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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 6 — Mar. 24, 2014
  • pp: 7269–7283
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System performance enhancement with pre-distorted OOFDM signal waveforms in DM/DD systems

C. Sánchez, B. Ortega, and J. Capmany  »View Author Affiliations


Optics Express, Vol. 22, Issue 6, pp. 7269-7283 (2014)
http://dx.doi.org/10.1364/OE.22.007269


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Abstract

In this work we propose a pre-distortion technique for the mitigation of the nonlinear distortion present in directly modulated/detected OOFDM systems and explore the system performance achieved under varying system parameters. Simulation results show that the proposed pre-distortion technique efficiently mitigates the nonlinear distortion, achieving transmission information rates around 40Gbits/s and 18.5Gbits/s over 40km and 100km of single mode fiber links, respectively, under optimum operating conditions. Moreover, the proposed pre-distortion technique can potentially provide higher system performance to that obtained with nonlinear equalization at the receiver.

© 2014 Optical Society of America

1. Introduction

Due to the emergence of multimedia and bandwidth intensive services, the development of efficient short-range (<100km) optical communication systems for its employment in metro and access networks has motivated lot of research and effort. In this cost-sensitive communication scenario intensity modulation and direct detection (DD) represents an appropriate solution for the provision of broadband services to end users, as it offers further reductions in the system complexity and maintenance cost, without considerably sacrificing the system flexibility and performance robustness. In combination with low-cost transmitters and bandwidth limited transceiver electronics, the generation of high capacity signals, such as those provided by orthogonal-frequency-division multiplexing (OFDM), is mandatory to achieve the stringent transmission rate requisites. The use of OFDM offers us interesting features such as high spectral efficiency values, adaptability to system impairments through adaptive bit and power loading techniques, and good compatibility with both conventional time division multiplexing (TDM) PONs and wavelength division multiplexing (WDM) PONs.

Several solutions have been proposed in order to overcome the system performance limitations imposed by nonlinear distortion in intensity modulated optical systems [2

2. Z. Liu, M. A. Violas, and N. B. Carvalho, “Digital predistortion for RSOAs as external modulators in radio over fiber systems,” Opt. Express 19(18), 17641–17646 (2011). [CrossRef] [PubMed]

9

9. W. Yan, T. Tanaka, B. Liu, M. Nishihara, L. Li, T. Takahara, Z. Tao, J. C. Rasmussen, and T. Drenski, “100 Gb/s optical IM-DD transmission with 10G-class devices enabled by 65 G samples/s CMOS DAC core,” in Proceedings of OFC/NFOEC2013 (OM3H1).

]. For example, digital-predistortion (DPD) technique was used to mitigate the nonlinearity of an externally modulated reflective semiconductor optical amplifier in [2

2. Z. Liu, M. A. Violas, and N. B. Carvalho, “Digital predistortion for RSOAs as external modulators in radio over fiber systems,” Opt. Express 19(18), 17641–17646 (2011). [CrossRef] [PubMed]

], of a DML [3

3. T. Alves, J. Morgado, and A. Cartaxo, “Linearity improvement of directly modulated PONs by digital predistortion of coexisting OFDM-based signals,” in Proceedings of Advanced Photonics Congress, (Optical Society of America, 2012), AW4A.2.

], and electro-absorption modulated lasers and Mach-Zehnder modulators [4

4. Y. Bao, Z. Li, J. Li, X. Feng, B. Guan, and G. Li, “Nonlinearity mitigation for high-speed optical OFDM transmitters using digital pre-distortion,” Opt. Express 21(6), 7354–7361 (2013). [CrossRef] [PubMed]

]. In [5

5. D. Lam, A. M. Fard, B. Buckley, and B. Jalali, “Digital broadband linearization of optical links,” Opt. Letters 38(4), 446–448 (2013). [CrossRef]

] a multi-stage digital postprocessing linearization technique based on the iterative substraction of distortion due to the Mach-Zehnder modulation and fiber propagation is proposed. In [6

6. C-C. Wei, “Analysis and iterative equalization of transient and adiabatic chirp effects in DML-based OFDM transmission sytems,” Opt. Express 20(23), 25774–25789 (2012). [CrossRef] [PubMed]

], an analytical model for the characterization of the nonlinear distortion in a DML-based OOFDM system is proposed and it is employed at the receiver-end side for the reconstruction of the interference terms and subsequent substraction using a decision-feedback equalizer; in [7

7. D-Z. Hsu, C-C. Wei, H-Y. Chen, Y-C. Lu, C-Y. Song, C-C. Yang, and J. Chen, “SSII cancellation in an EAM-based OFDM-IMDD transmission system employing a novel dynamic chirp model,” Opt. Express 21(1), 533–543 (2013). [CrossRef] [PubMed]

] this technique is adapted to an electro-absorption modulated laser and the laser chirp analytical model is improved to achieve higher nonlinear distortion efficiency values in a 100km-haul link. In [8

8. N. S. André, K. Habel, H. Louchet, and A. Richter, “Adaptive nonlinear volterra equalizer for mitigation of chirp-induced distortions in cost effective IMDD OFDM systems,” Opt. Express 21(18), 20999–21009 (2013). [CrossRef]

,9

9. W. Yan, T. Tanaka, B. Liu, M. Nishihara, L. Li, T. Takahara, Z. Tao, J. C. Rasmussen, and T. Drenski, “100 Gb/s optical IM-DD transmission with 10G-class devices enabled by 65 G samples/s CMOS DAC core,” in Proceedings of OFC/NFOEC2013 (OM3H1).

