## Abstract

In this paper, we have experimentally demonstrated the feasibility of a LMS-Volterra based joint MIMO equalizer in multiband super-Nyquist carrierless amplitude phase modulation visible light communication system. To obtain higher spectrum efficiency, overlapping between different sub-bands is introduced in this experiment. By using joint MIMO equalizer, an aggregate data rate of 1.26 Gb/s is successfully achieved in 1-m indoor free space transmission with the BER below the 7% FEC limit of 3.8 × 10^{−3}. To our best knowledge, this is the first time that our proposed joint MIMO equalizer is used to equalize multiband super-Nyquist data in VLC system.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Visible light communication (VLC) technology based on light emitting diodes (LEDs) is being paid more and more attention due to no electromagnetic interference, green environmental protection and suitable for various access scenes [1-2]. Compared with traditional light sources, LED has the advantages of high luminous efficiency, energy saving and environmental protection. In addition, LED can respond to the driving signal quickly, so it is widely used in the visible light communication system. VLC can provide simultaneous illumination and communication with a lower cost. In the receiving system, it is the photodiode that plays a major role. Photodiodes are devices that convert light signals into electrical signals. In VLC systems, photodiodes are required to have a sufficiently fast response speed to support high speed or broadband systems. With the increasing of mobile terminals, how to realize large capacity transmission and multi-user access under limited modulation bandwidth will be an urgent problem to solve in VLC systems.

As a single carrier modulation technology, carrierless amplitude phase (CAP) modulation has a small peak to average power ratio (PAPR), and is more resistant to the nonlinear effect. In addition, CAP modulation has higher spectral efficiency and spectral flexibility. Therefore, CAP modulation technology has great potential for application in high speed VLC systems. In [3], an aggregate data rate of 8 Gb/s is successfully achieved over 1-m indoor free space transmission with a hybrid post equalizer in a high-order CAP modulation based VLC system. In [4], a 10 Gb/s CAP16 modulation system is experimentally demonstrated in a fiber transmission system. However, these systems are single-band transmission and cannot be used in multiuser access system.

A possible way to enhance the spectrum efficiency (SE) is flexible multi-band transmitter based on a super-channel, being the essence of high speed VLC system. The transmitter has a suitable granularity between different sub-bands, which can realize multiuser distribution and lower the complexity of the system. A high speed WDM VLC system based on 3-bands CAP64 modulation using a single RGB LED is experimentally demonstrated in [5]. In [6], a novel WDM-CAP PON based on multi-band CAP is demonstrated and 55 sub-bands in the downstream is successfully transmitted over 40 km in single mode fiber(SMF) system. In [7], multiband CAP modulation has been proposed as a solution for beyond 100 Gb/s short range optical data links and 15 km optical link is realized with a total bitrate of 102 Gb/s using only a single wavelength and direct detection. Besides, a MIMO VLC system employing ASK modulation is proposed in [8] and a new detection mechanism aims at reducing interference from different colors to the detected one is also illustrated. Although these systems have realized multi-band signal transmission, the SE of the system can be further improved. Overlapping can be introduced between the multi-bands to further improve the system SE and realize multiuser access [9]. However, because of the existence of the overlapping, each sub-band will be affected by neighbor sub-bands and the performance of the system will be deteriorated with the increase of the degree of overlapping.

In this paper, a joint multiple input multiple output (MIMO) algorithm used for multiband super-Nyquist VLC systems is proposed. The algorithm can effectively mitigate the interference between adjacent sub-bands and the nonlinearity of the system. At the transmitter, the SE of the system is improved by adjusting the degree of overlapping between the adjacent sub-bands. At the receiver, the joint MIMO algorithm is used to equalize the data received from different sub-bands. The data rate of 1.26 Gb/s in 1-m indoor free space transmission is successfully achieved with the bit error rate (BER) less than 3.8 × 10^{−3}, which is under 7% FEC limit [10] when the two bands CAP16 are at 5% overlapping. To our best knowledge, this is the first time that our proposed joint MIMO algorithm is used to equalize multiband super-Nyquist data in VLC systems.

## 2. Principle

The structure of the proposed joint MIMO equalizer is shown in Fig. 1. In this paper, two independent bands are generated by the transmitter, which can be regard as multiple input signals [11]. Because of the overlapping between the sub-bands, the proposed joint MIMO algorithm can be used to equalize the two bands [12]. In the transmitter, if the carrier frequencies of the two sub-bands are *f _{1}* and

*f*, the

_{2}*S*is the input signal and

_{in}*B*is the main lobe width of the two independent sub-bands.

*S*is expressed using the following equation:

_{in}Where ${\phi}_{1}(t)$and ${\phi}_{2}(t)$ are the phase modulation components of the two sub-band signals respectively. Besides, *f _{2}-f_{1}<B* is satisfied to obtain higher SE and the degree of overlapping can be controlled by adjusting the two carrier frequency.

