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Abstract
Superposed constellation combined with spatial multiplexing multiple-input multiple-output (MIMO) techniques have been increasingly utilized in visible light communication (VLC) systems, as multiplexing gains can be achieved regardless of the correlation extent of the VLC channel. Herein, we propose a novel superposed 64-quadrature amplitude modulation (QAM) constellation scheme for 2 × 2 MIMO VLC systems. Considering the nonlinearity of light-emitting diodes (LEDs), two geometrically shaped 8QAM constellations are introduced to reduce the peak-to-average power ratio at the transmitter. Because the two 8QAM constellations are superposed in an interleaved manner, the required power ratio between two transmitted signals is 1, which further reduces the risk of nonlinear distortion and avoids signal-to-noise ratio deterioration induced by power competition. The proposed superposed 64QAM constellation scheme is experimentally investigated comprehensively, where the system performance is evaluated under different transmitted powers, direct current bias currents, and driving peak-to-peak voltages (Vpps). The experimental results show that the proposed scheme achieves better bit error rate (BER) performance than the traditional superposed 64QAM constellation schemes. Below the 7% pre-forward error correction BER threshold of 3.8 × 10−3, the dynamic range of the driving Vpps of the two LEDs improves from 0.06 to 0.4 V and 0.23 to 0.4 V when the optimal power ratio is achieved.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, the evolving explosion in high-data-rate services and applications has resulted in a high demand for wireless communication technologies [1]. Among the new technologies, visible light communication (VLC), which utilizes a light emitting diodes (LEDs) to deliver information, exhibits high potential. Compared with radio-frequency (RF) networks, VLC networks offer higher data rates, higher energy efficiencies, free spectrum licenses, and immunity to electromagnetic interference [2–4]. Consequently, it has emerged as the most compelling wireless communication technology for the fifth generation and beyond.
However, the modulation bandwidth of commercial LEDs is limited, where signals modulated at high frequencies are attenuated significantly. Consequently, the high data rate is restricted to point-to-point VLC networks. Hence, multiple-input multiple-output (MIMO) techniques, which have been widely used in RF communications, are considered one of the most promising solutions [5–7]. By equipping multiple LEDs and photodiodes (PDs) simultaneously, MIMO techniques can significantly improve the data rate without requiring additional spectrum resources.
Currently, MIMO has been highlighted in studies pertaining to multiple-point VLC networks. In MIMO VLC systems, intensity modulation and direct detection techniques create a highly correlated channel, where the channel gains tend to be similar, particularly when the LEDs or PDs are placed close to each other [8]. Consequently, the well-known MIMO scheme, i.e., spatial multiplexing (SMP), cannot be implemented in a VLC system because the receiver fails to separate independent data streams; hence, the bit error rate (BER) performance becomes deteriorated significantly [8]. To overcome issues concerning channel correlation, other MIMO options have been proposed for VLC systems. Imaging MIMO can create an uncorrelated channel using lenses [9,10]. However, it requires precise alignment for focusing an LED image onto a dedicated detector, thereby rendering it unfeasible in practice. Transmit diversity (TD), which sends the same information-bearing signals from multiple LEDs, exploits immunity to the channel correlation but lacks multiplexing gains [11]. Spatial modulation achieves a higher data rate than TD by extending the signal constellation to the spatial dimension [12]. Nevertheless, it is still impaired by a high channel correlation. Moreover, the required number of LEDs increases exponentially with the data rate.