] the employment of a nonlinear adaptive Volterra equalizer at the receiver-end side with low-cost optical modulators is investigated for short-reach links.

In this paper, a pre-distortion technique which aims to mitigate the nonlinear distortion in DM/DD OOFDM systems is presented. This pre-distortion technique operates in the frequency domain (before the transmitter inverse Fourier transform), is based on the analytical model reported in [10

10. C. Sánchez, J. L. Wei, B. Ortega, and J. Capmany, “Comprehensive impairment and performance description of directly modulated/detected OOFDM systems,” J. Lightw. Technol. 31(20), 3277–3288 (2013). [CrossRef]

] for the reconstruction of the interference, and takes advantage of the channel state information (CSI) provided by the feedback link. Unlike the previously mentioned references about digital pre-distortion, the technique here proposed aims to mitigate the nonlinear distortion with an end-to-end perspective, rather than only that originated by the optical modulator. The system performance of the OOFDM system with the pre-distortion technique is evaluated for different operating conditions (clipping ratio, laser bias point and laser modulation depth). The results obtained with the pre-distortion technique are compared with those obtained in a conventional DM/DD OOFDM system, and with those obtained when nonlinear distortion cancellation at the receiver-end side is employed.

The paper is structured as follows: in Section II, we provide a description of the DM/DD OOFDM system and the proposed pre-distortion technique. Section III presents the results of extensive simulations using the analytical model of the system reported in [10

10. C. Sánchez, J. L. Wei, B. Ortega, and J. Capmany, “Comprehensive impairment and performance description of directly modulated/detected OOFDM systems,” J. Lightw. Technol. 31(20), 3277–3288 (2013). [CrossRef]

] and employing the proposed pre-distortion technique. In Section IV, the system performance of a conventional DM/DD OOFDM system, that with the proposed technique and that obtained with nonlinear equalization at the receiver are compared. Finally, in section V, we outline the conclusions and future work.

2. OFDM system and proposed pre-distortiont technique

2.1. Description of the OOFDM system and analytical assesment

A directly modulated OOFDM communication system consists of an OFDM transmitter, a DML, an optical transmission link, a photodetection stage, and, finally, an OFDM receiver, as shown in Fig. 1.

Fig. 1 OOFDM system. Blocks in red: parts due to the proposed pre-distortion technique.

For the generation of an OFDM symbol, a block of information binary stream is translated into the information QAM-modulated symbols X1, X2,. . ., XN, being N the number of sub-carriers with data. The information complex symbols may belong to different M-QAM formats when bit loading technique is employed. The subcarriers which correspond to dc- and Nyquist frequencies are set to zero, and the complex information symbols X1, X2,. . ., XN are arranged with Hermitian symmetry at the input of the inverse fast Fourier transform (IFFT) to get real-valued time-samples at the IFFT output. The size of the IFFT is denoted as FS. In order to ease subsequent analog filtering, a certain number of subcarriers closer to Nyquist frequency are usually set to zero. The generated OFDM symbol is given by:
x[n]=2Re{k=1NXkexp(j2πknFS)}
(1)
where Re{·} is the real part of a complex quantity. Cyclic pre- and post-fixes with a number of samples equal to Npre = ηpre · FS and Npos = ηpos · FS, respectively, are appended to the original OFDM symbol (ηpre and ηpos represent their lengths as a fraction of the original OFDM symbol length, FS) in order to combat inter-symbol and inter-carrier interference (ISI and ICI, respectively) caused by the transmitter, channel and receiver filtering effects. Hard clipping at the digital domain is also performed in order to limit the amplitude of the discrete signal. The clipping ratio, CR, is related to the maximum amplitude of the signal after clipping, Aclip, through CR2=Aclip2/x2[n], where 〈x2[n]〉 is the variance of the discrete signal x[n]. Finally, the signal is interpolated and low-pass filtered. The OFDM symbol starting at t=0 and with duration T may be expressed as:
s(t)k=1N|Xk|cos(Ωkt+φXk)*htrx(t)+nclip(t),0tT
(2)
where Xk = |Xk|ej·φXk are the information complex symbols, Ωk is the angular frequency of the kth subcarrier, htrx(t) is the impulse response of the transmitter filter and nclip(t) is a noisy term due to clipping. Please note that we have not considered quantization noise. The value of the discrete frequency Ωk is given by k·ΔΩ, where ΔΩ is the spacing angular frequency between consecutive subcarriers. The spacing angular frequency ΔΩ is easily calculated from the available electrical bandwidth, BW, and the (I)FFT size as ΔΩ = 2π · BW/(FS/2). The analog OFDM signal is then scaled to yield a certain value of peak current and a dc value is added to operate the optical source. The input current to the laser is then given by:
i(t)=i0+im(t)=i0+m(k=1N|Xk|cos(Ωkt+φXk)*htrx(t)+ntrx(t))=i0+k=1N2ikcos(Ωkt+φik)+ntrx(t),0tT
(3)
where i0 represents the dc-offset added just before the laser, m is the scaling factor determined by the electrical attenuation to operate the laser within a certain region (|im(t)| ≤ Δi), and ik · exp((−) ik) is the driving current coefficient at frequency (−)Ωk.

