OFDM has been successfully applied to a wide variety

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1 1 Theoretical Analysis of the Effect of onlinear Clipping oise on the BER Performance of -Biased Optical OFDM Systems Mohammed S. A. Mossaad Abstract A theoretical analysis of the -biased optical OFDM O-OFDM transmission system is presented. In particular, the effect of both the bias the subsequent clipping, introduced at the transmitter, on the bit error rate BER performance metric is analyzed. The statistics of the nonlinear clipping noise are derived used in our derivation of the analytical epression for the BER. Our analytical results are compared to the corresponding simulation results for different design parameters. It is shown that both analytical simulation results are in good agreement. An additive white Gaussian noise AWG channel model, commonly used with wireless optical systems, is assumed. In addition, an implicit epression for the optimal value of the bias as a function of the signal-to-awg ratio is given. Inde Terms OFDM, intensity modulated direct detection, -biased optical OFDM, nonlinearities. I. ITRODUCTIO OFDM has been successfully applied to a wide variety of digital communications systems over the past years. It has been adopted in several broadb wireless communications cable stards. Two of its major advantages in wireless communications are its robustness against multipath dispersion ease of channel estimation in a time-varying environment. OFDM has been recently proposed for communication over optical fiber links to combat channel dispersion in fiber media which limits the data rate length of optical fiber links. Optical OFDM solutions can be broadly divided into two types: optical OFDM using intensity modulation IM optical OFDM using linear field modulation. In this paper, we focus on intensity modulation with direct detection IM/DD systems 1,, 3, 4. Intensity modulation implies that the power of the optical signal in the fiber is proportional to the OFDM information signal to be transmitted. However, the OFDM signal is generally a comple signal optical power must be real positive. To solve this problem, some conditions must be imposed on the OFDM subcarriers data so that the IFFT operation produces a real signal. In an OFDM frame, if the data symbols on the subcarriers have Hermitian symmetry, then the output of the IFFT operation is real, though not necessarily positive. To make the OFDM signal positive, we add a suitable bias clip the parts of the signal that are still negative, forcing them to zero 5. Then the OFDM signal is set to modulate an optical source. At the receiver, after photodetection, the bias is subtracted before the FFT operation. The clipping introduces nonlinear distortion LD noise. In this paper, we provide a theoretical characterization of the LD effects on the optical OFDM signal. onlinear effects in non-optical OFDM systems have been etensively studied 6, 7, 8, 9. 6 etends Bussgang s theorem its applications 10, 11, 1 to bpass memoryless nonlinearities with comple Gaussian nonzeromean nonstationary inputs. Clipping effects have been addressed in optical OFDM systems 3, 4. 4 compares between two types of IM/DD systems: -biased optical OFDM O-OFDM asymmetrically clipped optical OFDM ACO-OFDM. BER curves were obtained through simulations the BER performance of the two systems was compared. o analytical formulas were obtained for the BER, however. There are studies that have obtained BER formulas in the case of coherent optical OFDM systems 13. A recent study considered the clipping noise in an ACO-OFDM system a formula for the BER has been derived 14. But, to our knowledge, no previous studies have derived analytical results for BER in a O-OFDM system. In this paper, we derive an analytical epression for the BER of the O-OFDM system. The BER epression quantitatively shows how the LD noise affects the BER performance. In particular, we compare our analytical results obtained to the simulation results in 4. An additive white Gaussian noise AWG channel is assumed. This model is used for freespace optical FSO communication systems where the main source of noise is the electrical receiver front-end 4. The procedure we follow consists