Recently, researchers have focused on using a superposed constellation combined with the SMP scheme in MIMO VLC systems as this approach allows multiplexing gains to be realized even when the channel is highly correlated. In [13], a superposed constellation scheme was proposed for a 2 × 1 multiple-input single-output (MISO) VLC system, where two independent signals modulated with quadrature phase-shift keying and 16-quadrature amplitude modulation (QAM) were transmitted from two LEDs. Using this scheme, the relationship between the different transmitted power ratios and the resulting superposed constellation was analyzed, and the MIMO decoding algorithm based on a look-up table and successive interference cancelation was investigated. However, the assumption of MISO channels with the same channel gains restricts the application of the scheme. Meanwhile, the two signals exhibit different modulation orders, which results in a higher peak-to-average power ratio (PAPR) in the signal with the higher modulation order. Subsequently, a novel square-shaped 32QAM superposed constellation scheme for a 2 × 2 MIMO VLC system was proposed, which was the first investigation of the constellation superposition of the odd-order QAM [14]. In this study, a square-shaped 8QAM constellation was introduced to reduce the PAPR at the transmitter, which also benefited from the maximum minimum Euclidean distance (MED) at the receiver. Moreover, the advantages of the superposed constellation were analyzed comprehensively; not only was the performance of the SMP scheme unaffected by the channel correlation, but also a higher-order modulation can be employed without nonlinear distortions in VLC systems. However, nonlinearity and power competition are more likely to occur because of imbalanced power allocation. Hence, Zou et al. used two eight-pulse amplitude magnitude (8PAM) signals to superpose a 64QAM constellation [15]. Although the optimal power ratio was allocated equally, the significant increase in the PAPR of the 8PAM signals resulted in more serious nonlinear distortions. Therefore, a high-complexity post-equalizer MIMO multi-branch hybrid neural network was proposed to achieve good performance. In [16], the authors presented an optimization problem to determine sub-constellations with the highest MED values of the superposed constellation at the receiver under power constraints. Nevertheless, the effect of nonlinearity was not considered, i.e., the PAPRs of the constellations were not measured and imbalanced power allocation remained.
Based on the studies above, we conclude that a superior superposed constellation scheme should satisfy the following conditions: First, the PAPR of the transmitted signals should be minimized to reduce nonlinear distortions. Second, a greater MED of the superposed constellation is preferred to resist channel noise in the receiver. Third, the power ratio between the two transmitted signals should be approximately 1 to reduce nonlinearities at the transmitter and avoid power competition in the receiver. For the superposed constellation scheme of different modulation orders, it is necessary to take all of the factors into consideration to achieve an optimal solution.
Herein, we propose a novel superposed 64QAM constellation scheme for 2 × 2 MIMO VLC systems, where two geometrically shaped 8QAM constellations are designed at the transmitter to superpose a square-shaped 64QAM constellation in the receiver. The superiority of the proposed scheme can be explained as follows: First, the selected QAM format of the same order ensures that both transmitted signals are modulated in a low order. Therefore, the PAPR of the 8QAM signals is lower than that of the 16QAM signals in [13] for its lower order, which is also much lower than the PAPR of the 8PAM signals in [15] because two-dimensional amplitude modulation is used. Moreover, compared with the traditional 8QAM constellation, the PAPR of the proposed 8QAM constellations decreases further owing to geometrical shaping. Consequently, the nonlinear distortion caused by the non-ideal transmission characteristics of LEDs can be reduced significantly. Second, the two 8QAM constellations are proposed to be superposed in an interleaved manner, which is different from the separate superposition manner in [13] and [14]. As such, the necessary imbalanced power allocation because of using the separate superposition manner can be avoided, and the optimal 64QAM constellation with uniformly distributed constellation points is achieved when two 8QAM signals are equally allocated in terms of power. Therefore, power competition is not introduced, and nonlinearity is reduced concurrently. Using the concept of interleaved superposition, superposed signals are proposed to detect based on the maximum likelihood (ML) criterion by setting up a look-up table in the receiver, where the complete channel information is provided to achieve more accurate detection. The performance of the proposed scheme was first investigated via theoretical analysis and compared with those of the two traditional superposed 64QAM constellation schemes. Subsequently, the proposed system was experimentally investigated comprehensively, where the system performance was evaluated under different transmitted powers, direct current (DC) bias currents, and driving peak-to-peak voltages (Vpps). Compared with the traditional superposed 64QAM schemes, the dynamic range of the driving Vpps of the two LEDs improved from 0.06 to 0.4 V and 0.23 to 0.4 V under a 7% pre-forward error correction (pre-FEC) BER threshold of 3.8 × 10−3.
