Hybrid time-frequency domain equalization for LED nonlinearity mitigation in OFDM-based VLC systems Jianfeng Li, Zhitong Huang, Xiaoshuang Liu, and Yuefeng Ji* State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China * [email protected]
Abstract: A novel hybrid time-frequency domain equalization scheme is proposed and experimentally demonstrated to mitigate the white light emitting diode (LED) nonlinearity in visible light communication (VLC) systems based on orthogonal frequency division multiplexing (OFDM). We handle the linear and nonlinear distortion separately in a nonlinear OFDM system. The linear part is equalized in frequency domain and the nonlinear part is compensated by an adaptive nonlinear time domain equalizer (NTDE). The experimental results show that with only a small number of parameters the nonlinear equalizer can efficiently mitigate the LED nonlinearity. With the N-TDE the modulation index (MI) and BER performance can be significantly enhanced. ©2015 Optical Society of America OCIS codes: (230.3670) Light-emitting diodes; (060.4080) Modulation; (060.4510) Optical communications.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
IEEE 802.15.7 Working group for WPAN, “Short-range wireless optical communication using visual light,” (2011), http://www.ieee802.org/15/. L. Hanzo, H. Haas, S. Imre, D. O’Brien, M. Rupp, and L. Gyongyosi, “Wireless myths, realities, and futures: from 3G/4G to optical and quantum wireless,” Proc. IEEE 100(13), 1853–1888 (2012). C. G. Gavrincea, J. Baranda, and P. Henarejos, “Rapid prototyping of standard-compliant visible light communications system,” IEEE Commun. Mag. 52(7), 80–87 (2014). Z. T. Huang and Y. F. Ji, “Design and demonstration of room division multiplexing-based hybrid VLC network,” Chin. Opt. Lett. 11(6), 060603 (2013). A. M. Khalid, G. Cossu, R. Corsini, P. Choudhury, and E. Ciaramella, “1-Gb/s transmission over a phosphorescent white LED by using rate-adaptive discrete multitone modulation,” IEEE Photon. J. 4(5), 1465– 1473 (2012). G. Cossu, A. M. Khalid, P. Choudhury, R. Corsini, and E. Ciaramella, “3.4 Gbit/s visible optical wireless transmission based on RGB LED,” Opt. Express 20(26), B501–B506 (2012). F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, Z. Y. Chen, H. T. Huang, and S. Chi, “Performance comparison of OFDM signal and CAP signal over high capacity RGB-LED-based WDM visible light communication,” IEEE Photon. J. 5(4), 7901507 (2013). D. Tsonev, H. Chun, S. Rajbhandari, J. D. Mckendry, S. Videv, E. Gu, M. Haji, S. Watson, A. E. Kelly, G. Faulkner, M. D. Dawson, H. Haas, and D. O’Brien, “A 3-Gb/s single-LED OFDM-based wireless VLC wink using a gallium nitride μLED,” IEEE Photon. Technol. Lett. 26(7), 637–640 (2014). I. Neokosmidis, T. Kamalakis, J. W. Walewski, B. Inan, and T. Sphicopoulos, “Impact of nonlinear LED transfer function on discrete multitone modulation: analytical approach,” J. Lightwave Technol. 27(22), 4970–4978 (2009). B. Inan, S. C. Jeffrey Lee, S. Randel, I. Neokosmidis, A. M. Koonen, and J. W. Walewski, “Impact of LED nonlinearity on discrete multitone modulation,” J. Opt. Commun. Netw. 1(5), 439–451 (2009). H. Elgala, R. Mesleh, and H. Haas, “Non-linearity effects and predistortion in optical OFDM wireless transmission using LEDs,” Int. J. Ultra Wideband Commun. Syst. 1(2), 143–150 (2009). R. Mesleh, H. Elgala, and H. Haas, “LED nonlinearity mitigation techniques in optical wireless OFDM communication systems,” J. Opt. Commun. Netw. 4(11), 865–875 (2012). G. Stepniak, J. Siuzdak, and P. Zwierko, “Compensation of a VLC phosphorescent white LED nonlinearity by means of volterra DFE,” IEEE Photon. Technol. Lett. 25(16), 1597–1600 (2013). H. Elgala, R. Mesleh, and H. Haas, “An LED model for intensity-modulated optical communication systems,” IEEE Photon. Technol. Lett. 22(11), 835–837 (2010).
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Received 12 Dec 2014; revised 3 Jan 2015; accepted 4 Jan 2015; published 9 Jan 2015 12 Jan 2015 | Vol. 23, No. 1 | DOI:10.1364/OE.23.000611 | OPTICS EXPRESS 611
15. H. Q. Zhao and J. S. Zhang, “A novel adaptive nonlinear filter-based pipelined feed-forward second-order Volterra architecture,” IEEE Trans. Signal Process. 57(1), 237–246 (2009). 16. A. Zhu, P. J. Draxler, J. J. Yan, T. J. Brazil, D. F. Kimball, and P. M. Asbeck, “Open-loop digital predistorter for RF power amplifiers using dynamic deviation reduction-based Volterra series,” IEEE Trans. Microw. Theory Tech. 56(7), 1524–1534 (2008). 17. R. A. Shafik, S. Rahman, and R. Islam, “On the extended relationships among EVM, BER and SNR as performance metrics,” in Proceedings of International Conference on Electrical and Computer Engineering. (IEEE, 2006), pp. 408–411. 18. L. N. Peng, S. Haese, and M. Helard, “Frequency domain LED compensation for nonlinearity mitigation in DMT systems,” IEEE Photon. Technol. Lett. 25(20), 2022–2025 (2013).
