An adaptive scaling and biasing scheme for OFDM-based visible light communication systems

Orthogonal frequency-division multiplexing (OFDM) has been widely used in visible light communication systems to achieve high-rate data transmission. Due to the nonlinear transfer characteristics of light emitting diodes (LEDs) and owing the high peak-to-averagepower ratio of OFDM signals, the transmitted signal has to be scaled and biased before modulating the LEDs. In this contribution, an adaptive scaling and biasing scheme is proposed for OFDM-based visible light communication systems, which fully exploits the dynamic range of the LEDs and improves the achievable system performance. Specifically, the proposed scheme calculates near-optimal scaling and biasing factors for each specific OFDM symbol according to the distribution of the signals, which strikes an attractive trade-off between the effective signal power and the clipping-distortion power. Our simulation results demonstrate that the proposed scheme significantly improves the performance without changing the LED’s emitted power, while maintaining the same receiver structure. © 2014 Optical Society of America OCIS codes: (060.0060) Fiber optics and optical communications; (060.2605) Free-space optical communication; (060.4510) Optical communications. References and links 1. A. Jovicic, J. Li, and T. Richardson, “Visible light communication: opportunities, challenges and the path to market,” IEEE Commun. Magazine 51(12), 26–32 (2013). 2. Q. Wang, Z. Wang, S. Chen, and L. Hanzo, “Enhancing the decoding performance of optical wireless communication systems using receiver-side predistortion,” Opt. Express 21(25), 30295–30395 (2013). 3. J. Vučić, C. Kottke, S. Nerreter, K. Langer, and J. W. Walewski, “513 Mbit/s visible light communications link based on DMT-modulation of a white LED,” J. Lightwave Technol. 28(24), 3512–3518 (2010). 4. Z. Wang, C. Yu, W. Zhong, and J. Chen, “Performance improvement by tilting receiver plane in M-QAM OFDM visible light communications,” Opt. Express 19(14), 13418–13427 (2011). 5. 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 Photonics J. 4(5), 1465–1473 (2012). 6. 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). 7. Y. Wang, N. Chi, Y. Wang, R. Li, X. Huang, C. Yang, and Z. Zhang, “High-speed quasi-balanced detection OFDM in visible light communication,” Opt. Express 21(23), 27558–27564 (2013) 8. H. Elgala, R. Mesleh, and H. Haas, “Non-linearity effects and predistortion in optical OFDM wireless transmission using LEDs,” Inderscience International J. Ultra Wideband Commun. Syst. 1(2), 143–150 (2009). #208416 $15.00 USD Received 17 Mar 2014; revised 20 Apr 2014; accepted 27 Apr 2014; published 16 May 2014 (C) 2014 OSA 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.012707 | OPTICS EXPRESS 12707 9. S. Dimitrov, S. Sinanovic, and H. Haas, “Clipping noise in OFDM-based optical wireless communication systems,” IEEE Trans. Commun. 60(4), 1072–1081 (2012). 10. J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol. 27(3), 189–204 (2009). 11. T. Komine, J. H. Lee, S. Haruyama, and M. Nakagawa, “Adaptive equalization system for visible light wireless communication utilizing multiple white LED lighting equipment,” IEEE Trans. Wirel. Commun. 8(6), 2892– 2900 (2009). 12. J. Li, X. Zhang, Q. Gao, Y. Luo, and D. Gu, “Exact BEP analysis for coherent M-ary PAM and QAM over AWGN and Rayleigh fading channels,” in Proc. IEEE VTC-Spring, 390–394 (2008). 13. S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University, 2004). 14. J. G. Proakis and M. Salehi, Digital Communications, 5th ed. (McGram-Hill, 2008).