2. Principle
2.1 Principle of proposed superposed 64QAM constellation scheme
The principle of the proposed superposed 64QAM constellation scheme is illustrated in Fig. 1. Because of the superiority of the scheme in terms of the MED, the same square-shaped 64QAM constellation as in [13] and [15] was selected as the target constellation in the receiver. As shown, it was superposed by two geometrically shaped 8QAM constellations, one of which can be obtained by rotating the other by 90°. Furthermore, Fig. 1 shows that the two 8QAM constellations are superposed in an interleaved manner, unlike the traditional schemes. For comparison, we present two superposed 64QAM constellation schemes in Fig. 2, both of which are based on the concept of the existing superposed constellations [13,14]. For both schemes, a constellation with lower power is attached to each point of the constellation with higher power to form a superposed constellation, where constellations with lower power are separated. Figure 2(a) shows the superposed 64QAM constellation designed by ourselves, which is superposed by two different 8QAM constellations in a separate manner. The superposed 64QAM constellation shown in Fig. 2(b) is composed of 4QAM and 16QAM, which is the same as the scheme in [13]. As the constellations were superposed separately, power imbalance inevitably occurred between the two signals. Hereinafter, we refer to the proposed scheme as interleaved superposition (IS) and the traditional scheme as separate superposition (SS). Therefore, the proposed scheme can be abbreviated as IS-8QAM-8QAM, and the two traditional schemes are denoted as SS-8QAM-8QAM and SS-16QAM-4QAM, separately. In Table 1, the specific coordinates of different superposed 64QAM constellation schemes are listed, where SI and SQ represent the real and imaginary parts of the QAM signal, respectively. It is noteworthy that all the coordinate values were calculated under the assumption of constellation power normalization.
Table 1. Coordinates of different superposed 64QAM constellation schemes
Before evaluating the performance of the superposed constellation scheme quantitatively, we established a mathematical model of the superposed 64QAM signal; it comprised two transmitted signals, which can be written as
where S1 denotes the QAM signal sent from one LED (Tx1), and S2 represents the QAM signal transmitted from the other LED (Tx2). They are linearly superposed into a 64QAM signal and denoted as S64QAM. In addition, we define a scaling factor β to measure the power ratio between the two transmitted signals. Based on Eq. (1), the scaling factor is crucial as it determines the distribution of the constellation points in the superposed 64QAM constellation. Because the MED varies with the distribution of the constellation points, different BER performances are achieved.In Fig. 3, superposed 64QAM constellations are plotted with different power ratios under the condition of constellation power normalization. As can be seen, the maximum MED is achieved when constellation points are uniformly distributed in superposed 64QAM constellation. In this case, β is equal to 1, which is called the optimal power ratio. When β is lower than 1, MED of the constellation decreases because the distance between the constellation points close to the Y axis becomes smaller. However, when β is larger than the optimal power ratio, MED of the constellation still decreases because the constellation points near the X axis get closer.
Table 2 further lists the essential parameters for evaluating the performance of different superposed 64QAM constellation schemes. As shown, the optimal power ratio of the IS-8QAM-8QAM scheme is 1, whereas those of the other two schemes are much higher, equal to 6 and 3.2, respectively. Consequently, nonlinear distortions tend to occur on the SS-based schemes, since one of the signals must multiply the transmitted power to obtain the superposed 64QAM constellation with the maximum MED. Moreover, power competition would be introduced in the receiver owing to the significant power diversity between the two signals, where the signal-to-noise ratio (SNR) of the signals with lower power would further deteriorate. Comparing the three schemes, only the two transmitted signals of the proposed scheme achieved the lower PAPR values, indicating that the proposed scheme was more resistant to nonlinear distortions.