The photon density, p(t), and carrier density, n(t), in the laser cavity, as well as the output optical phase, ϕ(t), are governed by the following rate equations [11

11. G. P. Agrawal and N. K. Dutta, Semiconductor Lasers (Van Nostrand Reinhold, 1993).

]:
dp(t)dt=[ΓG(n,p)γ]p(t)+Rsp(n)dn(t)dt=i(t)eVγe(n)G(n,p)p(t)dϕdt=12αΓvgag(n(t)nt)
(4)
where p(t), n(t) are the photon and carrier densities in the laser active region, respectively, ϕ(t) is the phase of the output optical signal, Γ is the confinement factor, vg is the group velocity, ag is the linear material gain coefficient, V is the volume of the active region, i(t) is the driving current fed into the laser, e is the electron charge, nt is the transparency carrier density, α is the linewidth enhancement factor, G(n, p) is the optical gain, Rsp(n) is the spontaneous emission rate, γ is the photon decay rate and γe is the carrier-recombination rate.

The complex electrical field amplitude at the laser output is given by E(t,z=0)=P(t,z=0)exp(jϕ(t)) where P(t, z = 0) = Cp · p(t) is the output optical intensity and Cp is the photon-to-intensity conversion factor.

In [10

10. C. Sánchez, J. L. Wei, B. Ortega, and J. Capmany, “Comprehensive impairment and performance description of directly modulated/detected OOFDM systems,” J. Lightw. Technol. 31(20), 3277–3288 (2013). [CrossRef]

], we proposed an analytical model to account for several impairments which affect the received symbols Y[k] and get a reasonable estimation of the performance. Such estimation is obtained by calculating the following ratio:
SNR[k]=|H[k]|2|X[k]|2σclip2[k]+σISI&ICI2[k]+σs&t2+σIMD2[k],k=1,2,N
(6)
where H[k] is the k-th coefficient transfer function from the transmitter IFFT to the receiver FFT, σclip2 is the variance of the clipping noise added as a result of the clipping at the transmitter, σISI&ICI2 is the variance of the ISI and ICI caused by filtering through the communication system, and σs&t2=σshot2+σther2 is the variance of the shot and thermal noises at the receiver. Finally, σIMD2 is the variance of the nonlinear distortion which falls on the k-th subcarrier, σIMD2=|I[k]|2, k = 1, 2,...N, where:
I[k]=Ip,DML[k]+Iϕ,DML[k]+Ip/ϕ,β2[k]+Iϕ,β2[k]+Ip,β2[k],k=1,2N
(7)
where Ip,DML and Iϕ,DML account for the laser intensity and phase modulation nonlinearities, respectively, Iϕ,β2, Ip,β2 and Ip/ϕ,β2 are the interference terms due to the dispersion-induced imbalance on the intensity, phase and intensity/phase spectral components of the optical signal, respectively. The expressions for the interference terms Ip,DML[k], Iϕ,DML[k], Ip/ϕ,β2 [k], Iϕ,β2 [k] and Ip,β2 [k] can be consulted in [10

10. C. Sánchez, J. L. Wei, B. Ortega, and J. Capmany, “Comprehensive impairment and performance description of directly modulated/detected OOFDM systems,” J. Lightw. Technol. 31(20), 3277–3288 (2013). [CrossRef]

].

Finally, the transmitter uses bit-loading and the order of the modulation format on each sub-carrier is changed accordingly to the communication conditions [1

1. W. Shieh and I. Djordjevic, OFDM for Optical Communications (Elsevier/Academic Press, 2009).

]. A feedback-path from the transmitter to the receiver is thus assumed to make the transmitter able to be adapted to the communication system conditions (see Fig. 1). The decision on using a format for a certain subcarrier is based on the calculated bit-error-rate (BER) of that particular subcarrier, BER[k]. Under the Gaussian assumption for the noise distribution, the BER is directly determined once we have calculated SNR[k]. The modulation format of the subcarrier with the minimum value of BER is increased provided that the total BERT does not exceed a certain threshold. The achieved information transmission rate, R, and the total BER, BERT, are calculated as:
R(bits/s)=k=1Nlog2(M[k])(BW/(FS/2))1(1+ηpre+ηpos)
(8)
BERT=k=1Nlog2(M[k])BER[k]k=1Nlog2(M[k])
(9)
where M[k] stands for the constellation size of the QAM format used at the kth subcarrier.

2.2. Predistortion technique

In order to outperform the performance of the basic DM/DD OOFDM system, a pre-distortion technique is proposed in this paper. The principle is rather simple and is based on the reconstruction of the interference I[k] with k = 1, 2...N and proper substraction at the transmitter. The motivation for such strategy relies on the potential knowledge available at the transmitter of the interference impairing the detected signal at the receiver end-side and, therefore, the possibility of achieving the capacity of the Gaussian channel without interference under a proper design [12

12. M. Costa, “Writing on dirty paper,” IEEE Trans. Inform. Theory 29(3), 439–441 (1983). [CrossRef]

].

