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Abstract
Multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) has been widely used to improve data rate in visible-light communication (VLC) systems. However, the high correlation of channels restricts the application of MIMO. A superposed constellation, combined with MIMO, can achieve considerable diversity gain even in highly correlated MIMO channels. In this study, what we believe to be novel superposed three-dimensional 64-quadrature amplitude modulation (3D-64QAM) constellation schemes are proposed for MIMO-OFDM VLC systems. First, a superposed 3D-64QAM constellation scheme using two transmitted light emitting diodes (LEDs) is proposed, where two independent signals with 3D-4QAM and 3D-16QAM modulation formats are superposed to form a 3D-64QAM signal at the receiver. Then, for what we believe is the first time, we expand the superposed constellation solution to three-LED application scenarios, wherein the 3D-64QAM constellation is superposed by three different 3D-4QAM constellations. Both schemes benefit from a higher minimum Euclidean distance of 3D-64QAM constellation, 1.67 times that of traditional two-dimensional (2D) 64QAM constellation. Meanwhile, the equal-power superposition design of transmitted signals reduces the nonlinearity of LEDs and power competition of photodiodes. Moreover, the three-LED scheme further improves the transmitted power without increasing the risk of nonlinear distortion. To improve spectral efficiency and reduce complexity, we also propose a 3D OFDM modulation scheme. The superposed 3D-64QAM schemes are first studied through theoretical analysis and computer simulation. Then, an experimental demonstration is established to investigate the system performance comprehensively. Experimental results prove that the superposed 3D-64QAM constellation schemes achieve a superior bit error rate (BER) performance than the traditional superposed 2D-64QAM constellation scheme. Compared with two-LED scheme, the three-LED scheme not only obtains a lower BER, but also improves the dynamic range of driving peak-to-peak voltage significantly.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the rapid development of modern applications such as internet of things, smart city, smart medical and industry 4.0, the demand for high quality of service and high data rate has grown exponentially, leading to a higher shortage of radio-frequency spectrum [1,2]. Visible light communication (VLC), which utilizes light emitting diodes (LEDs) to deliver information, has amassed increasing attention in both academia and industry. Owing to many advantages, including rich spectrum resources, no electromagnetic interference, safety and energy saving, VLC has become a compelling candidate for the next generation of B5G and 6 G communications [3].
The biggest challenge for a high-speed VLC system is the limited modulation bandwidth of the commercial LED, where signals modulated at high frequencies are attenuated significantly, causing a serious intersymbol interference (ISI). Several technologies have been proposed to improve the data rate of VLC systems, such as multiple input multiple output (MIMO), orthogonal frequency division multiplexing (OFDM), carrier-less amplitude phase modulation, software and hardware pre-equalization, and so on [4–6]. Among them, MIMO and OFDM, which form a MIMO-OFDM VLC system, have attracted the greatest attention. OFDM eliminates the ISI by dividing the channel into parallel frequency-flat sub-channels. Meanwhile, MIMO multiplies the data rate by transmitting independent data streams simultaneously. However, high channel correlation causes failure of MIMO detection because receivers cannot separate the data streams with similar channel links, which is common in VLC systems. Owing to the limitations in the size and power consumption of the terminals, multiple photodiodes (PDs) must be integrated together, and the close placement of PDs always produces highly correlated channels [7].