Table 2. Essential parameters of different superposed 64QAM constellation schemes
2.2 Principle of proposed MIMO VLC system and detection algorith
We constructed a 2 × 2 MIMO VLC system based on the concept of the superposed 64QAM constellation. The system block diagram is shown in Fig. 4. To suppress the PAPR and mitigate nonlinearity in the LEDs, discrete Fourier transform spread orthogonal frequency division multiplexing modulation was implemented in the system [17]. QAM signals were first transformed from the time domain to the frequency domain using the M-point discrete Fourier transform (DFT) to generate DFT spread signals. Subsequently, a serial-parallel conversion was performed, where the channel was partitioned into N frequency-flat sub-channels. After inserting the training sequence and performing up-sampling in the frequency domain, the Hermitian symmetry was imposed, and an inverse fast Fourier transform (IFFT) was executed to obtain real-valued OFDM signals. Finally, a cyclic prefix (CP) was attached to alleviate inter-symbol interference, and signals to be transmitted were generated.
Fig. 4. System block diagram of superposed 64QAM constellation scheme for 2 × 2 spatial multiplexing MIMO VLC system.
In the channel, crosstalk occurred because a single LED illuminated multiple PDs. Therefore, one receiver received the superposition of two transmitted signals. Demodulation in the receiver is an inverse process of modulation at the transmitter. The starting positions of the data streams were detected via frame synchronization using the training sequence. Next, the received signals from the two receivers were combined. After CP removal, down-sampling, and OFDM demodulation, the MIMO channel was estimated based on the orthogonally designed training sequence and then applied for equalization. Subsequently, the signals were converted to the time domain via inverse discrete Fourier transform (IDFT). Finally, two data streams were separated through MIMO detection, and the original signals were recovered via QAM de-mapping.
Based on the proposed system, the received signals on each sub-channel in the frequency domain can be expressed as follows:
For SMP MIMO VLC systems with superposed constellation, MIMO detection is based on the concept of constellation de-mapping for overcoming channel correlation, instead of the direct separation of data streams. Because the proposed scheme is superposed in an interleaved manner, using the look-up table is a straightforward approach to separate the superposed signals based on a one-to-one mapping relation, where the ML is selected as the optimal criterion for MIMO detection. The specific detection procedures are as follows:
First, the received signals are merged based on the equal-gain combining criterion to achieve additional diversity gain [18]; this can be expressed as
Subsequently, channel estimation and equalization are implemented to set up the look-up table. Although the channel is highly correlated in the MIMO VLC system, a slight difference might still exist between the channel links. As a result, the complete channel information is estimated by orthogonally designed training sequences in the proposed system, where two LEDs are alternately activated to transmit pilots for two consecutive symbol durations. The channel gains can be estimated easily based on the least-squares criterion, which is expressed as
After channel estimation, the equalized signals can be obtained as follows:
Then, a look-up table can be set up based on the estimated power ratio and transmitted constellations to achieve more accurate detection in the time-domain, which is expressed as
Subsequently, the equalized signals are converted to the time domain via an M-point IDFT, and the ML criterion is used to achieve an optimal estimation. The estimations of Tx1 and Tx2 are expressed as follows:
3. Experimental setup
To verify the superiority of the superposed 64QAM constellation scheme in the MIMO VLC system, an experimental demonstration was conducted, as depicted in Fig. 5. The offline-generated transmitted signals were uploaded to an arbitrary function generator (AFG: Tektronix AFG3252C). Subsequently, the electrical signals were amplified using an electrical amplifier (EA: Mini-Circuit ZHL-6A-S+), and the DC power supplied by the DC bias (Mini-Circuit ZFBT-4R2GWFT+) was offset to ensure that the signals were positive. Subsequently, the mixed signals were used to drive the red-light LED (Cree XLamp XP-E). Each LED was equipped with a reflection cup to focus the light beam. After a 1.5 m free-space propagation, the optical signals were detected via two APD modules (Hamamatsu C 12702-11) and then converted to electrical signals. The effective bandwidth of the APD was approximately 100 MHz, and the sensitivity was approximately 0.42A/W at a wavelength of 620 nm. The two APD modules were placed close to each other to simulate an integrated APD array, which enables a small area and low power consumption in practical applications. Between the LEDs and APDs, lenses are placed to focus the light and improve the received SNR, whereas diaphragms are used to avoid the saturation of the APDs caused by excessive optical power. Finally, the electrical signals were recorded using a high-speed oscilloscope (OSC: Tektronix MDO4104C) and forwarded for offline processing.