The reconstruction of the interfering term I[k] = Ip,DML[k] + Iϕ,DML[k] + Ip/ϕ,β2 [k] + Iϕ,β2 [k] + Ip,β2 [k] with k = 1, 2,...N is based on the analytical model reported in [10

10. C. Sánchez, J. L. Wei, B. Ortega, and J. Capmany, “Comprehensive impairment and performance description of directly modulated/detected OOFDM systems,” J. Lightw. Technol. 31(20), 3277–3288 (2013). [CrossRef]

]. For the sake of clarity, we indicate that Ip/ϕ,β2, Iϕ,β2 and Ip,β2 are functions of the first order laser transfer functions Hp1k) and Hϕ1k), whilst Ip,DML and Iϕ,DML find their origin in the laser non-linearities, and, thus, are functions of the second order transfer functions Hp11k, Ωl) and Hϕ11k, Ωl) [10

10. C. Sánchez, J. L. Wei, B. Ortega, and J. Capmany, “Comprehensive impairment and performance description of directly modulated/detected OOFDM systems,” J. Lightw. Technol. 31(20), 3277–3288 (2013). [CrossRef]

,13

13. C. Sánchez, B. Ortega, J. L. Wei, J. Tang, and J. Capmany, “Analytical formulation of directly modulated OOFDM signals transmitted over an IM/DD dispersive link,” Opt. Express 21(6), 7651–7666 (2013). [CrossRef] [PubMed]

]. Thereby, in order to reconstruct I[k], we need to know the fiber length L, the fiber group velocity dispersion parameter β2, the fiber intensity attenuation coefficient αfib, the average optical power P0, and the laser intensity and phase modulation transfer functions Hp1k), Hp11k, Ωl) and Hϕ1k), Hϕ11k, Ωl), respectively.

Fig. 2 shows a block diagram of the proposed pre-distortion technique in order to clarify the steps to obtain the pre-distorted symbols to be transmitted on each OFDM subcarrier. The part at the right side of Fig. 2 aims to provide updated estimations of the nonlinear transfer function coefficients for the reconstruction of the interference term. Denoting as Xk0 the original information symbols Xk, once the symbols Xk0, k = 1, 2,...N are generated (block (I) in Fig. 2), the interference term Irec0[k], k = 1, 2,...N is reconstructed (block (II) in Fig. 2) as:
Irec0[k]=l=1k/21(Hp/ϕ,β2{1,1}(Ωl)Hp/ϕ,β2{1,1}(Ωkl)+Hϕ,β2{1,1}(Ωl)Hϕ,β2{1,1}(Ωkl)+Hp,β2{1,1}(Ωk)Hp,β2{1,1}(Ωkl)+Hp,DML(Ωk)Hp,DML{1,1}(Ωl)Hp,DML{1,1}(Ωkl)+Hϕ,DML(Ωk)Hϕ,DML{1,1}(Ωl)Hϕ,DML{1,1}(Ωkl))Xl0Xkl0+l=k+1N(Hp/ϕ,β2{1,1}(Ωl)Hp/ϕ,β2{1,1}(Ωlk)+Hϕ,β2{1,1}(Ωl)Hϕ,β2{1,1}(Ωlk)+Hp,β2{1,11}(Ωk)Hp,β2{1,1}(Ωlk)+Hp,DML(Ωk)Hp,DML{1,1}(Ωl)Hp,DML{1,1}(Ωlk)+Hϕ,DML(Ωk)Hϕ,DML{1,1}(Ωl)Hϕ,DML(Ωlk))Xl0(Xlk0)*,k=1,2,N
(12)
where the nonlinear transfer function coefficients in Eq. (12) account for the effects of the electrical and optical (chromatic dispersion and fiber attenuation) parts of the communication system. Hp/ϕ,β2{1,±1} are the coefficients for the reconstruction of Ip/ϕ,β2, and similarly for the rest of coefficients Hϕ,β2{1,±1}, Hp,β2{1,±1}, Hϕ,DML{1,±1}, H′ϕ,DML{1, ±1}, Hp,DML{1,±1} and H′p,DML{1, ±1}.

Fig. 2 Block diagram of the proposed pre-distortion technique.

The interference term just computed, Irec0[k], is divided by the total linear transfer function (block (III) in Fig. 2). Finally, the values Irec0[k]/H[k], k = 1, 2,...N are subtracted from the information complex symbols (block (IV) in Fig. 2):
Xk1=Xk0Irec0[k]/H[k],k=1,2,N
(13)
Next, we denote as I0[k] the nonlinear distortion which actually impairs the information signal in the DM/DD OOFDM system when Xk0 are transmitted. As result of the transmission of Xk1 instead of Xk0, we have at the output of the communication system:
Y[k]=H[k]Xk1+I1[k]=H[k]Xk0Irec0[k]+I1[k],k=1,2,N
(14)
where the interference I1[k] can be expressed in function of I0[k] as I1[k] = I0[k] + χ1[k], where χ1[k] is a difference term due to the transmission of Xk1, k = 1,..N instead of Xk0, k = 1, 2,...N through the nonlinear communication system.

With this technique, the system performance increases provided that the reconstructed interference Irec0[k] is sufficiently close to the actual interference I0[k] and the magnitude of the additional nonlinear term χ1[k] is smaller than I0[k], which is a reasonable assumption in a communication system using high order QAM modulation formats and the symbols must be weakly impaired in order to assure a certain performance (e.g., BERT ≤ 10−4). Under the first assumption:
Y[k]=H[k]Xk0Irec0[k]+I0[k]+χ1[k]H[k]Xk0+χ1[k],k=1,2,N
(15)

Provided that the reconstruction of the interference is sufficiently accurate and Irec0[k]I0[k], it may be convenient to go further and proceed iteratively. By doing so, we can transmit Xk1=Xk0Irec1[k], where Irec1[k] is now the reconstructed interference when Xk1 are sent, and calculated by substituting Xk0 by Xk1, k = 1, 2,...N in Eq. (12).

