## System performance enhancement with pre-distorted OOFDM signal waveforms in DM/DD systems |

Optics Express, Vol. 22, Issue 6, pp. 7269-7283 (2014)

http://dx.doi.org/10.1364/OE.22.007269

Acrobat PDF (3914 KB)

### 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

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]

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]

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]

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]

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]

## 2. OFDM system and proposed pre-distortiont technique

### 2.1. Description of the OOFDM system and analytical assesment

*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]: 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,

*v*is the group velocity,

_{g}*a*is the linear material gain coefficient,

_{g}*V*is the volume of the active region,

*i*(

*t*) is the driving current fed into the laser,

*e*is the electron charge,

*n*is the transparency carrier density,

_{t}*α*is the linewidth enhancement factor,

*G*(

*n*,

*p*) is the optical gain,

*R*(

_{sp}*n*) is the spontaneous emission rate,

*γ*is the photon decay rate and

*γ*is the carrier-recombination rate.

_{e}*P*(

*t*,

*z*= 0) =

*C*·

_{p}*p*(

*t*) is the output optical intensity and

*C*is the photon-to-intensity conversion factor.

_{p}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]

*H*[

*k*] is the

*k*-th coefficient transfer function from the transmitter IFFT to the receiver FFT,

*k*-th subcarrier,

*k*= 1, 2,...

*N*, where: where

*I*and

_{p,DML}*I*account for the laser intensity and phase modulation nonlinearities, respectively,

_{ϕ,DML}*I*

_{ϕ,β2},

*I*

_{p,β2}and

*I*

_{p/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

*I*[

_{p,DML}*k*],

*I*[

_{ϕ,DML}*k*],

*I*

_{p/ϕ,β2}[

*k*],

*I*

_{ϕ,β2}[

*k*] and

*I*

_{p,β2}[

*k*] can be consulted in [10

**31**(20), 3277–3288 (2013). [CrossRef]

*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

*BER*does not exceed a certain threshold. The achieved information transmission rate,

_{T}*R*, and the total BER,

*BER*, are calculated as: where

_{T}*M*[

*k*] stands for the constellation size of the QAM format used at the

*k*th subcarrier.

### 2.2. Predistortion technique

*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]

*I*[

*k*] =

*I*[

_{p,DML}*k*] +

*I*[

_{ϕ,DML}*k*] +

*I*

_{p/ϕ,β2}[

*k*] +

*I*

_{ϕ,β2}[

*k*] +

*I*

_{p,β2}[

*k*] with

*k*= 1, 2,...

*N*is based on the analytical model reported in [10

**31**(20), 3277–3288 (2013). [CrossRef]

*I*

_{p/ϕ,β2},

*I*

_{ϕ,β2}and

*I*

_{p,β2}are functions of the first order laser transfer functions

*H*

_{p1}(Ω

*) and*

_{k}*H*

_{ϕ1}(Ω

*), whilst*

_{k}*I*and

_{p,DML}*I*find their origin in the laser non-linearities, and, thus, are functions of the second order transfer functions

_{ϕ,DML}*H*

_{p11}(Ω

*, Ω*

_{k}*) and*

_{l}*H*

_{ϕ11}(Ω

*, Ω*

_{k}*) [10*

_{l}**31**(20), 3277–3288 (2013). [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]

*I*[

*k*], we need to know the fiber length

*L*, the fiber group velocity dispersion parameter

*β*

_{2}, the fiber intensity attenuation coefficient

*α*, the average optical power

_{fib}*P*

_{0}, and the laser intensity and phase modulation transfer functions

*H*

_{p1}(Ω

*),*

_{k}*H*

_{p11}(Ω

*, Ω*

_{k}*) and*

_{l}*H*

_{ϕ1}(Ω

*),*

_{k}*H*

_{ϕ11}(Ω

*, Ω*

_{k}*), respectively.*

_{l}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]

*L*,

*β*

_{2}, and

*α*. As it can be observed in Fig. 1, the laser output signal is divided into two signals by means of an optical power divider with constant

_{fib}*κ*: one is fed into the optical link for data communication, and the other is directly fedback into an OOFDM receiver. From the feedback signal, the average optical power

*P*

_{0}[14] and

*H*

_{p1}(Ω

*)*

_{k}*k*= 1, 2...

*N*can be determined.

*P*

_{0}and

*H*

_{p1}(Ω

*)*

_{k}*k*= 1, 2...

