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\title{Performances of OFDM/OQPSK Modulation for Optical High Speed Transmission in Long Haul Fiber over 1600 Km}
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             \author[1]{SANOU Serge-Roland  }

             \author[2]{Serge Roland  Sanou}

             \affil[1]{  University of Ouagadougou}

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\date{\small \em Received: 9 December 2013 Accepted: 31 December 2013 Published: 15 January 2014}

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\begin{abstract}
        


Orthogonal Frequency Division Multiplex (OFDM) is a high-speed transmission technique widely studied in wireless networks. Its potential presents it as an ideal solution for high-speed transmission in optical fiber networks. This study presents the OFDM modulation associated with Offset Quadrature Phase Shift Keying (OQPSK) filtered using a filter banks for an optical transmission at the rate of 10 GB/s over 1600 Km in a single mode fiber (SMF). The simulations are performed in the VPI Photonics software environment. The results show that the filtered OFDM/OQPSK provides better transmission performance than the Classical OFDM/QPSK firstly because it does not require equalization to certain distances; secondly distances are greater than those achieved with the conventional OFDM in similar studies. In this study the bandwidth is maximized because we do not use the cyclic prefix (CP). Moreover the complexity of transmitters and receivers is reduced, which shows OFDM/OQPSK as an effective solution to combat the effects of the chromatic dispersion (CD), the polarization mode dispersion (PMD), the inter-symbol interference (ISI) and nonlinearities.

