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A novel frequency domain nonlinear compensation method, FD-NC, is proposed for orthogonal frequency division multiplexing (OFDM) based visible light communication (VLC) system. By tackling the memory nonlinear impairments from light emitting diodes (LEDs) in the frequency domain rather than in the time domain, the proposed method has much lower computational complexity than the conventional time domain Volterra nonlinear compensation method (TD-NC). Both theoretical derivation and experimental investigation of the proposed method in OFDM based VLC systems with four types of commercial LEDs are presented. The results of experiments show that the proposed low-complexity FD-NC method with a moderate truncation factor achieves a performance comparable to that of the TD-NC. The application of FD-NC method in the bit-power loading OFDM VLC system is also experimentally demonstrated. Compared with the linear equalization case, at a bit error rate (BER) of 3.8 × 10−3 (a), the transmission distance of a 960 Mbps VLC system can be extended from 0.7 m to 1.8 m by the FD-NC, and (b) the achievable system capacity can be enhanced by 18.7%~36.5% for transmission distance in the range of 0.5 m~2 m with the FD-NC. The complexity analysis shows that the required number of real-valued multiplications (RNRM) of the FD-NC is independent of linear or nonlinear memory length. The reduction of RNRM achieved by the FD-NC over the TD-NC becomes more profound for a larger nonlinear memory length or a smaller truncation factor.
© 2017 Optical Society of America
1. Introduction
Visible light communication (VLC) using energy-efficient light emitting diodes (LEDs) has been regarded as one promising technology for high-speed indoor wireless communication [1, 2]. Compared with wireless communication systems based on radio frequency carrier, high-speed VLC systems with optical carrier can offer high security and are inherently tolerant to electromagnetic interference. To enhance the system capacity which is severely constrained by the modulation bandwidth of LEDs (e.g., the typical 3-dB bandwidth of a commercial LED is on the order of 10 to 100 MHz [3]), advanced modulation formats, such as orthogonal frequency division multiplexing (OFDM) and carrierless amplitude phase modulation (CAP) [4,5], have been adopted. As in VLC systems the signal-to-noise ratio (SNR) at the receiver can be degraded by both the linear and nonlinear impairments, various channel equalization methods have also been proposed to improve the transmission performance. Unlike the linear impairments that can be tackled using classical linear equalization methods [6], the nonlinear impairment in VLC systems is unique as the major nonlinearity source are the LED [7], which is a more complex issue to be mitigated.
Several nonlinearity compensation methods based on various theoretical models have been devised for VLC systems. By assuming the nonlinearity in the VLC system to be frequency independent, i.e., memoryless nonlinearity, pre-distortion using Taylor expansion has been proposed [8]. Nonlinear equalizers based on reproducing kernel Hilbert space (RKHS) techniques have been investigated in single carrier VLC systems by simulations [9,10], where various sparsification criteria are proposed to reduced complexity. A hybrid method based on time domain memoryless nonlinear equalization and frequency domain linear equalization has been demonstrated in an OFDM based VLC system [11]. Nevertheless, the frequency dependent nonlinear effect (i.e., memory nonlinearity) becomes more profound when a large modulation bandwidth (e.g., > 100 MHz) is utilized in a high-speed VLC system [12]. Recent investigations [6,13] show that the memory nonlinearity of LED can be well described using the Volterra series model. Time domain memory nonlinear equalization based on Volterra series model has been experimentally demonstrated in high-speed CAP based VLC systems [6]. However, since the number of Kth order nonlinearity kernels with memory length of M (e.g., M = 25 for the 2nd order kernels in [6]) grows as O(), the complexity of the time domain Volterra nonlinear equalizer is significantly higher than the conventional linear equalizer (i.e., K = 1). To reduce complexity, adaptive time domain post nonlinear equalizer [14] based on memory polynomial considering only the diagonal kernels has been proposed and investigated in a OFDM based VLC system with a LED of Winner model by simulation. Though in general memoryless nonlinear equalizers (i.e., M = 1) are less complicate than the memory ones, they are only the special cases of the latter ones. In other words, the effectiveness of the memoryless nonlinear equalizer depends on the nonlinear characteristic of the specific LEDs employed in VLC systems, while the memory nonlinear equalizer is a generic tool for LED VLC system.