Fig. 5. Experimental setup of superposed constellation scheme for 2 × 2 spatial multiplexing MIMO VLC system.
The system parameters used in the experiments are listed in Table 3. In each OFDM symbol, only 122 subcarriers were used to transmit the signals, where six subcarriers at low frequencies were zero-padded because of the poor response of the EA.
Table 3. Experimental parameters
4. Experimental result and discussion
4.1 Nonlinear response of system
In VLC systems, nonlinear distortions occur because of nonlinear components such as LEDs, EAs, and APDs. Among them, the nonlinearity caused by LEDs is the most significant. Considering the V–I characteristic curve of an LED, the nonlinear relationship between the driving voltage and forward current causes two types of signal distortion. One is nonlinear mapping in the electrical-to-optical conversion within the dynamic range, and the other is the hard clipping of signals when the voltage is less than the turn-on voltage or above the maximum permissible voltage [19,20]. As shown in Figs. 6(a), (b), and (c), the system nonlinearity was measured by the relationship between the transmitted and received signals. In the experiments, the DC bias current was set to 50 mA, whereas Vpp was set to 0.3, 0.6, and 0.9 V, separately. Each point was plotted with the normalized amplitude of the transmitted and received signals on the horizontal and vertical axes, respectively, where the different colors indicate the different densities of the points. To further measure the nonlinearity, we approximated the function of the transmitted and received signals as a power series with L+1 initially unknown coefficients, which can be expressed as
Based on Eq. (8), the fitting results were plotted, as shown by the dashed curves in Figs. 6(a), (b), and (c), where L is 3, and the coefficients an were calculated based on a least-squares fitting of the power series expansion to the measured data. The fitting curve in Fig. 6(a) shows that the amplitude response was linear when Vpp was 0.3 V. As the Vpp increased to 0.6 V, the received signals did not exhibit complete linearity to the transmitted signals, as shown by the fitting curve in Fig. 6(b). When Vpp increased to 0.9 V, the fitting curve exhibited apparent nonlinearity, as illustrated in Fig. 6(c).
Fig. 6. Nonlinear characteristics of system. Normalized amplitude response when Vpp is (a) 0.3 V, (b) 0.6 V, and (c) 0.9 V. SNR of each subcarrier when Vpp is (d) 0.3 V, (e) 0.6 V, and (f) 0.9 V.
The SNR was measured to evaluate the system nonlinearity, as shown in Figs. 6(d), (e), and (f). The SNR on the ith subcarrier is expressed as [21]
4.2 Power competition of system
In MIMO VLC systems, power competition is derived from the significant power diversity between two transmitted signals, which results in the SNR deterioration of the signal with a lower power. As shown in Fig. 7, we measured the amplitude–frequency responses of the MIMO VLC channels under different power ratios to verify the power competition. In the experiment, the Vpp and DC bias currents of the two transmitted signals were fixed to 0.3 V and 50 mA, respectively, to ensure that the LEDs were operating in the linear region. The Tx1 power was fixed to -20.52 dBm, which was the total power of the two receivers when only Tx1 was operated. The Tx2 power, which is the total received power when only Tx2 is active, was changed by adjusting the aperture size of the diaphragm. Because |H11| is similar to |H12| and |H21| is similar to |H22| when the two PDs are placed close to each other, only the estimated amplitude–frequency responses of |H11| and |H21| were plotted. The experimental results show that |H21| increased as the Tx2 power increased from −20.93 to −15.77 dBm. However, the value of |H11| decreased, although the Tx1 power was fixed. The results reveal that power competition occurred when power diversity occurred between the two signals. The SNR of the signal with a lower power continued to decrease as the power ratio increased.