Therefore, two kinds of optical spatial superposition schemes have recently been proposed to overcome channel correlation in VLC systems. One is spatial summing modulation [8,9]. In this scheme, signals are generated through different light intensities by controlling the number of alight LED chips in an LED array. In this way, the receiver only needs to detect the signals based on the superposed light intensity. However, the modulation bandwidth of LED would be reduced for grouped LEDs due to the connections of LEDs and driving transistors. The other is superposed constellation technique, where LEDs are driven separately and transmitted simultaneously. With a specific constellation design, MIMO detection is realized simply by constellation demapping of superposed signals rather than separating the data streams. In [10], Qiao et al. first proposed a superposed constellation scheme for the 2 × 1 MISO VLC system. Then, a superposed 32QAM constellation scheme was proposed for the 2 × 2 MIMO-OFDM VLC system, wherein the geometrically shaped 8-quadrature amplitude modulation (8QAM) constellation was introduced to increase the minimum Euclidean distance (MED) of the superposed constellation [11]. The MED of the superposed constellation was further improved by optimizing the sub-constellations at individual LEDs in [12]. Later, a scalar-superposed 64QAM constellation scheme using two 8-pulse amplitude magnitude (8PAM) signals was proposed in [13]. The study confirmed that the requirement for equal power of the transmitted signals reduced the nonlinearity of LEDs and the power competition of PDs. However, the adjacent constellation points were more likely to overlap when using scalar superposition with PAM signals. Consequently, two geometrically shaped 8QAM signals of equal powers were designed to superpose the 64QAM constellation in an interleaved manner [14]. Further, we proposed a flipped superposed constellation scheme, which is valid for superposed MQAM constellation of any order [15]. In addition to meeting the requirement of equal power, the scheme also provided a thorough Gray coding gain and improved the received signal-to-noise ratio (SNR).
In summary, the performance of the superposed constellation scheme is determined by many factors, with the most critical factors being the MED of the superposed constellation and the power ratio of the transmitted signals for superposition. The MED of the superposed constellation should be maximized to resist channel noise. The power ratio of the transmitted signals should be approximately one to reduce nonlinearity of LEDs and avoid power competition of PDs. Recently, three-dimensional (3D) constellations have been used in different optical communication systems [16–20]. They greatly increase constellation MED by extending constellation points from the two-dimensional (2D) plane to the 3D space, thus improving BER performance of the system. Moreover, more LEDs are preferred to improve the transmitted power without increasing the risk of nonlinear distortion in VLC systems. While keeping the data rate constant, lower-order modulation can further reduce the nonlinear distortion. To the best of our knowledge, existing superposed constellation schemes use only two transmitted LEDs.
In this paper, we propose two novel superposed 3D-64QAM constellation schemes for MIMO-OFDM VLC systems, wherein the same cube-shaped 64QAM constellation is selected as the target constellation in the receiver. The contributions of the proposed schemes can be explained as follows: First, the MED of the cube-shaped 3D-64QAM constellation was 1.67 times that of the square-shaped 2D-64QAM constellation in the case of power normalization, which significantly improved the BER performance of the system. Second, a superposed 3D-64QAM constellation scheme using two transmitted LEDs was proposed. By designing 3D-4QAM and 3D-16QAM signals at the transmitter, the required power ratio of the two transmitted signals was approximately one. Thus, the nonlinear distortion of LEDs and the power competition of PDs could be avoided as much as possible. Third, for the first time, we extended the superposed constellation to three-LED application scenarios. Three different 3D-4QAM signals were introduced at the transmitter to obtain a 3D-64QAM signal at the receiver, which also satisfied the requirement of equal power superposition. The employment of more transmitted LEDs increased the transmitted power. Meanwhile, the nonlinear distortion was reduced because the modulation order was reduced for a constant data rate. Fourth, 3D OFDM modulation was proposed, which is realized by a 3D signal mapper and one-dimensional (1D) fast Fourier transform (IFFT). Compared with the existing solutions, the spectral efficiency was doubled, while the complexity was reduced. The performance of the proposed superposed 3D-64QAM constellation schemes was first studied through theoretical analysis and computer simulation. Subsequently, the proposed system was experimentally investigated comprehensively. Experimental results confirmed that both two-LED and three-LED superposed 3D-64QAM constellation schemes achieved superior BER performance than the traditional superposed 2D-64QAM constellation scheme. Compared with the two-LED superposed 3D-64QAM constellation scheme, the three-LED scheme improved the dynamic range of driving peak-to-peak voltage (Vpp) by 250 and 350 mV, respectively, when the LEDs worked in linear and nonlinear regions.