The process could be repeated over and over again, but the nonlinear distortion is considerably reduced after the first iteration, and the remaining distortion is hardly reduced without a further refinement of the algorithm aimed to increase its efficiency. The limitation on the efficiency comes from the assumptions made for the simplification of the analytical model for the reconstruction of the nonlinear distortion and the transfer function estimations. In a real scenario, we should also add the tolerances and deviations of a practical implementation as another reason more for not going beyond in the iterative process.

Before the pre-distortion technique, the signal-to-noise ratio of the k-th subcarrier SNR[k] is given by Eq. (6). The signal-to-noise ratio of the k-th subcarrier after application of the pre-distortion is denoted as SNRprd[k] and is given by:
SNRprd[k]=κ2|H[k]|2|X[k]|2κ2(σclip2[k]+σISI&ICI2[k]+σshot2)+ηcanc[k]σIMD2[k]+σther2,k=1,2,N
(16)
where ηcanc[k], k = 1, 2...N is the ratio between the nonlinear distortion power with and without using the pre-distortion technique, ηcanc[k]=σIMD2|prd[k]/σIMD2[k], k = 1, 2...N.

2.3. Complexity of the proposed technique

Digital techniques aimed to the mitigation of nonlinear distortion in OOFDM systems are rather complex due to the mixing of the information transmitted in parallel by multiple information channels. Regarding the technique proposed in this work, we have two differentiated parts, as shown in Fig. 2: the right side aims to provide updated nonlinear transfer coefficients, and the left side aims to reconstruct the interference term.

The update of the nonlinear transfer function coefficients in Eq. (12) may be performed every certain number of OFDM symbols, and, thus, the added complexity is less important compared to that added by the part at the left side of Fig. 2.

Since the interference term depends on the information symbols to be transmitted, it must be calculated for each OFDM symbol. The calculation of Irec0[k], with k = 1, 2,...N represents the more complex part of the pre-distortion technique: its direct calculation as Eq. (12) would require a number of complex multiplications proportional to N2 (≈ 7(inner products) ( 12N22(firstsum)+N22(secondsum))+ 2 · N(outer products, first sum) + 2 · N(outer products, second sum)). Once obtained the values of I[k], k = 1, 2,...N, N complex divisions further are needed to calculate Irec0[k]/H[k], k = 1, 2,...N.

3. Results

3.1. System parameter values

Table 1. Laser parameters

table-icon
View This Table

The fiber chromatic dispersion D is set to 17ps/(km · nm) and its attenuation coefficient is equal to 0.2dB/km. The responsivity of the photodiode ℜ is set to 1A/W. After photodetection, shot and thermal noises [17

17. G. P. Agrawal, Fiber-optic Communications Systems (Wiley, 1997).

] have been considered, being 10pA/Hz the thermal noise spectral density.

3.2. System performance improvement

3.2.1. Nonlinear distortion ratio

In order to evaluate the system performance of the OOFDM system through Eq. (16), the nonlinear distortion cancellation ratio of the predistortion technique, ηcanc[k], k = 1, 2...N, must be calculated. It is worthy to remark that for its computation one must turn to computationally time exhausting numerical simulations of the DM/DD OOFDM system in Fig. 1. In Fig. 3 we show the value of ηcanc[k] for a fiber length equal to 40km and two different laser bias points (i0 = 45mA and i0 = 85mA). Within each figure, the clipping ratio CR and the amplitude swing of the laser modulating signal Δi are changed.

Fig. 3 Nonlinear distortion cancellation ratio ηcanc for a) i0 = 45mA and b) i0 = 85mA. Optical fiber length equals to 40km.

In general, we can observe that the pre-distortion technique does not work appropriately at low frequencies, but this incorrect behavior is limited to a few number of the lowest sub-carriers, where the nonlinear distortion is typically low [15

15. W. Yan, B. Liu, L. Li, Z. Tao, T. Takahara, and J. C. Rasmussen, “Nonlinear distortion and DSP-based cmpensation in metro and access networks using discrete multi-tone,” at ECOC 2012, Mo.1.B.2.

]. As expected, the nonlinear cancellation ratio of the proposed technique depends on the system parameters employed, such as the clipping introduced at the transmitter. This is clearly observed in Fig. 3(a), where a value for CR equals to 9dB yields higher values for ηcanc than for CR = 13.5dB. In particular, values around 0.1585 (10−0.8) are obtained for CR = 9dB, and values within a range of [0.025, 0.1259] ([10−1.6, 10−0.9]) are obtained for CR = 13.5dB. On the other hand, the trend with Δi is not so clear: a higher value for Δi may not be convenient because the analytical model is less accurate and higher nonlinear distortion is introduced (as it can be observed in Fig. 3(a) for CR = 9dB), but it can also help through an increase of the optical modulation efficiency (as it can be observed in Fig. 3(b) for CR = 13.5dB). Apart from these aspects, the proposed technique achieves a considerable reduction of the nonlinear distortion, ranging from ηcanc = 10−1.7 = 0.02 to ηcanc = 10−0.9 = 0.126 for CR = 13.5dB and i0 = 45mA, and values around ηcanc = 10−1.5 = 0.031 in most of the subcarriers for CR = 13.5dB and i0 = 85mA.