Introduction
Light emitting diodes (LEDs) have emerged as a power-efficient alternative to replace incandescent bulbs for illumination owing to their inherent benefits of bright output and long lifetime.Furthermore, LEDs are increasingly applied for visible light communications (VLC) as a benefit of their low cost [1,2].In order to achieve high-rate transmission, orthogonal frequencydivision multiplexing (OFDM), which is also known as discrete multi-tone modulation (DMT), is commonly used in VLC, whereby gigabit transmissions have been reported in [3][4][5][6][7].
In contrast to radio frequency (RF) systems where the signal modulates the carrier in the electronic domain, in VLC systems the signal modulates the light emitted by the optical emitter and the light-intensity of LEDs is proportional to the power of the transmitted signal.At the receiver, the optical signal is detected by photodiodes (PDs) or avalanche photodiodes (APDs) and converted to the electronic signal, whose amplitude is proportional to the received optical power.Therefore, the transmitted signal has to be real-valued and non-negative.Apart from these requirements, due to the nonlinear transfer characteristics of the LEDs, the transmitted signal is constrained in a limited range even after pre-distortion [8], which limits the performance of OFDM due to its inherently high peak-to-average-power ratio (PAPR).In current OFDM-based VLC systems, the time-domain OFDM signal is firstly scaled by a constant factor and clipped according to the predefined dynamic range.Then a DC bias is added to shift the transmitted signal into the non-negative linear range of LEDs [5,6].Given that the expectation of the time-domain OFDM symbol is zero, when the 0th subcarrier is set to zero, the scaling factor does not change the LED's emitted power, provided that the signal is symmetric in the predefined dynamic range.A larger scaling factor results in a higher effective power at the receiver [9], which mitigates the effect of the receiver's noise, but it also imposes higher clipping distortion at the transmitter.Therefore, a trade-off has to be struck between the effective power and the clipping distortion, when choosing an appropriate scaling factor.Similarly, the DC bias must also be carefully selected to minimize the clipping distortion, which is usually set to the mid-point of the LED's linear range.However, the signal distribution is different within each specific OFDM symbol, since different OFDM symbols contain different transmitted information.Consequently, using constant scaling and biasing factors throughout the entire transmission period cannot fully exploit the linear range of LEDs, and will hence impose a performance degradation.
In this contribution, a novel adaptive scaling and biasing scheme is proposed for OFDMbased VLC systems, which fully exploits the dynamic range of the LEDs for each individual OFDM symbol in order to enhance the achievable system performance.The basic idea of the proposed scheme is based on the observation that different OFDM symbols require different optimal scaling and biasing factors for fully exploiting the linear range of the LEDs.More specifically, the proposed scheme calculates near-optimal scaling and biasing factors for each specific OFDM symbol according to the signal's distribution, which strikes an attractive compromise between the effective electronic power and the clipping distortion power.The proposed adaptive scaling and biasing scheme does not change the LED's emitted power at the transmitter.Furthermore, since no extra operations are needed at the receiver, the receiver structure also remains unchanged.Our simulation results show that this adaptive scaling and biasing scheme significantly improves the performance of OFDM-based VLC systems.
The remainder of this treatise is organized as follows.In Section 2, the conventional OFDMbased VLC system is presented, while in Section 3, our proposed adaptive scaling and biasing scheme is described.In Section 4, the performance of the proposed VLC system is compared to that of the conventional OFDM VLC method, whilst our conclusions are drawn in Section 5.