of tracing the signal as it is transmitted through the O-OFDM system up to the decision device at the receiver. Our goal is to statistically characterize the effects of the LD noise at the input of the decision device. We prove that each data-carrying OFDM subcarrier is subject to a multiplicative scaling factor K, which is a constant independent of the subcarrier number, an additive Gaussian noise term whose variance is dependent on the subcarrier number. We evaluate K the LD noise variance use them to obtain an epression for the BER. From the BER epression, the optimal value for the bias is derived. The remainder of this paper is organized as follows. The system model is described qualitatively in Section II. A detailed mathematical analysis of the O-OFDM signal before clipping is carried out in Section III. A detailed mathematical analysis of the O-OFDM signal at the output of the L block is provided in Section IV. The statistics of the decision variable at the receiver are derived in Section V. Based on this statistical characterization, a formula for the bit error

2 probability is given in Section VI, the optimal value of the bias is derived. In Section VII, we compare our analytical results with simulation results. Finally our conclusions are given in Section VIII. II. SYSTEM MODEL The system block diagram is presented in Fig. 1. A m k represents the information symbols, which come from a square QAM constellation. Superscript m denotes the OFDM frame number, whereas subscript k 0, 1,,..., 1 denotes the subcarrier number. is the number of OFDM subcarriers. In order to suit the implementation of optical IM, the output of the IFFT should be real. It can be shown in a straightforward manner that this necessitates the following two conditions. In each OFDM frame a Hermitian symmetry condition must hold for k 0, / such that A m k A m k 1 In addition the 0 th / th subcarriers are set to zero, that is, A m 0 A m / 0 For each OFDM frame, the IFFT operation is carried out to transform comple numbers, the information symbols A m k, k 0, 1,,..., 1 to real numbers, the samples of the OFDM signal in time domain m n. Thus, m n 1 A m k e jπkn/ 3 k0 for n 0, 1,..., 1. It is noted here that, due to the central limit theorem, m n has a Gaussian distribution, provided is sufficiently large. Since is typically equal to 64, 18, etc., the Gaussian assumption is valid. All samples m n are real, but some samples are negative hence not suitable for intensity modulation. To overcome this problem, a bias B is added to m n to produce o m n : o m n m n B 4 We define the factor α as the ratio between B the RMS value of m n. Thus: B α E m n 5 We define the bias in db, B db, as: B db 10 log 10 E o m n E m n 10 log 10 α 1 6 Some samples o m n may still be negative. Therefore, the samples o m n are clipped, that is, all negative samples are set to zero. At the receiver, the bias is subtracted before the samples are fed to the FFT block. But the clipping causes loss of information in the sense that, ignoring all other sources of noise error, the recovered symbols at the receiver will be noisy versions of those transmitted due to clipping. We develop an analytical approach to characterize this noise component its effect on BER performance. We also emphasize the effect of the bias on the clipping noise. Clearly, the larger the bias, the smaller the clipping noise. But a large bias would mean increased transmission power. So there is a trade-off between power BER performance. Thus, the value of B should be optimized according to system requirements. It is noted that the input sample suffers clipping only when its value is less than. The OFDM signal is then used to modulate an optical source which is assumed to be ideal, achieving a linear transformation between the input signal the output optical power. An AWG channel is assumed. At the receiver, after ideal photodetection, the signal vt is sampled the samples vn m are fed to the FFT block which is followed by the symbol detector. III. MATHEMATICAL AALYSIS OF THE O-OFDM SIGAL BEFORE CLIPPIG In this section, we provide a complete statistical description of the O-OFDM signal at the input of the clipping device. It is necessary to obtain the input statistics, in