1. Introduction Visible light communication (VLC) based on light emitting diode (LED) can provide licensefree bandwidth, high signal-to-noise rate, low-cost front-ends and high modulation power. These properties facilitate the potentiality of VLC to become an effective complement to radio frequency (RF) signal transmission [1–4]. Recently, there has been increasing interest in utilizing multi-carrier modulation for VLC systems such as discrete multi-tone (DMT) and orthogonal frequency division multiplexing (OFDM) modulation [5–8]. However, the influence of LED nonlinearity is not taken into account in these reports. The LED nonlinearity is a major challenge for the OFDM-based VLC system due to its sensitivity to the resulting distortion [9, 10]. The output optical power of LED is nonlinear with the driving current, therefore, the biasing current should be carefully selected to force signal magnitude in the maximum linear interval. Elgala et al. employed a time domain pre-distortion technique to compensate the nonlinear distortion of OFDM symbols [11]. However, the LED transfer function should be known as a priori information. In [12], the OFDM symbols in the time domain were divided into multiple parts to drive multiple LEDs respectively. Although the nonlinearity is mitigated by the multiple transmitters, multiple LEDs will increase the system complexity. In [13], decision feedback equalizer (DFE) with nonlinear Volterra feed-forward was introduced to mitigate the LED nonlinearity. However, the number of the Volterra coefficients increases geometrically with the delays and orders increasing, which is prohibitive for most practical applications. Therefore, an efficient and low complex compensation scheme is quite important to mitigate the LED nonlinearity for the OFDM-based VLC system. In this paper, a hybrid timefrequency domain equalization scheme is proposed and experimentally demonstrated to decrease the LED nonlinearity. We use a commercially available white-LED with a 3dB bandwidth of 20 MHz. The linear distortion is equalized in frequency domain and the nonlinear distortion is mitigated by an adaptive nonlinear time domain equalizer (N-TDE) whose optimum coefficients are found via the least mean squares (LMS) algorithm. The experimental results show that the N-TDE only with a very small number of parameters can efficiently eliminate the effects of the LED nonlinearity. 2. Modulation scheme and LED nonlinearity In a nonlinear OFDM system, distortions can be divided into two types: linear distortions and nonlinear distortions. Linear distortions produced by channel fading can be equalized easily in the frequency domain. However, nonlinear distortions which cause interferences between subcarriers are very difficult to be compensated in frequency domain. In the scheme we proposed, the linear distortion is compensated by the frequency domain equalization (FDE) and the nonlinear distortion is equalized by the N-TDE. Two OFDM schemes (fixed-rate and bit-power loading) have been utilized for maximizing the capabilities for VLC systems [8]. Both of the approaches are tested with the N-TDE in our experiments. The block diagram of the OFDM-based VLC system with the N-TDE is presented in Fig. 1. After the operation of the quadrature amplitude modulation (QAM), the pre-frequency domain equalization (preFDE) or the adaptive power loading is operated. Then, Hermitian symmetry of complex signals is used before inverse fast Fourier transform (IFFT) to produce a real time domain output signal. The cyclic prefix (CP) is inserted to mitigate inter-symbol interference. At the receiver, after synchronization, three equalization approaches are compared (without TDE, #230559 - $15.00 USD © 2015 OSA
Received 12 Dec 2014; revised 3 Jan 2015; accepted 4 Jan 2015; published 9 Jan 2015 12 Jan 2015 | Vol. 23, No. 1 | DOI:10.1364/OE.23.000611 | OPTICS EXPRESS 612
linear TDE and N-TDE). In our experiments, the LED frequency response is feedback to the transmitter, which is used to equalize the linear distortion in frequency domain. The linear TDE (L-TDE) is just used to demonstrate that linear distortions have already been indeed compensated in frequency domain. The optimum coefficients of the L-TDE and N-TDE are found by the LMS algorithm.
Fig. 1. The schematic of nonlinear compensation for OFDM systems (fixed-rate or adaptive bit-power loading). PA: power amplifier; Bias-T: bias tee; APD: avalanche photo diode.
In VLC systems, the nonlinearity mainly origins from LEDs. Thermal aspects of LEDs leading to a drop in the electrical-to-optical (E/O) conversion efficiency (light output of the LED decreases and slowly approaches a steady-state value; LED self heating characteristic) is the major source of the LED nonlinearity [14]. In Fig. 2(a), the E/O characteristic of a commercially available white-LED (Cree PLCC4) is measured with different biasing currents and the strong nonlinearity is observed. In Fig. 2, we can see that in VLC systems, the positive and unipolar signal is needed to be modulated onto the LED luminous intensity. The direct-current-bias (DC-bias) is always used to shift negative values to positive values for the bipolar signal. Therefore, there are two factors dominate the nonlinear distortion: ΔPsignal (peak-to-peak of the signal) and DC-bias. To study the nonlinear phenomenon still further, the modulation index (MI) and DC-bias index (DI) are defined in Fig. 2(b), which are measured by an avalanche photo diode (APD) in our experiments.
Fig. 2. (a) The measured optical power vs the LED current; (b) The schematic diagram of MI and DI.