System model
A typical OFDM-based VLC system is depicted in Fig. 1.The transmitted bit stream is mapped to the complex-valued symbols, X(m), according to the chosen modulation scheme, such as pulse amplitude modulation (PAM), quadrature amplitude modulation (QAM) or phase shift keying (PSK).For an OFDM symbol with the N subcarriers and the bandwidth of B, N symbols are assigned to all the subcarriers, each having a bandwidth of B/N.To guarantee that the timedomain OFDM signal is real-valued, however, Hermitian symmetry is imposed on the OFDM subcarriers where we have and the 0th as well as the N/2th subcarriers are set to zero.Therefore, only N/2 − 1 symbols are actually contained in an OFDM symbol with N subcarriers.The time-domain OFDM signal is obtained by the inverse fast Fourier transform (IFFT) as [10] x which follows a Gaussian distribution according to the central limit theorem (CLT).Due to the nonlinear transfer characteristics of the LEDs, the transmitted time-domain signal is constrained in a limited range even after pre-distortion, which is denoted as [z min , z max ] [9].Therefore, a linear transformation is performed on the time-domain signal x(k), and the linearly transformed signal should be clipped, when it is outside the predefined range.We denote the scaling and biasing factors of this linear transformation by α and x bias , respectively.The clipped signal x c (k) is then given by (3) A cyclic prefix (CP) is added to the beginning of each time-domain OFDM symbol to eliminate the inter-symbol interference (ISI) at the receiver.The clipped signal is then parallel to serial (P/S) converted into a single signal stream, which is then biased and used for modulating the LEDs.
At the receiver, the signal is detected by APDs and converted to the electronic signal.Both shot-noise and thermal-noise are then introduced at the receiver, which may be modeled by an additive white Gaussian noise (AWGN) process [11].After serial-to-parallel (S/P) conversion and CP removal, the received signals y(0), y(1), • • • , y(N − 1) are then transformed to the frequency domain by FFT according to which are used to demodulate according to the modulation scheme employed.
Noting that the bias x bias introduced at the transmitter only affects the 0th subcarrier, which is not used to carry useful information.Therefore, the effective electronic power at the receiver is only determined by the transmitter's scaling factor α.After the FFT operation, the zero-mean complexvalued AWGN, which models the receiver's shot-noise and thermal-noise, has a two-sided power spectral density of N 0 /2 per dimension and a variance of σ 2 AW GN = BN 0 .The clippingdistortion n c (k) introduced at the transmitter may also be modeled by a Gaussian distribution with a variance of σ 2 clip owing to Central Limit Theorem (CLT), which has been studied in [9].For an M-QAM OFDM-based VLC system, the bit error ratio (BER) performance can be formulated as [12] where Γ b(elec) denotes the effective electronic signal-to-noise ratio (SNR) at the receiver, which is defined as where P s is the average effective electrical power at the receiver.The specific linear transformation invoked at the transmitter directly influences both the effective electronic power and the clipping-distortion power.For a given dynamic range of the LEDs, the clipping-distortion is determined by both the scaling and biasing factors, α and x bias .For a small scaling factor, the clipping-distortion is also small and may even become negligible in comparison to the shot-noise and thermal-noise at the receiver.But the effective electronic power at the receiver is also small given a small α, hence the overall effective electronic SNR at the receiver becomes low.By contrast, increasing the scaling factor increases the effective electronic power at the receiver, but it also results in a signal, which is more likely to be outside the linear range of the LEDs, which in turn increases the clipping-distortion.Therefore, striking a compromise between the effective electronic power and the clipping-distortion is necessary, when choosing appropriate values for the scaling and biasing factors, in order to maximize the effective electronic SNR and to achieve good BER performance.

Proposed scheme
In current OFDM-based VLC systems [5], the "optimal" fixed scaling and biasing factors are found by minimizing the BER, which is equivalent to choosing the fixed scaling and biasing factors that maximize the average effective electronic SNR, and the scaling and biasing factors remain unchanged throughout the entire transmission period.However, the signal distributions are different for individual OFDM symbols according to Eq. ( 2).More specifically, for an OFDM-based VLC system relying on M-QAM and N subcarriers, the OFDM symbol assumes one of M N/2−1 possible signals Figure 2 shows the dynamic range of x(k) in 10000 OFDM symbols with M = 16 and N = 64 as well as M = 64 and N = 256, where the average electronic power of x(k) is normalized.The dynamic range of x(k) varies for different OFDM symbols and hence using constant scaling and biasing factors cannot fully exploit the linear range of LEDs, hence imposing a performance degradation.An exhaustive search could be carried out to find the optimal scaling and biasing factors α (l) and x (l) bias for the individual signal states x (l) ∈ X by maximizing the individual effective electronic SNRs 2 denote the effective electronic power and the clipping-distortion power for the signal state x (l) , respectively.When the OFDM symbol takes the value of x (l) , the corresponding scaling and biasing factors α (l) and x (l) bias are applied.Such an exhaustive search would indeed, find the true optimal solution but its computational complexity may become prohibitive, since the size of the signal state set M N/2−1 is typically excessive.
Our proposed adaptive scaling and biasing scheme is computationally much simpler and it calculates near-optimal scaling and biasing factors for each OFDM symbol according to the distribution of the time-domain OFDM signals.In particular, the scaling factor is chosen to strike a compromise between the effective electronic power and the clipping-distortion power, while the biasing factor is determined by minimizing the clipping-distortion, given the selected scaling factor.In the following, the calculation of the scaling and biasing factors is detailed.