\end{abstract}


\keywords{ber, high-speed, OFDM, OQPSK, optical fiber.}

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\let\tabcellsep& 	 	 		 
\section[{INTRODUCTION}]{INTRODUCTION}\par
FDM multicarrier modulation techniques have been used to transmit information using various channel transmission networks such as Wi-Fi (IEEE 802.11) or new mobile networks \hyperref[b0]{[1]}, \hyperref[b1]{[2]}. Application to optical fiber networks is new and raises new issues as the transmission channel has different characteristics \hyperref[b2]{[3]}, \hyperref[b3]{[4]}. Techniques related to the conventional OFDM like the implementation of an appropriate channel coding (COFDM) is used to improve the performance of OFDM on an optical medium. COFDM has been studied in our previous works \hyperref[b4]{[5]}, \hyperref[b5]{[6]}. New solutions that can save the cyclic prefix, OFDM/OQPSK, are based on a prototype function which is better localized in time and frequency domain. Another approach is related to the use of OQPSK modulation with a filter banks to perform a good signal processing which can achieve a better performance than the classical OFDM with cyclic prefix. In fact, the idea of using filtered OFDM/OQPSK by a filter banks is based on the fact that OFDM is a common choice that can now be replaced or supplemented by Filter Bank-based Multicarrier (FBMC) techniques which have some very interesting characteristics, like the results showed by M. Bellanger \hyperref[b6]{[7]}, \hyperref[b7]{[8]}. Then, it seems to us as a good idea to investigate the combination of the two techniques where an OFDM/OQPSK signal is filtered by a filter banks.\par
Filter Banks Multicarrier approach can be seen as an evolution and an extension of the FFT approach of the OFDM. In order to keep the same size as the FFT used in OFDM, we implemented a polyphase structure.\par
In this context, we used to modulate subcarriers by QPSK for the generation of the OFDM baseband signal before applying the OQPSK and filter banks process.\par
Performance tests of the transmission chain were carried out on the basis of the Error Vector Magnitude (EVM), the Q factor (Qeff) and Bit Error Rate (BER). All these tests were performed according to the Optical Signal to Noise Ratio (OSNR). 
\section[{II.}]{II.} 
\section[{MATERIAL AND METHODOLOGY a) OFDM/OQPSK data structure}]{MATERIAL AND METHODOLOGY a) OFDM/OQPSK data structure}\par
The principle of the OFDM is based on the division of the transmitted signal into many sub-carriers, which makes it less sensitive to frequency selectivity, and by the extension of the OFDM symbol duration using a Cyclic Prefix (CP) of sufficient length to avoid ISI. The OFDM signal is in baseband time domain \hyperref[b2]{[3]}:( ) ( ) ( ) S k SC SC iT t f j S ki N k N k i OFDM e iT t C t S ? = + ? = +? ?? = ? ? = ? ? ? 2 2 / 1 2 / (1) ( ) ( ) ( ) S k iT t f j S S k e iT t iT t S ? ? ? = ? ? 2 (2) S k t k f 1 ? = ( ) ( ) ( ) S G S G t t t t t t ? ? , , 0 , 1 ? ? ? ? ? ? ? ? ? = ? (3)\par
where S OFDM (t) is the OFDM signal, Î?" G is the guard interval characterizing the cyclic prefix CP and ?(t) the rectangular function taking into account the guard interval. C ki is the i-th information symbol of the kth subcarrier, S k (t) is the waveform of the k-th subcarrier, N SC is the number of carriers, f k is the frequency of the  
\section[{Performances of OFDM/OQPSK Modulation for Optical High Speed Transmission in Long Haul}]{Performances of OFDM/OQPSK Modulation for Optical High Speed Transmission in Long Haul}\par
Fiber over 1600 Km k-th subcarrier, T S is the symbol period, t s is the observation period of the OFDM symbol.\par
In the context of OFDM/OQPSK, we don't use the cyclic prefix, so Î?" G = 0. The signal at the output of the optical receiver is:) ( . ) ( 0 ) ( t r e t r t j off ? ? ? + = (4) ) ( * ) ( ) ( 0 t h t S t r OFDM = (5)\par
with ? Off = ? LD1? LD2 and ??= ? LD1? LD2; ? LD1 and ? LD1 are respectively frequency and phase angular of the transmitter laser. ? LD2 and ? LD2 are respectively frequency and phase angular of the receiver laser. The symbol * represents the convolution product and h(t) is the impulse response of the optical fiber channel (SMF fiber).\par
OFDM has many variants and especially the one where the Cyclic Prefix is suppressed and adding an extension of the FFT approach, like FBMC. There are mainly three FBMC techniques that have been studied in the literature: Offset Quadrature Amplitude Modulation (OQAM), Cosine Modulated multi Tone (CMT), and Filtered Multi Tone (FMT). The term 'offset' refers to the time shift of half the inverse of the sub-channel spacing between the real part and the imaginary part of a complex symbol. Our goal is to address OQPSK which is a variant using QPSK modulation.\par
Contrary to OFDM, which transmits complexvalued symbols at a given symbol rate, OQPSK transmits real-valued symbols by introducing a half symbol space delay between the in-phase and quadrature components of QPSK symbols, it is possible to achieve a baud-rate spacing between adjacent subcarrier channels and recover the information symbol, free of ISI and Inter-Carrier Interference (ICI). The OQPSK transmitter structure used is the one presented in Figure \hyperref[fig_1]{1}. In the Receiver in Figure \hyperref[fig_2]{2}, the inverted process is achieved using an analysis filter bank.  ? ? ? ? ? ? + ? + = ? ? = ? ? ) 1 ( 2 cos ] [ ) 1 ( 2 ] 0 [ ] [ 1 1 m KM k k P P m P k K k ? (6)\par
With m =0,1,?, KM-2, the prototype filter length is L = KM±1 with M the number of subchannels and K the overlapping factor.\par
The frequency coefficients of the half-Nyquist filter obtained for K=4 are used for the prototype filter in the simulation and are given in Table1. The kth synthesis filter is defined by \hyperref[b9]{[10]}:? ? ? ? ? ? ? ? ? ? = ) 2 1 ( 2 exp ] [ ] [ p k L m M k j m P m g ? (7)\par