To model most nonlinear systems, a widely used nonlinear system representation is the Volterra series expansion. However, direct use of the Volterra series is rather impractical because the number of parameters increases exponentially with the degree of nonlinearity and memory length of the system [15, 16]. The Volterra series contains a linear convolution and a nonlinear power series, which is shown as
#230559 - $15.00 USD © 2015 OSA
Received 12 Dec 2014; revised 3 Jan 2015; accepted 4 Jan 2015; published 9 Jan 2015 12 Jan 2015 | Vol. 23, No. 1 | DOI:10.1364/OE.23.000611 | OPTICS EXPRESS 613
T −1
T −1 T −1
k =0
k1 = 0 k2 = k1
y (t ) = h0 + h1 (k ) x(t − k ) + T −1
+ + k1 = 0
T −1
k p = k p −1
h (k , k ) x(t − k ) x(t − k ) 2
1
2
1
2
(1)
hp (k1 , k p ) x(t − k1 ) x(t − k p )
where h0 is a constant, {hi(k1,…, ki), 1 ≤ i ≤ p} is the set of ith order Volterra kernel coefficients, and T is the memory length of the equalizer. In fact, the Volterra series is a memory polynomial. To decrease the computational complexity of the Volterra series, we make an effective reduction that the part of time delay convolution in the Volterra series is omitted, which is used to compensate linear distortions for the frequency-selective fading channel (memory channel). However, for the frequency flat channel (memoryless channel), the output y(t) is only relevant to the current input x(t), so the time delay convolution can be omitted. In OFDM systems, the frequency flat channel is easily obtained by the pre-FDE. Therefore, the Volterra series without the time delay convolution is expressed as y (t ) = h0 + h1 (0) x(t ) + h2 (0, 0) x 2 (t ) + + hp (0, 0) x(t ) p
(2)
After the reduction, the Volterra series become a simplistic memoryless polynomial. According to Eq. (2), a nonlinear adaptive equalizer is constructed. The structure of the nonlinear equalizer we proposed is shown in Fig. 3. The output yout (t) with L taps (Lth order) is expressed as
yout (t ) = w1 x(t ) + w2 x 2 (t ) + w3 x3 (t ) + wL x L (t ) − I DC
(3)
where x(t) is the input nonlinear signal, L is the number of taps, w denotes the equalizer weight and IDC is the intensity of DC-bias. In our experiments, the error signal e(t) and weight vector w(t) for N-TDE at the tth iteration are estimated by LMS algorithm e(t ) = d (t ) − yout (t ) + I DC
(4)
w(t + 1) = w(t ) + μ e(t ) x(t )
(5)
where d(t) is the expected output and μ is the step size.
Fig. 3. The structure of the N-TDE.
3. Experimental setup and results
The experimental setup is presented in Fig. 4. The OFDM symbols from an arbitrary waveform generator (AWG, Tektronix AWG5012) working at 1GS/s sampling rate are amplified by a power amplifier (PA, Mini-Circuits ZHL-6A + ) and then superimposed onto the LED by aid of a bias-T, (Mini-Circuits ZFBT-6GW + ). A blue-filter of 400-480 nm is utilized to filter out the yellow light. A commercially available APD (Hamamatsu, S866420K) is used to detect the optical signals from DC to 280 MHz. The effective area of the APD is 3.14 mm2. The received signal is amplified by a PA (Mini-Circuits ZFL-1000LN + ). The ZFL-1000LN + is a low noise and wideband amplifier, which is used to amplify the small
#230559 - $15.00 USD © 2015 OSA
Received 12 Dec 2014; revised 3 Jan 2015; accepted 4 Jan 2015; published 9 Jan 2015 12 Jan 2015 | Vol. 23, No. 1 | DOI:10.1364/OE.23.000611 | OPTICS EXPRESS 614
signal. Moreover, the impedance matching between ZFL-1000LN + (50Ω) and oscilloscope (OSC, LeCroy 735Zi, 50Ω) is always perfect. Then the analog signal is connected to the OSC (1GS/s). In the experiments, the FFT size is NFFT = 2048, the bias current is fixed at 100mA (3.8V, DI ≈0.7), the transmission distance is fixed at 35cm and the experimental results are obtained at an illuminance level of 730 lux.
Fig. 4. Experimental setup of the LED communication.
Fig. 5. (a) The channel gain of VLC links (blue line) and the power loading of pre-FDE (red line); (b) The measured BER versus the MI with the fixed-rate (M = 400, D = 1.1Gbps).
In the first experiment, the fixed-rate modulation format of 64QAM is used. Each OFDM symbol consists of M = 400 subcarriers within a bandwidth of B = 195 MHz. The overall data rate achieves D = 1.1Gbps. The total transmission sequence is 1000 OFDM symbols. The frequency response of the overall system on each subcarrier is estimated by the binary phaseshift keying (BPSK). The measured channel gain and power loading of pre-FDE are shown in Fig. 5(a). Figure 5(b) illustrates the BER performance versus MI. Starting from MI ≈10%, without TDE the BER performance is improved by increasing the MI. Further increasing the MI, the BER performance begins to degenerate. With the power increasing, the amplitudes of the OFDM symbols exceed the maximum linear interval and work at a nonlinear range. The L-TDE (time delay taps = 8) has a close BER performance compared to without TDE, which illustrates that linear distortions have already been compensated by pre-FDE and post-FDE. Therefore, the system bottleneck is the nonlinear distortion. However, when the N-TDE is operated, the BER performance can be significantly enhanced. The N-TDE is trained with a training sequence of 5 OFDM symbols. The N-TDE of 2nd order (2 taps) has a close performance to the N-TDE with 3rd order, which implies that the 2nd order term harmonics is the major part in the nonlinear distortion. When the MI is greater than 36%, the driving signal will exceed the dynamic range of PA (ZHL-6A + ) which can introduce damage to the signal.
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Received 12 Dec 2014; revised 3 Jan 2015; accepted 4 Jan 2015; published 9 Jan 2015 12 Jan 2015 | Vol. 23, No. 1 | DOI:10.1364/OE.23.000611 | OPTICS EXPRESS 615
Fig. 6. The measured spectra (fixed-rate of 64QAM) of: (a) without N-TDE, (b) with N-TDE; The nonlinear noise spectra of: (c) without N-TDE, (d) with N-TDE.
The nonlinear distortion can cause interferences both inside and outside the signal bandwidth. Figures 6(a) and 6(b) show the OFDM spectra when MI is equal to ~36%. It is seen from Fig. 6(b) the out-band noise is eliminated when the N-TDE is used. Figures 6(c) and 6(d) illustrate the noise spectra. The noise signal xnoise is obtained by xnoise (t ) = x(t ) − ρ xo (t )
(6)
where xo(t) is original signal, ρ is a linear correlation coefficient between x(t) and xo(t). The nonlinearity noise is clearly visible in Fig. 6(c). It is observed that the noises of in-band and out-band all can be eliminated respectively in Fig. 6(d). Finally, the measured BERs versus the MI with different subcarrier numbers are depicted in Fig. 7. In this experiment, the BER performance with respect to subcarrier numbers are presented. The N-TDE of 3rd order is carried out. The BER performance is improved by reducing the subcarrier numbers and the optimal MI is shifted toward the higher MI. The reason of this phenomenon can be attributed to the reduction of the peak-to-average power ratio (PAPR). The fewer subcarriers have lower data rate and PAPR, which suffers less nonlinearity. If we reduce the subcarriers number even more, the better BER performance can be obtained, but the lower data rate is achieved.