2. Principle
2.1. Principle of the proposed superposed 3D-64QAM constellation schemes
The principle of the superposed 3D-64QAM constellation scheme using two LEDs is illustrated in Fig. 1, where 3D-4QAM and 3D-16QAM constellations are superposed to form a 3D-64QAM constellation. Further, we propose a three-LED superposed 3D-64QAM constellation scheme, as depicted in Fig. 2, which shows that three different 3D-4QAM constellations were designed and were located in the xoy-, xoz-, and yoz-planes. Owing to the advantage of MED, the cube-shaped 3D-64QAM constellation was selected as the target constellation in both schemes. Meanwhile, 3D QAM modulation was adopted at the transmitter, i.e., each modulated signal contained three components, even though one or two components may be equal to 0. Hereinafter, for simplicity, 3D-MQAM is abbreviated as MQAM, and the two superposed 3D-64QAM constellation schemes are abbreviated as 3D-4QAM-16QAM and 3D-4QAM-4QAM-4QAM, respectively.
Before evaluating the performance of the proposed schemes quantitatively, we established a mathematical model of the superposed 3D-64QAM signals. For the two-LED scheme, the superposed signals can be written as follows:
For the three-LED scheme, the superposed signals are denoted by
where S1, S2, and S3 represent the 3D modulated signals transmitted from three LEDs. They are linearly superposed into a 3D-64QAM signal and denoted as S64QAM. The superscript denotes the index of the LED. The signal power of S2 is normalized. β1 and β2 are power coefficient ratios, representing the square root of the power ratios of S1 to S2 and S3 to S2, respectively. According to Eq. (1) and (2), the value of 3D-64QAM signal is related to the power coefficient ratio. Consequently, the power coefficient ratio determines the distribution of the constellation points, which in turn affects the MED of the superposed constellation. Generally, the MED is maximized when the constellation points are uniformly distributed. Thus, we define the corresponding power coefficient ratio as the optimal power coefficient ratio. Considering the nonlinearity of LED and the power competition of PD, the optimal power coefficient ratio of one is more optimal. When the power coefficient ratio is not equal to one, a power imbalance between the transmitted signals occurs. The further the power coefficient ratio deviates from one, the more likely the high-power signal is to fall into the nonlinear region of the volt–ampere characteristic curve of an LED. Meanwhile, large power diversity leads to power competition of PD, i.e., the received SNR of low-power signals becomes worse.Table 1 lists the essential parameters of different superposed constellation schemes. The traditional superposed 2D-64QAM constellation scheme consisting of two 8QAM signals in [14] is also selected for comparison. Notably, the MED was calculated assuming an optimal power coefficient ratio. Evidently, the MED of 3D-64QAM constellation is 1.67 times that of the 2D-64QAM constellation, which greatly improves the ability of the received signal to resist noise. All schemes are designed with an optimal power coefficient ratio of one to reduce performance losses due to nonlinearity and power competition. In addition, the peak-to-average power ratios (PAPRs) of the constellations are the lowest in the 3D-4QAM-4QAM-4QAM scheme.
Table 1. Essential parameters of different superposed 64QAM constellation schemes
2.2. Principle of 3D OFDM modulation
Further, we proposed a 3D OFDM modulation to realize the OFDM modulation of 3D MQAM signals, which is implemented by the 3D signal mapper and 1D IFFT. The 3D signal mapper reorganizes the 3D MQAM signals into complex signals and assigns them to different sub-carriers. Compared with the previous solutions [19,20], the spectral efficiency is doubled since the complex signals are produced. Then, we used 1D IFFT instead of 2D IFFT to generate the time-domain OFDM symbols, which reduces the complexity without sacrificing the BER performance.
