# Maximization of Visible Light Communication Capacity Employing Quasi-Linear Preequalization with Peak Power Limitation

Authors: Yingjun Zhou; Jianyang Shi; Zhixin Wang; Junwen Zhang; Xingxing Huang; Nan Chi
Journal: Mathematical Problems in Engineering
 (2016)

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## Abstract

We propose quasi-linear preequalization to be used for high speed visible light communication (VLC) system. Compared with zero-forcing preequalization, this kind of preequalization method is more suitable for a real VLC experimental system with peak power limitation. We carry out simulations and experiments to test the performance of quasi-linear preequalization. With this equalizer, the 3 dB bandwidth of the system can be extended from 17 MHz to 450 MHz. We implement 2.32 Gbit/s phosphorescent white light-emitting diode (LED) VLC transmission over 1 m distance with quasi-linear equalizer, bit and power loading OFDM, differential amplification positive intrinsic negative diode (PIN) receivers, and maximum ratio combining algorithm. To our knowledge, this is the highest transmission data rate based on a phosphorescent white LED VLC system.


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## Body

## 1. Introduction

With the advantage of combining lighting and communication, VLC has become more and more attractive. Compared with other wireless communication technologies, VLC is preferred due to its low cost, high accuracy, high security, immunity to electromagnetic interference, and long life [1–4]. The key challenge in high speed VLC system based on commercial phosphorescent white LEDs is the limited bandwidth from 3 MHz to 20 MHz [5, 6]. Many approaches such as preequalization and high order modulation have been applied in VLC system for higher modulation bandwidth of LEDs and higher transmission data rate. Preequalization is utilized by attenuating low frequency components and enhancing high frequency components. Recent research results applying preequalization is summarized in Table 1. These results are all implemented using hardware preequalization. Compared with RGB LEDs, phosphorescent white LEDs are more promising because of its low cost and complexity.Table 1
Recent research results applying preequalization.
LED type Modulation format Data rate Distance Data source White OOK-NRZ 80 Mbit/s 10 cm ECOC 2008 [7] RGB red OOK 614 Mbit/s 40 cm ECOC 2012 [8] RGB red OOK-NRZ 477 Mbit/s 40 cm OFC 2013 [9] RGB blue OOK-NRZ 662 Mbit/s 15 cm ECOC 2014 [10] White OOK-NRZ 200 Mbit/s 110 cm COL 2014 [11] White OOK-NRZ 550 Mbit/s 60 cm OE 2014 [12] White OFDM 225 Mbit/s 66 cm OE 2013 [1] White DMT 1 Gbit/s 10 cm PTL 2015 [13] White 16QAM-OFDM 1.6 Gbit/s 1 m OE 2015 [14] White BPL OFDM 2 Gbit/s 1.5 m PJ 2015 [15]In this paper, we carry out simulations and implement a high speed VLC system based on a phosphorescent white LED utilizing quasi-linear software preequalization. Instead of hardware equalization circuits reported in most recent high speed experiments based on phosphorescent white LED, we employ software equalization to provide more accurate and complex preequalization. Zero-forcing preequalization will bring the most flat received spectrum theoretically; however it is not the most suitable software preequalization method in a practical VLC experimental system considering the constrained peak and total power. We select three kinds of linear preequalization lines to be the software equalizer. We test the system performance using the lines through simulation and experiment demonstration. Besides, we also apply maximum ratio combining (MRC) algorithm, differential amplification PIN receivers, and adaptive bit and power loading orthogonal frequency division multiplexing (OFDM) for better system performance. We successfully carry out the experimental demonstration of 2.32 Gbit/s VLC transmission utilizing a phosphorescent white LED over 1 m free space transmission distance with bit error rate (BER) lower than 3.8 × 10−3. To our knowledge, this is the highest transmission data rate based on a phosphorescent white LED VLC system.