Fig. 7. The measured BER versus the MI with different subcarrier numbers.
In the second experiment, the scheme of bit-power loading is carried out. Both the order and the energy of QAM on each subcarrier are determined based on the achievable signal-to-
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Received 12 Dec 2014; revised 3 Jan 2015; accepted 4 Jan 2015; published 9 Jan 2015 12 Jan 2015 | Vol. 23, No. 1 | DOI:10.1364/OE.23.000611 | OPTICS EXPRESS 616
noise ratio (SNR). In this experiment, a single OFDM symbol consists of 512 subcarriers within a bandwidth B = 250 MHz. The total transmission sequence is 1000 OFDM symbols. The SNR on each subcarrier applying BPSK modulation is estimated by the error vector magnitude (EVM) of the received constellations [17], which is depicted in Fig. 8(a). Figure 8(b) shows the optimal bit loading distribution. The loading algorithm aims to ensure a constant SNR on all received subcarriers with the same constellation size. To employ the NTDE we proposed, the channel gain has to be flat (memoryless channel). Therefore, the method of power loading combining the pre-FDE is used in our experiment, which has been reported in [18]. Figure 9 shows the assigned energy on each subcarrier. With this optimized modulation, the overall data rate achieves 1.3Gbps in this experiment.
Fig. 8. (a) The measured SNR versus frequency; (b) Optimal bit loading distribution.
Fig. 9. Optimal power loading distribution.
Figure 10 shows the BER performance versus MI with the scheme of bit-power loading. It is seen that the bit-power loading has similar experimental results compared to fixed-rate. The L-TDE also has a close performance to without TDE, which implies that the nonlinear noise dominates the system performance. With the increasing of the MI, the nonlinear noise will increase gradually. With the MI increasing, the amplitudes of the OFDM symbols exceed the maximum linear interval and work at a nonlinear range. However, when the nonlinear compensation is operated, the BER performance can be significantly enhanced and the constellations can be clearly recognized. The training sequence of N-TDE contains 5 OFDM symbols.
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Received 12 Dec 2014; revised 3 Jan 2015; accepted 4 Jan 2015; published 9 Jan 2015 12 Jan 2015 | Vol. 23, No. 1 | DOI:10.1364/OE.23.000611 | OPTICS EXPRESS 617
Fig. 10. The measured BER versus the MI with the scheme of bit-power loading (D = 1.3Gbps).
Figures 11(a) and 11(b) show the OFDM spectra of the bit-power loading when the MI is equal to ~36%. When the N-TDE is used, the out-band noise is eliminated in Fig. 11(b). In Fig. 11(c), the noise spectra is described, which can be obtained by Eq. (6). The nonlinear noises of in-band and out-band are clearly visible in Fig. 11(c). The out-band noise in the higher frequency will exceed the detection range of the APD (DC-280MHz) we used. Figure 11(d) illustrates that with the operation of N-TDE, the nonlinear noises can be eliminated respectively. In Fig. 12, the data rate versus MI is presented. In this experiment, the BER is restricted at ~10−4 and the different bit loading scheme is operated according to the MI.
Fig. 11. The measured spectra of bit-power loading (MI ≈36%, D = 1.3Gbps) of: (a) without N-TDE, (b) with N-TDE; The nonlinear noise spectra of: (c) without N-TDE, (d) with N-TDE.
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Received 12 Dec 2014; revised 3 Jan 2015; accepted 4 Jan 2015; published 9 Jan 2015 12 Jan 2015 | Vol. 23, No. 1 | DOI:10.1364/OE.23.000611 | OPTICS EXPRESS 618
Fig. 12. The measured data rate versus the MI with adaptive bit-power loading (BER ≈10−4).
Finally, the convergence of N-TDE is presented in terms of the mean square error (MSE) between the ideal and received symbol (bit-power loading, D = 1.3Gbps, MI ≈36%). The NTDE is trained with a sequence of 5 OFDM symbols. Figures 13(a) and 13(b) show the convergence speed and steady state error performance of the N-TDE of 2nd order and 3rd order. The N-TDE of 3rd order can reduce the MSE, but the number of iterations required for convergence is higher than the N-TDE of 2nd order. It is observed that the steady state error can be achieved by only one OFDM symbol, which will be interesting for practical implementations.
Fig. 13. MSE as a function of the iteration number: (a) N-TDE of 2nd order; (b) N-TDE of 3rd order.
4. Conclusion
An efficient nonlinear compensation scheme for OFDM-based VLC systems has been presented in this paper. Two separate approaches (fixed-rate and adaptive bit-power loading) are tested with the hybrid nonlinear equalization we proposed. The experiments show that the N-TDE is an efficient, low complex and adaptive equalizer to mitigate the LED nonlinearity. Only using a very small number of parameters the nonlinear distortion can be significantly reduced. It is demonstrated that with the N-TDE the optimal MI of LED and the BER performance can be largely enhanced. With the nonlinear compensation, not only the in-band noise, but also the out-band noise can be eliminated. It is worth noting that the proposed nonlinear compensation scheme can be used for the other optical OFDM systems. Acknowledgments
This research was supported in part by National 973 Program (No. 2013CB329205), National Natural Science Foundation of China (No. 61401032), and National 863 Program (No. 2013AA013601).