order to derive the output statistics the statistics of the decision variable at the receiver in Section V. The O-OFDM signal, before clipping, is given by: t m m n g t nt mt 7 where m n is given in 3. T is the channel symbol time, gt is the pulse shaping function introduced when converting the signal from digital to analog after IFFT. g t is chosen to be limited in time, that is, g t 0 for t > T/. For simplicity, we choose g t to be a rectangular pulse of unity amplitute a duration of T, centered at t 0. Therefore, g t can be epressed as: { 1 for T/ t < T/ g t Π t 8 0 for t < T/ or t T/ Symbols A m k belong to an alphabet A of M elements, which depend on the modulation format, have the same probability. In order for t to be real, conjugate symmetry conditions are imposed on the subcarrier data the 0 th / th subcarriers are set to zero as described by Eqs. 1. Considering square QAM constellations, A m k can be written in terms of its real imaginary parts: A m k X m k jy m k 9 where the real imaginary parts; X k Y k, respectively; are zero-mean rom variables with E Xk m E Yk m 10 E Xk m E Yk m P k 0, / 11 where P is the average energy per symbol in the constellation. It follows from that: E Xk m E Yk m P/ k 0, / 1

3 3 Fig. 1. System block diagram. Also, for a square QAM constellation, assuming all information symbols are sent with equal probabiliy: More generally, E X m k Y m k 0 13 E X m k Y l h 0 14 for every k, h 0, 1,..., 1 for every m l. It follows from the conjugate symmetry condition that: E Xk m X k l {P/ for m l k 0, / 0 otherwise E Yk m Y k l { P/ for m l k 0, / 0 otherwise Based on Eqs , the following relations hold for every k, h 0, 1,..., 1 for every m l: E A m k 0 17 E A m k A l {P for m l h k, k 0, / h 0 otherwise { 18 E A m k A l P for m l h k, k 0, / h 0 otherwise 19 The mean of the sample m n is: β E m n 1 E A m k e jπkn/ 0 0 k0 where 17 was used. The mean square value of the sample m n is computed as follows: σ E m n 1 1 k0 h0 k1 k / 1 E A m k A m h e jπkhn/ P e jπk kn/ P 1 where the second line follows from 18 the factor in the last line accounts for the two subcarriers set to zero. The covariance of two samples of t, m n m p, taken at t m n nt mt t m p pt mt, respectively, is given by: µn, p E m n m p 1 1 P k0 h0 k1 k / k1 k / E A m k A m h e jπknhp/ P e jπkn kp/ e jπkn p/ P 1 e jπkn p/ e jπ kn p/ k1 1 P for n p P for n p even n p 0 for n p odd where the third equality follows from 18. Eqs. 0, 1,, the Gaussian assumption provide a complete statistacal description of the rom signal t its samples m n up to the second order statistics. The correlation coefficient of the two samples m n m p is given by: µn, p ρn, p σ 1 for n p 1 1 for n p even, n p 3 0 for n p odd In the net section, we consider the effects of the nonlinear clipping device on the statistics of the O-OFDM signal. IV. MATHEMATICAL AALYSIS OF THE O-OFDM SIGAL AT THE OUTPUT OF THE OLIEAR BLOCK We focus our attention on the output of the nonlinear block ut. Our goal is to represent this output as u t F t K t d t 4

4 4 where F. is the nonlinear clipping function, dt is a suitably introduced additive noise term, K is a deterministic function. The cross-correlation between the input to the nonlinear clipping device t delayed by τ the output u t is evaluated using their joint statistics as follows: Eutt τ EF tt τ 5 Denote t as 1 t τ as for simplicity. Thus, we can write: Eutt τ EF 1 F 1 f X1X 1, d 1 d 6 1 are jointly Gaussian RVs with zero means. Each has a variance of σ. Let µ E 1 be the covariance of 1 ρ µ σ be their correlation coefficient. The bivariate Gaussian distribution is defined in terms of these parameters: 1 f X1 X 1, πσ ep 1 ρ 1 1 ρ 1 ρ 7 The nonlinear clipping function is given by: { for < F 8 for Substituting from 8 into 6, we get: EF 1 B 1 f X1 X 1, d 1 d 1 f X1 X 1, d 1 d 9 Carrying out the integrations, we get: E F 1 ρσ B ep πσ 1 3 γ π, B B 1 30 where γs, 0 ts 1 e t dt t s 1 e t dt is the 0 lower incomplete Gamma function. But ρσ E 1 Ett τ µ. Thus, 30 can be written as: B EF 1 ep B πσ 1 3 γ π, B 1 µ KE 1 31 where K B ep B πσ 1 3 γ π, B 1 3 From 31, F 1 can be epressed as: F 1 K 1 d 1 33 or F t Kt dt 34 where d 1 dt is an additive noise term uncorrelated with t τ. That is: Ed 1 Edtt τ 0 