The joint MIMO algorithm we proposed is based on the LMS-Volterra and both the linear and nonlinear parts of the data can be equalized. For a practical nonlinear system, the higher order terms in the Volterra series is, the more accurate of the system's nonlinear estimation is. However, the computational complexity of the system will increase rapidly [13]. In order to balance the system performance and the computational complexity, the nonlinear terms higher than 2rd-order are not considered. Then the received two bands signal can be expressed as:

Here, N and L are the tap numbers of the linear and nonlinear equalizers, respectively. For each received band, the first term is the linear term and the second term is the linear interference term. The nonlinear term and nonlinear interference term are the third term and the forth term respectively. Since the algorithm is based on LMS-Volterra, training sequence are used to update the taps according to the error function of LMS. As a quasi-static transmission system, the updated weight coefficients can be used for a long time after training process is finished [14]. As depicted in Fig. 1, for one received signal and the neighboring sub-band, the cross-talk from the neighboring sub-band signal can be mitigated by the joint MIMO equalizer. In systems with a weak nonlinear effect, it is simple to do the equalization in the time domain because there is no need to do FFT and IFFT transformation on the data. The MIMO equalizer proposed and used in our system is based on time domain. The MIMO equalizer can greatly improve the performance of super Nyquist modulated signal at the cost of relatively higher computation complexity.

## 3. Experimental setup

Figure 2 shows the experimental setup of multiband VLC super-Nyquist system. At transmitter side, the original sequence is mapped into quadrature amplitude modulation (QAM) signals firstly. After upsampling, the complex signal passes through a pair of orthogonal shaping filter. The shaping filter used in this system is square-root raised-cosine function. To obtain a high SE, the roll-off coefficient of the square-root raised-cosine function for CAP modulation is set as 0.01 [3]. After shaping filters, the signal is divided into real part and imaginary part. Compared to single-band CAP, multi-band CAP offers the flexibility of multi-user allocation. Two bands are generated and transmitted in this system. To obtain higher SE than the multiband CAP systems introduced in [5–7], overlapping is introduced in our experiment. The central frequency difference of the two sub-band is less than the main lobe width of one sub-band.

In this paper, Tektronix arbitrary waveform generator (AWG) 710 is used to generate the two bands CAP16 signal and the signal voltage peak-to-peak value (Vpp) can be adjusted by the AWG. The T-based hardware pre-equalizer [15] is used to equalize the data. After that, electrical amplifier (EA) is used to amplify the signal. The amplified signal and direct current (DC) bias voltage are combined by a bias tee. Then, the signal is loaded into the red LED. In this paper, a commercial RGBA LED (LZ4-00MA00) is utilized as the transmitter. The emission wavelength range is from 618 to 630nm. The frequency characteristics of the electro-optical-electro channel for LED chips are measured and shown in [2]. Obviously severe frequency fading exists at high frequency part therefore appropriate equalization scheme at frequency domain is necessary. In front of the PIN, a lens (15-mm focus length, 75-mm diameter) is used to focus a high proportion of light onto the PIN photosensitive surface. The experiment was carried out in the free space in the room and only red LED was used in the experiment. In indoor environment, ambient light has little effect on system performance, so it is not necessary to filter out ambient light with filters. However for a blue phosphor LED, an optical filter is required to suppress the ambient light and to achieve higher bandwidth. The transmission distance is set at 1m.

At receiver side, a commercial differential outputs PIN photodiode is used to realize photo-electric signal conversion. A commercial PIN photodiode (Hamamatsu 10784) is used as the receiver. The responsivity of PIN at red wavelength is around 0.45 A/W. EAs are employed to amplify the differential output signals and the signals are recorded by two different channels of a digital storage oscilloscope (OSC) for further offline demodulation and signal processing. In [16], a 6 sub-band VLC system is realized. In [17], a maximum of 20 sub-bands CAP system is studied. The −3dB modulation bandwidth of commercial LED ranges from 3MHz to 20MHz, but in our group previous work, constant-resistance symmetrical bridged-T amplitude equalizer is proposed to extend LEDs’ −3dB modulation bandwidth [15]. By using the hardware pre-equalization technique, the modulation bandwidth of LED increases from 15MHz to 315MHz and is sufficient to support modulation and transmission of multiband signals. It should be noted that our PIN receiver bandwidth is about 500MHz, which can totally support the 315MHz multi-band signal detection. The LED frequency channel response is a kind of exponential fading. The system distortion can be compensated by two ways. Firstly the hardware pre-equalization is applied in the transmitter to boost the transmitter bandwidth from 15MHz to 315MHz. Secondly, the channel deterioration can be eliminated by our proposed joint MIMO equalizer. By using both pre- and post-equalization, the super-Nyquist multi-band CAP signal can be successfully transmitted and detected with the measured BER below HD-FEC threshold. In offline signal processing, a pair of matched filters are used to separate the in-phase and quadrature components of the signal. After down-sampling, joint MIMO equalizer is employed to equalize the two bands. Cascaded multi-modulus algorithm (CMMA) [18] is used to realize post-equalization. After de-mapping, the bit error rate (BER) of the system can be calculated.