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Received 12 Dec 2014; revised 3 Jan 2015; accepted 4 Jan 2015; published 9 Jan 2015 12 Jan 2015 | Vol. 23, No. 1 | DOI:10.1364/OE.23.000611 | OPTICS EXPRESS 619
Abstract: A novel hybrid time-frequency domain equalization scheme is proposed and experimentally demonstrated to mitigate the white light emitting diode (LED) nonlinearity in visible light communication (VLC) systems based on orthogonal frequency division multiplexing (OFDM). We handle the linear and nonlinear distortion separately in a nonlinear OFDM system. The linear part is equalized in frequency domain and the nonlinear part is compensated by an adaptive nonlinear time domain equalizer (NTDE). The experimental results show that with only a small number of parameters the nonlinear equalizer can efficiently mitigate the LED nonlinearity. With the N-TDE the modulation index (MI) and BER performance can be significantly enhanced. ©2015 Optical Society of America OCIS codes: (230.3670) Light-emitting diodes; (060.4080) Modulation; (060.4510) Optical communications.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
IEEE 802.15.7 Working group for WPAN, “Short-range wireless optical communication using visual light,” (2011), http://www.ieee802.org/15/. L. Hanzo, H. Haas, S. Imre, D. O’Brien, M. Rupp, and L. Gyongyosi, “Wireless myths, realities, and futures: from 3G/4G to optical and quantum wireless,” Proc. IEEE 100(13), 1853–1888 (2012). C. G. Gavrincea, J. Baranda, and P. Henarejos, “Rapid prototyping of standard-compliant visible light communications system,” IEEE Commun. Mag. 52(7), 80–87 (2014). Z. T. Huang and Y. F. Ji, “Design and demonstration of room division multiplexing-based hybrid VLC network,” Chin. Opt. Lett. 11(6), 060603 (2013). A. M. Khalid, G. Cossu, R. Corsini, P. Choudhury, and E. Ciaramella, “1-Gb/s transmission over a phosphorescent white LED by using rate-adaptive discrete multitone modulation,” IEEE Photon. J. 4(5), 1465– 1473 (2012). G. Cossu, A. M. Khalid, P. Choudhury, R. Corsini, and E. Ciaramella, “3.4 Gbit/s visible optical wireless transmission based on RGB LED,” Opt. Express 20(26), B501–B506 (2012). F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, Z. Y. Chen, H. T. Huang, and S. Chi, “Performance comparison of OFDM signal and CAP signal over high capacity RGB-LED-based WDM visible light communication,” IEEE Photon. J. 5(4), 7901507 (2013). D. Tsonev, H. Chun, S. Rajbhandari, J. D. Mckendry, S. Videv, E. Gu, M. Haji, S. Watson, A. E. Kelly, G. Faulkner, M. D. Dawson, H. Haas, and D. O’Brien, “A 3-Gb/s single-LED OFDM-based wireless VLC wink using a gallium nitride μLED,” IEEE Photon. Technol. Lett. 26(7), 637–640 (2014). I. Neokosmidis, T. Kamalakis, J. W. Walewski, B. Inan, and T. Sphicopoulos, “Impact of nonlinear LED transfer function on discrete multitone modulation: analytical approach,” J. Lightwave Technol. 27(22), 4970–4978 (2009). B. Inan, S. C. Jeffrey Lee, S. Randel, I. Neokosmidis, A. M. Koonen, and J. W. Walewski, “Impact of LED nonlinearity on discrete multitone modulation,” J. Opt. Commun. Netw. 1(5), 439–451 (2009). H. Elgala, R. Mesleh, and H. Haas, “Non-linearity effects and predistortion in optical OFDM wireless transmission using LEDs,” Int. J. Ultra Wideband Commun. Syst. 1(2), 143–150 (2009). R. Mesleh, H. Elgala, and H. Haas, “LED nonlinearity mitigation techniques in optical wireless OFDM communication systems,” J. Opt. Commun. Netw. 4(11), 865–875 (2012). G. Stepniak, J. Siuzdak, and P. Zwierko, “Compensation of a VLC phosphorescent white LED nonlinearity by means of volterra DFE,” IEEE Photon. Technol. Lett. 25(16), 1597–1600 (2013). H. Elgala, R. Mesleh, and H. Haas, “An LED model for intensity-modulated optical communication systems,” IEEE Photon. Technol. Lett. 22(11), 835–837 (2010).
#230559 - $15.00 USD © 2015 OSA
Received 12 Dec 2014; revised 3 Jan 2015; accepted 4 Jan 2015; published 9 Jan 2015 12 Jan 2015 | Vol. 23, No. 1 | DOI:10.1364/OE.23.000611 | OPTICS EXPRESS 611
15. H. Q. Zhao and J. S. Zhang, “A novel adaptive nonlinear filter-based pipelined feed-forward second-order Volterra architecture,” IEEE Trans. Signal Process. 57(1), 237–246 (2009). 16. A. Zhu, P. J. Draxler, J. J. Yan, T. J. Brazil, D. F. Kimball, and P. M. Asbeck, “Open-loop digital predistorter for RF power amplifiers using dynamic deviation reduction-based Volterra series,” IEEE Trans. Microw. Theory Tech. 56(7), 1524–1534 (2008). 17. R. A. Shafik, S. Rahman, and R. Islam, “On the extended relationships among EVM, BER and SNR as performance metrics,” in Proceedings of International Conference on Electrical and Computer Engineering. (IEEE, 2006), pp. 408–411. 18. L. N. Peng, S. Haese, and M. Helard, “Frequency domain LED compensation for nonlinearity mitigation in DMT systems,” IEEE Photon. Technol. Lett. 25(20), 2022–2025 (2013).
