation than RF technologies in some non-terrestrial scenarios, such as aerospace and underwater [3].

Some studies have demonstrated VLC transmissions using commercial single light-emitting diodes (LED) [7–9]. In order to produce white light, a blue LED with phosphor was considered. Despite being relatively simple and cheap, this type of LEDs is characterized by a very low bandwidth due to the low response time of the yellow phosphor [7]. In 2012, Khalid et al. has demonstrated a VLC system with 1 Gbit/s transmitting over a distance of 10 cm using a phosphor-based white LED [8]. Huang et al. achieved 2 Gbit/s over 1.5 m of free space using a single commercially available phosphorescent white LED [9]. However, to compensate the low bandwidth of the source, typically a few tens of MHz, a wavelength division multiplexing (WDM) using RGB (red, green and blue) LEDs has been widely employed, to obtain white light. In 2013, Wu et al. demonstrate 3.22 Gb/s with the referred RGB-LED-based VLC system [10]. Later on, in 2016, Chun et al. presented a considerably higher data rate using a similar system, achieving 10.4 Gbit/s [11].

Despite the numerous research efforts on LED-based VLC, its fundamental bandwidth bottleneck represents a major technological threat, mainly when compared with currently available multi-gigabit RF communications. Therefore, in order to unlock the full capacity of these systems, novel VLC approaches have been recently proposed, resorting to the use of laser diodes (LDs) [2,12–15]. Benefitting from their fundamental working principle, even visible light low-cost LDs typically provide a usable communication bandwidth in the GHz range, thus representing a major leap over LED systems. Gunawan et al. [12] and Wei et al. [13] presented both an RGB LD system. The first achieved a data rate of 28.4 Gbit/s with a 1.25 m free-space transmission distance, and the second demonstrated 40.665 Gbit/s through 2 m using dual-polarization. Another alternative to obtain white light is to use an RGBV (red, green, blue and violet) LD as suggested by Chow et al. in 2020 [14]. However, these high data rate VLC communication systems are obtained using a point-to-point link, not making them suitable for illumination. Therefore, the light needs to be diverged using a diffuser to be used for lighting and communication, allowing to cover a wide area and providing a high-capacity wireless connection for multiple users [2]. In 2017, Wu et al. recorded a total transmission data rate of 8.8 Gbit/s at a distance of 0.5 m of free space distance where the light is diffused using frosted glass [15]. And Chun et al. proposed an RGBV VLC transmission system that achieves 35.6 Gbit/s over 4 m [2].

The frequency response of a visible light communication channel presents significant fading at high frequency, mainly due to the optical transceivers, which have low bandwidth. Therefore, if we use the same quadrature amplitude modulation (QAM) format in all subcarriers of a multi-carrier signal, the performance would be affected due to the non-uniform channel response. To improve the overall link bit rate and mitigate the impact of distortions on the system performance, some works have proposed the use of adaptive power loading (PL) and bit loading (BL) [16–18]. Although the application of PL and BL improves the performance of the system, it has some limitations. The main disadvantage is associated with the difference between the throughput and the channel capacity, since it is not possible to continuously adjust the entropy of the source. Therefore, an entropy loading (EL) method based on probabilistic constellation shaping (PCS) was proposed to overcome this limitation [19]. Contrary to the typical QAM modulation formats, where all symbols have the same probability, PCS can load continuous entropies instead of discrete numbers of bits per subcarrier by assigning a probability distribution function to its constellation symbols [20].