Before introducing the 3D signal mapper, we first define the 3D MQAM signal, which is represented as
where xk, yk, and zk express the components on the x, y, and z axes, respectively.Then, the complex 3D signals are reorganized. Two consecutive 3D signals form a 3D complex signal as
Afterward, the three components of the complex 3D signal are separately mapped to the same sub-carrier of three successive OFDM signals. Suppose that the number of sub-carriers is N, the 3D OFDM symbol in the frequency domain after 3D signal mapping can be given by
Note that Hermitian symmetry is applied in Eq. (5) to obtain the real-valued OFDM symbols in the time domain. After 3D signal mapping, 3D OFDM symbols are converted from the frequency domain to time domain by using 1D IFFT. The time-domain 3D OFDM symbol is denoted as
The three rows of the generated signals in T could be used to drive three independent physical components. In this paper, for simplicity, the generated signals are time-division multiplexed and serialized into a sequence. Consequently, the net data rate is reduced to two-third that of the traditional 2D OFDM system. Nevertheless, the proposed 3D signals achieve great advantage in improving the MED. Moreover, the net data rate can be increased by employing wavelength division multiplexing technology, when RGB-LED is employed as a transmitter in a VLC system.
3. Simulation results
In this section, the performance of the proposed schemes is investigated via computer simulations. In comparison with the superposed 2D-64QAM constellation scheme, the superiority of the proposed superposed 3D-64QAM constellation schemes was verified.
To provide a more clear comparison, the PAPR performance for different schemes is presented in terms of complementary cumulative distribution function (CCDF) in Fig. 3. CCDF indicates the probability that the PAPR of the OFDM symbol exceeds a given PAPR0. In this simulation, we aim to study the PAPR performance of different constellations. Consequently, we calculated the CCDF of PAPRs for different constellations in a single-carrier system, because the PAPR performance of a multi-carrier system mainly depends on the number of subcarriers [21]. As the consisted constellations of 3D-4QAM-4QAM-4QAM and 2D-8QAM-8QAM differ only in phase, one CCDF curve is required for each scheme. Two CCDF curves were plotted for 4QAM and 16QAM of the 3D-4QAM-16QAM scheme, respectively. As shown, the simulation results are consistent with those in Table.1. The PAPR values of 4QAM signals are the lowest, while the PAPR performance of 16QAM signals is the worst.
Then, the BER performance of the superposed 3D-64QAM constellation schemes is evaluated at different power coefficient ratios in Figs. 4 and 5. In the simulation, an additive white Gaussian noise (AWGN) channel was assumed, i.e., the non-ideal impacts, such as the nonlinearity of LED and the power competition of PD were not considered. The received SNR remained constant at 18 dB when the power coefficient ratio changed. Therefore, the BER performance mainly depends on the value of power coefficient ratio. Figure 4 presents the BER curves of the 3D-4QAM-16QAM and 2D-8QAM-8QAM schemes. The BER of both schemes decreased first and then increased, which was optimized when the power coefficient ratio was about one. Compared with the superposed 2D-64QAM constellation scheme, the 3D-4QAM-16QAM scheme reached a considerably lower BER due to its higher MED. Figure 5(a) depicts the BER performance of the 3D-4QAM-4QAM-4QAM scheme versus the power coefficient ratios β1 and β2. In order to show the relationship between BER and power coefficient ratios more clearly, Fig. 5(b) further presents the BER curves of different β1 values under a certain β2. As shown in the figures, the power coefficient ratios β1 and β2 jointly determined the BER performance. Only when β1 and β2 are simultaneously equal to the optimal value will BER reach the minimum value.
In Fig. 6, the BER performance of different schemes was compared when noise variance changed in the AWGN channel. In the simulation, the optimal power coefficient ratio was assumed for all the schemes, where the power of each transmitted signal was set to one. Thus, the 3D-4QAM-4QAM-4QAM scheme owns the highest transmitted power, since an additional LED is used. The simulation results confirmed that the SNR of 3D-4QAM-4QAM-4QAM was improved compared with the two-LED schemes, as shown by the dashed lines in Fig. 6. Therefore, the BER of 3D-4QAM-4QAM-4QAM was lower than that of 3D-4QAM-16QAM. The 3D-4QAM-16QAM and 2D-8QAM-8QAM schemes achieved the same SNR owing to the same transmitted power, but the 3D-4QAM-16QAM scheme still benefited from a higher MED.