1. Introduction Visible light communication (VLC) based on light emitting diode (LED) can provide licensefree bandwidth, high signal-to-noise rate, low-cost front-ends and high modulation power. These properties facilitate the potentiality of VLC to become an effective complement to radio frequency (RF) signal transmission [1–4]. Recently, there has been increasing interest in utilizing multi-carrier modulation for VLC systems such as discrete multi-tone (DMT) and orthogonal frequency division multiplexing (OFDM) modulation [5–8]. However, the influence of LED nonlinearity is not taken into account in these reports. The LED nonlinearity is a major challenge for the OFDM-based VLC system due to its sensitivity to the resulting distortion [9, 10]. The output optical power of LED is nonlinear with the driving current, therefore, the biasing current should be carefully selected to force signal magnitude in the maximum linear interval. Elgala et al. employed a time domain pre-distortion technique to compensate the nonlinear distortion of OFDM symbols [11]. However, the LED transfer function should be known as a priori information. In [12], the OFDM symbols in the time domain were divided into multiple parts to drive multiple LEDs respectively. Although the nonlinearity is mitigated by the multiple transmitters, multiple LEDs will increase the system complexity. In [13], decision feedback equalizer (DFE) with nonlinear Volterra feed-forward was introduced to mitigate the LED nonlinearity. However, the number of the Volterra coefficients increases geometrically with the delays and orders increasing, which is prohibitive for most practical applications. Therefore, an efficient and low complex compensation scheme is quite important to mitigate the LED nonlinearity for the OFDM-based VLC system. In this paper, a hybrid timefrequency domain equalization scheme is proposed and experimentally demonstrated to decrease the LED nonlinearity. We use a commercially available white-LED with a 3dB bandwidth of 20 MHz. The linear distortion is equalized in frequency domain and the nonlinear distortion is mitigated by an adaptive nonlinear time domain equalizer (N-TDE) whose optimum coefficients are found via the least mean squares (LMS) algorithm. The experimental results show that the N-TDE only with a very small number of parameters can efficiently eliminate the effects of the LED nonlinearity. 2. Modulation scheme and LED nonlinearity In a nonlinear OFDM system, distortions can be divided into two types: linear distortions and nonlinear distortions. Linear distortions produced by channel fading can be equalized easily in the frequency domain. However, nonlinear distortions which cause interferences between subcarriers are very difficult to be compensated in frequency domain. In the scheme we proposed, the linear distortion is compensated by the frequency domain equalization (FDE) and the nonlinear distortion is equalized by the N-TDE. Two OFDM schemes (fixed-rate and bit-power loading) have been utilized for maximizing the capabilities for VLC systems [8]. Both of the approaches are tested with the N-TDE in our experiments. The block diagram of the OFDM-based VLC system with the N-TDE is presented in Fig. 1. After the operation of the quadrature amplitude modulation (QAM), the pre-frequency domain equalization (preFDE) or the adaptive power loading is operated. Then, Hermitian symmetry of complex signals is used before inverse fast Fourier transform (IFFT) to produce a real time domain output signal. The cyclic prefix (CP) is inserted to mitigate inter-symbol interference. At the receiver, after synchronization, three equalization approaches are compared (without TDE, #230559 - $15.00 USD © 2015 OSA
Received 12 Dec 2014; revised 3 Jan 2015; accepted 4 Jan 2015; published 9 Jan 2015 12 Jan 2015 | Vol. 23, No. 1 | DOI:10.1364/OE.23.000611 | OPTICS EXPRESS 612
linear TDE and N-TDE). In our experiments, the LED frequency response is feedback to the transmitter, which is used to equalize the linear distortion in frequency domain. The linear TDE (L-TDE) is just used to demonstrate that linear distortions have already been indeed compensated in frequency domain. The optimum coefficients of the L-TDE and N-TDE are found by the LMS algorithm.
Fig. 1. The schematic of nonlinear compensation for OFDM systems (fixed-rate or adaptive bit-power loading). PA: power amplifier; Bias-T: bias tee; APD: avalanche photo diode.
In VLC systems, the nonlinearity mainly origins from LEDs. Thermal aspects of LEDs leading to a drop in the electrical-to-optical (E/O) conversion efficiency (light output of the LED decreases and slowly approaches a steady-state value; LED self heating characteristic) is the major source of the LED nonlinearity [14]. In Fig. 2(a), the E/O characteristic of a commercially available white-LED (Cree PLCC4) is measured with different biasing currents and the strong nonlinearity is observed. In Fig. 2, we can see that in VLC systems, the positive and unipolar signal is needed to be modulated onto the LED luminous intensity. The direct-current-bias (DC-bias) is always used to shift negative values to positive values for the bipolar signal. Therefore, there are two factors dominate the nonlinear distortion: ΔPsignal (peak-to-peak of the signal) and DC-bias. To study the nonlinear phenomenon still further, the modulation index (MI) and DC-bias index (DI) are defined in Fig. 2(b), which are measured by an avalanche photo diode (APD) in our experiments.
Fig. 2. (a) The measured optical power vs the LED current; (b) The schematic diagram of MI and DI.