The kth analysis filter is simply a time-reversed and complex-conjugated version of the corresponding synthesis filter. So it is as follows:] 1 [ ] [ * m L g m f p k k ? ? = (8) ? ? ? ? ? ? ? ? ? ? = ) 2 1 ( 2 exp ] [ ] [ p k L m M k j m P m f ? (9) b) Optical transmission chain\par
The digital optical transmission channel used is illustrated in Figure  {\ref 3}.\par
OFDM optical transmission chain is simulated in VPITransmissionMaker 9.1, [11] and Matlab cosimulation environments. OQPSK modulations are not available in VPITransmissionMaker. So cosimulation with Matlab is used to add specific processing.\par
The developed processing platform is a universe of interconnected modules where some new galaxies were created. The processing chain used is shown in     We monitor the OSNR so as to fix its successive values at the transmitter side which can influence the calculation of BER, modeling the variable effect of imperfections in the optical transmission channel. For this the galaxy Set\textunderscore OSNR is used. The performances are evaluated using the OSNR measured at the receiver side before the entrance of the signal in the photodiode, by using an OSNR meter.\par
In order to use the successive values of OSNR in the Decoder galaxy, the OSNR meter uses a variable called OSNR that is also used as the parameter of the Const module in the global transmission chain.\par
An equalization process is added to the global chain to illustrate the impact of equalization in the calculation of EVM, BER and Qeff factor. For the simulation, we used the new DFE equalizer module which implements a Volterra equalization process available in VPITransmissionMaker 9.1. 
\section[{c) Estimation of the EVM, BER, Qeff factor and OSNR}]{c) Estimation of the EVM, BER, Qeff factor and OSNR}\par
The EVM is a measure of the quality of the transmission through the quality of the demodulation.\par
EVM RMS is the value of the root square (Root Mean Square) of the difference between the received symbols and ideals symbols, normalized. It is given by \hyperref[b10]{[13]}: \hyperref[b9]{(10)} with ? r I and r Q ? the real and imaginary part of the r-th received symbol. I r and Q r are the real and imaginary part of the r-th ideal symbol corresponding to the r-th received one. The calculation of EVM RMS is performed in the receiver decoding process.( ) 2 / 1 1 2 2 1 2 2 1 1 ? ? ? ? ? ? ? ? ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? + ? ? ? ? ? ? ? = ? ? = = ? ? N r r r N r r r r r RMS Q I N Q Q I I N EVM\par
The Bit Error Rate (BER) is the measuring parameter the best known of the quality of a digital transmission, and represents the ratio between the number of erroneous bits and the total number of bits transmitted. The determination of the BER is based on the following definition: For a better estimation of BER, we used a Monte Carlo approach, which consists in a stochastic simulation with a large number of random symbols, to estimate the behavior of the system. Therefore, we can estimate that:) ( N N BER err N MC Lim +? ? = (12)\par
Q factor (Qeff) calculation is based on the above BER formulas [3]: with Ps the power of the optical signal, P Noise the total power of the noise which models the accumulation of all the noises associated with the optical transmission chain.? ? ? ? ? ? ? ? = 2 2 1 eff Q erfc BER (13) ( ) BER erfcinv Q eff * 2 . 2 = (14) 
\section[{III.}]{III.} 
\section[{RESULTS}]{RESULTS}\par
The simulations helped us to plot the evolution curves of EVM as a function of OSNR. Similarly, the estimations of evolution of the BER and Q factor curves were performed according to the OSNR.  The results show that the Q factor, after some values, became infinite as the better quality is achieved.\par
IV. 
\section[{CONCLUSION}]{CONCLUSION}\par
networks. The idea of using variants of OFDM is influenced by the need to strengthen the transmission capacity and the use of new modulation schemes like OQPSK that can be implemented without the use of a cyclic prefix and equalization in some cases.\par
The simulations showed the superiority of OFDM/OQPSK than standard OFDM with cyclic prefix for optical communications, in term of covering long distance without the need of an equalization process for modulations like QPSK. This can be useful for simple applications with the use of less complex receivers. The equalization process is mandatory for higher level modulation scheme.\par
Furthermore, the study of FBMC techniques for optical communication is beginning and it opens new ways of research and applications that can be used to maximize the bandwidth with better qualities of transmission for photonics networks.\begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_1}Figure 1 :}\end{figure}
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\caption{\label{fig_3}Figure 4 .}\end{figure}
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 \begin{figure}[htbp]
\noindent\textbf{5}\includegraphics[]{image-6.png}
\caption{\label{fig_5}Figure 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{73}\includegraphics[]{image-7.png}
\caption{\label{fig_6}Figure 7 :Figure 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{8}\includegraphics[]{image-8.png}
\caption{\label{fig_7}Figure 8 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-9.png}
\caption{\label{fig_9}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{10}\includegraphics[]{image-10.png}
\caption{\label{fig_10}Figure 10 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{12}\includegraphics[]{image-11.png}
\caption{\label{fig_11}Figure 12 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.03777777777777778\textwidth}P{0.056666666666666664\textwidth}P{0.4155555555555555\textwidth}P{0.1511111111111111\textwidth}P{0.18888888888888888\textwidth}}
\tabcellsep \tabcellsep \multicolumn{2}{l}{Coefficients}\tabcellsep \\
K\tabcellsep H0\tabcellsep H1\tabcellsep H2\tabcellsep H3\\
4\tabcellsep 1\tabcellsep 0.971960\tabcellsep ?2 / 2\tabcellsep 0.235147\end{longtable} \par
 
\caption{\label{tab_0}Table 1 :}\end{figure}
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