In [7], Xie et al. demonstrated for the first time the application of EL in a VLC system using an LED with a bandwidth of 45 MHz and experimentally verified a 26.8% improvement in comparison with the bit-loading technique over 1 m free-space transmission. However, the EL scheme based on PCS was previously proposed by Di Che and William Shieh as a capacity-approaching technique for colored signal-to-noise ratio (SNR) optical channels with band-limited cascaded-reconfigurable optical add-drop multiplexers (ROADM) [19]. And they extended their work in [21], confirming that the EL method is an optimum solution to decrease the gap between the throughput and the capacity in bandwidth-limited channels. Furthermore, Guiomar et al. have experimentally demonstrated the application of time-adaptive PCS to change the bit rate according to the conditions of an outdoor free-space optics (FSO) channel [20], while Xing et al. proposed and experimentally demonstrated a PCS-based VLC system [22], optimizing the data rate transmission for different distances, thus enabling 3.37 Gbit/s for 1-meter free-space distances using a single blue LED. In [23] the authors applied entropy loading for a VLC system by using a single 450 nm GaN LD with collimated light, achieving 10.23 Gbit/s for a 1.2 m distance between the transmitter and the receiver.

In this work, we experimentally demonstrate the application of the EL technique for the RGB-based LD VLC system. In the proposed EL method, the probability distribution for the M-QAM symbols was adapted for all subcarriers, maximizing the net bit rate of the system. Using red, green and blue lasers with a bandwidth of 1 GHz and a free space distance of 0.90 m we demonstrated bit rates greater than 30 Gbit/s. Despite the aforementioned papers use PCS in VLC, this work has a different approach, since it uses three LDs, thus allowing the generated diffused white light to be used for lighting and communications. To the best of the authors’ knowledge, this corresponds to the highest bit rate demonstrated so far using a single-polarization RGB-based LD VLC system with diffused light.

2. Enabling techniques: multi-carrier modulation and entropy loading

2.1 Multi-carrier modulation via digital subcarrier multiplexing

Digital subcarrier multiplexing (DSCM) is a multi-carrier modulation technique that has been recently proposed to enhance the performance of fiber optic systems, providing an alternative to single-carrier (SC) systems [24–26]. DSCM signals are obtained by dividing the high symbol rate SC signal into multiple low symbol rate subcarriers. After optimizing the number of subcarriers in the DSCM signal, higher robustness to fiber nonlinearities is expected due to better control of the peak-to-average-power ratio (PAPR) [26]. Although nonlinearities in a VLC system are smaller than in high-speed fiber optic communication systems, a high number of subcarriers results in lower performance, mainly due to high PAPR. Furthermore, with this subcarrier approach, we are allowed to adapt the spectral efficiency across the frequency axis by applying the aforementioned PL, BL and EL methods [24]. However, contrarily to orthogonal frequency division multiplexing (OFDM), in DSCM signals the subcarriers are generated and multiplexed resorting to quasi-Nyquist pulse shaping, and thus can be separated and processed independently using SC-compatible DSP algorithms, thus avoiding the use of fast-Fourier transform (FFT) or inverse FFT (IFFT) [24,25].

In Fig. 1 a) and Fig. 1 b), the multiplexing and de-multiplexing processes of an DSCM signal are depicted, respectively. Initially, $N_{\mathrm {SC}}$ independent data sequences are generated and mapped to a QAM constellation. Afterwards, the symbols of each subcarrier are up-sampled to 2 samples per symbol, in order to be pulse shaped by a root raised-cosine (RRC) filter with a given roll-off factor. Then, each subcarrier is up-sampled by a factor of $N_{\mathrm {SC}}$ and shifted to its respective frequency. Finally, the DSCM signal is re-sampled to the digital-to-analog converter (DAC) sample rate, so it is ready to be transmitted to the channel after digital-to-analog conversion. Regarding the demodulation of the DSCM signal, it is first digitized by the analog-to-digital converter (ADC) and re-sampled to $N_{\mathrm {SC}}$ samples per symbol. Thereafter, each subcarrier is downconverted to the baseband and filtered with a matched filter. This process ends with a down-sample of $N_{\mathrm {SC}}$ times and with the demodulation of the QAM symbols [25,27].

 

Fig. 1. Diagram of the DSCM a) multiplexing and b) the de-multiplexing.

