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

We propose quasi-linear preequalization to be used for high speed visible light communication (VLC) system. Comparedwith zeroforcing 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 17MHz to 450MHz.We implement 2.32Gbit/s phosphorescent white lightemitting diode (LED) VLC transmission over 1m 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.


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][2][3][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.
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.

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 Figure 1.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].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)   represents the received th normalized symbol and  0, is the corresponding normalized constellation point. is the number of constellation symbols.If bit error rate (  ) is 3.8 × 10 −3 , this subcarrier's allocated bit number can be computed using (2) [18]. is the level number in each dimension of the desired -ary QAM modulation system.The bit number  allocated for this subcarrier is calculated utilizing .By setting appropriate value of   and decreasing SNR which can be lower than the measured SNR,  can be adjusted to an integer: The total data rate is calculated using (3). is the total data rate of the system,  represents the bandwidth of the system,  is the subcarrier number, and   is the allocated bit number for the th subcarrier: The frequency of a phosphorescent white LED is modeled using (4) [19].  is the fitted coefficient and is set as 2 × 15.5 × 10 6 rads/s: The thermal noise variance of PIN receivers is computed using (5) [20].  represents Boltzmann's constant,   represents the absolute temperature,  represents open loop voltage gain,  represents the photo-detector's fixed capacitance per unit area,  is the photo-detector area,  represents the channel noise factor of field-effect transistor,   is the transconductance of field-effect transistor,  2 is noise bandwidth factor, and  3 = 0.868:

Simulation and Results
We propose three kinds of quasi-linear software equalization lines shown in Figure 2 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. is used to denote the slope of the oblique line part.
is also used to denote the slope of the linear kind.To test the system performance employing different software preequalization lines, we carry out simulations.The simulation setup is shown in Figure 3 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 Calculate bit numbers for each subcarrier Algorithm 1: Preequalization with peak power limitation.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.We use linear kind with different slope  and different intercept  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  and  in the lower right corner for better receiving performance and  should not be too large compared with the value of .
Then, we simulate the system using two-staged oblique line equalizer to find the best combination of  1 and  2 ( 1 represents the slope of the first oblique line part and  2 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  1 approximately equals 0.1 and the values of  2 are relatively small compared with  1 .So, the value of  2 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.We select  = 0.01, 0.1, and 1 to test the performance of different equalization lines which is shown in Figure 6.As  increases, the performance of the concave kind becomes better and then worse.When  is small, the performance of the linear kind is better than the other two kinds.But as  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 .

Experimental Setup and Results
The block diagram with quasi-linear equalizer and experimental setup of VLC system are shown in Figures 7 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.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].total data rate includes 3% cyclic prefix and 7% forward error correction overhead.Measured spectra (spectrum analyzer, HP8562A) are shown in Figure 9. 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.Quailinear 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 10 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  = 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  = 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 -ary QAM system constellations of the convex kind equalization with  = 0.1 are also shown in Figure 10.There is a mapping between bit number and 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.
The bit allocation using three kinds of preequalization is shown in Figure 11.To achieve the maximum data rate of each equalization kind,  is set as 0.1 for the linear kind and convex kind and  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.

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.When  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.

Figure 4 :
Figure 4: Average bit numbers using different  and  for linear kind equalization.

Figure 5 :Figure 6 :
Figure 5: Average bit numbers using different  1 and  2 for twostaged oblique line equalization.

Figure 10 :Figure 11 :
Figure 10: Comparison of experimental data rate using linear kind, concave kind, and convex kind equalization.