To model most nonlinear systems, a widely used nonlinear system representation is the Volterra series expansion. However, direct use of the Volterra series is rather impractical because the number of parameters increases exponentially with the degree of nonlinearity and memory length of the system [15, 16]. The Volterra series contains a linear convolution and a nonlinear power series, which is shown as
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Received 12 Dec 2014; revised 3 Jan 2015; accepted 4 Jan 2015; published 9 Jan 2015 12 Jan 2015 | Vol. 23, No. 1 | DOI:10.1364/OE.23.000611 | OPTICS EXPRESS 613
T −1
T −1 T −1
k =0
k1 = 0 k2 = k1
y (t ) = h0 + h1 (k ) x(t − k ) + T −1
+ + k1 = 0
T −1
k p = k p −1
h (k , k ) x(t − k ) x(t − k ) 2
1
2
1
2
(1)
hp (k1 , k p ) x(t − k1 ) x(t − k p )
where h0 is a constant, {hi(k1,…, ki), 1 ≤ i ≤ p} is the set of ith order Volterra kernel coefficients, and T is the memory length of the equalizer. In fact, the Volterra series is a memory polynomial. To decrease the computational complexity of the Volterra series, we make an effective reduction that the part of time delay convolution in the Volterra series is omitted, which is used to compensate linear distortions for the frequency-selective fading channel (memory channel). However, for the frequency flat channel (memoryless channel), the output y(t) is only relevant to the current input x(t), so the time delay convolution can be omitted. In OFDM systems, the frequency flat channel is easily obtained by the pre-FDE. Therefore, the Volterra series without the time delay convolution is expressed as y (t ) = h0 + h1 (0) x(t ) + h2 (0, 0) x 2 (t ) + + hp (0, 0) x(t ) p
(2)
After the reduction, the Volterra series become a simplistic memoryless polynomial. According to Eq. (2), a nonlinear adaptive equalizer is constructed. The structure of the nonlinear equalizer we proposed is shown in Fig. 3. The output yout (t) with L taps (Lth order) is expressed as
yout (t ) = w1 x(t ) + w2 x 2 (t ) + w3 x3 (t ) + wL x L (t ) − I DC
(3)
where x(t) is the input nonlinear signal, L is the number of taps, w denotes the equalizer weight and IDC is the intensity of DC-bias. In our experiments, the error signal e(t) and weight vector w(t) for N-TDE at the tth iteration are estimated by LMS algorithm e(t ) = d (t ) − yout (t ) + I DC
(4)
w(t + 1) = w(t ) + μ e(t ) x(t )
(5)
where d(t) is the expected output and μ is the step size.
Fig. 3. The structure of the N-TDE.
3. Experimental setup and results
The experimental setup is presented in Fig. 4. The OFDM symbols from an arbitrary waveform generator (AWG, Tektronix AWG5012) working at 1GS/s sampling rate are amplified by a power amplifier (PA, Mini-Circuits ZHL-6A + ) and then superimposed onto the LED by aid of a bias-T, (Mini-Circuits ZFBT-6GW + ). A blue-filter of 400-480 nm is utilized to filter out the yellow light. A commercially available APD (Hamamatsu, S866420K) is used to detect the optical signals from DC to 280 MHz. The effective area of the APD is 3.14 mm2. The received signal is amplified by a PA (Mini-Circuits ZFL-1000LN + ). The ZFL-1000LN + is a low noise and wideband amplifier, which is used to amplify the small
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Received 12 Dec 2014; revised 3 Jan 2015; accepted 4 Jan 2015; published 9 Jan 2015 12 Jan 2015 | Vol. 23, No. 1 | DOI:10.1364/OE.23.000611 | OPTICS EXPRESS 614
signal. Moreover, the impedance matching between ZFL-1000LN + (50Ω) and oscilloscope (OSC, LeCroy 735Zi, 50Ω) is always perfect. Then the analog signal is connected to the OSC (1GS/s). In the experiments, the FFT size is NFFT = 2048, the bias current is fixed at 100mA (3.8V, DI ≈0.7), the transmission distance is fixed at 35cm and the experimental results are obtained at an illuminance level of 730 lux.
Fig. 4. Experimental setup of the LED communication.
Fig. 5. (a) The channel gain of VLC links (blue line) and the power loading of pre-FDE (red line); (b) The measured BER versus the MI with the fixed-rate (M = 400, D = 1.1Gbps).
In the first experiment, the fixed-rate modulation format of 64QAM is used. Each OFDM symbol consists of M = 400 subcarriers within a bandwidth of B = 195 MHz. The overall data rate achieves D = 1.1Gbps. The total transmission sequence is 1000 OFDM symbols. The frequency response of the overall system on each subcarrier is estimated by the binary phaseshift keying (BPSK). The measured channel gain and power loading of pre-FDE are shown in Fig. 5(a). Figure 5(b) illustrates the BER performance versus MI. Starting from MI ≈10%, without TDE the BER performance is improved by increasing the MI. Further increasing the MI, the BER performance begins to degenerate. With the power increasing, the amplitudes of the OFDM symbols exceed the maximum linear interval and work at a nonlinear range. The L-TDE (time delay taps = 8) has a close BER performance compared to without TDE, which illustrates that linear distortions have already been compensated by pre-FDE and post-FDE. Therefore, the system bottleneck is the nonlinear distortion. However, when the N-TDE is operated, the BER performance can be significantly enhanced. The N-TDE is trained with a training sequence of 5 OFDM symbols. The N-TDE of 2nd order (2 taps) has a close performance to the N-TDE with 3rd order, which implies that the 2nd order term harmonics is the major part in the nonlinear distortion. When the MI is greater than 36%, the driving signal will exceed the dynamic range of PA (ZHL-6A + ) which can introduce damage to the signal.
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Received 12 Dec 2014; revised 3 Jan 2015; accepted 4 Jan 2015; published 9 Jan 2015 12 Jan 2015 | Vol. 23, No. 1 | DOI:10.1364/OE.23.000611 | OPTICS EXPRESS 615
Fig. 6. The measured spectra (fixed-rate of 64QAM) of: (a) without N-TDE, (b) with N-TDE; The nonlinear noise spectra of: (c) without N-TDE, (d) with N-TDE.
The nonlinear distortion can cause interferences both inside and outside the signal bandwidth. Figures 6(a) and 6(b) show the OFDM spectra when MI is equal to ~36%. It is seen from Fig. 6(b) the out-band noise is eliminated when the N-TDE is used. Figures 6(c) and 6(d) illustrate the noise spectra. The noise signal xnoise is obtained by xnoise (t ) = x(t ) − ρ xo (t )
(6)
where xo(t) is original signal, ρ is a linear correlation coefficient between x(t) and xo(t). The nonlinearity noise is clearly visible in Fig. 6(c). It is observed that the noises of in-band and out-band all can be eliminated respectively in Fig. 6(d). Finally, the measured BERs versus the MI with different subcarrier numbers are depicted in Fig. 7. In this experiment, the BER performance with respect to subcarrier numbers are presented. The N-TDE of 3rd order is carried out. The BER performance is improved by reducing the subcarrier numbers and the optimal MI is shifted toward the higher MI. The reason of this phenomenon can be attributed to the reduction of the peak-to-average power ratio (PAPR). The fewer subcarriers have lower data rate and PAPR, which suffers less nonlinearity. If we reduce the subcarriers number even more, the better BER performance can be obtained, but the lower data rate is achieved.