3.2.2. OOFDM system with bit-loading and pre-distortion

Fig. 4 Transmission information rate as a function of CR and Δi for L = 40km a) i0 = 45mA, b) i0 = 65mA, c) i0 = 85mA, and L = 100km e) i0 = 45mA, f) i0 = 65mA, g) i0 = 85mA.

The transmission information rate ranges from 21.18Gbits/s to 34.44Gbits/s for L = 40km, whilst for L = 100km, R reduces substantially due to the higher attenuation and the accumulated dispersion, ranging from 6.53Gbits/s to 15.3Gbits/s.

For L = 40km, it can be observed that a reduction of the value for CR is detrimental due to the clipping noise. This is clearly observed in Figs. 4(b) and (c) by the fact that a reduction of CR from 11dB to 9dB leads to smaller values of R, but an increase of the amplitude swing of the laser modulating signal, Δi, has marginal effects. The increase of Δi and the consequent higher impact of nonlinearities is evident for i0 = 45mA (Fig. 4(a)). An increase of the laser bias point to 65mA (Fig. 4(b)), and 85mA (Fig. 4(c)) seems to be beneficial and results in higher values of transmission information rate than for i0 = 45mA. A reasonable value for the clipping ratio equals to 12dB, i0 = 65mA and Δi = 10mA can provide us a transmission information rate around 34.4Gbits/s.

For L = 100km, an increase of the value of CR leads generally to a reduction of the obtained transmission information rate because of the optical modulation efficiency loss. Remarkably, in Fig. 4(d) we can observe two different regions which lead to transmission information rates around 14Gbits/s, which is the result of the trade-offs between modulation effiency/receiver noise/nonlinear distortion/nonlinear distortion cancellation efficiency obtained the proposed pre-distortion technique. Similarly to L = 40km, an increase of the laser bias point to 65mA (Fig. 4(e)), and 85mA (Fig. 4(f)) gives us higher values of transmission information rate. By setting i0 = 65mA, CR = 12dB and Δi = 12mA, one can theoretically achieves a transmission information rate around 15.3Gbits/s.

In order to fully obtain the maximum system performance in terms of transmission rate, we study the obtained values for R when the length of the cyclic extensions Npre and Npos is changed in order to reduce as much as possible the number of redundant samples. With the values for i0, CR and Δi set to the previously selected values, the obtained results are shown in Fig. 5 for both optical fiber lengths, L = 40km and L = 100km.

Fig. 5 a) Information transmission rate achieved in function of the number of samples for the cyclic extensions, b) BER of each subcarrier and corresponding modulation format. Blue: optical fiber length equals to 40km. Red: optical fiber lengths equals to 100km.

From Fig. 5(a) it is clear than smaller values for Npre and Npos can be used without falling into a penalty due to ISI & ICI effects. It is worth mentioning that bit loading may be also helping to overcome ISI & ICI effects by allocating more bits into those subcarrier more weakly impaired. Concretely, a value of Npre = Npos = 4 can be used, leading to a transmission information rate equal to 40Gbits/s for L = 40km, whilst a value of Npre = Npos = 2 leads to a transmission information rate equals to 18.5Gbits/s for L = 100km. Using these cyclic extension lengths, the obtained BER and the modulation format employed of each subcarrier is shown in Fig. 5(b). For L = 40km, a modulation format as high as 512-QAM can be used in most of the signal bandwidth, and for L = 100km, 4-QAM, 16-QAM and 32-QAM are used for the information transmission.

4. Comparison with brute force simulations

Fig. 6 a) System transfer function of the conventional system, b) SNR of the conventional system, c) System transfer function of the system with pre-distortion technique, d) SNR of the system with pre-distortion technique (SNRprd).

Fig. 7 Obtained BER values obtained through brute force simulations.

We observe from Fig. 7 that the obtained BER values are close to the objective BER = 10−4. As predicted by the simulations with the simplified model, the achieved transmission information rates when the pre-distortion technique is used are considerably higher. With the nonlinear equalizer at the receiver, the transmission information rates are equal to 33.08Gbits/s and 14.49Gbits/s for L=40km and L=100km, respectively. Though the values obtained with the nonlinear equalizer at the receiver are not the result of a so exhaustive system parameter optimization, the values shown in Fig. 7 show an intuitively clear issue: a nonlinear equalization at the receiver can improve the quality of the detected signal, but, since the interference reconstruction depend on decisions about the received information signal, the obtained performance will eventually depend on the signal quality of the conventional DM/DD OOFDM system.

In Fig. 8 we show the constellation diagrams of the 62th–110th subcarriers in order to get a visual impression of the improvement achieved by means of the proposed pre-distortion technique.

Fig. 8 Constellation diagrams of the 62th to 110th subcarriers for L = 40km. a) Conventional DM/DD OOFDM system (128-QAM), b) DM/DD OOFDM system without pre-distortion technique (512-QAM), and c) DM/DD OOFDM system with pre-distortion technique (512-QAM).

