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Abstract
Multiple-input multiple-output (MIMO) visible-light communication (VLC) systems based on the concept of superposed constellation have attracted increasing attention because multiplexing gains can be achieved even in a highly correlated MIMO channel. In this paper, a novel superposed constellation scheme is proposed for 2×2 MIMO VLC systems, where a 2n-order quadrature amplitude modulation (QAM) signal is obtained by superposing 4QAM and processed 2n−2-order QAM signals. Based on the original 2n−2-order QAM signal, the processed signal is generated by adding an optimal offset, power normalization, and flipping according to the value of the 4QAM signal. Thus, the required power ratio between the two superposed signals is equal to 1, which not only avoids the power competition in the receiver, but also reduces the risk of the nonlinear distortion of the light-emitting diode at the transmitter. Moreover, benefitting from the flipped superposition method, two additional performance gains are provided. First, thorough Gray coding can be achieved. Second, the received power can be improved because the two transmitted signals are correlated. An algorithm for solving the optimal offset is proposed based on the target of the equal power ratio, and the expression of the received power is derived as well. Then, the performance of the proposed scheme is investigated using detailed simulations in an additive white Gaussian noise channel, where the superposed 64QAM constellation is assumed as an example. Further, we perform an experimental demonstration and examine the performance of the proposed system when a practical optical channel is considered, where nonideal impacts, such as nonlinearity and power competition, may occur. The experimental results confirm that the proposed scheme achieves a lower bit error rate (BER) and a larger dynamic range of driving peak-to-peak voltage compared with the existing superposed constellation schemes. Considering the 7% pre-forward error correction BER threshold of 3.8 × 10−3, the proposed superposed 64QAM constellation system can achieve a maximum transmission rate of 3 Gb/s.
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1. Introduction
The recent visual networking index published by Cisco Systems has predicted that mobile data traffic will account for 71% of Internet protocol traffic, and more than 80% of mobile data traffic will be consumed indoors [1]. The exponential growth of mobile data traffic poses considerable challenges to traditional radio-frequency (RF) systems. Visible-light communication (VLC), which integrates both lighting and communication services, is emerging as a solution to overcome the crowded radio spectrum for wireless communication systems. As a short-range wireless communication technology, VLC offers several advantages over traditional RF communications, such as a high data rate, free spectrum license, the ability to be used in RF-restricted areas, and the capability of providing secure wireless communications [2–4]. Therefore, VLC has become a research hotspot in both academia and industry.
One of the greatest challenges in high-speed VLC systems is the development of new technologies that can improve data rates under the limited modulated bandwidth of commercial light-emitting diodes (LEDs). Enabling technologies have been studied for high-speed VLC systems beyond gigabit per second, including adaptive bit loading orthogonal frequency-division multiplexing (OFDM), advanced modulation formats, software and hardware pre-equalization, post-equalization, and spatial multiplexing (SMP) multiple-input multiple-output (MIMO) [5–8]. Among these technologies, SMP MIMO is considered a particularly promising solution. As multiple LEDs are necessary to provide sufficient illumination, the MIMO technique can be implemented to realize parallel data transmission. However, the use of intensity modulation and direct detection techniques may create a correlated channel in VLC systems [9]. In particular, limited by the size and power consumption of the terminal, multiple photodiodes (PDs) need to be integrated together, and the close placement of the PDs causes a highly correlated channel. Thus, the bit error rate (BER) performance deteriorates dramatically as the receivers fail to separate the parallel data streams when the channel links between transmitters and receivers are similar to each other.
Therefore, several techniques have been proposed to reduce channel correlations. Link blockage is a straightforward way to decrease channel correlation by placing an opaque boundary to block a particular link from an LED to a PD [9]. This simple method restricts the receiver from moving around the room freely. Imaging MIMO can create an uncorrelated channel by producing an approximate image of the source array on a detector array using lenses [10]. However, this method is difficult to apply in practice because precise alignment is necessary to create an LED image on a detector. An angle diversity receiver is another way to reduce the channel correlation, where PDs can be oriented with different inclination angles to achieve high-rank MIMO channels [11]. However, the structure of the receiver becomes more complicated.