*N*are known, using the optical link attenuation and the accumulated dispersion,

*H*

_{ϕ1}(Ω

*)*

_{k}*k*= 1, 2...

*N*can be estimated from the total transfer function

*H*(Ω

*)*

_{k}*k*= 1, 2...

*N*.Then, we can reconstruct the nonlinear distortion due to chromatic dispersion on the intensity and frequency modulated parts of the transmitted optical signal,

*I*

_{p/ϕ,β2}[

*k*],

*I*

_{ϕ,β2}[

*k*] and

*I*

_{p,β2}[

*k*] with

*k*= 1, 2,...

*N*.

*I*and

_{p,DML}*I*, can be also partially mitigated. As previously said, they depend on the second order laser transfer functions

_{ϕ,DML}*H*

_{p11}(Ω

*, Ω*

_{k}*) and*

_{l}*H*

_{ϕ11}(Ω

*, Ω*

_{k}*). A possible approach for their calculation is the probing of the system with all the possible pairs of tones, though this approach would be time consuming and inefficient. However, the second order laser intensity transfer function can be expressed as*

_{l}*H*

_{p11}(Ω

*, Ω*

_{l}

_{k}_{−}

*) =*

_{l}*H′*

_{p11}(Ω

*) ·*

_{k}*H*

_{p1}(Ω

*)*

_{l}*H*

_{p1}(Ω

_{k}_{−}

*) and therefore the nonlinear distortion term*

_{l}*I*can be written as [10

_{p,DML}**31**(20), 3277–3288 (2013). [CrossRef]

*cos*(

*θ*) =

_{k}*cos*(0) = 1) offers a way to get an estimation of

*H′*

_{p11}(Ω

*),*

_{k}*k*= 1, 2...

*N*, and, therefore, of the second order nonlinear distortion transfer function

*H*

_{p11}(Ω

*, Ω*

_{l}

_{k}_{−}

*),*

_{l}*k*= 1, 2...

*N*, used finally to reconstruct

*I*. Regarding the interfering term

_{p,DML}*I*, the perturbative analysis of the equation system in Eq. (4) yields the next expression for the second order laser phase transfer function

_{ϕ,DML}*H*

_{ϕ11}:

*n*

_{0}and

*p*

_{0}the carrier and photon density steady-state values, respectively,

*I*[

_{ϕ,DML}*k*],

*k*= 1, 2...

*N*.

*X*, once the symbols

_{k}*k*= 1, 2,...

*N*are generated (block (I) in Fig. 2), the interference term

*k*= 1, 2,...

*N*is reconstructed (block (II) in Fig. 2) as:

*H*

_{p/ϕ,β2{1,±1}}are the coefficients for the reconstruction of

*I*

_{p/ϕ,β2}, and similarly for the rest of coefficients

*H*

_{ϕ,β2{1,±1}},

*H*

_{p,β2{1,±1}},

*H*

_{ϕ,DML}_{{1,±1}},

*H′*

_{ϕ,DML}_{{1, ±1}},

*H*

_{p,DML}_{{1,±1}}and

*H′*

_{p,DML}_{{1, ±1}}.

*k*= 1, 2,...

*N*are subtracted from the information complex symbols (block (IV) in Fig. 2): Next, we denote as

*I*

^{0}[

*k*] the nonlinear distortion which actually impairs the information signal in the DM/DD OOFDM system when

*I*

^{1}[

*k*] can be expressed in function of

*I*

^{0}[

*k*] as

*I*

^{1}[

*k*] =

*I*

^{0}[

*k*] +

*χ*

_{1}[

*k*], where

*χ*

_{1}[

*k*] is a difference term due to the transmission of

*k*= 1,..

*N*instead of

*k*= 1, 2,...

*N*through the nonlinear communication system.

*I*

^{0}[

*k*] and the magnitude of the additional nonlinear term

*χ*

_{1}[

*k*] is smaller than

*I*

^{0}[

*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.,

*BER*≤ 10

_{T}^{−4}). Under the first assumption:

*k*= 1, 2,...

*N*in Eq. (12).

*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

*SNR*[

_{prd}*k*] and is given by:

*η*[

_{canc}*k*],

*k*= 1, 2...

*N*is the ratio between the nonlinear distortion power with and without using the pre-distortion technique,

*k*= 1, 2...

*N*.