To balance the complexity and generality, in this paper we propose a novel frequency domain nonlinear compensation (FD-NC) method for OFDM based LED VLC systems. By estimating and compensating the nonlinearity in frequency domain rather than time domain, the required number of real-valued multiplications (RNRM) can be significantly reduced when the memory length of nonlinearity is non-trivial. The performance of the proposed FD-NC method is experimentally investigated in OFDM based high-speed VLC systems with four different commercial LEDs. The application of FD-NC in the adaptive bit-power loading OFDM VLC system is also demonstrated. The results show that compared with the time domain Volterra nonlinear equalizer, the proposed FD-NC method with a moderate truncation factor offers a similar performance but with much lower complexity.
2. Principle of the proposed frequency domain nonlinear compensation method FD-NC
The nonlinearity of an indoor VLC system is mainly introduced by the electrical-to-optical (E-O) conversion with the LED at the transmitter [7]. As a practical VLC system may use various types of LEDs with different nonlinearity characteristics (e.g., Weiner nonlinearity [14], Hammerstein nonlinearity [7], etc.), the Volterra series model is employed to give a general description of such nonlinearity [13]. Based on the Volterra series model, the discrete time domain signal y(n) after O-E conversion at the receiver can be expressed as:
where is a constant, is the Kth order Volterra kernel corresponding to the linear (K = 1) or nonlinear effect (K >1), is the memory length of the Kth order term, is the OFDM signal before E-O conversion at the transmitter. To relieve the complexity issue in memory nonlinearity compensation, we only consider the effects with K to be no larger than 2. By rearranging the 2nd order term in Eq. (1), we have:By defining and , Eq. (2) can be rewritten as:Equation (3) shows that the 2nd order terms of the Volterra series model can be obtained via multiple linear convolution operations. Figure 1 shows the temporal structure of the which is involved in the linear convolution in Eq. (3). As illustrated in Fig. 1(a), the product of OFDM signal x(n) and its delayed version x(n-L) still exhibits certain cyclicality in the time domain when the length of cyclic prefix LCP in x(n) is larger than the delay L. The length of remaining cyclic block is L1 = Lcp – Max (N1, N2).
Fig. 1 Illustration of (a) the temporal structure of xL(n) in the Volterra series model, and (b) the cyclicality of the 2nd order nonlinearity term.
In order to compensate for the nonlinear distortion in y(n), the 2nd order inverse of nonlinearity method [6,12] can be used by feeding y(n) into a Volterra nonlinear equalizer. The corresponding output z(n) after nonlinearity compensation is:
where , is the linear convolution operator, is the direct current (DC) term, is the ith kernel of linear equalizer, is the ith kernel of the 2nd order nonlinear equalizer for with 0 ≤ i ≤ M2-1-L and 0 ≤ L ≤ M2-1. The memory length is set to M1 (M2) for the 1st (2nd) order kernels of the Volterra equalizer. As the number of kernels for equals to M2-1-L and the amplitude of is expected to be small for a large L [12], the right hand side of Eq. (4) can be truncated by including only the first α convolution terms of the 2nd order operation to balance the complexity and performance. After truncation, Eq. (4) becomes:In case the maximum memory length of the nonlinear equalizer does not exceed the length of cyclic blocks in y(n), i.e., Max(M1, M2) ≤ L2, the linear convolutions in Eq. (5) can be convert to circular convolutions for samples inside the length-N discrete Fourier transform (DFT) window. With such observation, the truncated frequency domain nonlinear equalization can be realized in with parallel one-tap equalizers:
where Z(n), Am(n) and Ym(n) are the length-N DFT of z(n), βm(n) and ym(n), respectively. Zero padding of βm(n) is used in the DFT operations. To make Eq. (6) valid, the length of cyclic prefix of OFDM signal x(n) should be longer than the sum of the maximum memory length of channel and the maximum memory length of the equalizer. Figure 2 shows the schematic diagram of frequency domain nonlinear equalizer based on Eq. (6). The DFT is implemented with fast Fourier transform (FFT). The first term on the right hand side of Eq. (6) A0 can be removed by a digital DC blocker and is omitted hereafter.The kernel Am(n) can be obtained by training with a certain estimation method at the beginning of transmission. In this paper recursive least squares (RLS) method [15] is utilized for kernel estimation for fast convergence [16]. The procedure of RLS estimation is summarized as:
where is the identity matrix of rank α, Ai(n) = [Ai0(n), Ai20(n), ..., Ai2(α-1)(n)]T is the vector consisting all the linear and nonlinear kernels for nth subcarrier after ith update,is the vector consisting of the nth element of the DFT of the ith received symbol and the nth elements of the DFT of corresponding the 2nd order nonlinear products, Si(n) and are the training data and the output of the equalizer for the nth subcarrier in the ith OFDM training symbol, and are predefined constants before initialization. After obtaining kernels by RLS estimation, the received signal can be equalized by using Eq. (6).3. Experimental investigation
3.1 Experimental setup
The performance of the proposed FD-NC algorithm is experimentally investigated in an OFDM based VLC system. Figure 3 shows the schematic diagram of experimental setup and the digital signal processing (DSP) flow. The DSP at the transmitter and receiver are implemented offline using Matlab. At the transmitter side, the frequency domain symbols are converted to time domain samples using 1024-point inverse fast Fourier transform (IFFT). The 512 subcarriers around DC except for the central 14 ones are utilized to carry the information symbols with Hermitian symmetry. A length-64 cyclic prefix (CP) is added after parallel-to-serial (P/S) conversion. The real-valued OFDM signal is loaded into an arbitrary waveform generator (AWG, AWG7122C) with a sampling rate of 640 MS/s for digital-to-analog conversion. This results in a baseband OFDM signal with an effective bandwidth of 160 MHz (i.e., from 5 MHz to 165 MHz). The output signal is amplified by an electrical amplifier (Mini circuit ZHL-32A-S). An electrical tunable attenuator is used after the amplifier to optimize the power of driving signal. The OFDM signal and the DC bias are combined by a bias-tee before applying to the LED. Four different types of commercial LEDs, including a phosphor-based white LED (Cree XPE) and red/green/blue LEDs (three chips on a RGB LED, Cree CLV6A-FKB), are used in the experiments to show the wide applicability of the proposed nonlinearity compensation method. The measured illumination levels at the transmission distance of 50 cm are 46 lx, 14 lx, 20 lx and 21 lx for the white/red/green/blue LEDs, respectively.
The receiver consists of a focusing lens (f = 70 mm) and an avalanche photodiode (APD, HAMAMATSU, C12702-11). For the system with the phosphor-based white LED, one blue filter is placed before the APD, while no filter is employed for the systems with the other LEDs. The optical-to-electrical converted signal from APD is captured and digitalized by a real-time oscilloscope (DSO73304D) and downsampled to 640MS/s. The signals are then processed offline with Matlab. The DSP flow at the receiver side starts with symbol synchronization. Channel equalization is carried out afterwards to mitigate the linear/nonlinear distortion. The performance of various channel equalizers based on either the proposed FD-NC method or conventional methods, including the TD-NC based on Eq. (4) with RLS estimation and the linear one-tap equalization method FDE [17], are investigated. The equalized signals go through hard-decision and are finally demapped to bits.