Recently, a novel technique called superposed constellation has attracted increasing attention, and it can be combined with SMP MIMO to achieve multiplexing gains even in a highly correlated channel. In [12], the principle of a superposed 64 quadrature amplitude modulation (64QAM) constellation was first proposed for 2×1 multiple-input single-output VLC systems, where various superposed signal structures were analyzed depending on the power ratio between two transmitters. Subsequently, the constellation superposition of the odd-order QAM, namely, a superposed 32QAM constellation scheme, was studied for the first time, where geometrical shaping was introduced to improve the performance [13]. However, signals were superposed in a separate manner in both the above schemes, and therefore required an imbalanced power allocation. Consequently, an inevitable signal-to-noise ratio (SNR) deterioration occurred owing to the power competition in the receiver and the risk of nonlinear distortion of the LEDs increased [14–16]. Instead of power allocation, the authors proposed designing the sub-constellations at each LED to increase the minimum Euclidean distance (MED) of the superposed constellation at the receiver in [17]. However, only the effect of MED on system performance was considered, the nonlinearity of the LED and power competition of the receiver were not referred. Besides, the imbalance of the signal power remained. Hence, Zou et al. proposed the use of two eight-pulse amplitude magnitude (8PAM) signals to superpose into a 64QAM signal with equal power allocation [18]. However, one-dimensional modulated 8PAM signals produced a high peak-to-average power ratio (PAPR), which induced the nonlinear distortion of the LEDs. Consequently, a high-complexity post-equalizer MIMO multi-branch hybrid neural network was proposed to compensate for the nonlinear distortion. Subsequently, two geometrically shaped 8QAM signals were proposed to superpose into a 64QAM signal in an interleaved manner, which not only satisfied the requirement of an equal power ratio, but also achieved a much lower PAPR of the transmitted signals [16]. However, the adjacent constellation points are more likely to overlap because of interleaved superposition. Consequently, the BER performance decreased dramatically when the power ratio was not equal to 1.
In this paper, a flipped superposed constellation scheme is proposed for 2×2 MIMO VLC systems, which is valid for a superposed 2n-order QAM constellation of any order with n greater than 2. In this scheme, we propose the use of a processed 2n−2-order QAM signal and a 4QAM signal at the transmitter to superpose into a 2n-order QAM signal at the receiver. Based on the original 2n−2-order QAM signal, a new 2n−2-order QAM signal is generated by adding an optimal complex offset, power normalization, and flipping according to the value of the 4QAM signal superposed with it. Consequently, the proposed scheme is equivalent to the flipped superposition of 2n−2-order QAM and 4QAM signals to form a 2n-order QAM signal. The advantages of the proposed scheme are as follows: First, the proposed flipped superposition takes advantage of both separate and interleaved superpositions. It maintains the equal power ratio requirement of the interleaved superposition to avoid power competition and reduce the nonlinear distortion concurrently. Moreover, it can be used over a wide range of power ratios because the 2n−2-order QAM constellations are located in four quadrants after superposed with 4QAM signal of four quadrants, which is the same as the separate superposition. Second, thorough Gray coding of the superposed QAM constellation is realized in the receiver because the 2n−2-order QAM signals are flipped to be superposed with the 4QAM signal. Compared with the existing schemes that can only achieve the Gray coding of transmitted constellations, an additional Gray coding gain is provided. Third, benefitting from the correlation of the transmitted signals owing to the flipped superposition, the received power increases, which further improves the BER performance. Based on the target equal power ratio of the two superposed signals, an algorithm for solving the optimal offset is proposed, and the expression of the received power is also derived. Then, a comprehensive simulation is conducted to investigate the performance of the proposed scheme in an additive white Gaussian noise (AWGN) channel by changing the SNR and power coefficient ratios. The simulation results confirm the performance gains introduced by the Gray coding and the improved received power. Finally, the proposed scheme is evaluated by setting up a 2×2 MIMO VLC experimental demonstration system, where nonideal impacts, such as nonlinearity and power competition, are considered. The experimental results confirm that the proposed scheme not only obtains a much lower BER, but also realizes a larger dynamic range of the driving peak-to-peak voltages (Vpps) compared with the existing schemes. Considering the 7% pre-forward error correction (pre-FEC) BER threshold of 3.8 × 10−3, the proposed superposed 64QAM constellation system achieves a maximum transmission rate of 3 Gb/s.
The remainder of this paper is organized as follows. In Section 2, we present the principle of the proposed superposed constellation scheme and an algorithm to solve the optimal offset. In Section 3, the performance of the proposed scheme is investigated using a theoretical simulation. The experimental setup and results are discussed in Section 4. Finally, we conclude the paper in Section 5.