## 2. Principle

Preequalization aims at attenuating low frequency components and amplifying high frequency components which can flatten the whole receiving spectrum for better system performance. Zero-forcing preequalization is the most traditional way. The principle of applying zero-forcing equalization in VLC system is shown in Figure1. A represents low frequency components and B represents high frequency components. Zero-forcing preequalization attenuates A region greatly and amplifies B region significantly to make the final receiving spectrum flat. Although zero-forcing preequalization can lead to the most flat received spectrum theoretically, it is not the most suitable software preequalization method in a practical VLC experimental system due to the large difference between low frequency components and high frequency components of the receiving signal. The difference may exceed the dynamic range of PIN receivers; thus PIN receivers can not detect low frequency components with higher signal to noise ratio (SNR) linearly [16]. The detected low frequency components are distorted which leads to worse receiving performance. Thus, we design quasi-linear preequalization to achieve relatively small difference between low and high components of the receiving signals which does not exceed the dynamic range of PIN receivers and improve the receiving performance of middle frequency components at the same time. Therefore, the whole receiving performance is improved significantly. This VLC system is a total power and peak power constrained system. Applying bit and power loading OFDM becomes a constraint problem of rate maximization (RM) [17].Figure 1
Zero-forcing preequalization.SNR of each subcarrier is estimated using BPSK-OFDM to implement adaptive bit and power loading in VLC system. SNR is computed with estimation of error vector magnitude (EVM) using [18] (1)EVM=1/N∑n=1NSn-S0,n21/N∑n=1NS0,n2,SNR≈1EVM2.S n represents the received nth normalized symbol and S0,n is the corresponding normalized constellation point. N is the number of constellation symbols. If bit error rate (Pb) is 3.8 × 10−3, this subcarrier’s allocated bit number can be computed using (2) [18]. L is the level number in each dimension of the desired M-ary QAM modulation system. The bit number b allocated for this subcarrier is calculated utilizing M. By setting appropriate value of Pb and decreasing SNR which can be lower than the measured SNR, b can be adjusted to an integer:(2)Pb=21-1/Llog2LQ3log2LL2-12SNRlog2M,Qx=∫x∞12πe-y2/2dy,b=log2M.The total data rate is calculated using (3). R is the total data rate of the system, B represents the bandwidth of the system, m is the subcarrier number, and bi is the allocated bit number for the ith subcarrier: (3)R=B∑i=1mbim.The frequency of a phosphorescent white LED is modeled using (4) [19]. ωb is the fitted coefficient and is set as 2π  × 15.5 × 106 rads/s: (4)Hbω=e-ω/ωb.The thermal noise variance of PIN receivers is computed using (5) [20]. kB represents Boltzmann’s constant, TkB represents the absolute temperature, G represents open loop voltage gain, δ represents the photo-detector’s fixed capacitance per unit area, A is the photo-detector area, E represents the channel noise factor of field-effect transistor, gm is the transconductance of field-effect transistor, I2 is noise bandwidth factor, and I3=0.868:(5)σthermal2=8πkBTkBGδAI2Ben2+16π2kBTkBEgmδ2A2I3Ben3.


