OFDM is efficient approaches to deal with inter symbol interference due to CD and PMD. By providing that the guard interval is larger than the combined delay spread due to CD and maximum DGD, the ISI can be eliminated successfully. However, the four-wave mixing (FWM) between different subcarriers and its interplay with CD and PMD will result in different subcarriers being affected differently. Even though that most of the subcarriers are without errors, the overall BER will be dominated by BER of the worst subcarriers. In order to avoid this problem, the use of forward error correction (FEC) is essential. The use of advanced FEC schemes is needed to provide that BER performance of an OFDM system that is determined by the average received power rather than by the power of the weakest sub carrier. In this paper, we describe coded OFDM with direct detection.
In this paper, we describe how to optimally combine modulation with channel coding, and describe several coded-modulation schemes such as coded orthogonal frequency division multiplexing (OFDM) . Using this approach, modulation, coding, and multiplexing are performed in a uniï¬ed fashion so that, effectively, the transmission, signal processing, detection, and decoding are done at much lower symbol rates. At these lower rates, dealing with the nonlinear effects and polarization mode dispersion (PMD) is more manageable, while the aggregate data rate per wavelength is maintained above 100Gb/s.
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The paper is organized as follows. In Section 2we describe M-ary quadrature amplitude multiplexing (QAM), M-ary phase shift keying (PSK), and we describe multidimensional coded modulation as an efficient way to increase the spectral efficiency. We describe coded OFDM as an efficient way to compensate simultaneously for chromatic dispersion (CD) and PMD, and to increase the spectral efficiency. Section 3 is results & Discussion, Section 4 is future Scope & Section 5 gives the references which conclude the paper.
2. Coded OFDM in Fiber-optics Communication Systems with Direct Detection & its implementation
The transmitter and receiver configurations of an OFDM  system with direct detection [2, 16] and format of the transmitted OFDM symbol are shown in Fig.1a-c, respectively. On the transmitter side the information-bearing streams at 10 Gb/s are encoded using identical LDPC codes. The outputs of these LDPC encoders are demultiplexed and parsed into groups of B bits corresponding to one OFDM frame. The B bits in each OFDM frame are subdivided into K subchannels with the i th subcarrier carrying bi bits, so that B= âˆ‘bi The bi bits from the i th sub channel are mapped into a complex-valued signal from a 2 bi -point signal constellation such as M-ary QAM and M-ary PSK. For example, bi D 2 for QPSK and bi D 4 for 16-QAM. The complex-valued signal points from subchannels are considered to be the values of the fast Fourier transform (FFT) of a multicarrier OFDM signal. By selecting the number of subchannels K, sufficiently large, OFDM symbol interval can be made significantly larger than the dispersed pulse-width of an equivalent single carrier system, resulting in ISI reduction. The OFDM symbol, shown in Fig. 1c, is generated as follows: NQAM.= K input QAM symbols are zero-padded to obtain NFFT input samples for IFFT, NG nonzero samples are inserted (as explained below) to create the guard interval, and the OFDM symbol is multiplied by the window function. The OFDM symbol windowing is illustrated in Fig. 1d. The purpose of cyclic extension is to preserve the orthogonality among sub carriers even when the neighboring OFDM symbols partially overlap due to dispersion, and the role of windowing is to reduce the out-of-band spectrum. For efficient chromatic dispersion and PMD compensation, the length of cyclically extended guard interval should be larger than the spread due to chromatic dispersion and PMD.
The cyclic extension, illustrated in Fig. 1.c, is accomplished by repeating the last NG/2 samples of the effective OFDM symbol part (NFFT samples) as a prefix, and repeating the first NG/2 samples as a suffix. After D/A conversion and RF up conversion, the RF signal can be mapped to the optical domain using one of two possible options: (1) the OFDM signal can directly modulate a DFB laser, or (2) the OFDM signal can be used as the RF input of a Mach-Zehnder modulator (MZM). A DC bias component is added to the OFDM signal in order to enable recovery of the QAM symbols incoherently. In what follows, three different OFDM schemes are described. The first scheme is based on direct modulation, and shall be referred to as the "biased-OFDM" (B-OFDM) scheme. Because bipolar signals cannot be transmitted over an IM/DD link, it is assumed that the bias component is sufficiently large so that when added to the OFDM signal the resulting sum is nonnegative. The main disadvantage of the B-OFDM scheme is its poor power efficiency. To improve the OFDM power efficiency, two alternative schemes can be used. The first scheme, which we shall refer to as the "clipped-OFDM" (C-OFDM) scheme, is based on single-sideband (SSB) transmission, and clipping of the OFDM signal after bias addition. The bias is varied in order to find the optimum one for fixed optical launched power. It was found that the optimum bias is one in which _50% of the total electrical signal energy before clipping is allocated for transmission of a carrier. The second power-efficient scheme, which we shall refer to as the "unclipped-OFDM" (U-OFDM) scheme, is based on SSB transmission using a LiNbO3 MZM. To avoid distortion due to clipping at the transmitter, the information is mapped into the optical domain by modulating the electrical field of the optical carrier (instead of intensity modulation employed in the B-OFDM and C-OFDM schemes). In this way, both positive and negative portions of the electrical OFDM signal are transmitted to the photo detector. Distortion introduced by the photo detector, caused by squaring, is successfully eliminated by proper filtering, and recovered signal does not exhibit significant distortion. It is important to note, however, that the U-OFDM scheme is slightly less power efficient than the C-OFDM scheme.