2. Principle
2.1 Principle of proposed superposed constellation scheme
The principle of the proposed superposed QAM constellation scheme is illustrated in Fig. 1. As shown, two independent data streams are first modulated using 4QAM and 2n−2-order QAM with normalized power. Then, an optimal complex offset is added to the 2n−2-order QAM signal, where the real and imaginary parts are assumed to be equal. Thus, the required power ratio between the two superposed signals may be equal to 1 when the optimal superposed 2n-order QAM constellation is obtained. As the additional offset increases the power of the 2n−2-order QAM signal, power normalization is performed again. Subsequently, the 2n−2-order QAM signal is flipped along the X- or Y-axis, depending on the value of the corresponding 4QAM signal superposed with it. As the 2n−2-order QAM constellation is asymmetrical after the offset is added, the 2n−2-order QAM signal must be flipped and superposed with a 4QAM signal to achieve a symmetric target constellation at the receiver. The detailed flipped criterion is defined as follows:
The superposed 64QAM constellation scheme is depicted as an example in Fig. 1. Because of the superiority in terms of the MED, the same square-shaped 64QAM constellation as in [12] and [16] was selected as the target constellation in the receiver. As shown in Fig. 1(e), the processing of the 16QAM signals results in a geometrically shaped 64QAM constellation, where the purple points represent the 16QAM signals superposed with the 4QAM signals in the first quadrant. Points A1, A2, A3, and A4 in Fig. 1(e), respectively, represent the positions of the original point A1 in Fig. 1(b) that flipped according to different values of the 4QAM signals. After free-space transmission, square-shaped 64QAM signals are formed by the superposition of the geometrically shaped 64QAM signal and the corresponding 4QAM signal, which is equivalent to the 16QAM signal that has undergone flipped superposition with the 4QAM signals. The 16QAM signal after superposition is located in different quadrants, determined by the quadrant of the 4QAM signal superposed with it. In Fig. 1(f), the purple points denote the resulting points superposed by the processed 16QAM and 4QAM signals in the first quadrant. Points A1, A2, A3, and A4 represent the results of the original point A1 in Fig. 1(b) superposed with a different 4QAM signal. As evident, because of the flipped superposition, the adjacent points of the superposed constellation near the coordinate axes correspond to the same 16QAM signal and different 4QAM signals. The adjacent points of the superposed constellation in the same quadrant correspond to the same 4QAM signal and different 16QAM signals. Consequently, thorough Gray coding of the superposed 64QAM constellation is achieved, provided that the original 4QAM and 16QAM constellations are both Gray-coded. Moreover, different offsets lead to different shapes of the superposed 64QAM constellations. Thus, we define an optimal offset by which a superposed constellation with uniformly distributed constellation points can be obtained when two signals are superposed with equal power. Consequently, the key problem of the proposed scheme is to solve the optimal offset.
2.2 Algorithm for solving the optimal offset
In this section, an algorithm for the optimal offset is derived. Without loss of generality, we consider the superposed 64QAM constellation scheme as an example. As discussed above, the optimal offset leads to a superposed constellation with uniformly distributed constellation points at the receiver. Therefore, once the optimal offset is reached, the superposed constellation should satisfy the following relationship:
where points A1 and A2 are shown in Fig. 1(f). d2 represents the MED of the 16QAM constellation in Fig. 1(d), which is also the MED of the superposed 64QAM constellation.To solve Eq. (2), the values of points A1 and A2 are required, which can be deduced from the processing of the 16QAM signal at the transmitter, as shown in Figs. 1(b)–(e).
In Step 1, the binary data stream is modulated using 16QAM. For any point A1 of the 16QAM constellation, its value can be represented by a complex number as
where i is the imaginary unit, and x1 and y1 represent the real and imaginary parts of point A1, respectively. Note that all the values are obtained when the constellation power is normalized. The MED of the constellation is denoted as d1.In Step 2, assuming that both the real and imaginary parts of the offset are equal to a, the value of point A1 after adding the offset becomes
In Step 3, the power of the 16QAM signals is normalized again because the addition of the offset increases the power. After power normalization, the MED is reduced to d2, which is given by
Thus, the value of the point A1 is denoted by
In Step 4, the 16QAM signals are flipped based on the criterion in Eq. (1). Point A1, originally in the second quadrant, may remain in the second quadrant, or move to the first, third, and fourth quadrants marked as points A2, A3, and A4, depending on the values of the 4QAM signals. The values of points A1, A2, A3, and A4 can be expressed as follows:
In the receiver, the 64QAM signal can be regarded as a linear superposition of the two transmitted signals, and is given by
By substituting the values of points A1 and A2 into Eq. (2), the optimal offset can be solved as follows:
According to Eq. (10), the optimal offset of the superposed 64QAM constellation scheme was 0.4348.
Further, the power of the superposed 64QAM signal is derived as
Equation (11) confirms that the power of the received signals is higher than that of the traditional schemes in which the signals are transmitted independently. This is because the flipped superposition correlated with the two transmitted signals. Assuming that p1 and p2 are equal to 1 and the optimal offset is reached, the received power of the proposed scheme is approximately three times that of the traditional schemes.
3. Simulation results
In this section, we examine the performance of the proposed superposed constellation scheme through computer simulation, where the superposed 64QAM constellation scheme is used as an example. In the simulations, the superiority of the proposed scheme is verified via a comparison with the existing superposed 64QAM constellation schemes in [12] and [16]. Hereinafter, we refer to the proposed scheme as flipped superposition (FS), and the superposed 64QAM constellation schemes in [12] and [17] as separate superposition (SS) and interleaved superposition (IS), respectively. Thus, the proposed scheme is denoted as FS-16QAM-4QAM, and the two traditional schemes are denoted as IS-8QAM-8QAM and SS-16QAM-4QAM, respectively. Note that all the simulations were implemented in an AWGN channel. Consequently, nonideal impacts, such as the nonlinearity of the LED and the power competition of the PD, are not considered in the simulations.