Download Full Size | PDF

2.2 Digital subcarrier multiplexing versus OFDM

Note that, although the majority of recent VLC works tend to use OFDM (possibly inspired by modern RF wireless systems), in this work we propose to explore a different flavour of multi-carrier modulation, using DSCM, which has recently gained significant popularity within the framework of modern optical fiber systems [25,28]. In a quick technical comparison against OFDM, the main distinctive aspects of DSCM can summarized as follows:

Although these two modalities of multi-carrier modulation actually share many similarities, DSCM might provide some practical advantages over OFDM in optical communication scenarios, namely:

Besides these technical benefits, it is also important to note that DSCM has been recently widely applied to multiple optical fiber systems scenarios, from long-haul [29] to short-reach/access networks [30]. Therefore, by applying DSCM to VLC systems, we are also promoting an enhanced compatibility with the fiber-based distribution network, which is expected to be installed in most modern buildings (fiber-to-the-room).

Following these premises, in this work we carry out a pioneering study exploiting the use of DSCM for VLC systems together with optimized entropy loading per subcarrier, in which we aim to find the key requirements in terms of frequency granularity (i.e. minimum required bandwidth per subcarrier) that enables a capacity-achieving VLC solution.

Finally, it is worth mentioning that the concept of DSCM exposed in section 2.1 and generally employed in optical fiber systems is actually very similar to the generalized frequency division multiplexing (GFDM) waveform [31], which is currently being proposed as a potential candidate for beyond 5G communications. The main difference between these modulation options lies on their practical implementation and complexity: while DSCM employs single-carrier-like DSP per subcarrier, GFDM includes the use of a cyclic prefix together with 1-tap FFT-based equalization for a low-complexity operation. This is also linked to the fact that DSCM is typically utilized with wider-band subcarriers (from 100 MHz up to few GHz) than GFDM (which typically uses sub-MHz subcarriers), which therefore prevents DSCM to use single-tap equalization within each subcarrier band.

2.3 Probabilistic constellation shaping and associated performance metrics

In additive white Gaussian noise (AWGN) channels, the best probability distribution for the M-QAM symbols that requires the minimum transmitted signal energy to achieve a given bit-rate is given by the Maxwell-Boltzmann (MB) distribution [32]:

It represents the information rate that can be sent by the transmitter, and it only depends on the probability distribution. Thereby, the net bit rate of a system with PCS and forward error correction (FEC) is calculated as follows [20]:

A common approach in optical communication systems is to assign a maximum value of the bit error rate (BER) without FEC encoding and decoding, so that, after the application of an FEC code, the value of the BER is reduced to a certain desired value. In this scenario, the BER values after the application of the FEC code (post-FEC BER) are in the order of $10^{-12}$ or $10^{-15}$, which would make it impossible to perform tests in a short time [35]. Therefore, the use of pre-FEC BER was introduced to decrease the computation complexity and latency associated with the application of the FEC code. However, in [35], it is shown that this paradigm is not the most adequate for systems relying on bitwise soft decoding. Alternatively, it is suggested the use of generalized mutual information (GMI) as a prediction of post-FEC BER. The GMI is a bitwise performance metric that provides an estimate of the achievable information rate (AIR) in bits per channel use (bpcu) [21]. Furthermore, Cho et al. showed that the normalized GMI (NGMI) is also an excellent post-FEC BER predictor for probabilistically shaped QAM signals [36]. The NGMI represents the maximum number of fractional information bits per transmit bit [21], taking values in the range of [0,1]. The NGMI can be expressed as follows:

Finally, the ideal FEC overhead, which guarantees error-free decoding, can be obtained from the NGMI [7]:

2.4 Entropy loading

Bringing together DSCM-based multi-carrier modulation and probabilistic constellation shaping opens up the opportunity to implement frequency-resolved entropy loading with fine bit-rate granularity enabled by PCS. The proposed EL scheme in this paper is based on the works developed independently by Jorge Campello de Souza and Howard E. Levin, known as Levin-Campello algorithm [37,38]. This algorithm was originally developed to calculate the ideal modulation format in the bit loading technique. Therefore, only integer entropy values are considered. Thus, we adapted the algorithm to the EL technique to obtain the entropy per subcarrier that guarantees a target NGMI given the estimated SNR per subcarrier. We decided to implement this simple algorithm instead of more complex algorithms, due to simplicity of the proposed problem. In other scenarios, for example, where multiple transceivers are considered, the use of other advanced optimization methods, namely resorting to artificial intelligence, such as genetic algorithms and particle swarm optimization, might provide a more robust solution [39,40].