Scaling factor calculation
For a time-domain OFDM symbol {x(k), k = 0, 1, • • • , N − 1}, let us denote the maximum and minimum of the symbol by x max and x min , respectively.If the symbol is linearly transformed from [x min , x max ] to [z min , z max ], i.e. the scaling factor is given by α min = z max − z min x max − x min (10) and the corresponding biasing factor is x bias = z min − α min x min , the transformed signals fully exploit the linear range of LEDs and no clipping is needed at the transmitter.In other words, the clipping-distortion power becomes zero.However, the effective electronic power is also small.On the other hand, if we inclrease the scaling factor, the effective electronic power is increased, but the clipping-distortion power is also increased.Instead of performing a complicated optimization to find the optimal scaling factor that strikes the optimal trade off between the effective electronic power and the clipping-distortion power, for implementational convenience, we simply set the scaling factor to where x smax and x smin represents the second largest and second smallest signals of {x(k), k = 0, 1, • • • , N − 1}, respectively.In general, the choice of α in Eq. ( 11) is not optimal.Heuristically, we can justify that this choice strikes a good compromise between the effective electronic power and the clipping-distortion power, yielding a near-optimal result.Clearly, this α value is larger than that given in Eq. ( 10) and, therefore, it yields a higher effective electronic power.On the other hand, this α value is not too large and, consequently, only a few signals with large absolute value are clipped.Thus, the clipping-distortion power is kept small.This may result in a favorable near-optimal effective electronic SNR.Using Eq. ( 5) and noting that X(0) = X(N/2) = 0, we have which shows that the scaling factor does not change the optical power of the unclipped signal.
Although the pilot in the OFDM symbol is scaled at the transmitter, the receiver does not need any knowledge about the scaling factor.This is because the scaling factor can be considered as part of the scaled channel state information (CSI), and the channel estimator at the receiver estimates this scaled CSI for equalization.Thus, no extra operation is required at the receiver.

Biasing factor calculation
The biasing factor only affects the clipping-distortion and makes no contribution to the effective electronic power.Therefore, the selection of the biasing factor is based on minimizing the clipping-distortion power for the given scaling factor, and the optimal biasing factor is expressed as xbias = arg min where f (x) denotes the power of the clipping-distortion for each time-domain symbol, defined by The optimization problem in Eq. ( 13) can be solved by numerical algorithms, such as Newton's methods [13].However, the complexity associated with a numerical optimization algorithm can be high, especially because the number of subcarriers used in an OFDM-based VLC system is usually large.Note that given the chosen scaling factor in Eq. ( 11), only a few signals with a large absolute value are clipped at the transmitter.Therefore, we may consider simply the maximum and minimum of {x(k), k = 0, 1, • • • , N − 1} to directly derive a near-optimal biasing factor for solving the optimization of Eq. ( 13) as As discussed in Section 2, the bias only affects the 0th subcarrier, which is not used to carry the information.After the FFT operation at the receiver, the biasing factor is automatically removed.Therefore, the receiver does not have to know the biasing factor and no extra operation is needed at the receiver.

Computational complexity
As detailed in the previous two subsections, the proposed adaptive scaling and biasing scheme does not impose any extra operation at the receiver.Let us now summarize the computational requirements of this adaptive scheme at the transmitter.For the time-domain OFDM symbol {x(k), k = 0, 1, • • • , N − 1} to be transmitted, our adaptive scaling and biasing scheme first finds the largest, second largest, smallest and second smallest signals, x max , x smax , x min and x smin , of which involves a modest computational complexity.The calculation of the scaling factor of Eq. ( 11) requires just one multiplication and three additions, as 2(z max − z min ) is a known value, while the calculation of the biasing factor of Eq. ( 15) needs only two multiplications and two additions, since (z min + z max )/2 is a known value too.Clearly, this adaptive scaling and biasing scheme has an extremely low complexity.