In Fig. 2, the BERs of the different superposed 64QAM constellation schemes with optimal power coefficient ratios are presented. The optimal power coefficient ratio is defined as the power coefficient ratio when the points of the superposed constellation are distributed uniformly. The optimal power coefficient ratios for FS-16QAM-4QAM, IS-8QAM-8QAM, and SS-16QAM-4QAM were 1, 1, and 1.79, respectively. We maintain the same received power in all the schemes, which produces the same superposed 64QAM constellation. Figure 2 shows that the proposed scheme achieves the best BER performance, although the same superposed 64QAM constellation is reached. This is because only the proposed scheme takes advantage of the thorough Gray coding, which leads to a performance gain of approximately 0.5 dB.
Then, the BER performance is evaluated for different power coefficient ratios, as shown in Fig. 3. In the simulation, the power coefficient ratio is defined as the ratio of the power of the 4QAM signal to that of the 16QAM signal for the FS-16QAM-4QAM and SS-16QAM-4QAM schemes. It is the ratio of the power of one 8QAM signal to that of the other 8QAM signal for the IS-8QAM-8QAM scheme. Similar to the above simulation, the received power is also maintained the same in all the schemes, where the received SNR is set to 25 dB. As evident, the BER performance mainly depends on the power coefficient ratio when the received power is constant. The simulation results prove that the FS-16QAM-4QAM and IS-8QAM-8QAM schemes achieve the best BER performance when the power coefficient is equal to 1, whereas the optimal power coefficient ratio for the SS-16QAM-4QAM scheme is 1.79. The BER of the proposed scheme is slightly lower than that of the other two schemes because of the Gray coding gain when the optimal power coefficient ratio is obtained. Moreover, the power coefficient ratios of the FS-16QAM-4QAM and SS-16QAM-4QAM schemes have a similar operating range, which is much larger than that of the IS-8QAM-8QAM scheme. This result is confirmed by the detailed constellations, as the constellations of the FS-16QAM-4QAM and SS-16QAM-4QAM schemes are almost the same. When the power coefficient ratio is small, the MED is reduced because the constellation points near the coordinate axes become close. After the BER reaches the minimum value, it increases again as the power coefficient ratio increases. This is because the power of the 16QAM signal decreases as the total power is fixed, leading to a reduction in the MED. However, for the IS-8QAM-8QAM scheme, the constellation points tend to overlap in the same manner, regardless of whether the power coefficient ratio increases or decreases.
In Fig. 4, the BERs for the two data streams are depicted separately, which can further reveal the differences among the three schemes. Comparing Figs. 4(a) and (c), the BER curves of the 4QAM signals are similar, but those of the 16QAM signals are different. When the power coefficient ratio is small, the BER of the 16QAM signals for the FS-16QAM-4QAM scheme is much lower than that of the SS-16QAM-4QAM scheme. This result once again proves the advantage of Gray coding in the proposed scheme, where only one bit of the adjacent points near the coordinate axes is different owing to the different 4QAM signals. Therefore, the overlap of the constellation points near the X- and Y-axes would not cause errors in the 16QAM signals. As for the IS-8QAM-8QAM scheme, the two 8QAM signals are equivalent, and the two BER curves are almost the same as those of the IS scheme.
Fig. 4. BER performance versus different power coefficient ratios for two data streams: (a) FS-16QAM-4QAM, (b) IS-8QAM-8QAM, and (c) SS-16QAM-4QAM.
In Fig. 5(a), the BER performance versus different power coefficient ratios for the different schemes is compared when the noise power is maintained the same. The power coefficient ratio is increased by increasing the power of the 16QAM signals, where the power of the 4QAM signals is fixed at 1. Here, the power coefficient ratio is defined as the ratio of the power of the 4QAM signal to that of the 16QAM signal for the FS-16QAM-4QAM and SS-16QAM-4QAM schemes. In the IS-8QAM-8QAM scheme, the power of any 8QAM signal is fixed at 1 because the two 8QAM signals are equivalent. The BER curves versus the received SNRs are illustrated in Fig. 5(b). Consistent with the result in Fig. 4, the simulation results show that the BER decreases first and then increases again as the power coefficient ratio increases. This indicates that the BER performance is mainly determined by the power coefficient ratio, although the received SNR continues to increase. However, in contrast to the result in Fig. 4, the proposed scheme achieves a much lower BER than the other two schemes when the optimal power coefficient ratio is obtained. This can be deduced from the results in Fig. 5(b). As evident, the received SNR of the FS-16QAM-4QAM scheme is higher than that of the IS-8QAM-8QAM scheme, although the transmitted power and noise power are the same in both schemes. The result confirms that the received SNR can be improved because the two transmitted signals are correlated in the FS-16QAM-4QAM scheme. Consequently, the BER performance is improved as well. The BER performance of the SS-16QAM-4QAM scheme is even worse than that of the IS-8QAM-8QAM scheme, as the lower power of the 16QAM signals is set to satisfy the required power coefficient ratio under the constraint of the power of the 4QAM signals.
Fig. 5. BER performance when the power of the 4QAM signals is fixed: (a) BER versus different power coefficient ratios, (b) BER versus different power coefficient ratios.