35 The mean of ut is computed as follows: Eut EF t EF 1 1 πσ 1 πσ σ ep π ep 1 ep B σ F 1 f X1 1 d 1 1 d 1 1 σ σ 1 B erfc d 1 B 36 From 33, Eut EF 1 KE 1 Ed 1 Ed 1 as E 1 β 0. Therefore, the mean, β d, of the noise term dt is: β d Edt Ed 1 σ ep B π 1 B B erfc 37 The representation of the output of the nonlinear clipping device given by 34 indicates that the effect of the clipping on the input O-OFDM signal is a scaling factor K an additive noise term d t. For the probability of error to be properly evaluated, the effects of K d t on the input to the decision device at the receiver should be carefully considered. This is treated in the net section. V. STATISTICAL CHARACTERIZATIO OF THE DECISIO VARIABLES AT THE RECEIVER Assuming an additive white Gaussian noise AWG channel, the signal before the sampling at the receiver is given by: vt ut wt Kt dt wt 38 where wt is a zero-mean white Gaussian noise signal having a single-sided power spectral density of 0. Since the main noise source is electrical rather than optical, the AWG is bipolar, rather than unipolar. Sampling at t m n nt mt, we get the samples that are fed to the FFT operation: v m n u m n w m n K m n d m n w m n 39

5 5 The FFT output is, hence: where Vk m 1 vn m e jπkn/ 1 K m n e jπkn/ 1 d m n e jπkn/ 1 wn m e jπkn/ KA m k D m k W m k 40 Dk m 1 d m n e jπkn/ 41 is the clipping noise component at the k th subcarrier at the output of the FFT block Wk m 1 wn m e jπkn/ 4 is the AWG component. The variance of W m k, σ W, is computed as follows: σ W EW m k W m k 1 p0 1 E w m n Ew m n w m p e jπkn p/ σ w 43 where we have used the fact that Ewn m wp m 0 for n p as we have white noise uncorrelated from sample to sample. Here σw E wn m 0 is the variance of the AWG sample wn m. To obtain a formula for the BER, we also have to evaluate σd, the variance of Dm k. First, we compute the mean of Dk m: EDk m 1 Ed m n e jπkn/ { βd for k 0 0 for k 1,,..., 1 44 Thus, only the LD noise component affecting the 0 th subcarrier that does not carry any data symbols has a non-zero mean. We then proceed by computing the mean-square value of Dk m: E Dk m E Dk m Dk m 1 E d m n p0 1 E d m n d m p 1 E d m n d m p Ed m n d m p e jπkn p/ n p odd n p even p0 n p odd p0 n p even It can be easily shown that, for k 0, /: p0 n p odd p0 n p even e jπkn p/ e jπkn p/ 45 e jπkn p/ 0, 46 e jπkn p/. 47 Substituting from into 45, we get: E Dk m E where E d m n d m p d m n E d m n d m n p p even 48 n p even is to be evaluated using a corre- lation coefficient ρn, p 1 1 ρ according to 3. The first term of the right-h side of 48 is: where E d m n E u m n K m n E u m n E u m n E F 1 K E m n KEu m n m n 49 E m n σ, 50 f X1 1 d 1 1f X1 1 d 1 B B πσ 1 πσ 1 B erfc σ ep 1 1 ep B B 1 1 π γ d 1 1 σ d 1 3, B, 51

6 6 Eu m n m n EF f X1 1 d 1 1f X1 1 d 1 1 d 1 B 1 ep πσ 1 1 ep 1 πσ d 1 σ B ep B πσ 1 3 γ π, B 1 Kσ. 5 Substituting 50-5 into 49, we get, after a few algebraic manipulations: E d m n 1 B erfc σ 1 π γ B 3, B σ 1 K 53 Turning our attention to the second term of the right-h side of 48, we have: Ed m n d m p Eu m n K m n d m p Eu m n d m p where Eu m n u m p K m p Eu m n u m p KEu m n m p Eu m n u m p KEK m n d m n m p Eu m n u m p K E m n m p 54 E m n m p µ ρ σ, 55 Eu m n u m p EF 1 F B 1 B B 1 1 B B σ π f X1X 1, d 1 d f X1 X 1, d 1 d 1 f X1 X 1, d 1 d 1 f X1 X 1, d 1 d ρ 1 ρ B σ π 1 1 erfc B σ π 1 ρ ρ σ ρ σ π erfc ρ B σ 1 ρ e B σ e σ d B 1 ρ 1 ρ 1 ρ 1 ρ 1 ρ σ π ep B σ 1 ρ e B B σ erfc 1 1 erfc B γ 3, ρ B 1 ρ e σ d. σ Substituting from 55 into 54, we get: 56 Ed m n d m p Eu m n u m p ρ K σ 57 oting that, for k 0, the variance of Dk m : σd E Dk m E Dk m E D m k E Dk m 58 due to 44, then substituting from into 48, we get: σd E Dk m 1 B B erfc 1 3 σ π γ, B 1 1 ρ K E u m n u m p 59 The variance of the noise term Dk m affecting the kth subcarrier represents the energy of the noise term. Applying the central limit theorem to 41, the pdf of Dk m approaches a Gaussian pdf, the approimation gets closer to the true pdf as increases. This approimation causes a discrepancy between the BER simulation results our derived BER formula which assumes the nonlinear clipping noise is Gaussian. It is noticeable only in the high SR regime where the nonlinear clipping noise dominates over the AWG.