3.2 Results of experiments and discussion
We first optimize the power of driving signal at the transmitter. Figure 4 shows the measured average signal-to-noise ratio (SNR) of the recovered signal with different channel equalization methods versus power attenuation of driving signal at the transmitter. The M1 and M2 are set to 10 and 7 for the TD-NC, respectively. The number of training symbols is set to 30 for kernel estimation. For the FD-NC, the results under different truncation factor α (from 1 to 7) are included. The optimized power is larger when the nonlinear equalizer is employed instead of the linear equalizer FDE. This attributes to the fact that with nonlinear equalizers the system has a larger tolerance to the nonlinear distortion which is non-trivial when a large driving signal is employed (e.g., with power attenuation < 14/8/12/12 dB in Figs. 4(a)-4(d), respectively). Compared with FDE case, the maximum SNR gain with the proposed FD-NC equalizer are about 4.22 dB, 2.13 dB, 3.68 dB and 5.65 dB for the red, white, green and blue LEDs, respectively. When the truncation factor is sufficient large (i.e., α > 4 for all LEDs), the proposed FD-NC has a performance fairly close to that of the TD-NC with full memory.
Fig. 4 Average SNR versus power attenuation for VLC system with (a) red (b) white (c) green and (d) blue LEDs.
Figure 5 shows the average SNR versus the 2nd order nonlinearity memory length M2 for the TD-NC and truncation factor α for the FD-NC. It is clear that VLC systems with different LEDs have different sensitivities to the selection of M2 or α. Compared with the worst case [i.e., M2 = 1 in Fig. 5 (a), α = 1 in Fig. 5 (b)], the maximum average SNR gain with optimal M2 (α) are about 6.08 dB, 4.01 dB, 4.48 dB and 6.85 dB (1.85 dB, 1.26 dB, 1.25 dB and 3.92 dB) with the TD-NC (FD-NC) for the red, white, green and blue LEDs. The performance of both the TD-NC and the FD-NC become converged when the M2 or α exceed certain values. We fix M2 to 7 for the TD-NC in the left experiments. For all LEDs, a moderate α is found to be sufficient to achieve the optimal performance with the FD-NC.
Fig. 5 Average SNR versus (a) the memory length of the 2nd order nonlinearity M2 for the TD-NC and (b) truncation factor α for the FD-NC.
We also investigate the performance of nonlinear equalizers under IEEE 802.15 WAPN VLC channels [18] by simulations. Two different multi-path channels corresponding to the test points D6 in the “open office” and D7 in the “office with cubicles” [18] are employed. The LED is modeled by cascading a 3-tap FIR filter (the coefficients are [1, 0.15, 0.1]) with a memoryless Rapp nonlinearity model (the keen factor k = 2, the maximum allowable current Imax = 0.5 A and the turn-on voltage VTOV = 0.2 V) [14]. The bias voltage and the peak-to-peak amplitude of driving signal are 0.6 V and 0.5 V, respectively. The simulated OFDM parameters are chosen as: the FFT length is 1024, the number of used subcarriers is 450, the cyclic prefix length is 64, the modulation format is 64 QAM and the sampling period is 4 ns. The corresponding electrical bandwidth and transmission rate are about 110 MHz and 659 Mbps, respectively. The schematic description of simulation setup is the same as Fig. 1 in [9]. The received SNR without the impact of LED nonlinearity is set to 26 dB. The recovered average SNR with linear equalizer FDE are 17.68 dB and 17.57 dB for the two channels, respectively. The large SNR degradations show the strong impact of LED nonlinearity. For the cases with nonlinear equalization, the recovered average SNR with different M2 in the TD-NC and different truncation factor α for the FD-NC are shown in Fig. 5 (dash lines). The simulation results verify that the performance of the FD-NC (TD-NC) is improved with a larger truncation factor α (memory length M2). The FD-NC with α = 7 and the TD-NC with M2 = 7 have similar performance, which offer about 5.8 dB and 4.6 dB SNR gain over FDE under the two channels, respectively. By comparing the results under two different channels, it is observed that the interplay between the nonlinearity of LED and multi-path transmission has a larger impact on the system performance when the channel has a larger RMS delay spread [18] (i.e., D7 in the “office with cubicles”).