Finally, the BER performance versus different power coefficient ratios is shown in Fig. 6, where the power of the 16QAM signals and noise power are fixed. Thus, the power coefficient ratio is changed by increasing the power of the 4QAM signals. In this simulation, the definition of the power coefficient ratio is the same as that in Fig. 3. The simulation results show that the BER curves of the FS-16QAM-4QAM and SS-16QAM-4QAM schemes are different from those in Fig. 5. Initially, the errors are caused by the overlap of constellation points near the coordinate axes because of the lower power of the 4QAM signals. As the power coefficient ratio increases, the BER decreases until the BER floor appears. As the power of the 16QAM signals is constant, a fixed BER is induced by the errors in the 16QAM signals. Therefore, the best BER performance is obtained when the power of the 4QAM signals is sufficient to make the BER of the 4QAM signals zero, rather than when the optimal power coefficient is achieved. Moreover, the value of the BER floor for the SS-16QAM-4QAM scheme is lower than that of the proposed scheme. This is because the MED of the 16QAM constellation is reduced after adding the offset and power normalization, which can also be deduced from Eq. (5). Nevertheless, the required power of the SS-16QAM-4QAM scheme is much higher to achieve the best BER performance. The BER curve of the IS-8QAM-8QAM scheme is similar to that shown in Fig. 5. This result further proves that the two 8QAM signals are equivalent in the IS scheme, and increasing the power of any 8QAM signal results in the overlap of the constellation points.
Fig. 6. BER performance versus different power coefficient ratios when the power of the 16QAM signals is fixed.
4. Experimental set-up and results
4.1 Experimental set-up
We construct a 2×2 MIMO VLC system based on the concept of the proposed flipped superposition, where the discrete Fourier transform spread orthogonal frequency-division multiplexing modulation (DFT-S-OFDM) is performed owing to its considerable ability to suppress the PAPR [19]. The block diagram and experimental setup are shown in Fig. 7. At the transmitter, two independent binary data streams are modulated separately, one of which is mapped to the 4QAM signals and the other to the 2n−2-order QAM signals. Then, the 2n−2-order QAM signals are further processed by adding an offset, power normalization, and constellation flip. The discrete Fourier transform (DFT) was performed on each modulated data stream to produce DFT spread signals in the frequency domain. Subsequently, the frequency-domain signals were imposed symmetrically conjugated on parallel subchannels. After up-sampling, the real-valued OFDM signals were obtained via inverse fast Fourier transform and cyclic prefix (CP) attachment. The above signal processing was performed using MATLAB, and the offline transmitted signals were generated.
Fig. 7. System block diagram and experimental set-up of the proposed superposed constellation scheme.
The offline generated signals were loaded into an arbitrary waveform generator (AWG: Agilent M9502). Considering that the frequency response of an LED is attenuated dramatically with increasing frequency, a self-designed T-bridge passive hardware equalizer (Eq) was connected to pre-emphasize the high-frequency components of the signals to expand the bandwidth to approximately 500 MHz. The equalized signals were then amplified by an electrical amplifier (EA: Mini-Circuits ZHL-6A-S+) and coupled with direct current (DC) through a DC bias (Mini-Circuits ZFBT-4R2GWFT+) to drive the blue LED (manufactured by Nanchang University), where the signals were transmitted in the form of optical power. The light from a single LED falls on multiple PDs because the LED light diffuses through free-space transmission. Thus, the received signals can be regarded as a superposition of the two transmitted signals. Between the transmitters and receivers, lenses were placed to focus more light on the PDs to improve the intensity of the received signals. In the receiver, we designed a printed circuit board (PCB) consisting of a 2×2 integrated PD array and back-end amplifying circuit, as shown in Fig. 7. To realize a small size and low power consumption, the PDs were integrated together and placed at a very close distance of approximately 5 mm, which produced a highly correlated MIMO channel. The PDs (Hamamatsu S10784) convert optical signals into electrical signals. Finally, the electrical signals were amplified by the EA and recorded using a high-speed digital oscilloscope (OSC: Agilent 9254A) for offline demodulation.
Offline demodulation is the inverse process of modulation at the transmitter. Frame synchronization was performed to detect the starting positions of the data streams. Then, the two received signals were combined based on the equal-gain combining (EGC) criterion. OFDM demodulation was performed by removing the CP and applying a fast Fourier transform. After channel estimation, the signal distortion induced by the channel was eliminated by channel equalization. The time-domain signals were regained through an inverse DFT. Finally, the binary data streams were recovered based on the concept of superposed constellation de-mapping [16].
4.2 Experimental results and discussions
In the experiment, we also assume the superposed 64QAM constellation scheme as an example to examine the performance of the proposed system without loss of generality. The system parameters were set as follows: The number of DFT points was 127. The number of subchannels of the OFDM modulation was 256. The CP length was one-eighth of the length of the OFDM symbol. The upsampling rate was 2. The distance between the two LEDs was 0.9 m, and the transmission distance was approximately 1.2 m.