The conventional DM/DD OOFDM system, with the same system parameters as those used to obtain the results in Fig. 7, employs 128-QAM in the subcarriers ranging from 62 to 110, and the received symbols after equalization are shown in Fig. 8(a). Using this modulation format guarantees that the obtained BER does not exceed considerably the objective BERT = 10−4, situation which would occur if the modulation format order is increased to 512-QAM. The aim of the constellation diagrams Figs. 8(b)–8(c) is to show the effects of the proposed pre-distortion technique. Both of them show the constellation diagram for the same subcarriers (62 to 110), using 512-QAM as modulation format and employing the same system parameters as those used to obtain the results in Fig. 7 for the system with pre-distortion, but in Fig. 8(b) the pre-distortion technique is not used at all. It is clear that the quality of the received signal is ruined and it would lead to an unacceptable value of BERT. The use of the pre-distortion technique, Fig. 8(c), offers us a much clearer constellation diagram, and, similarly to Fig. 8(a), an appropriate quality of the received symbols is achieved and the value of the obtained BERT does not increase significantly. Evidently, the transmission information rate achieved with the proposed technique is higher than that in the conventional system as result of using higher modulation format orders.

5. Conclusions

We have proposed a novel pre-distortion technique which takes advantage of the relatively stable conditions in a directly modulated/detected system, in such a way the transmitter may know a priori the impairing nonlinear distortion at the transmitter. Its operation conditions have been studied in order to explore its potential performance and make comparisons with that obtained in a conventional DM/DD OOFDM system. The system performance has been greatly improved for different distances, allowing to employ higher modulation QAM formats on the OFDM subcarriers. Transmission information rates equal to 40Gbits/s and 18.5Gbits/s have been obtained for L=40km and L=100km, respectively, with a BER in the order of 10−4.

Finally, we have compared the results obtained with those from brute force simulations, demonstrating the feasibility of the simplified analytical model to predict the final system performance in front of varying system parameters. The results also show that the performance obtained with the pre-distortion technique proposed in this work outperforms that obtained with a nonlinear distortion canceller at the receiver: the pre-distorted waveform may be considered as a special modulation format, with particular optimum operating conditions, whilst the performance with a nonlinear distortion canceller at the receiver is unavoidably linked to the operating conditions/performance of the conventional OOFDM system to assure a certain level quality of the received signal.

The pre-distortion technique here proposed represents a valuable technique for its employment in optical metro/access networks, where the two-way end-to-end communications is a reasonable assumption, and, thus, the transmitter can extract information on the transmission channel. Its refinement through a higher accuracy of the simplified analytical model, better channel transfer function estimation algorithms and the cancellation of the harmonic distortion is therefore a promising line of research for the achievement of higher nonlinear distortion cancellation ratios and higher transmission information rates. Such refinement must be studied in combination with strategies for the reduction of the complexity in order to find an appropriate trade-off between reliability and implementation feasibility in real-time applications.

Acknowledgments

References and links

1.

W. Shieh and I. Djordjevic, OFDM for Optical Communications (Elsevier/Academic Press, 2009).

2.

Z. Liu, M. A. Violas, and N. B. Carvalho, “Digital predistortion for RSOAs as external modulators in radio over fiber systems,” Opt. Express 19(18), 17641–17646 (2011). [CrossRef] [PubMed]

3.

T. Alves, J. Morgado, and A. Cartaxo, “Linearity improvement of directly modulated PONs by digital predistortion of coexisting OFDM-based signals,” in Proceedings of Advanced Photonics Congress, (Optical Society of America, 2012), AW4A.2.

4.

Y. Bao, Z. Li, J. Li, X. Feng, B. Guan, and G. Li, “Nonlinearity mitigation for high-speed optical OFDM transmitters using digital pre-distortion,” Opt. Express 21(6), 7354–7361 (2013). [CrossRef] [PubMed]

5.

D. Lam, A. M. Fard, B. Buckley, and B. Jalali, “Digital broadband linearization of optical links,” Opt. Letters 38(4), 446–448 (2013). [CrossRef]

6.

C-C. Wei, “Analysis and iterative equalization of transient and adiabatic chirp effects in DML-based OFDM transmission sytems,” Opt. Express 20(23), 25774–25789 (2012). [CrossRef] [PubMed]

7.

D-Z. Hsu, C-C. Wei, H-Y. Chen, Y-C. Lu, C-Y. Song, C-C. Yang, and J. Chen, “SSII cancellation in an EAM-based OFDM-IMDD transmission system employing a novel dynamic chirp model,” Opt. Express 21(1), 533–543 (2013). [CrossRef] [PubMed]

8.

N. S. André, K. Habel, H. Louchet, and A. Richter, “Adaptive nonlinear volterra equalizer for mitigation of chirp-induced distortions in cost effective IMDD OFDM systems,” Opt. Express 21(18), 20999–21009 (2013). [CrossRef]

9.

W. Yan, T. Tanaka, B. Liu, M. Nishihara, L. Li, T. Takahara, Z. Tao, J. C. Rasmussen, and T. Drenski, “100 Gb/s optical IM-DD transmission with 10G-class devices enabled by 65 G samples/s CMOS DAC core,” in Proceedings of OFC/NFOEC2013 (OM3H1).

10.

C. Sánchez, J. L. Wei, B. Ortega, and J. Capmany, “Comprehensive impairment and performance description of directly modulated/detected OOFDM systems,” J. Lightw. Technol. 31(20), 3277–3288 (2013). [CrossRef]

11.

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers (Van Nostrand Reinhold, 1993).

12.

M. Costa, “Writing on dirty paper,” IEEE Trans. Inform. Theory 29(3), 439–441 (1983). [CrossRef]

13.

C. Sánchez, B. Ortega, J. L. Wei, J. Tang, and J. Capmany, “Analytical formulation of directly modulated OOFDM signals transmitted over an IM/DD dispersive link,” Opt. Express 21(6), 7651–7666 (2013). [CrossRef] [PubMed]

14.