The SNR distribution in frequency domain under the optimized driving signal power is shown in Fig. 6. The insets in Fig. 6 show the amplitude of corresponding FD-NC kernels, which illustrate the diversity of nonlinear characteristic of different types of LEDs. Compared with linear equalization case, the SNR of all subcarriers can be improved when nonlinearity is mitigated by FD-NC with a non-zero truncation factor α. The improvement of performance at the lower frequency band requires a larger truncation factor α, which gives a more accurate description of system nonlinearity, than that is required for the higher frequency band. According to Eqs. (4)-(6), for the same equalization process in Eq. (4), the TD-NC with the 2nd order memory length of M2 and the FD-NC without truncation (i.e., α = M2) are two equivalent equalizers. For the FD-NC, truncation increases the modeling error. However, when the kernels in Eq. (6) (n is the subcarrier index) are trivial for a certain L for most of the subcarriers, the truncation of terms associated with these kernels in the FD-NC causes only a small performance degradation. For the red/green/blue/white LEDs in our experiments, the mean amplitude of the normalized 2nd order kernels (L = 0, 1, 2, 3, 4, 5, 6) from channel estimation are [1.88, 0.83, 1.21, 1.28, 0.56, 0.97, 0.66], [2.54, 1.70, 0.61, 1.48, 1.31, 0.53, 0.90], [3.38, 1.87, 1.40, 2.37, 1.21, 0.81, 1.08], [2.00, 1.42, 0.73, 1.82, 2.08, 1.27, 0.93], respectively. Note that estimation error exists in the above results. Therefore, the performance of FD-NC with truncation factor α = 5 (i.e., terms with kernels are truncated if L ≥ 5) is comparable with that of the TD-NC with M2 = 7 for the four LEDs in our experiments.
Fig. 6 SNR distribution under the optimal driving signal power after the FD-NC and the TD-NC for the (a) red (b) white (c) green and (d) blue LED. The insets show the amplitude of the 1st and 2nd order kernels of FD-NC.
The convergence characteristic of the proposed FD-NC is also investigated. The normalized amplitude of kernels of three different subcarriers at the low/middle/high frequency range (i.e., A1 A20 ... A24 for the 15th, 120th and 230th subcarriers) as a function of the number of training symbols (i.e., number of iterations in RLS estimation) are shown in Fig. 7. For fair comparison, the amplitude of kernels of each subcarrier are normalized to the amplitude of its converged linear kernel (A1). Most of the estimated kernels are converged after 30 iterations. For each subcarrier, the linear kernel has the highest convergence speed for all listed kernels. The nonlinear kernels of the higher frequency subcarriers are found to be smaller than that of the lower frequency subcarriers. This is in consistent with the observation in Fig. 6 that the LED nonlinearity has a larger influence on the low frequency band [20].
Fig. 7 The convergence performance of the proposed FD-NC algorithm. The kernels of (a) the 15th subcarrier, (b) the 120th subcarrier and (c) the 230th subcarrier.
The dependence of the performance of the FD-NC on the length of training symbols is shown in Fig. 8. When the number of training symbols is large, a higher average SNR can be obtained by increasing the truncation factor α. In other words, with sufficient training symbols the highest average SNR is always achieved with the largest α for all types of LEDs (e.g., α = 7 with 60 training symbols). However, when the length of training symbols are set to be moderate to reduce the training overhead, the best performance is achieved with a moderate truncation factor α. For example, with 30 training symbols the optimal truncation factors α are 5, 5, 4, 5 for the red, white, green and blue LEDs, respectively.
Fig. 8 SNR performance of the FD-NC versus training symbol number with different α for the (a) red, (b) white, (c) green and (d) blue LEDs.