The flow chart of the proposed algorithm is shown in Fig. 2. The input parameters of the algorithm are the estimated SNR per subcarrier, obtained as follows:

 

Fig. 2. Flow chart of proposed algorithm to maximize the bit rate.

Download Full Size | PDF

Initially, the SNR required to allocate 2 bits/symbol to a subcarrier is calculated, since it represents the entropy of a QPSK constellation, which is the minimum value allowed for the PCS, symbolizing a single-amplitude scenario. To estimate the required SNR corresponding to a given allocated entropy, the following function was used:

If the required SNR ($\mathrm {SNR_{req}}(H=2)$) is greater than the SNR measured for the subcarrier under test, that subcarrier will not carry any information, being assigned 0 bits/symbol; otherwise, 2 bits/symbol are allocated. The next step is to estimate the required SNR when the entropy is increased by $\Delta H$:

This step is repeated, adding $\Delta H$ to the entropy on each iteration, until the available SNR is lower than the required SNR in the next iteration. Then, the entropy estimation is performed in all subcarriers. Note that, we adjust the modulation format to ensure that the difference between entropy and the maximum value for that modulation format is never lower than 1 bit, i.e. $\log _2(M)-H>1$. This avoids the use of uniform or quasi-uniform QAM signals, thus guaranteeing that the PCS shaping gain is preserved even for the subcarriers with better SNR. As an example, the highest allowed entropy for PCS-64QAM is 5 bits/sym. Furthermore, the modulation formats employed as PCS templates are chosen from a pool of square/cross $M$-QAM constellations (with integer $\log _2(M)$), ranging from 16QAM to 4096QAM.

The EL algorithm, assuming a 64QAM modulation format, subcarrier SNR of 15 dB, $\mathrm {NGMI_{th}}=0.9$ and $\Delta H$ =[0.001,0.01,0.1,0.5] was applied. Table 1 shows the estimated entropy, required SNR and number of iterations for the four corresponding $\Delta H$ values. Ideally, the calculated entropy should correspond to a required SNR that is equal to the available subcarrier SNR. However, for this to happen, we need a small $\Delta H$, which will take a long time to converge. Therefore, there is a trade-off between the number of iterations and the precision of the entropy estimation. Analyzing the table, we can conclude that both the 0.001 and 0.010 cases guarantee a good solution with a required SNR very close to the subcarrier SNR, but the second one with 10 times fewer iterations. Regarding the 0.100 and 0.500 scenarios, we can see that their speeds do not compensate the poor precision. Therefore, we decided to use $\Delta H=0.010$.