Fig. 7. Measured amplitude–frequency responses of MIMO VLC channels. (a) |H11| channel estimation; (b) |H21| channel estimation.
4.3 Experimental result of different superposed 64QAM schemes
Initially, the BER performance of the proposed IS-8QAM-8QAM scheme vs. different transmitted powers was investigated. As mentioned in Eq. (5), the power ratio of the received signals would not be exactly the same as that of the transmitted signals, which may occurs when the distance between two LEDs and the integrated APD array is different. As a result, it is necessary to evaluate the system performance when the power ratio deviates from the optimal value. In the experiment, the Vpps of Tx1 and Tx2 were fixed at 0.3 V, and their DC bias currents were set to 50 mA to ensure that the system was operating in the linear operation range. The transmitted power was changed by adjusting the aperture size of the diaphragm, where the Tx1 and Tx2 powers are defined as presented above. Figure 8 shows the BER performance vs. Tx2 power when the Tx1 power was −19.92 and −25.52 dBm. As shown, the BER first decreased and then increased in each curve. The best BER performance was achieved when the power ratio was approximately 1, which is consistent with the theoretical analysis. The detailed constellations confirmed the result, where the constellation points of the superposed 64QAM were uniformly distributed, and the MED of the constellation was maximized when the minimum BER was attained. For a specific Tx1 power, deviation from the optimal power ratio introduces constellation points that overlap horizontally or vertically, causing BER performance loss. Nevertheless, considering the 7% pre-FEC BER threshold of 3.8 × 10−3, it can be seen that the system can work in a large dynamic range although the power ratio is not always optimal. As the Tx1 power is equal to −19.52dBm, the Tx2 power can be changed from about −21dBm to −17dBm, which equates to a fourfold change in power. Moreover, the system performance can further be improved if the optimal power ratio is maintained in the receiver, which requires the feedback of the channel information to adjust the power ratio at the transmitter. Comparing the two curves, a greater Tx2 power was required to maintain a suitable power ratio when the Tx1 power was −19.52 dBm. Additionally, the BER performance improved by increasing the Tx1 power.
Next, we evaluated the system BER performance by changing the DC bias currents, as shown in Fig. 9, where the Vpps of Tx1 and Tx2 were set equally to 0.2 and 0.3 V for the two curves, respectively. As the DC offset increased, the BER decreased initially and then increased for each curve, which is similar to the results shown in Fig. 8. This phenomenon can be explained as follows: In this experiment, the BER performance depended primarily on the degree of nonlinearity. When the value of the DC offset was low, nonlinear distortion occurred because the signals were clipped when the voltage was less than the turn-on voltage. As the DC offset increased, the BER decreased because the LED was operating in the linear operation region. However, the BER increased again when the DC offset continued to increase. This indicates that the LED generated a non-linear mapping during the electrical-to-optical conversion, where the distortion became more severe as the DC offset increased. Once the voltage exceeded the maximum permissible voltage, the signals were clipped. The illustrated constellations confirmed the result, where the variation in the SNR indicates the degree of nonlinear distortion. Comparing the two curves, the BER curve with a Vpp of 0.3 V yielded better performance owing to the higher transmitted power.