For FD-NC equalizer based on the 2nd order inverse of nonlinearity, a larger truncation factor α gives a smaller modeling error and hence a better nonlinearity mitigation performance. Nevertheless, the number of the kernels to be estimated increases with a larger truncation factor α, which requires a longer training period to achieve a certain estimation accuracy. Another important observation is that for all LEDs the variation of average SNR is less than 0.3 dB when α exceeds 3 regardless of the number of training symbols employed. Since reducing the truncation factor helps to save computational resources, a moderate truncation factors can be used (i.e., α = 5, 5, 4, 5 for red, white, green and blue LEDs) to balance the performance and complexity. Note that wavelength-division-multiplexing (WDM) with R/G/B channels can be used to enhance the overall throughput of the VLC system [6]. Since the WDM channels can be well separated at the receiver using filters of different pass bands, the linear crosstalk due to wavelength multiplexing/demultiplexing can be very small [6]. On the other hand, as the red/green/blue LED chips are usually placed separately in a commercial RGB LED, good thermal and electrical insulation between R/G/B LED chips (i.e., negligible nonlinear crosstalk) can be achieved with a proper physical design. In this case, the nonlinear compensation of each WDM channels can be optimized independently using the method shown in this paper. If there is significant nonlinear crosstalk between different chips of a RGB LED due to poor thermal/electrical insulation, a joint optimization of nonlinear compensation of WDM channels (e.g., nonlinear compensation in MIMO system [19]) will be needed, which is left for future study.
By taking advantage of the SNR improvement in the whole frequency band with FD-NC, the system capacity can be improved using the adaptive bit-power loading method, such as the Chow algorithm [21]. We experimentally investigate an adaptive bit-power loading OFDM VLC system with FD-NC. Only the red LED is used as the light source in demonstration for concision. The measured bit error rate (BER) versus system capacity at transmission distance of 50 cm is shown in Fig. 9(a). Each BER result is measured over 3.6 × 106 bits. The estimated SNR and corresponding bit-power loading profile for a target capacity of 1.12 Gbps are shown in Fig. 9(b). The achievable capacity at BER of 3.8 × 10−3 are increased by about 20% with the FD-NC (α = 5) when compared with the FDE. The performance difference between the FD-NC (α = 5) and the TD-NC (M2 = 7) are negligible.
Fig. 9 (a) The measured BER versus system capacity at 50 cm, and (b) the corresponding bit-power loading profile with Chow algorithm for a system capacity of 1.12 Gbps.
Figure 10(a) shows the measured BER versus the transmission distance at a system capacity of 960 Mbps. The FD-NC (α = 5) and the TD-NC (M2 = 7) perform similarly. The distance at a BER of 3.8 × 10−3 can be extended from 0.7 m to 1.8 m when switching from FDE to FD-NC. Figure 10(b) plots the maximum capacity at BER of 3.8 × 10−3 with respect to the transmission distance. The capacity gap between FDE and FD-NC (α = 5) are larger than 175 Mbps in the whole range of transmission distance of interest (i.e., from 0.5 m to 2 m).
Fig. 10 (a) The measured BER performance at different transmission distance at system capacity of 960 Mbps, and (b) the maximum capacity at different transmission distance for the BER of 3.8 × 10−3.
4. Complexity analysis
The complexity of the proposed FD-NC method in terms of the required number of real-valued multiplication (RNRM) is presented in Table 1. For fair comparison, the time domain method TD-NC with truncation by including only the first α terms of the 2nd order operation on the right hand side of Eq. (4) is also included in Table 1. Both the TD-NC and FD-NC consist of two consecutive stages, namely the training stage and compensation stage. Since the nonlinearity of a typical indoor VLC systems changes slowly, a small training overhead on the magnitude of a few percentages is found to be sufficient (e.g., ≤ 4% in our experiments). Therefore, only the complexity of the compensation stage is considered in Table 1. In the TD-NC, the RNRM for each sample by Eq. (5) is t + α, where is the total number of kernels. Note that partial reuse of the yL(n) in the nonlinear compensation stage of next sample is assumed for the TD-NC to reduce the complexity. After all samples in the same OFDM symbol is processed with Eq. (4), one DFT operation is needed in the TD-NC to convert the signal from time domain to frequency domain for symbol decision.