Figure 7 studies the BER performance of the proposed 3D OFDM modulation, where the 3D-4QAM-16QAM scheme is assumed as an example. In the simulation, the theoretical model of VLC channel was established, and the exponential attenuation frequency response model of LED was also considered. The number of OFDM subcarriers was 256, and the length of CP was eight. The optimal power coefficient ratio was chosen. The existing 3D OFDM modulation in [17] was compared, wherein 1D IFFT was employed. The simulation results showed that the BER performance of the proposed 3D OFDM modulation was the same as that of the scheme in [17]. However, computational complexity was reduced by using 1D IFFT instead of 2D IFFT.
4. Experimental setup and results
4.1. Experimental setup
To verify the superiority of the proposed superposed 3D-64QAM constellation schemes, we built a MIMO VLC experimental system for demonstration. The system block diagram and experimental setup are shown in Fig. 8. First, binary data streams were modulated to 3D MQAM signals. Then, 3D MQAM signals were mapped to different sub-carriers, and the Hermitian symmetry was imposed. After up-sampling, 1D inverse fast Fourier transform (IFFT) was executed to obtain the real-valued OFDM signals. Finally, a CP was attached, and the transmitted signals were generated.
Fig. 8. System block diagram and experimental setup of the proposed superposed 3D-64QAM constellation schemes.
The offline generated signals were uploaded to arbitrary function generators (AFG1: Tektronix AFG3252C, AFG2: Tektronix AFG3252) for transmission. For the two-LED schemes, AFG1 was used to generate two signals. While for the three-LED scheme, three signals were sent from AFG1 and AFG2 simultaneously, of which AFG1 and AFG2 were required to be synchronized. The electrical signals were amplified using an electrical amplifier (EA: Mini-Circuit ZHL-6A-S+) and coupled with direct current (DC) through a DC bias (Mini-Circuits ZFBT-4R2GWFT+) to drive the red-light LEDs (Cree XLamp XP-E). Two PDs (Hamamatsu C 12702-11) were employed at the receiver to convert electrical signals into the optical signals after 1.4-m free-space transmission. The two PDs were placed approximately 1.5 cm apart to simulate an integrated PD array, which resulted in a highly correlated MIMO channel. Between the LEDs and PDs, lenses were placed to focus the light and improve the received SNR. The electrical signals were recorded using a high-speed oscilloscope (OSC: Tektronix MDO4104C) and forwarded for offline processing.
At the receiver, crosstalk occurred because a single LED illuminated multiple PDs. Each receiver received the superposition of multiple transmitted signals. Signal processing at the receiver is an inverse process of modulation at the transmitter. After synchronization, the two received signals were combined together. Then, OFDM demodulation was realized by down-sampling, CP removal, and FFT. The estimated superposed 3D constellation signals were obtained after channel estimation and equalization. Finally, the binary data streams were recovered via demapping and demodulation.
4.2. Experimental results and discussion
In the experiment, the system parameters were set as follows: the number of FFT points was 256, and the length of the CP was eight. Only 122 sub-carriers were used to transmit the signals, where six sub-carriers at low frequency were zero-padded because of the poor response of the EA. The DC bias current was set as 50 mA. The sampling rate of the AFG was set to 100 MHz. As mentioned above, because each 3D-QAM signal contains three components, the data rate of 3D OFDM system is reduced to two-third that of the traditional 2D OFDM system. Therefore, in order to ensure the same data rate, the 2D-8QAM-8QAM scheme adopted an up-sampling rate of six, while the 3D-4QAM-16QAM and 3D-4QAM-4QAM-4QAM schemes used an up-sampling rate of four. In this case, the modulation bandwidth of the 2D-8QAM-8QAM scheme was 17 MHz, and the modulation bandwidths of the 3D-4QAM-16QAM and 3D-4QAM-4QAM-4QAM schemes were both 25 MHz. All schemes achieved a net data rate of 48 Mbps. Note that, we do not expect to pursue higher data rates than those presented in the literature. Instead, we aim to demonstrate that the proposed superposed 3D-64QAM constellation scheme can significantly improve the BER performance compared with the existing schemes at the same data rate.