### 2.3. Complexity of the proposed technique

*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

*N*

^{2}(≈ 7(inner products) (

*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

*k*= 1, 2,...

*N*.

*𝒪*(

*N*

^{2}) the practical application of the algorithm, even for a modest number of subcarriers

*N*, is limited. Simplification of the algorithm must be carried out to achieve a reasonable applicability of the technique in a real-time transmission:

- By applying the pre-distortion technique selectively: in the previous subsection, we have pointed out the possibility of reducing interference terms of different nature, but, their impact is not necessarily equal and depends on the particular conditions of the communication system. If the predistortion is applied only for those with stronger power, some complexity reduction can be achieved. Moreover, the interference is not uniformly distributed with frequency [6, 15], which allows us to further reduce the complexity by applying the pre-distortion technique to those subcarriers more strongly impaired.
**20**(23), 25774–25789 (2012). [CrossRef] [PubMed] - As suggested in [6
**20**(23), 25774–25789 (2012). [CrossRef] [PubMed]*N̄*·*log*_{2}(*N̄*) complex multiplications (where*log*_{2}(*N̄*) is the minimum integer such that 2*N*≤*N̄*)). Since each of the two sums contains 5 inner terms, we would require to compute 10 forward and inverse Fourier transforms. However, the change of the complexity order from*N*^{2}to*N̄*·*log*_{2}(*N̄*) means a significant complexity reduction compared to its direct calculation for high and moderate values of*N*. Besides, as commented in the previous point, it may not be necessary to cancel all the interference terms in Eq. (7), which would reduce the number of forward and inverse Fourier transforms.

## 3. Results

### 3.1. System parameter values

*BW*) is equal to 5.5GHz; the inverse fast Fourier transform (IFFT) processor has a size of

*FS*= 256;

*N*= 110 subcarriers are used for information transmission; a cyclic pre- and post-fix of 32 samples (

*N*=

_{pre}*N*= 32,

_{pos}*η*=

_{pre}*η*= 1/8) are appended to each OFDM symbol; after digital-to-analog conversion, the obtained analog signal is adapted for laser driving by scaling it to yield a peak-to-peak value of Δ

_{pos}*i*and adding a dc-offset

*i*

_{0}. The laser parameters are shown in Table 1.

*A/W*. After photodetection, shot and thermal noises [17] have been considered, being

### 3.2. System performance improvement

#### 3.2.1. Nonlinear distortion ratio

*η*[

_{canc}*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

*η*[

_{canc}*k*] for a fiber length equal to 40km and two different laser bias points (

*i*

_{0}= 45mA and

*i*

_{0}= 85mA). Within each figure, the clipping ratio

*CR*and the amplitude swing of the laser modulating signal Δ

*i*are changed.

*CR*equals to 9dB yields higher values for

*η*than for

_{canc}*CR*= 13.5dB. In particular, values around 0.1585 (10

^{−0.8}) are obtained for

*CR*= 9

*dB*, 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 Δ

*i*is not so clear: a higher value for Δ

*i*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

*η*= 10

_{canc}^{−1.7}= 0.02 to

*η*= 10

_{canc}^{−0.9}= 0.126 for

*CR*= 13.5dB and

*i*

_{0}= 45mA, and values around

*η*= 10

_{canc}^{−1.5}= 0.031 in most of the subcarriers for

*CR*= 13.5dB and

*i*

_{0}= 85mA.

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

*η*for a set of system parameter values (

_{canc}*i*

_{0}= 45, 65, 75, 85

*mA*,

*CR*= 9, 10.5, 12, 13.5dB, Δ

*i*= 6, 8, 10, 12mA and

*L*= 40, 100km), a more exhaustive search for the optimum conditions is carried out using the simplified analytical model and the computation of the signal-to-noise ratio in Eq. (16). As it was mentioned in the subsection 2.1, bit-loading is used, leading to different values of transmission information rate according to the channel conditions. Setting an objective

*BER*equal to 10

_{T}^{−4}, the results obtained when

*CR*and Δ

*i*are changed are shown in Fig. 4.

*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.

*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, Δ

*i*, has marginal effects. The increase of Δ

*i*and the consequent higher impact of nonlinearities is evident for

*i*

_{0}= 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

*i*

_{0}= 45mA. A reasonable value for the clipping ratio equals to 12dB,

*i*

_{0}= 65mA and Δ

*i*= 10mA can provide us a transmission information rate around 34.4Gbits/s.