## 3. Simulation and Results

We propose three kinds of quasi-linear software equalization lines shown in Figure2 including linear kind, concave kind, and convex kind. This system uses 512 subcarriers. Concave kind and convex kind both have oblique line part and linear line part. k is used to denote the slope of the oblique line part. k is also used to denote the slope of the linear kind.Figure 2
Quasi-linear software equalizer lines.To test the system performance employing different software preequalization lines, we carry out simulations. The simulation setup is shown in Figure3 and the main algorithm applied for this simulation system is shown in Algorithm 1. If the transmitting signals exceed PIN receivers’ peak power, gain of the signals after preequalization will be adjusted automatically to find the maximum total allocated bit numbers for all subcarriers. BPSK-OFDM is applied to calculate the allocated bit number for each subcarrier according to LED response model. In the simulation system, up sample number is 3, data number of each subcarrier is 200, bandwidth is 450 MHz, and ratio of cyclic prefix is 1/32.Algorithm 1:Preequalization with peak power limitation.
Step  1. Generate BPSK-OFDM signal S Step  2. Use th pre-equalization lines Step  3. Amplify signal with gain G Step  4. Multiply S×th×G with LED transfer function H(ω) Step  5. Consider time domian signal Stime=IFFT[G×th×S×H(ω)] Step  6. If Stime peak power exceeds PIN peak power Step  7.  Go to step 3 and change G Step  8. Else calculate SNR Step  9.  Calculate bit numbers for each subcarrierFigure 3
Simulation setup.We use linear kind with different slopek and different intercept b to get the maximum average bit numbers of the system. As shown in Figure 4, the lower right corner has higher bit numbers. That is to say, we should choose the combinations of b and k in the lower right corner for better receiving performance and b should not be too large compared with the value of k.Figure 4
Average bit numbers using differentk and b for linear kind equalization.Then, we simulate the system using two-staged oblique line equalizer to find the best combination ofk1 and k2 (k1 represents the slope of the first oblique line part and k2 represents the slope of the second oblique line part). According to the results shown in Figure 5, we can find that the maximum average bit numbers can be achieved when k1 approximately equals 0.1 and the values of k2 are relatively small compared with k1. So, the value of k2 is set as 0 to simplify the problem. Then we only need to test the performance using different slope of the first oblique line part. Therefore, we propose the convex kind equalizer. The first 3/4 part of subcarriers uses oblique line equalization and the latter 1/4 part of subcarriers uses constant line equalizer. For symmetry, we propose the concave kind equalizer.Figure 5
Average bit numbers using differentk1 and k2 for two-staged oblique line equalization.We selectk=0.01, 0.1, and 1 to test the performance of different equalization lines which is shown in Figure 6. As k increases, the performance of the concave kind becomes better and then worse. When k is small, the performance of the linear kind is better than the other two kinds. But as k increases, the performance of the convex kind approaches the linear kind. Using the convex kind equalization can achieve the maximum average bit numbers with appropriate k.Figure 6
Average bit numbers using linear kind, concave kind, and convex kind equalization.