## 4. Experimental results and discussion

Overlapping is introduced between the two-bands to further improve the system SE in this system and the measured electrical spectra of received signal are presented in Fig. 3. When the baud rate of is set as 315MBaud and overlapping is not introduced, the measured electrical spectra of received signal is shown in Fig. 3(a). From Fig. 3(b) and 3(c), when the baud rate is 315MBaud, with the increase of the degree of aliasing, the transmission bandwidth of the system is gradually reduced. From Fig. 3(d) to 3(f), it can be clearly seen that when the overlapping is set as 6%, with the increase of the baud rate of the system, the transmission bandwidth of the system is gradually increasing. Figure 3(f) shows that, for two-band CAP16 with 6% overlapping, there is a peak between the joint of the two sub-bands. Compared Fig. 3(f) with Fig. 3(a), it can be concluded that 11% bandwidth is saved in this experiment.

In this experiment, in order to illustrate the convergence of the proposed MIMO equalizer, the error value vs. different iteration number is shown in Fig. 4. It can be clearly seen that whether it is for band 1 or band 2, the required iteration number of joint MIMO equalizer until desired convergence is about 6000, so 6000 symbols were used to update the weight coefficients according to the Least Mean Square (LMS) error function.

To render the LED working at the optimal condition, the influence of different bias voltages and input signal peak-to-peak values (Vpp) are investigated in this paper. BER of the system with different input signal Vpp and bias currents is measured and shown in Fig. 5. With the change of system current and signal Vpp, the performance of subband1 remains stable and the system BER is mainly decided by subband2. Therefore, only BER performance of subband2 is investigated in Fig. 5. Here, system baud rate is fixed at 300MBaud. When Vpp is fixed at 0.6V, the effect of current from 70mA to 110mA on system BER performance is studied firstly. From Fig. 5(a), it can be clearly seen that under this working condition, the joint MIMO algorithm we proposed can get a lower BER than CMMA algorithm and BER is below the threshold. When system current is fixed at 90mA, the effect of signal from 0.4V to 0.8V on system BER performance is shown in Fig. 5(b). It is obvious that when the system current is 90mA and signal Vpp is 0.6V, the BER is the lowest. It can be concluded that the optimal working point of this system is at 90mA current and 0.6 V input signal Vpp. When the system works at the optimal working point (90mA, 0.6Vpp), the illuminance is 563 lux and luminous flux is 24 lm. In addition, from the constellation diagram shown in Fig. 5, we can see that when the system works at the optimal condition, the constellation of subband2 after using joint MIMO algorithm is clearer than that of CMMA algorithm. It also proves that the proposed joint MIMO equalizer can improve the performance of the system. When the system is working at the optimal condition, the measured BER performance versus the system baud rate of the two-band at different sub-bands overlap is shown in Fig. 6.

From Fig. 6, we can see that with the increase of the overlapping degree, the performance of the proposed joint MIMO algorithm become worse. When the degree of overlapping is increasing, the sub-band is more affected by the neighbor sub-band. Thus, the equalization ability of joint MIMO algorithm is limited. When two bands CAP16 are at 5% overlapping, we can see from Fig. 6 that, in 330MB, within 330MBaud, the BER performance of the subband2 is almost stable. But when the two bands CAP16 at 5% overlapping, the maximum transmission baud rate of the system is 315Mbaud. With the two bands CAP16 at 6% overlapping, the maximum transmission baud rate of the system is 300Mbaud. The data rate of 1.26 Gb/s over 1m transmission for 11% bandwidth saving is successfully achieved with the bit error rate (BER) less than 3.8 × 10^{−3} when the two bands CAP16 are at 5% overlapping.

In order to make a clear comparison of the joint MIMO algorithm and CMMA algorithm, the measured system Q factor versus overlap of the two-band CAP16 system is presented in Fig. 7. From Fig. 7, we can see that with the increase of the overlapping degree, the Q factor of the two algorithms is decreasing, but we can also see that the Q factor of the joint MIMO algorithm is larger than that of the CMMA algorithm. Especially when the aliasing is 6%, joint MIMO equalizer can outperform the CMMA algorithm by Q factor of 1.16dB on subband1 and 1.68dB on subband2 respectively. An enhanced performance of the system is realized by the MIMO equalizer.

## 5. Conclusion

In this paper, for the first time, we experimentally demonstrate the feasibility of a LMS-Volterra based joint MIMO equalizer in multiband VLC super-channel system. The proposed joint MIMO equalizer is used to equalize the sub-band signal when overlap is introduced in two-band CAP16 system. The joint MIMO equalizer consists of a linear term, a linear interference term, a nonlinear term and a nonlinear interference term. The optimal bias voltages and input signal Vpp is investigated to find the optimal working condition. When the system is working at the optimal condition, the joint MIMO equalizer and CMMA algorithm are compared by calculating BER. By the joint MIMO equalizer, an aggregate data rate of 1.26 Gb/s is successfully achieved in 1-m indoor free space transmission with the BER below the 7% FEC limit of 3.8 × 10^{−3}.

## Funding

National Natural Science Foundation of China (NSFC) (61571133); National Key Research and Development Program of China (2017YFB0403603).

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