*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*= 40

*km*, 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

*i*

_{0}= 65

*mA*,

*CR*= 12

*dB*and Δ

*i*= 12mA, one can theoretically achieves a transmission information rate around 15.3Gbits/s.

*R*when the length of the cyclic extensions

*N*and

_{pre}*N*is changed in order to reduce as much as possible the number of redundant samples. With the values for

_{pos}*i*

_{0},

*CR*and Δ

*i*set to the previously selected values, the obtained results are shown in Fig. 5 for both optical fiber lengths,

*L*= 40km and

*L*= 100km.

*N*and

_{pre}*N*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

_{pos}*N*=

_{pre}*N*= 4 can be used, leading to a transmission information rate equal to 40Gbits/s for

_{pos}*L*= 40km, whilst a value of

*N*=

_{pre}*N*= 2 leads to a transmission information rate equals to 18.5Gbits/s for

_{pos}*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

*CR*= 12

*dB*, for

*L*= 40

*km*a transmission information rate equals to 31Gbits/s can be theoretically achieved with

*i*

_{0}= 45mA and Δ

*i*= 4mA, whilst the values found in the previous subsection (

*i*

_{0}= 65

*mA*and Δ

*i*= 10

*mA*) are employed in the pre-distorted system. As expected, the conventional system and that with pre-distortion do not have the same optimum operation conditions because of the mitigation of the nonlinear distortion and the change of the different system trade-offs involved in the performance of the two systems. The transfer functions and the obtained signal-to-noise ratio of the conventional system and that with pre-distortion are shown in Fig. 6 for L=40km. As expected, the results obtained through simulations are in good agreement with those obtained using the analytical model. The magnitude of the transfer function of the system with pre-distortion (Fig. 6(c)) reach higher values than that obtained in the conventional system (Fig. 6(a)) due to the higher laser modulation efficiency. However, the increase on the value of Δ

*i*does not lead to a reduction of the signal-to-noise ratio due to nonlinear distortion (Fig. 6(d)) thanks to the pre-distortion technique.

*L*= 100km, the conventional OOFDM system achieves a transmission information rate equal to 10Gbits/s with the optimized values

*i*

_{0}= 45mA and Δ

*i*= 7mA, whilst the values found in the previous section (

*i*

_{0}= 65

*mA*and Δ

*i*= 12

*mA*) are employed in the pre-distorted system. Additionally, we have also included the results obtained when a nonlinear equalizer is used at the receiver as reported in [6

**20**(23), 25774–25789 (2012). [CrossRef] [PubMed]

*i*and the laser bias current

*i*

_{0}as well as the modulation format profile across the OFDM subcarriers in order to maximize the transmission information rate.

*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.

*BER*= 10

_{T}^{−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

*BER*. 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

_{T}*BER*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.

_{T}## 5. Conclusions

*BER*in the order of 10

^{−4}.

## Acknowledgments

## References and links

1. | W. Shieh and I. Djordjevic, |

2. | Z. Liu, M. A. Violas, and N. B. Carvalho, “Digital predistortion for RSOAs as external modulators in radio over fiber systems,” Opt. Express |

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 |

5. | D. Lam, A. M. Fard, B. Buckley, and B. Jalali, “Digital broadband linearization of optical links,” Opt. Letters |

6. | C-C. Wei, “Analysis and iterative equalization of transient and adiabatic chirp effects in DML-based OFDM transmission sytems,” Opt. Express |

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 |

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 |

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. |

11. | G. P. Agrawal and N. K. Dutta, |

12. | M. Costa, “Writing on dirty paper,” IEEE Trans. Inform. Theory |

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 |

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. |

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, |

17. | G. P. Agrawal, |

**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

- W. Shieh, I. Djordjevic, OFDM for Optical Communications (Elsevier/Academic Press, 2009).
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- 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]
- 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]
- 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).
- 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]
- G. P. Agrawal, N. K. Dutta, Semiconductor Lasers (Van Nostrand Reinhold, 1993).
- M. Costa, “Writing on dirty paper,” IEEE Trans. Inform. Theory 29(3), 439–441 (1983). [CrossRef]
- 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]
- 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).
- 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.
- A. V. Oppenheim, R. W. Schaffer, J. R. Buck, Discrete-time signal processing (Prentice-Hall, 1999).
- G. P. Agrawal, Fiber-optic Communications Systems (Wiley, 1997).

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