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Fig. 1(a) Transmitter configuration, (b) receiver configuration, (c) OFDM symbol after cyclic extension, and (d) OFDM symbol after windowing. LDPCE LDPC encoder, LDPCD LDPC decoder, S=P serial-to-parallel converter, MZM Mach-Zehnder modulator, SMF single-mode optical fiber, PD photo detector, DSB double-sideband, SSB single-sideband
The SSB modulation can be achieved either by appropriate optical filtering the double-side band signal at MZM output (see Fig. 1a) or by using the Hilbert transformation of in-phase component of OFDM RF signal. The first version requires the use of only in-phase component of RF OFDM signal, providing that zero-padding is done in the middle of OFDM symbol rather than at the edges.
The transmitted OFDM signal can be written as
is defined for
t Ð„ [kT - TG/2- Twin; kT + TFFT+ TG/2 + Twin ]. In the above expression, Xi;k denotes the i th sub carrier of the k th OFDM symbol, w(t) is the window function, and fRF is the RF carrier frequency. T denotes the duration of the OFDM symbol, TFFT denotes the FFT sequence duration, TG is the guard interval duration (the duration of cyclic extension), and Twin denotes the windowing interval duration. D denotes the DC bias component, which is introduced to enable the OFDM demodulation using the direct detection
The PIN photodiode output current can be written as
Where SOFDM(t) denotes the transmitted OFDM signal in RF domain given by eq(2). D is introduced above, while RPIN denotes the photodiode responsivity. The impulse response of the optical channel is represented by h(t). The signal after RF down conversion and appropriate filtering, can be written as
Where he(t) is the impulse response of the low-pass filter, n(t) is electronic noise in the receiver, and kRF denotes the RF down-conversion coefficient. Finally, after the A/D conversion and cyclic extension removal, the signal is demodulated by using the FFT algorithm. The soft outputs of the FFT demodulator are used to estimate the bit reliabilities that are fed to identical LDPC iterative decoders implemented based on the sum-product with correction term algorithm as we explained above. For the sake of illustration, let us consider the signal waveforms and powerspectral densities (PSDs) at various points in the OFDM system given in Fig. 1. These examples were generated using SSB transmission in a back-to-back configuration. The bandwidth of the OFDM signal is set to B GHz, and the RF carrier to 0:75B; where B denotes the aggregate data rate. The number of OFDM subchannels is set to 64, the OFDM sequence is zero-padded, and the FFT is calculated using 128 points. The guard interval is obtained by a cyclic extension of 2 * 16 samples. The average transmitted launch power is set to 0 dBm. The OFDM transmitter parameters are carefully chosen such that RF driver amplifier and MZM operate in linear regime (see Fig. 2a-c). The PSDs of MZM output signal and the photo detector output signal are shown in Fig. 2d, e, respectively. The OFDM term after beating in the PD, the low-pass term, and the squared OFDM term can easily be identified.
Fig. 2 Waveforms and PSDs of SSB QPSK-OFDM signal at different points during transmission for electrical SNR (per bit) of 6 dB. (fc the optical carrier frequency, LD the laser diode.)
The received electrical field, at the input of the transimpedance amplifier (TA), in the presence of chromatic dispersion and first-order PMD, can be represented by
where Î²2 and Î²3 represent the group-velocity dispersion (GVD) and second-order GVD parameters, Ltot is the total SMF length, k is the splitting ratio between two principal states of polarization (PSPs), Î´ is the phase difference between PSPs, E0 is transmitted laser electrical field amplitude, and Nx and Ny represent x- and y polarization ASE noise components. With FT and FT-1 we denoted the Fourier transform and inverse Fourier transform, respectively. The TA output signal can be represented by v(t)= RF RPIN Ð†E(t)I2 + n(t), where RPIN is the photodiode responsivity, RF is the TA feedback resistor, and n(t) is TA thermal noise. For complete elimination of ISI, the total delay spread due to chromatic dispersion and DGD should be shorter than the guard interval:
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Where Dt is the accumulated dispersion, Î”f is the sub carrier spacing, c is the speed of the light, and âˆ†f is the central frequency set to 193.1 THz. The number of subcarriers NFFT, the guard interval TG, GVD and second-order GVD parameters were introduced earlier.