7 7 VI. EVALUATIO OF ERROR PROBABILITY The decision variable at the input of the decision device is given by: V m k KA m k D m k W m k 60 We divide by K so that the received constellation is a noisy, but not a scaled version of the transmitted constellation. The input to the decision device becomes: V m k A m k Dm k K W m k K 61 The symbol-error probability P e can be evaluated by considering error probabilities conditioned on the transmission of each symbol of the modulation alphabet, as follows P e 1 1 Prob { Vk m S A A m k A } 6 M A A where S A is the decision region for symbol A. It requires the statistical characterization of the decision variable Vk m. Starting from the epression of the decision variable at the input of the decision device given in 60, we can evaluate the bit-error probability as a function of the modulation format the signal-to-total-noise ratio S/ σ σ D /K σ W /K K σ σ D σ W 63 An epression of the bit-error probability can be derived for several modulation formats. In this paper, we specialize the derivation for square M-QAM constellations. In this case, the probability of error is given by 15: M 1 P e M log M erfc 3 S/ M 1 M 1 M log M erfc 3K σ M 1 σd σ W 64 The bit-error probability has an irreducible floor M 1 P efloor M log M erfc Kσ 3 σ D M 1 65 which depends on the signal-to-ld-noise ratio K /σ D. In the net section, we plot the bit-error probability epression obtained above versus E b / 0 where E b is the electrical energy per bit we compare to simulation results. We now eplain the procedure to obtain the optimal bias. Our first goal is to epress the AWG variance σ w as a function of the bias B. This is necessary for deriving an epression for the optimal bias, since all parameters affecting the probability of error must be epressed as a function of the bias. The signal-to-awg ratio per subcarrier σ B /0 equals the signal-to-awg ratio per bit E b / 0 times the number of bits per symbol log M. Thus, we have: σ B 0 E b 0 log M 66 from which 0 σ w σ B 10 E b/ 0 db/10 log M 67 et, the optimal bias B o can be found by maimizing the signal-to-total-noise ratio S/ given by 63 with respect to B. Differentiating with respect to B equating to zero, we get: K σ B D σw σ K D B σ w B B B o 0 68 Epressing K, σd, σ w as functions of B using 3, 56, 59, 67, making the approimation ρ 0 to simplify the result, carrying out the differentiations, we obtain the following implicit epression for the optimal bias B o : B o π ep B o Bo σ erfc σ π π ep σ π 10 E b/ 0 db/10 log M ep B o π σ ep B o Bo B o erfc Bo σ ep B o erfc π B o erfc B o 10 E b/ 0dB/10 log M 1 π γ σ 3, B o σ 3B o 1 σ Bo 0 69 Eq. 69 can be solved numerically for B o. The optimal bias B o is a function of the signal-to-awg ratio per bit E b / 0 the square QAM constellation size M. In the net section, the epression for B o is compared to simulation results. VII. UMERICAL RESULTS Results were obtained for, 048 subcarriers, with 4-QAM, 16-QAM, 64-QAM constellations. Linear field modulation bipolar 4-QAM where Hermitian symmetry is not imposed no bias clipping are needed is included for reference. A bias of 7 db is used. This is the same value used for the simulation in 4. We reproduce the simulation results in 4 compare them to the analytical BER epression given by 64 that we derived in the previous sections. The results are shown in Fig.. The analytical epression derived for the bit-error probability is plotted in red while the simulation results are shown in black. The results show close agreement. A small discrepancy arises, howerver, for small E b / 0 values. This is due to the fact that the BER formula used ignores symbol errors involving non-adjacent QAM symbols. Each of such errors corresponds to more than one bit in error assuming Gray coding is used. At low E b / 0 values, these errors are significant, but as E b / 0 increases beyond a few dbs, they can be safely ignored. Another small discrepancy occurs between the analytical BER formula the simulation results for large E b / 0 values, which is noticeable in the 64-QAM case as is clear in Fig..

8 8 Fig.. BER versus SR E b / 0 db curve: analytical epression in red simulation results in blue. Fig. 3. Plot of the simulated BER versus the Bias in db with 16-QAM different values of E b / 0 db. Also plotted for comparison is the analytical optimal bias the corresponding BER.