According to the system model in Fig. 7, the received signals in the frequency domain for each subchannel can be written as
Since the channel is highly correlated in the receiver, the received signals are merged based on the EGC criterion to achieve additional diversity gain with low complexity [13]. After EGC and channel equalization, the superposed signals are denoted as
Then, a look-up table is set up based on the estimated power ratio and transmitted constellations in the time domain, which is expressed as
Finally, after converting the equalized signal into the time domain via an IDFT, the maximum likelihood criterion is used to achieve an optimal estimation, which is given by
Initially, the different superposed 64QAM constellation schemes are compared for different transmitted power coefficient ratios, as depicted in Fig. 8. In the experiment, the 4QAM signals were transmitted from LED1, and the 16QAM signals were transmitted from LED2 in the FS-16QAM-4QAM and SS-16QAM-4QAM schemes. In the IS-8QAM-8QAM scheme, the two 8QAM signals were sent from LED1 and LED2 separately because they are equivalent. The transmission rate of the AWG was set to 1.8 Gb/s; thus, the available bandwidth was approximately 450 MHz. Vpp2 was fixed at 300 mV and the transmitted power coefficient ratio was changed by adjusting the value of Vpp1. The simulation results showed that the BER decreases first and then increases for each curve. The best BER performance was achieved when Vpp1 was set to 220 mV for the FS-16QAM-4QAM and IS-8QAM-8QAM schemes. The detailed constellations indicate that the received power coefficient ratio is close to 1 because the constellation points are uniformly distributed in this case. This is because the two LEDs were not placed symmetrically for the receivers, which usually occurs in practice. Therefore, the required Vpp1 was lower than Vpp2 when the channel gain corresponding to LED1 was larger than that corresponding to LED2. It indicates that the best BER performance is obtained when the optimal power coefficient ratio is realized in the receiver. Hence, to maintain optimal BER performance in practical optical channels, the channel information is necessary to be fed back to the transmitter to adjust the transmitted power. Benefitting from the higher received power, the optimal BER of the FS-16QAM-4QAM scheme was lower than that of the IS-8QAM-8QAM scheme. For the SS-16QAM-4QAM scheme, the lowest BER was obtained when Vpp1 was equal to 340 mV. As the optimal power coefficient ratio was 1.79, the required Vpp1 value of the SS-16QAM-4QAM scheme was much higher. The optimal BER of the SS-16QAM-4QAM scheme was the highest compared with that of the other two schemes. Moreover, the BER performance of the FS-16QAM-4QAM and SS-16QAM-4QAM schemes decreased after it reached the optimum, which is different from the simulation result in Fig. 6. These two phenomena indicate that nonlinearity and power competition appeared in the experiment. As a higher Vpp1 was required in the SS-16QAM-4QAM scheme, nonlinear distortion was more serious, thus inducing the deterioration of the received SNR. Meanwhile, when the power of the two received signals was different, the lower-power signals experienced a further reduction in power owing to the power competition. Consequently, the received power of the signals sent by LED2 decreased, although the value of Vpp2 was maintained constant. The detailed constellations depicted in Fig. 8 confirm this result. Compared with the other two schemes, the performance of the SS-16QAM-4QAM scheme degraded more seriously, because the higher power requirement of the 4QAM signals led to more severe nonlinear distortion and power competition. Considering the 7% pre-FEC BER threshold of 3.8 × 10−3, only the proposed scheme can operate in a large dynamic range of Vpp1 from 200 mV to 290 mV.
Subsequently, the BERs were measured when the value of Vpp2 changed, and Vpp1 was maintained constant at 260 mV. In Fig. 9, the experimental results show that the BER performance is improved first and then reduced again, which is consistent with the simulation result in Fig. 5. As the power of the 4QAM signals was fixed, the required power of the 16QAM signals in the SS-16QAM-4QAM scheme was the lowest, and the BER performance was the worst. The FS-16QAM-4QAM and IS-8QAM-8QAM schemes both achieved the best BER performance when Vpp2 was 320 mV, where the received power of the two signals was almost the same. With an increase in Vpp2, the power competition further reduces the signal power of LED1. Therefore, the increase in Vpp2 increases the signal power of LED2 and decreases the signal power of LED1 concurrently, both of which cause the overlap of the constellation points, as shown in Fig. 9. Compared with the IS-8QAM-8QAM scheme, the proposed scheme obtained a better BER, as a higher received SNR was realized.