Table 1. Levin-Campello algorithm for four $\Delta H$ values

View Table

3. VLC system sescription

The experimental setup of the VLC system is shown in Fig. 3 a). Initially, the baseband signal is generated offline in Matlab and is shifted to an intermediate frequency, making the signal real and allowing it to directly modulate the laser. Two arbitrary waveform generators (AWG, Keysight M8190A and Tektronix AWG70002A) operating at 8 GSa/s and 16 GSa/s with an analog bandwidth of 3.5 GHz and 8 GHz are used to generate the three waveforms. Note that two AWGs were needed since the utilized models only support 2 independent channels each. Then, the analog signals are amplified by linear RF amplifiers with variable gain up to 26 dB, 6 dB noise figure and 10 GHz bandwidth. The LDs used for blue, green and red colors are PLT5450B (OSRAM, 450 nm), L520P50 (Thorlabs, 520 nm) and L638P040 (Thorlabs, 638 nm), respectively. The three lasers use a laser diode mount (Thorlabs, LDM9T/M) with an integrated temperature controller and Bias-Tee Adapter for RF Modulation. The light from the LDs is collimated using aspheric lens (Thorlabs, C220TMD-A) and multiplexed by dichroic mirrors (Thorlabs, DMSP567T, DMSP490T) to produce white light. Finally, the white light is diffused (Thorlabs, ED1-C20-MD) in order to enable the illumination functionality of VLC systems, as can be seen in Fig. 3 b).

 

Fig. 3. a) Architecture of the experimental setup of the VLC system. Top view photos of the b) transmitter and c) receiver. d) Photo of the receiver from the transmitter. AWG: Arbitrary Waveform Generator; LD: Laser Diode, APD: Avalanche Photodiode; RTO: Real-Time Oscilloscope; DSP: Digital Signal Processing.

Download Full Size | PDF

At the receiver side, after 0.9 m of free space distance with diffused light, the white light is focused using a bi-convex lens (LB1106-A) to the dichroic mirrors to de-multiplex the red, green and blue colors, as shown in Fig. 3 c). The three optical signals are converted to electrical domain using avalanche photodiodes (APD), with a cutoff frequency of 1 GHz and an integrated low-noise amplifier (Hamamatsu, c5658). The electrical signals are received by a 4-channel real-time oscilloscope (RTO, Keysight DSO804A) with 8 GHz bandwidth operating at 20 Gsa/s. Thereafter, the receiver DSP is applied, with a downconversion to baseband, an adaptive least mean square (LMS) equalization with 51 taps, a re-sampling and a timing synchronization to finally de-map the received complex symbols. Lastly, performance metrics (for example EVM and NGMI) calculations are performed.

4. Results and discussion

In order to evaluate the VLC system and the entropy loading algorithm, we start by analyzing the received optical spectrums of a 16$\times$100 MHz signal for the red, green and blue colors. The green spectrum of Fig. 4 a) shows an almost flat channel up to 1 GHz, which corresponds to the bandwidth of the laser diode mount and the receiver module. For high frequencies, a considerable penalty is verified. A similar performance is seen for the red spectrum, but with higher power at low frequencies and a more significant filtering effect at high frequencies, while for the blue laser, a deformed spectrum is measured. These three distinct spectra are justified with the optical spectrum of the APD, presented in Fig. 4 b) (taken from the equipment datasheet [41]). The APD has a spectral response range between 400 and 1000 nm, with a peak at 800 nm. However, the photosensitivity at 450 nm (blue) and 520 nm (green) are 10 and 3 times lower compared to 650 nm (red), respectively. In Fig. 4 c), the estimated SNR per subcarrier is depicted. From this figure, we can see that the red color has the best performance at low frequencies, while the blue color yields the worst performance. Although the first three subcarriers of blue and red colors are at similar power levels (see 4 a)), the blue subcarriers show approximately 3 dB worse SNR. This behavior can be justified by the automatic power control implemented after the APD receiver: in order to equalize the powers among different colors, a higher gain is required for the blue component, thus leading to stronger noise enhancement, and consequently to a reduced performance.

 

Fig. 4. a) Received spectrum for red, green and blue colors. b) Spectral response of the APD. c) Estimated SNR per subcarrier.