Initially, BER performance was compared when using different receivers in Fig. 9. In the experiment, the 3D-4QAM-16QAM scheme was selected as an example. The 4QAM signal was sent from LED1, and the 16QAM signal was sent from LED2. The received SNR was varied by changing the driving Vpp of LED2 (Vpp2). The Vpp of LED1 (Vpp1) was set to approximately 1.069 times that of Vpp2 to meet the optimal power coefficient ratio. The red BER curve represented the BER measured when both PDs were used as receivers, and the green and blue curves denoted the BER performance when only PD1 (Rx1) or PD2 (Rx2) was used. As shown, the BER decreased first and then increased. At the beginning, the SNR improved and the BER decreased with Vpp2 growing. However, when Vpp2 was higher than 500 mV, the BER increased again due to the appearance of LED nonlinearity. The experimental results showed that the system with single receiver was also feasible because multiple data streams were detected by constellation demapping. Therefore, the number of receivers does not required to be greater than or equal to the number of transmitters, which can be considered another advantage of the superposed constellation scheme. The BER performance was almost the same when Rx1 or Rx2 was used. The reason is that the PDs were placed close together in the experiment, resulting in a high correlation of the received signals. However, compared with the single receiver system, the employment of two receivers can significantly improve the BER performance. This is because the use of multiple receivers obtains a receive diversity gain, thereby improving the received SNR. Since the nonlinearity of LED limits the transmitted power, it is a good choice to use multiple receivers to improve the system SNR.
In Fig. 10, BER performance comparison was made on different combining techniques by taking the 3D-4QAM-16QAM scheme as an example. The experimental settings were the same as those in Fig. 9. The well-known combining techniques maximal ratio combining (MRC) and equal gain combing (EGC) were compared in the experiment. The MRC is considered the optimal solution among the combining techniques, where signals of each receiver are weighted by their respective SNRs and then combined together. However, experimental results showed that the BER performance of the two techniques was almost the same. Because the received signals are highly correlated, the SNRs of the two receivers are also similar, leading to the same performance of the two techniques. Therefore, the EGC criterion is chosen owing to its lower complexity. In the following, MIMO system and EGC combining technique were adopted in all the experiments.
In Fig. 11, the performance of the superposed 64QAM constellation schemes using two transmitted LEDs with different power coefficient ratios were compared. 11. In the experiment, for 3D-4QAM-16QAM, the 4QAM signal was sent from LED1, and the 16QAM signal was sent from LED2. For the 2D-8QAM-8QAM scheme, two 8QAM signals were sent from LED1 and LED2, respectively. The Vpp2 was fixed at 400 mV, and the power coefficient ratio was changed by adjusting the value of Vpp1. The experimental results showed that the BER of both schemes first decreased first and then increased. The best BER performances of 3D-4QAM-16QAM and 2D-8QAM-8QAM were achieved when the Vpp1 values were set to 400 and 430 mV, respectively. The ratio of Vpp1 to Vpp2 is consistent with the optimal power coefficient ratio in Table 1. The detailed constellation diagrams confirmed that the constellation points were uniformly distributed in this case. Increasing or decreasing Vpp1 would cause the power coefficient ratio to deviate from the optimal value, resulting in a decrease in MED. Moreover, when Vpp1 continued to increase, nonlinearity of LED and power competition of PD occurred. The higher the value of Vpp1, the more serious the nonlinear distortion and power competition, and the worse the received SNR. Compared with the 3D-4QAM-16QAM scheme, the 2D-8QAM-8QAM scheme occupied a narrower modulation bandwidth at the same data rate. Consequently, the frequency response of the channel was better, because the LED frequency response decreased exponentially as the frequency increased. Nevertheless, the 3D-4QAM-16QAM still achieved a significantly better BER performance due to its superior performance on MED.