Further, the 4QAM and 16QAM signals are interchanged at the transmitter, where the 16QAM and 4QAM signals are sent from LED1 and LED2 separately for the FS-16QAM-4QAM and SS-16QAM-4QAM schemes. Moreover, the two 8QAM signals are interchanged. In the experiment, Vpp1 was set to 220 mV and Vpp2 was adjusted to change the power coefficient ratio. The experimental results in Fig. 10 show that the BER curves of the FS-16QAM-4QAM and IS-8QAM-8QAM schemes are similar to those in Fig. 8, except that the required Vpp1 is increased. The dynamic range of driving Vpp1 for the FS-16QAM-4QAM scheme was increased from 200 mV to 280 mV and from 290 mV to 400 mV. This is because the channel gain corresponding to the 4QAM signals was smaller than that of the 16QAM signals after interchanging the signals at the transmitter. Consequently, a higher power of the 4QAM signals was necessary to maintain the power coefficient ratio for the 16QAM signals at the receiver. However, the performance of the SS-16QAM-4QAM scheme was dramatically reduced. In addition to the inevitable power competition, this indicates that the requirement of a higher Vpp2 value introduces more severe nonlinearity.
In Fig. 11, the dynamic ranges of driving Vpp for different schemes are presented when the 7% pre-FEC BER threshold of 3.8 × 10−3 is considered. Figures 11(a), (b), and (c) show the results when 4QAM signals are sent from LED1 and 16QAM signals are sent from LED2. The results obtained when the two signals are interchanged at the transmitter are plotted in Figs. 11(d), (e), and (f). As evident, the proposed scheme not only exhibits the best BER performance, but also achieves the maximum dynamic range of driving Vpp in both cases. Owing to the flipped superposition method, the proposed scheme benefits from Gray coding and improved received power. Moreover, the requirement of an equal received power coefficient ratio reduces the performance loss owing to power competition. Comparing the results of Figs. 11(a) and (d), the operating range of Vpp in Fig. 11(d) is smaller. The asymmetric channel increases the required value of Vpp2, and consequently, the nonlinearity is more severe. Nevertheless, the proposed scheme is still considered more robust to different power coefficient ratios and channels compared with the other two schemes. The IS-8QAM-8QAM scheme also has the advantage of requiring an equal received power coefficient ratio. As shown in Figs. 11(b) and (e), similar results are achieved under the two channel conditions because the two transmitted 8QAM signals are equivalent and superposed in an interleaved manner. However, interleaved superposition limits the dynamic range of the driving Vpp. Compared with the above two schemes, the SS-16QAM-4QAM scheme is more vulnerable to performance loss owing to power competition because it requires a received power coefficient ratio of 1.79. In addition, the experimental results in Figs. 11(c) and (f) show that the SS-16QAM-4QAM scheme can only operate under the first channel condition, but fails to operate after the two signals are interchanged at the transmitter. The asymmetry of the first channel reduces the power requirement of the 4QAM signals, thus reducing the performance loss caused by the nonlinearity of the LED. However, the asymmetry of the second channel increases the power requirements of the 4QAM signals. Therefore, severe nonlinear distortion leads to the failure of the SS-16QAM-4QAM scheme.
Fig. 11. Contour of system BER performance for the different superposed 64QAM constellation schemes.
Finally, the BER performance versus data rate for the proposed scheme was evaluated under the constraint of transmitted power. In the experiment, the 4QAM and 16QAM signals were sent from LED1 and LED2, respectively. Vpp1 was set to 230 mV and Vpp2 was fixed at 320 mV, which ensured that the system was operated with equal received powers of the two signals. The experimental results in Fig. 12 show that the BER decreases first and then increases with an increase in data rate. As the transmitted power was maintained constant, the amplitude of the transmitted signal was high when the data rate was low. Consequently, nonlinear distortions of the LED were more likely to appear. The best BER performance was achieved when the data rate was 1.6 Gb/s. As the data rate continued to increase, the BER performance began to decline because a decrease in the signal amplitude led to SNR deterioration. When the data rate increased to 3.3 Gb/s, the available modulated bandwidth was 550 MHz, which exceeds the bandwidth of the hardware equalizer. Therefore, the BER increased dramatically. Considering the 7% pre-FEC BER threshold of 3.8 × 10−3, the proposed system can achieve a maximum transmission rate of 3 Gb/s.
5. Conclusion
In this paper, we proposed a flipped superposed constellation scheme for MIMO VLC systems. In this scheme, a 4QAM signal is superposed with a processed 2n−2-order QAM signal to form a 2n-order QAM signal, which is equivalent to the flipped superposition of a 4QAM signal with a 2n−2-order QAM signal. The proposed scheme can be applied to superposed 2n-order QAM constellations of any order with n greater than 2. In contrast to the traditional superposed constellation schemes, the proposed scheme benefitted from three aspects. First, thorough Gray coding of the superposed QAM constellation is performed to obtain the Gray coding gain. Second, the received power of the superposed QAM signals can be improved because the two transmitted signals are correlated. Third, the requirement of equal power for the two superposed signals can simultaneously reduce the nonlinear distortion and avoid power competition. Comprehensive theoretical simulations were performed to examine the performance of the proposed superposed 64QAM constellation scheme. The simulation results confirmed the advantages of the Gray coding and received power improvement. Further, the performance of the proposed system was experimentally investigated for two different channels by changing the driving Vpps. As the nonlinearity of the LED and the power competition of the PD are inevitable in the experiment, the proposed scheme exhibits superior performance. Experimental results showed that the proposed scheme not only achieves the best BER performance, but also maximizes the dynamic range of driving Vpp. This result indicates that the proposed scheme is more robust to different power coefficient ratios and channels. Considering the 7% pre-FEC BER threshold of 3.8 × 10−3, the proposed superposed 64QAM constellation scheme can achieve a maximum transmission rate of 3 Gb/s.