Implementation issues
Practical implementations of OFDM-based VLC systems have been reported in [5,6].In our proposed scheme, the receiver remains unaltered.For the transmitter of Fig. and biasing modules have to be slightly modified according to our method.To elaborate a little further, the adaptive scaling and biasing factor may be calculated with the aid of Eq. ( 11) and Eq. ( 15), which may be readily implemented using either field programmable gate arrays (FPGA) or digital signal processors (DSP).Furthermore, the adaptive scaling module can be realized by adjusting the gain of the power amplifier, while the adaptive biasing module relies on adjusting the current of the driver.Therefore, our proposed scheme has a convenient lowcomplexity implementation.

Simulation results
The BER performance of the proposed adaptive scaling and biasing scheme was evaluated by simulation, in comparison to the conventional OFDM-based VLC system [5].The bandwidth of the LEDs was set to 100 MHz, and the linear range of the LEDs after pre-distortion was 0-160 mA [5].Two different modulation schemes were used, namely, 16QAM with 64 subcarriers and 64QAM with 256 subcarriers, yielding the overall transmission rates of 387.5 Mbps and 595 Mbps, respectively.In the conventional OFDM-based VLC system, the biasing factor was set to the middle of the linear range of the LEDs, i.e. x bias = 80 mA [5].The standard deviation of x(k) was assumed to be 80 mA.The target BER was set to 10 −3 , which was within the error correction capability range of the conventional forward error correction (FEC) codes, such as convolutional codes, turbo codes or low density parity check codes [14].
The single fixed scaling factor used for the conventional OFDM-based VLC system was determined by minimizing the required average normalized optical SNR (OSNR) to attain the required BER level of 10 −3 , which was the ratio of the normalized emitted optical power to the electronic noise power at the receiver.The normalized OSNR values required for achieving the BER level of 10 −3 for the two different modulation schemes are illustrated in Fig. 3.The fixed optimal scaling factors were -7.8 dB and -9.2 dB for the two cases, respectively, which were employed by the corresponding conventional OFDM-based VLC benchmark systems.Figure 4 compares the BER performance of our OFDM-based VLC system employing the proposed adaptive scaling and biasing scheme to that of the conventional system using the optimal fixed scaling factor indicated in Fig. 3.In our proposed scheme, the scaling factor  was calculated by Eq. ( 11) for each OFDM symbol, while the biasing factor was either directly obtained by Eq. (15) (denoted as approximate biasing) or calculated by solving the optimization of Eq. ( 13) using a numerical algorithm (denoted as optimal biasing).It can be clearly seen from Fig. 4 that our adaptive system outperformed the conventional optimal system by about 1 dB in terms of the OSNR.It can also be seen that the proposed adaptive scheme using the approximate biasing factor of Eq. ( 15) attained almost the same performance as the proposed adaptive scheme with the optimal biasing factor.Therefore, the low-complexity approximation in Eq. ( 15) is deemed sufficiently accurate.

Conclusions
A low-complexity adaptive scaling and biasing scheme has been proposed for OFDM-based VLC systems, which fully exploits the dynamic range of LEDs and is capable of significantly improving the attainable system performance, while imposing an extremely low computational complexity at the transmitter and requiring no additional operation at the receiver.In our adaptive scheme, near-optimal scaling and biasing factors are calculated for each specific OFDM symbol according to the distribution of the signals with a few multiplications and additions, which strikes a beneficial compromise between the effective electronic power and the clippingdistortion power.Our simulation results have shown that the proposed adaptive system outperforms the current OFDM-based VLC system that employs the fixed optimal scaling and biasing factors over the entire transmission period.

Fig. 2 .
Fig. 2. The dynamic range of the time-domain signal x(k) in an OFDM-based VLC system with M-QAM and N subcarriers.

Fig. 3 .
Fig.3.The required normalized OSNR to achieve the BER level of 10 −3 as the function of scaling factor for the conventional OFDM-based VLC system with M-QAM and N subcarriers.
Fig.4.The BER performance comparison of the conventional OFDM-based VLC system and our system with the proposed adaptive scaling and biasing scheme.The both systems employ M-QAM with N subcarriers.