9 9 This is due to the the assumption used in the derivation of our BER formula, that Dk m has a Gaussian pdf. This discrepancy almost disappears if we simulate for 16, In this case, applying the CLT, the Gaussian pdf is very close to the true pdf, as is very large. In Fig. 3, the simulated BER is plotted versus the bias with 16-QAM for different values of E b / 0. It can be noticed that the curves have a minimum value at the optimal bias. Also, plotted in the same figure for comparison, is the analytical optimal bias given by 69 the corresponding analytical BER. The simulation analytical results closely agree. 10 A. Papoulis. Probability, Rom Variables, Stochastic Processes. ew York: McGraw-Hill, 3rd edition, H. E. Rowe. Memoryless nonlinearities with Gaussian inputs: Elementary results. Bell Syst. Tech. J., vol. 61, no. 7:pp , Sept J. Minkott. The role of AM-to-PM conversion in memoryless nonlinear systems. IEEE Trans. Commun., vol. COM-33:pp , Feb X. Yi, W. Shieh, Y. Ma. Phase noise effects on high spectral efficiency coherent optical ofdm transmission. IEEE Journal of Lightwave Technology, vol. 6, no. 10:pp , May Svilen Dimitrov Harald Haas. On the clipping noise in an acoofdm optical wireless communication system. In GLOBECOM, pages 1 5, Raed Mesleh, Hany Elgala, Harald Haas. On the performance of different ofdm based optical wireless communication systems. J. Opt. Commun. etw., vol. 3, no. 8:pp , August 011. VIII. COCLUSIOS In this paper, we have mathematically analyzed a O- OFDM system with the focus on the effect of the nonlinear clipping noise on the BER performance. Specifically, the clipping noise statistics were studied in details, an analytical formula was derived for use in the BER evaluation. The dependence of the BER on the bias, an important design parameter, is characterized in the BER formula. It can be seen that as the bias is increased, the transmitted power increases, but the nonlinear clipping noise is reduced leading to some sort of trade-off. Hence, the value of the bias should be optimized according to the system constraints the required BER performance. In the light of this observation, we have found the optimal value of the bias, the one that minimizes the probability of error for a given E b / 0 QAM constellation size M. Our analysis results provide a theoretical basis for the design implementation of O-OFDM systems. Our results are valid for wireless optical systems where the main source of noise is the electrical receiver front-end. Future work should consider optical fiber transmission include the optical effects of chromatic dispersion, polarization mode dispersion, fiber nonlinearity, amplified spontaneous emission ASE noise, etc. REFERECES 1 J. B. Carruthers J. M. Kahn. Multiple-subcarrier modulation for nondirected wireless infrared communication. IEEE J. Sel. Areas Commun., vol. 14:pp , O. Gonzalez, R. Perez-Jimenez, S. Rodriguez, J. Rabadan, A. Ayala. OFDM over indoor wireless optical channel. IEEE Proc. Optoelectronics, vol. 15:pp , J. Armstrong A. J. Lowery. Efficient optical OFDM. Electron. Lett., vol. 4:pp , J. Armstrong B. J. C. Schmidt. Comparison of asymmetrically clipped optical OFDM -biased optical OFDM in AWG. IEEE Commun. Lett., vol. 1:pp , Jean Armstrong. OFDM for optical communications. IEEE/OSA J. Lightwave Technol., vol. 7, no. 3:pp , February D. Dardari, V. Tralli, A. Vaccari. A theoretical characterization of nonlinear distortion effects in OFDM systems. IEEE Trans. Communications, vol. 48, no. 10:pp , A. R. S. Bahai, M. Singh, A. J. Goldsmith, B. R. Saltzberg. A new approach for evaluating clipping distortion in multicarrier systems. IEEE J. Sel. Areas Commun., vol. 0, no. 5:pp , Jun H. Ochiai H. Imai. Performance analysis of deliberately clipped OFDM signals. IEEE Trans. Commun., vol. 50, no. 1:pp , Jan Y. Ermolova. Analysis of OFDM error rates over nonlinear fading channels. IEEE Trans. Wireless Commun., vol. 9, no. 6:pp , June 010. Mohammed S. A. Mossaad was born in Aleria, Egypt, in He received the B.S. M.S. degrees in Electrical Engineering from Aleria University, Aleria, Egypt, in , respectively. He is currently working towards the PhD degree at the Department of Electrical Computer Engineering, McMaster University, Hamilton, Ontario, Canada. His current research interests include signaling design for visible light communications, OFDM for optical communications.