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.
References
1. “Cisco visual networking index: Forecast and trends, 2017–2022,” Cisco Tech. Rep. (2018).
2. A. Memedi and F. Dressler, “Vehicular Visible Light Communications: A Survey,” IEEE Commun. Surv. Tutorials 23(1), 161–181 (2021). [CrossRef]
3. N. Chi, Y. Zhou, Y. Wei, and F. Hu, “Visible Light Communication in 6G: Advances, Challenges, and Prospects,” IEEE Veh. Technol. Mag. 15(4), 93–102 (2020). [CrossRef]
4. L. Matheus, A. Vieira, L. F. M. Vieira, M. A. M. Vieira, and O. Gnawali, “Visible Light Communication: Concepts, Applications and Challenges,” IEEE Commun. Surv. Tutorials 21(4), 3204–3237 (2019). [CrossRef]
5. N. Chi, Y. Zhou, and J. Shi, “Enabling Technologies for High Speed Visible Light Communication (Invited paper),” in 2017 Optical Fiber Communications Conference & Exhibition (OFC), 16930111 (2017).
6. X. Guo, X. Li, and R. Huang, “Adaptive multiple-input multiple-output mode switching for indoor visible light communication system with orthogonal frequency division multiplexing modulation,” Chin. Opt. Lett. 15(11), 110604 (2017). [CrossRef]
7. X. Huang, S. Chen, Z. Wang, J. Shi, Y. Wang, J. Xiao, and N. Chi, “2.0-Gb/s Visible Light Link Based on Adaptive Bit Allocation OFDM of a Single Phosphorescent White LED,” IEEE Photonics J. 7(5), 7904008 (2015). [CrossRef]
8. H. G. Olanrewaju, J. Thompson, and W. O. Popoola, “Pairwise Coding for MIMO-OFDM Visible Light Communication,” IEEE Trans. Wireless Commun. 19(2), 1210–1220 (2020). [CrossRef]
9. T. Fath and H. Haas, “Performance comparison of MIMO techniques for optical wireless communications in indoor environments,” IEEE Trans. Commun. 61(2), 733–742 (2013). [CrossRef]
10. K. Werfli, P. Chvojka, Z. Ghassemlooy, N. B. Hassan, S. Zvanovec, and A. Burton, “Experimental Demonstration of High-Speed 4 × 4 Imaging Multi-CAP MIMO Visible Light Communications,” J. Lightwave Technol. 36(10), 1944–1951 (2018). [CrossRef]
11. A. Nuwanpriya, S.-W. Ho, and C. S. Chen, “Indoor MIMO Visible Light Communications: Novel Angle Diversity Receivers for Mobile Users,” IEEE J. Select. Areas Commun. 33(9), 1780–1792 (2015). [CrossRef]
12. L. Qiao, X. Lu, S. Liang, J. Zhang, and N. Chi, “Performance analysis of space multiplexing by superposed signal in multi-dimensional VLC system,” Opt. Express 26(16), 19762–19772 (2018). [CrossRef]
13. X. Guo and N. Chi, “Superposed 32QAM constellation design for 2 × 2 spatial multiplexing MIMO VLC systems,” J. Lightwave Technol. 38(7), 1702–1711 (2020). [CrossRef]
14. Y. Wang, N. Chi, Y. Wang, L. Tao, and J. Shi, “Network Architecture of a High-Speed Visible Light Communication Local Area Network,” IEEE Photonics Technol. Lett. 27(2), 197–200 (2015). [CrossRef]
15. M. Gao, C. Li, and Z. Xu, “Optimal transmission of VLC System in the presence of LED non-linearity and APD module saturation,” IEEE Photonics J. 10(5), 7907514 (2018). [CrossRef]
16. X. Guo, Y. Yuan, C. Pan, and J. Xiao, “Interleaved superposed-64QAM-constellation design for spatial multiplexing visible light communication systems,” Opt. Express 29(15), 23341–23356 (2021). [CrossRef]
17. M. Le-Tran and S. Kim, “Superposed constellation design for spatial multiplexing visible light communication systems,” Opt. Express 28(25), 38293–38303 (2020). [CrossRef]
18. P. Zou, Y. Zhao, F. Hu, and N. Chi, “Enhanced performance of MIMO multi-branch hybrid neural network in single receiver MIMO visible light communication system,” Opt. Express 28(19), 28017–28032 (2020). [CrossRef]
19. N. Chi and M. Shi, “Advanced modulation formats for underwater visible light communications (Invited),” Chin. Opt. Lett. 16(12), 120603 (2018). [CrossRef]