As shown in Fig. 10, the performance of the proposed IS-8QAM-8QAM scheme was investigated for different Vpps, where Vpp1 and Vpp2 denote the Vpps of Tx1 and Tx2, respectively. In the experiment, the DC bias currents were fixed to 50 mA. By setting different Vpps, different transmitted powers can be realized for the two signals. Consequently, the BER curves were similar to those shown in Fig. 8, where the BER decreased first and then increased for a specific Vpp1. The best BER performance was achieved when the ratio of Vpp1 to Vpp2 was approximately 1. Moreover, the illustrated constellations accounted for the BER result with varying Vpp2. Comparing the different BER curves, the average BER first decreased and then increased again when Vpp1 was increased. This is because an increase in Vpp1 not only changed the signal power, but also introduced nonlinear distortions to the system. Initially, the BER performance improved because of the increase in the SNR. However, nonlinear distortions appeared when Vpp1 continued to increase, resulting in performance loss. Considering the 7% pre-FEC BER threshold of 3.8 × 10−3, the dynamic range of Vpp2 reached the maximum value of 0.12 V when Vpp1 was set to 0.38 V. Concurrently, the BER was 10−4 when Vpp1 was 0.34 V.
Subsequently, the proposed superposed 64QAM constellation scheme based on the concept of interleaved superposition was compared with the two traditional schemes, SS-8QAM-8QAM and SS-16QAM-4QAM. Because of the different optimal power ratios for the three schemes, we normalized the power of the generated data before loading them into the AFG. In this experiment, we set Vpp1 and Vpp2 to 0.3 V and the DC bias current to 50 mA, which guaranteed that the LEDs were operating in the linear range. The Tx1 power was fixed at −19.92 dBm. The transmitted power was changed by adjusting the aperture size of the diaphragm. Figure 11 shows the BER curves of different superposed 64QAM schemes vs. the Tx2 power. As shown, the BER decreased first and then increased in all the three schemes. When the optimal power ratio was achieved for each scheme, the minimum BER was attained. An increase or decrease in the power ratio resulted in a reduced MED and a deteriorated BER performance. A comparison of the three schemes shows that a much lower Tx2 power is required in the IS-8QAM-8QAM scheme to superpose the 64QAM constellation. Consequently, the BER performance of the IS-8QAM-QAM scheme is the best for avoiding the loss of power competition. In fact, a significant performance loss due to the considerable power diversity was observed in the SS-8QAM-8QAM and SS-16QAM-4QAM schemes. When the Tx2 power differed significantly from the Tx1 power, the SNR deteriorated, as depicted in the detailed constellations.
Fig. 11. BER comparison of different superposed 64QAM schemes vs. different Tx2 powers when Tx1 power is -19.92 dBm.
Separate BERs for the two independent data streams are presented in Figs. 12(a) and (b). Because the two 8QAM constellations were superposed in an interleaved manner for the IS-8QAM-8QAM scheme, the BERs of Tx1 and Tx2 were similar, although the power ratio changed. However, different results were obtained for the SS-based schemes. The BER curves of the two data streams were different because the constellations were superposed separately. As the Tx2 power increased, the Tx2 BER decreased owing to the improvement in the SNR. The trend of the Tx1 BER was similar to that of the average BER shown in Fig. 11 because of the same reason.
Fig. 12. BER comparison of different superposed 64QAM schemes vs. different Tx2 powers when Tx1 power is −19.92 dBm. BERs of (a) Tx1 and (b) Tx2.
Figure 13 shows a comparison of the three superposed 64QAM constellation schemes vs. Vpp2. In the experiment, the DC bias currents of Tx1 and Tx2 were set to 50 mA, and Vpp1 was 0.3 V. As mentioned above, varying the value of Vpp not only changed the transmitted power, but also introduced nonlinearities. Consequently, the trend of the BER curves was similar to that shown in Fig. 10 because of the changes in the power ratio, except that the performance gap among different schemes increased. The performance advantage was derived from two aspects. The proposed scheme benefited from the low PAPR of the two 8QAM signals, which reduced the risk of nonlinear distortion. Concurrently, a much lower Vpp2 was necessitated in the IS-8QAM-8QAM scheme to reduce nonlinear distortions at the transmitter and prevent power competition in the receiver. The detailed constellations confirmed the result, where the SS-8QAM-8QAM scheme achieved the worst BER performance for the highest power ratio.