Subsequently, the BER of the 3D-4QAM-4QAM-4QAM scheme was measured when Vpp2 was fixed at 400 mV, as presented in Fig. 12. In the experiment, different 3D-4QAM signals were transmitted from three LEDs separately. The experimental results indicated that the BER is related to two power coefficient ratios in the three-LED scheme. BER reached the optimal value only when Vpp1 and Vpp of LED3 (Vpp3) were equal to 400 mV, concurrently. The constellation points tended to overlap when Vpp1 or Vpp3 deviated from the optimal values. Meanwhile, when Vpp1 or Vpp3 was high, the nonlinearity of LED and power competition of PD would also worsen the system performance. In addition, the optimal BER performance of 3D-4QAM-16QAM was about 3 × 10−4, while the minimum BER value of 3D-4QAM-4QAM-4QAM was around 1 × 10−4. The result proved that the 3D-4QAM-4QAM-4QAM scheme achieves better BER performance under the optimal power coefficient ratio due to the increase in the received SNR.
To further demonstrate the superiority of the proposed schemes, Figs. 13 and 14 depict the dynamic ranges of driving Vpps for different superposed 64QAM constellation schemes, considering the 7% pre-forward error correction (pre-FEC) BER threshold of 3.8 × 10−3. In Fig. 13, the dynamic ranges of driving Vpp1 and Vpp2 were measured for the 3D-4QAM-16QAM and 2D-8QAM-8QAM schemes. Obviously, the available dynamic range of 3D-4QAM-16QAM was considerably larger than that of 2D-8QAM-8QAM. In addition, the 3D-4QAM-16QAM achieved significantly better BER performance, due to the advantage of MED. Figure 14 presents the dynamic ranges of driving Vpp1 and Vpp3 with different Vpp2 values. As evident, with Vpp2 increasing, the overall BER performance first increased and then decreased. Initially, the BER performance improved as the received SNR increased with Vpp2. However, when Vpp2 continued to increase, the overall BER performance of the system decreased. The result proved again that nonlinearity and power competition lead to considerable performance loss when the values of driving Vpps are high. Compared with 3D-4QAM-16QAM, the 3D-4QAM-4QAM-4QAM scheme obtained a larger dynamic range of driving Vpps. When Vpp2 was equal to 500 mV, the Vpp1 dynamic range of 3D-4QAM-16QAM was about 350 mV. Meanwhile, 3D-4QAM-4QAM-4QAM increased the available dynamic range of Vpp1 to around 600 mV. When Vpp2 was increased to 800 mV, nonlinearity occurred. In this case, the advantage of 3D-4QAM-4QAM-4QAM is even more significant, when the Vpp1 dynamic range of 3D-4QAM-16QAM is reduced to 250 mV, while the Vpp1 dynamic range of 3D-4QAM-4QAM-4QAM is maintained at 600 mV.
5. Conclusion
In this paper, novel superposed 3D-64QAM constellation schemes by using two and three LEDs are proposed for MIMO-OFDM VLC systems. The MED of the target cube-shaped 3D-64QAM constellation is 1.67 times that of the traditional 2D-64QAM constellation, which greatly improves the anti-noise ability of the system. 3D-64QAM constellation is superposed by 3D-4QAM and 3D-16QAM constellations in the two-LED scheme and by three different 3D-4QAM constellations in the three-LED scheme. Both schemes meet the requirement for equal power superposition of transmitted signals. Consequently, the nonlinearity of LED can be reduced, and the power competition of PD can be avoided. Without increasing the risk of nonlinear distortion, the employment of three LEDs increases the transmitted power to achieve a superior BER performance. Further, a 3D OFDM modulation is proposed, consisting of a 3D signal mapper and 1D IFFT. Compared with the existing solution, it improves the spectral efficiency and reduces complexity while maintaining the BER performance of the system. Theoretical simulation evaluates the performance of the proposed schemes under different power coefficient ratios and noise powers. Finally, detailed explorations of the proposed system performance were experimentally investigated by changing the driving Vpps. Experimental results showed a dramatic performance improvement of the superposed 3D-64QAM constellation schemes over the traditional 2D-8QAM-8QAM scheme. Compared with 3D-4QAM-16QAM, the 3D-4QAM-4QAM-4QAM scheme achieves lower BER and a larger dynamic range of driving Vpps. Especially when the LEDs operate in the nonlinear region, the Vpp dynamic range can be increased from 250 to 600 mV.
Funding
National Natural Science Foundation of China (61501296).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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