Download Full Size | PDF

Figure 5 a) depicts the bit rate obtained after applying the EL algorithm as a function of the number of 100 MHz subcarriers. This means that the first test was done to identify the optimum bandwidth. For the three colors, a bit rate improvement was verified up to the 16 subcarrier signal; for higher values there is no increase. Therefore, we decided to use a signal with the same bandwidth of a 16$\times$100 MHz with 0.05 roll-off (1.68 GHz). Note that, the estimated bandwidth guarantees the highest bit rate, but does not correspond to the highest spectral efficiency because there is a large entropy difference between the best and worst subcarriers, as can be seen in Fig. 5 b). In the second test, the ideal number of subcarriers was studied for blue, green and red LDs with $\mathrm {NGMI_{th}}=0.90$, shown in Fig. 5 c). For that, signals with the aforementioned bandwidth and with 1, 2, 4, 8, 16 and 32 subcarriers were tested. Analyzing the figure, we can see that, ideally, the greater the frequency domain granularity, i.e., the lower the bandwidth of the subcarriers (greater number of subcarriers), the better is the adaptation to bandwidth-limited channels, allowing for continuous adaptation of entropy across the entire spectrum. Therefore, using a low number of subcarriers (1 and 2 subcarriers) does not allow to differentiate between spectral regions with high and low SNR, thus an intermediate entropy has to be assigned, considerably decreasing the system performance. However, a very high number of subcarriers causes an excessive PAPR, as happens with OFDM. In this way, it is concluded that it is best to use an intermediate value, corresponding to the value of 8 subcarriers verified at the peak. Furthermore, as we saw in the received spectra, the red LD outperforms the other two colors, with the blue LD having the worst bit rate.

 

Fig. 5. Achievable bit rate for red, green and blue colors as a function of a) the number of 100 MHz subcarriers and c) the number of subcarriers in a 1.68 GHz bandwidth signal. b) Spectral efficiency as a function of the number of 100 MHz subcarriers.

Download Full Size | PDF

In Fig. 6 it is shown the aggregated achievable bit rates corresponding to the individual red, green and blue results from the previous figures. In this test, four NGMI threshold values were considered in order to obtain the highest bit rate per color. The used $\mathrm {NGMI_{th}}$ values vary between 0.8 and 0.95, which corresponds an ideal FEC overhead between 25% and 5%. A peak value of 31.2 Gbit/s was measured, corresponding to three signals with 1.68 GHz bandwidth, 8 subcarriers and an $\mathrm {NGMI_{th}} = 0.9$. This maximum bit rate was achieved by using a tricolor signal with 12.3 Gbit/s for the red signal, 10.8 Gbit/s for the green and 8.1 Gbit/s for the blue. It should be noted that although we have only studied the performance for a channel with a fixed distance of 90 cm and a diffuser with an angle of 20$^{\circ }$, different scenarios can be considered. It is expected a bit rate reduction for higher distances and diffusing angles, due to a lower estimated SNR per subcarrier which results in a lower allocated entropy by the proposed entropy loading algorithm.

 

Fig. 6. Aggregated achievable bit rate for four NGMI target values.

Download Full Size | PDF

Finally, in Fig. 7, we can see the assigned entropies and the corresponding used QAM modulation format at the peak aggregated achievable bit rate. Once again, we verify that the highest entropies are attributed to the red LD, with values above 10 bits per symbol with a PCS-4096QAM modulation format. For better visual perception of the entropy loading scheme, in Fig. 7 c) we plot the received constellations corresponding to the blue color.

 

Fig. 7. Experimental a) entropy and b) QAM modulation format per subcarrier. c) Received constellations of the blue color.

Download Full Size | PDF

5. Conclusion

In this paper, we present an experimental setup of a visible light communications system capable of both lighting and >30 Gbit/s communications. To that end, we present an entropy loading technique based on probabilistic constellation shaping for multi-carrier signals. This method maximizes the bit rate considering a given pre-estimated SNR per subcarrier. A bit rate of 31.2 Gbit/s over 0.90 m of free space distance was recorded for tricolor RGB LDs systems. The aggregated 31.2 Gbit/s RGB visible light transmission is divided into 12.3 Gbit/s, 10.8 Gbit/s and 8.1 Gbit/s for the red, green and blue colors, respectively. To the best of the authors’ knowledge, these results represent the highest capacity demonstrated so far for a single-polarization RGB-VLC system.