Table 1. Complexity analysis of two nonlinearity compensation methods
Unlike the TD-NC, the complexity of the FD-NC method is mainly induced by calculating YL(n) with DFT. In the FD-NC, α + 1 times of DFT operation are conducted for one OFDM symbol. Nevertheless, only additional α + 1 multiplications are needed for nonlinear compensation in each subcarrier in the FD-NC as shown in Eq. (6). Unlike the TD-NC case, the RNRM of the FD-NC is independent of linear or nonlinear memory length. By taking advantage of the efficient implementation of DFT, such as split-radix FFT algorithms [22], the proposed frequency domain nonlinearity compensation method (FD-NC) can achieve a lower complexity than the time domain compensation method (TD-NC).
To show the complexity saving of the FD-NC over the TD-NC in a typical indoor VLC system, Fig. 11 depicts the ratio of RNRM of the TD-NC over that of the FD-NC with respect to truncation factor α [Fig. 11(b)] and the memory length of the 2nd order nonlinearity [Fig. 11(a)]. The system parameters are: oversampling factor S/N is 2, and memory length of linear equalizer M1 is 10. Note that oversampling is required to avoid aliasing between the out-of-band nonlinear interference and the information bearing baseband signal [23]. The RNRM of the proposed FD-NC is lower than the TD-NC for all cases shown in Fig. 11. With α = 5 and M2 = 7 used for the commercial LEDs in our experiments, the RNRM of the proposed FD-NC is 29.9% lower than that of the TD-NC. In case a small performance degradation is allowed with a small α, the complexity saving becomes much more significant. For example, when chose α to be 2 instead of 5, which results in 0.54 dB average SNR degradation in Fig. 8(a), the RNRM can be reduced approximately by half with the FD-NC when compared with the TD-NC. It is also shown that complexity saving increases with a larger memory length if a LED with stronger memory nonlinearity is used. For example, when the memory length M2 increases from 7 to 13 while α remains to be 5, the saving of RNRM with the FD-NC increases to 58.5%.
Fig. 11 Ratio of the RNRM of the TD-NC and FD-NC in one OFDM symbol with different (a) truncation factors α and (b) the memory length of the 2nd order nonlinearity M2. The oversampling ratio S/N is 2.
5. Conclusion
In this paper, we proposed a novel frequency domain method, FD-NC, to mitigate the nonlinearity in OFDM based VLC system. The proposed FD-NC method can be implemented with a tunable truncation factor α to balance the performance and complexity. The performance of the proposed method is investigated experimentally with four types of LEDs of different nonlinearity characteristics. The results of experiments show that the average SNR can be significantly improved by 4.22 dB, 2.13 dB, 3.68 dB and 5.65 using the FD-NC with moderate truncation factors rather than the linear equalization for red, white, green and blue LEDs, respectively. The compatibility of the proposed FD-NC method with bit-power loading OFDM VLC system is demonstrated with a red LED, which shows 2.5 times longer transmission distance for system capacity of 960Mbps with the FD-NC (α = 5). Compared with the case of linear equalization, the system capacity increases by about 18.7% (36.5%) for the transmission distance of 0.5 m (2 m). The complexity analysis shows that the frequency domain method requires less real-valued multiplications than the conventional time domain nonlinearity compensation method. For example, with the measured memory length of the 2nd order nonlinearity M2 of 7 and the truncation factor α of 5, the FD-NC saves 29.9% real-valued multiplications than the TD-NC. The saving of complexity is more significant for a larger memory length of nonlinearity or a smaller truncation factor.
Funding
National Natural Science Foundation of China (NSFC) (61605047, 61550110240, 61671212); Science and Technology Department of Zhejiang Province; Natural Science Foundation of Guangdong Province (2016A030313438, 2016A030313445); China Scholarship Council; Göran Gustafsson Stiftelse.
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