W-P. Peng, B. Zhang, K-M. Feng, X. Wu, A. E. Willner, and S. Chi, “Spectrally efficient direct-detected OFDM transmission incorporating a tunable frequency gap and an iterative detection techniques,” J.Lightw. Technol. 31(20), 3277—3288 (2013).

15.

W. Yan, B. Liu, L. Li, Z. Tao, T. Takahara, and J. C. Rasmussen, “Nonlinear distortion and DSP-based cmpensation in metro and access networks using discrete multi-tone,” at ECOC 2012, Mo.1.B.2.

16.

A. V. Oppenheim, R. W. Schaffer, and J. R. Buck, Discrete-time signal processing (Prentice-Hall, 1999).

17.

G. P. Agrawal, Fiber-optic Communications Systems (Wiley, 1997).

OCIS Codes
(060.2330) Fiber optics and optical communications : Fiber optics communications
(060.4080) Fiber optics and optical communications : Modulation
(060.3510) Fiber optics and optical communications : Lasers, fiber

ToC Category:
Optical Communications

History
Original Manuscript: February 6, 2014
Revised Manuscript: March 12, 2014
Manuscript Accepted: March 13, 2014
Published: March 20, 2014

Citation
C. Sánchez, B. Ortega, and J. Capmany, "System performance enhancement with pre-distorted OOFDM signal waveforms in DM/DD systems," Opt. Express 22, 7269-7283 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-6-7269


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References

  1. W. Shieh, I. Djordjevic, OFDM for Optical Communications (Elsevier/Academic Press, 2009).
  2. Z. Liu, M. A. Violas, N. B. Carvalho, “Digital predistortion for RSOAs as external modulators in radio over fiber systems,” Opt. Express 19(18), 17641–17646 (2011). [CrossRef] [PubMed]
  3. T. Alves, J. Morgado, A. Cartaxo, “Linearity improvement of directly modulated PONs by digital predistortion of coexisting OFDM-based signals,” in Proceedings of Advanced Photonics Congress, (Optical Society of America, 2012), AW4A.2.
  4. Y. Bao, Z. Li, J. Li, X. Feng, B. Guan, G. Li, “Nonlinearity mitigation for high-speed optical OFDM transmitters using digital pre-distortion,” Opt. Express 21(6), 7354–7361 (2013). [CrossRef] [PubMed]
  5. D. Lam, A. M. Fard, B. Buckley, B. Jalali, “Digital broadband linearization of optical links,” Opt. Letters 38(4), 446–448 (2013). [CrossRef]
  6. C-C. Wei, “Analysis and iterative equalization of transient and adiabatic chirp effects in DML-based OFDM transmission sytems,” Opt. Express 20(23), 25774–25789 (2012). [CrossRef] [PubMed]
  7. D-Z. Hsu, C-C. Wei, H-Y. Chen, Y-C. Lu, C-Y. Song, C-C. Yang, J. Chen, “SSII cancellation in an EAM-based OFDM-IMDD transmission system employing a novel dynamic chirp model,” Opt. Express 21(1), 533–543 (2013). [CrossRef] [PubMed]
  8. N. S. André, K. Habel, H. Louchet, A. Richter, “Adaptive nonlinear volterra equalizer for mitigation of chirp-induced distortions in cost effective IMDD OFDM systems,” Opt. Express 21(18), 20999–21009 (2013). [CrossRef]
  9. W. Yan, T. Tanaka, B. Liu, M. Nishihara, L. Li, T. Takahara, Z. Tao, J. C. Rasmussen, T. Drenski, “100 Gb/s optical IM-DD transmission with 10G-class devices enabled by 65 G samples/s CMOS DAC core,” in Proceedings of OFC/NFOEC2013 (OM3H1).
  10. C. Sánchez, J. L. Wei, B. Ortega, J. Capmany, “Comprehensive impairment and performance description of directly modulated/detected OOFDM systems,” J. Lightw. Technol. 31(20), 3277–3288 (2013). [CrossRef]
  11. G. P. Agrawal, N. K. Dutta, Semiconductor Lasers (Van Nostrand Reinhold, 1993).
  12. M. Costa, “Writing on dirty paper,” IEEE Trans. Inform. Theory 29(3), 439–441 (1983). [CrossRef]
  13. C. Sánchez, B. Ortega, J. L. Wei, J. Tang, J. Capmany, “Analytical formulation of directly modulated OOFDM signals transmitted over an IM/DD dispersive link,” Opt. Express 21(6), 7651–7666 (2013). [CrossRef] [PubMed]
  14. W-P. Peng, B. Zhang, K-M. Feng, X. Wu, A. E. Willner, S. Chi, “Spectrally efficient direct-detected OFDM transmission incorporating a tunable frequency gap and an iterative detection techniques,” J.Lightw. Technol. 31(20), 3277—3288 (2013).
  15. W. Yan, B. Liu, L. Li, Z. Tao, T. Takahara, J. C. Rasmussen, “Nonlinear distortion and DSP-based cmpensation in metro and access networks using discrete multi-tone,” at ECOC 2012, Mo.1.B.2.
  16. A. V. Oppenheim, R. W. Schaffer, J. R. Buck, Discrete-time signal processing (Prentice-Hall, 1999).
  17. G. P. Agrawal, Fiber-optic Communications Systems (Wiley, 1997).

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