The received QAM symbol of i th subcarrier in the kth OFDM symbol is related to transmitted QAM symbol Xi;k by
Where hi is channel distortion introduced by PMD and chromatic dispersion, and Î¸i is the phase shift of i th subcarrier due to chromatic dispersion. Î¦k represents the OFDM symbol phase noise due to SPM and RF down-converter, and can be eliminated by pilot-aided channel estimation. Notice that in direct detection case, the laser phase noise is completely cancelled by photo detection. To estimate the channel distortion due to PMD, hi and phase shift due to chromatic dispersion Î¦i , we need to pretransmit the training sequence. Because in ASE noise dominated scenario (considered here) the channel estimates are sensitive to ASE noise, the training sequence should be sufficiently long to average the noise. For DGDs up to 100 ps, the training sequence composed of several OFDM symbols is sufficient. For larger DGDs longer OFDM training sequence is required; alternatively, the channel coefficients can be chosen to maximize the LLRs or someone can use the PBS to separate the x- and y-polarization components, and consequently process them. The phase shift of i th subcarrier due to chromatic dispersion can be determined from training sequence as difference of transmitted and received phase averaged over different OFDM symbols. Once the channel coefficients and phase shifts due to PMD and chromatic dispersion are determined, in a decision-directed mode, the transmitted QAM symbols are estimated by
The symbol LLRs Î»(q) ; (q = 0,1,. . . . . 2b -1) can be determined as
where Re and Im denote the real and imaginary part of a complex number, QAM denotes the QAM-constellation diagram, N0 denotes the PSD of an equivalent Gaussian noise process, and map.q/ denotes a corresponding mapping rule (Gray mapping is applied here). (b denotes the number of bits per constellation
point.) Let us denote by vj the j th bit in an observed symbol q binary representation v =(v1, v2, . . . , vb). The bit LLRs needed for LDPC decoding are calculated from symbol LLRs by
Therefore, the j th bit reliability is calculated as the logarithm of the ratio of a probability that vj = 0 and probability that vj = 1. In the nominator, the summation is done over all symbols q having 0 at the position j, while in the denominator over all symbols q having 1 at the position j .
3. Results & Discussion
The results of simulation, for ASE noise-dominated scenario and single wavelength channel transmission, are shown in Figs. 3-5, for the LDPC coded SSB OFDM system with aggregate rate of 10 Gb/s, 512 subcarriers, RF carrier frequency of 10 GHz, over sampling factor of 2, and cyclic extension with 512 samples. The modulation format being applied is QPSK. The LDPC (16935, 13550) code of girt-10, code rate 0.8, and column-weight 3 is used. In Fig. 3, we show the BER performance for DGD of 100 ps, without residual chromatic dispersion. We see that un coded case faces significant performance degradation at low BERs. On the other hand, the LDPC-coded case has degradation of 1.1 dB at BER of 10-9 (when compared to the back-to-back configuration). In Fig. 7, we show the BER performance after 6,500 km of SMF (without optical dispersion compensation), for a dispersion map composed of 65 sections of SMF with 100 km in length. The noise figure of erbium-doped fiber amplifiers (EDFAs), deployed periodically after every SMF section, was set to 5 dB. To achieve the desired OSNR, the ASE noise loading was applied on receiver side, while the launch power was kept below 0 dBm. We see that LDPC-coded OFDM is much less sensitive to chromatic dispersion compensation than PMD. Therefore, even 6,500 km can be reached without optical dispersion compensation with penalty within 0.4 dB at BER of 10-9, when LDPC-coded OFDM is used.
Fig. 3 BER performance of LDPC-coded OFDM system with aggregate rate of 10 Gb/s, for DGD of 100 ps
Fig. 4 BER performance of LDPC-coded OFDM system with aggregate rate of 10 Gb/s, after 6,500 km of SMF
Fig. 5 BER performance of LDPC-coded OFDM system with aggregate rate of 10 Gb/s, after 6,500 km of SMF and for DGD of 100 ps
In Fig. 5, the efficiency of LDPC-coded OFDM in simultaneous chromatic dispersion and PMD compensation is studied. After 6,500 km of SMF (without optical dispersion compensation) and for DGD of 100 ps, the LDPC-coded OFDM has the penalty within 1.5 dB. It has been noticed that coded turbo equalization cannot be used at all for this level of residual chromatic dispersion and DGD. It can also be noticed that, from numerical results presented here, that the major factor of performance degradation in LDPC-coded OFDM with direct detection, in ASE noise-dominated scenario, is PMD.
4. Future Scope
To improve the tolerance to PMD someone may use longer training sequences and redistribute the transmitted information among the subcarriers less affected by DGD, or to use the PBS and separately process x- and y-PSPs, in a fashion similar to that proposed for OFDM with coherent detection as described in next section; however, the complexity of such a scheme would be at least two times higher. Notice that for this level of DGD, the redistribution of power among subcarriers not being faded away is not needed. For larger values of DGDs, the penalty due to DGD grows as DGD increases, if the redistribution of sub carriers is not performed.