Fig. 13. BER comparison of different superposed 64QAM schemes vs. different Tx2 powers when Vpp1 is 0.3 V.
Figure 14 illustrates the specific BERs of the two independent data streams vs. Vpp2. Compared with the result shown in Fig. 12, the BER floor of Tx2, which was induced by highly nonlinear distortions, appeared in the two SS-based schemes, as shown in Fig. 14(b). Meanwhile, the Tx1 BERs deteriorated significantly because of nonlinearity. However, the proposed IS-8QAM-8QAM scheme maintained its excellent performance when the power ratio was approximately 1.
Fig. 14. BER comparison of different superposed 64QAM schemes vs. different Tx2 powers when Vpp1 is 0.3 V. BERs of (a) Tx1 and (b) Tx2.
Finally, the BER performances of different superposed 64QAM constellation schemes were compared when the optimal power ratio was guaranteed. In this case, the BER performance was unaffected by the overlap of the constellation points but was primarily determined by the SNR. In the experiment, the DC bias current was set to 50 mA. As shown in Fig. 15(a), Vpp1 is plotted on the horizontal axis, and the values of Vpp2 for the different schemes are different to ensure the optimal power ratio. Similarly, the horizontal axis in Fig. 15(b) is represented by Vpp2, where Vpp1 is determined by the optimal power ratio. The BER performance of all the schemes first improved and then deteriorated. For each scheme, the BER decreased because the SNR improved when Vpp1 or Vpp2 increased. However, the BER performance loss was caused by nonlinearity when Vpp1 or Vpp2 continued to increase. Furthermore, the experimental results show that the proposed IS-8QAM-8QAM scheme yielded the best performance owing to the lower nonlinearity and immunity to power competition. It not only achieved the lowest BER, but also provided the maximum dynamic ranges of Vpp1 and Vpp2. Considering the 7% pre-FEC BER threshold of 3.8 × 10−3, the dynamic ranges of Vpp1 and Vpp2 improved from 0.06 to 0.4 V and from 0.23 to 0.4 V, respectively, when compared with those of the SS-8QAM-8QAM scheme.
Fig. 15. BER comparison of different superposed 64QAM schemes when optimal power ratio was achieved. (a) BER vs. Vpp1 (b) BER vs. Vpp2.
5. Conclusion
Herein, we proposed a novel superposed 64QAM constellation scheme for 2 $\times$ 2 MIMO VLC systems that can achieve multiplexing gains, including in highly correlated VLC channels. In this scheme, two independent signals modulated with two geometrically shaped 8QAM constellations were transmitted from two LEDs and spatially multiplexed in the receiver to superpose a square-shaped 64QAM signal after free-space transmission. In contrast to the traditional superposed 64QAM constellation schemes, the two 8QAM constellations were superposed in an interleaved manner. Hence, the proposed scheme benefitted from two aspects. First, the PAPRs of the proposed geometrically shaped 8QAM constellations were much lower than those of the existing schemes, thereby affording improved robustness to system nonlinearities. Second, the same power required for the two signals simultaneously reduced nonlinear distortions and avoided power competition. Using the concept of interleaved superposition, superposed signals were detected based on the ML criterion by setting up a look-up table. A comprehensive experimental investigation was conducted to investigate the performance of the proposed superposed 64QAM constellation scheme by changing the transmitted power, DC bias currents, and driving Vpps. The experimental results confirmed that the proposed IS-8QAM-8QAM scheme achieved better BER performance than the traditional SS-based schemes, where the dynamic range of the driving Vpp1 and Vpp2 improved from 0.06 to 0.4 V and from 0.23 to 0.4 V under a 7% pre-FEC with a BER threshold of 3.8 $\times$ 10−3, respectively, when the optimal power ratio was assumed. Finally, it is worth noting that the proposed interleaved superposition manner can be extended to other modulation orders to achieve the balanced power allocation. Further work includes the study of the optimal interleaved superposition schemes for other modulation orders by combining the geometrical shaping technology.
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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