## 4. Experimental Setup and Results

The block diagram with quasi-linear equalizer and experimental setup of VLC system are shown in Figures7 and 8, respectively. This system also employs differential amplification PIN receivers applying MRC algorithm and adaptive bit and power loading OFDM. Adaptive bit and power loading OFDM is implemented in this system. SNR of each subcarrier is measured using error vector magnitude (EVM) method [17] and BPSK (bipolar phase shift keying) symbols through the experimental system. The bit number allocated for each subcarrier is calculated according to SNR of each subcarrier. QAM mapping for each subcarrier is implemented according to the corresponding allocated bit number.Figure 7
Block diagram with quasi-linear equalizer.Figure 8
Experimental setup of VLC system.Quasi-linear equalization is implemented by a Matlab program. Then the signal is loaded into AWG (Tektronix AWG710). After being amplified by EA (Electrical Amplifier, 25 dB gain, 50 Ω input impedance, and 50 Ω output impedance), the signal is coupled with direct current by Bias Tee. Then, it is applied to a phosphorescent white LED (OSRAM, LCWCRDP.EC-KULQ-5L7N-1, luminous flux about 120 lm at 350 mA). The 3 dB bandwidth of this LED is about 17 MHz [13]. At the receiving end, two lenses are used for focusing light and two blue filters are used for filtering out the light’s slow responding component and increasing modulation bandwidth. Differential amplification PINs include PINs (HAMAMATSU S10784, 0.45 A/W sensitivity with −3 dB bandwidth of 300 MHz at 660 nm) and TIA (tansimpedance amplifier) modules. PINs achieve the function of detecting signals and TIA modules generate differential outputs. Besides, MRC algorithm is applied in this system for better receiving performance. The transmission distance is 1 m. OSC (digital real-time oscilloscope, Agilent 54855A) captures the signals. The sample rate of AWG is 1.35-GS/s and the sample rate of OSC is 2 GS/s with 450 MHz modulation bandwidth. Offline signal processing is then implemented utilizing the captured signals from OSC. The total data rate includes 3% cyclic prefix and 7% forward error correction overhead.Measured spectra (spectrum analyzer, HP8562A) are shown in Figure9. Figures 9(a), 9(b), 9(d), 9(f), and 9(h) show the transmitting spectrum before VLC system without preequalization, with zero-forcing preequalization, with linear preequalization, with convex preequalization, and with concave preequalization, respectively. Figures 9(c), 9(e), 9(g), and 9(i) show the receiving spectrum after VLC system with zero-forcing preequalization, with linear preequalization, with convex preequalization, and with concave preequalization, respectively. Vpp is 0.7 V and the driving current of the phosphorescent white LED is 94 mA. Quasi-linear software equalizer achieves attenuating low frequency components and amplifying the high frequency components and has more high gain area than using zero-forcing preequalization. Quai-linear preequalization achieves relatively small difference between low and high components of the receiving signals and improves the receiving performance of middle frequency components at the same time. Among the three kinds of quasi-linear equalizer, convex equalization has the largest high gain area.Figure 9
Measured electrical spectra before VLC system (a) without preequalization, (b) with zero-forcing preequalization, (d) with linear preequalization, (f) with convex preequalization, and (h) with concave preequalization and receiving electrical spectra after VLC system (c) with zero-forcing equalization, (e) with linear preequalization, (g) with convex preequalization, and (i) with concave preequalization.
(a) (b) (c) (d) (e) (f) (g) (h) (i)Figure10 shows the simulation data rate and experimental data rate using different kinds of quasi-linear equalizer. Simulation results are shown using colorful curves and experimental results are marked with scatter symbols. We select k=0.01, 0.1, and 1 to test the performance of different equalization lines. According to Figure 10, the simulation results and experimental results are matched. Zero-forcing equalization only achieves 0.5 Gb/s data rate. The convex kind implements the highest experimental data rate 2.32 Gb/s over 1 m distance when k=0.1 with BER lower than 3.8 × 10−3. To our knowledge, this is the highest transmission data rate based on a phosphorescent white LED VLC system. The results also verify that zero-forcing preequalization is not suitable for experimental VLC systems because of peak power limitation caused by PIN receivers and quasi-linear preequalization can improve system performance greatly. The corresponding M-ary QAM system constellations of the convex kind equalization with k=0.1 are also shown in Figure 10. There is a mapping between bit number and M-ary QAM, such that 1 bit stands for BPSK, two bits stand for QPSK, three bits stand for 8QAM, four bits stand for 16QAM, and so on. The total bit error rate of the system is 3.7 × 10−3 under the limitation of forward error correction.Figure 10
Comparison of experimental data rate using linear kind, concave kind, and convex kind equalization.The bit allocation using three kinds of preequalization is shown in Figure11. To achieve the maximum data rate of each equalization kind, k is set as 0.1 for the linear kind and convex kind and k is set as 0.01 for the concave kind. According to the results, convex kind has the maximum average bit numbers and the largest high gain area.Figure 11
Bit allocation for 512 subcarriers applying linear kind, concave kind, and convex kind equalization.


## 5. Conclusions

In this work, we propose quasi-linear preequalization for high speed visible light communication system. Compared with zero-forcing preequalization, this kind of preequalization method can improve system performance significantly because of the peak power limitation caused by the PIN receivers in VLC system. Adaptive bit and power loading OFDM, differential amplification receivers, and MRC algorithm are also applied in this system for better performance. We carry out both simulation and experimental demonstration to test and verify the performance of different kind of quasi-linear preequalization. According to the results, the performance of the concave kind is worse than the linear and the convex kind. Whenk increases, the performance of the convex kind approaches the linear kind. With this equalizer, the 3 dB bandwidth of the system can be extended from 17 MHz to 450 MHz. A total data rate of 2.32 Gb/s of VLC transmission over 1 m transmission distance based on a phosphorescent white LED with BER under 3.8 × 10−3 is experimentally achieved for the first time. To our knowledge, this is the highest transmission data rate based on a phosphorescent white LED VLC system.



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