Fig. 7. The measured BER versus the MI with different subcarrier numbers.
In the second experiment, the scheme of bit-power loading is carried out. Both the order and the energy of QAM on each subcarrier are determined based on the achievable signal-to-
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Received 12 Dec 2014; revised 3 Jan 2015; accepted 4 Jan 2015; published 9 Jan 2015 12 Jan 2015 | Vol. 23, No. 1 | DOI:10.1364/OE.23.000611 | OPTICS EXPRESS 616
noise ratio (SNR). In this experiment, a single OFDM symbol consists of 512 subcarriers within a bandwidth B = 250 MHz. The total transmission sequence is 1000 OFDM symbols. The SNR on each subcarrier applying BPSK modulation is estimated by the error vector magnitude (EVM) of the received constellations [17], which is depicted in Fig. 8(a). Figure 8(b) shows the optimal bit loading distribution. The loading algorithm aims to ensure a constant SNR on all received subcarriers with the same constellation size. To employ the NTDE we proposed, the channel gain has to be flat (memoryless channel). Therefore, the method of power loading combining the pre-FDE is used in our experiment, which has been reported in [18]. Figure 9 shows the assigned energy on each subcarrier. With this optimized modulation, the overall data rate achieves 1.3Gbps in this experiment.
Fig. 8. (a) The measured SNR versus frequency; (b) Optimal bit loading distribution.
Fig. 9. Optimal power loading distribution.
Figure 10 shows the BER performance versus MI with the scheme of bit-power loading. It is seen that the bit-power loading has similar experimental results compared to fixed-rate. The L-TDE also has a close performance to without TDE, which implies that the nonlinear noise dominates the system performance. With the increasing of the MI, the nonlinear noise will increase gradually. With the MI increasing, the amplitudes of the OFDM symbols exceed the maximum linear interval and work at a nonlinear range. However, when the nonlinear compensation is operated, the BER performance can be significantly enhanced and the constellations can be clearly recognized. The training sequence of N-TDE contains 5 OFDM symbols.
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Received 12 Dec 2014; revised 3 Jan 2015; accepted 4 Jan 2015; published 9 Jan 2015 12 Jan 2015 | Vol. 23, No. 1 | DOI:10.1364/OE.23.000611 | OPTICS EXPRESS 617
Fig. 10. The measured BER versus the MI with the scheme of bit-power loading (D = 1.3Gbps).
Figures 11(a) and 11(b) show the OFDM spectra of the bit-power loading when the MI is equal to ~36%. When the N-TDE is used, the out-band noise is eliminated in Fig. 11(b). In Fig. 11(c), the noise spectra is described, which can be obtained by Eq. (6). The nonlinear noises of in-band and out-band are clearly visible in Fig. 11(c). The out-band noise in the higher frequency will exceed the detection range of the APD (DC-280MHz) we used. Figure 11(d) illustrates that with the operation of N-TDE, the nonlinear noises can be eliminated respectively. In Fig. 12, the data rate versus MI is presented. In this experiment, the BER is restricted at ~10−4 and the different bit loading scheme is operated according to the MI.
Fig. 11. The measured spectra of bit-power loading (MI ≈36%, D = 1.3Gbps) of: (a) without N-TDE, (b) with N-TDE; The nonlinear noise spectra of: (c) without N-TDE, (d) with N-TDE.
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Received 12 Dec 2014; revised 3 Jan 2015; accepted 4 Jan 2015; published 9 Jan 2015 12 Jan 2015 | Vol. 23, No. 1 | DOI:10.1364/OE.23.000611 | OPTICS EXPRESS 618
Fig. 12. The measured data rate versus the MI with adaptive bit-power loading (BER ≈10−4).
Finally, the convergence of N-TDE is presented in terms of the mean square error (MSE) between the ideal and received symbol (bit-power loading, D = 1.3Gbps, MI ≈36%). The NTDE is trained with a sequence of 5 OFDM symbols. Figures 13(a) and 13(b) show the convergence speed and steady state error performance of the N-TDE of 2nd order and 3rd order. The N-TDE of 3rd order can reduce the MSE, but the number of iterations required for convergence is higher than the N-TDE of 2nd order. It is observed that the steady state error can be achieved by only one OFDM symbol, which will be interesting for practical implementations.
Fig. 13. MSE as a function of the iteration number: (a) N-TDE of 2nd order; (b) N-TDE of 3rd order.
4. Conclusion
An efficient nonlinear compensation scheme for OFDM-based VLC systems has been presented in this paper. Two separate approaches (fixed-rate and adaptive bit-power loading) are tested with the hybrid nonlinear equalization we proposed. The experiments show that the N-TDE is an efficient, low complex and adaptive equalizer to mitigate the LED nonlinearity. Only using a very small number of parameters the nonlinear distortion can be significantly reduced. It is demonstrated that with the N-TDE the optimal MI of LED and the BER performance can be largely enhanced. With the nonlinear compensation, not only the in-band noise, but also the out-band noise can be eliminated. It is worth noting that the proposed nonlinear compensation scheme can be used for the other optical OFDM systems. Acknowledgments
This research was supported in part by National 973 Program (No. 2013CB329205), National Natural Science Foundation of China (No. 61401032), and National 863 Program (No. 2013AA013601).
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Received 12 Dec 2014; revised 3 Jan 2015; accepted 4 Jan 2015; published 9 Jan 2015 12 Jan 2015 | Vol. 23, No. 1 | DOI:10.1364/OE.23.000611 | OPTICS EXPRESS 619
