Andrew M. Weiner, Editor-in-Chief
Gal Shulkind and Moshe Nazarathy
Gal Shulkind and Moshe Nazarathy*
EE Dept., Technion, Israel Institute of Technology, Haifa 32000, Israel
*Corresponding author: firstname.lastname@example.org
DFT-spread (DFT-S) coherent optical OFDM was numerically and experimentally shown to provide improved nonlinear tolerance over an optically amplified dispersion uncompensated fiber link, relative to both conventional coherent OFDM and single-carrier transmission. Here we provide an analytic model rigorously accounting for this numerical result and precisely predicting the optimal bandwidth per DFT-S sub-band (or equivalently the optimal number of sub-bands per optical channel) required in order to maximize the link non-linear tolerance (NLT). The NLT advantage of DFT-S OFDM is traced to the particular statistical dependency introduced among the OFDM sub-carriers by means of the DFT spreading operation. We further extend DFT-S to a unitary-spread generalized modulation format which includes as special cases the DFT-S scheme as well as a new format which we refer to as wavelet-spread (WAV-S) OFDM, replacing the spreading DFTs by Hadamard matrices which have elements +/−1 hence are multiplier-free. The extra complexity incurred in the spreading operation is almost negligible, however the performance improvement with WAV-S relative to plain OFDM is more modest than that achieved by DFT-S, which remains the preferred format for nonlinear tolerance improvement, outperforming both plain OFDM and single-carrier schemes.
© 2012 OSA
Alex Tolmachev and Moshe Nazarathy
Opt. Express 19(26) B370-B384 (2011)
Xi Chen, An Li, Guanjun Gao, and William Shieh
Opt. Express 19(27) 26198-26207 (2011)
Jair A. L. Silva, Adolfo V. T. Cartaxo, and Marcelo E. V. Segatto
J. Opt. Commun. Netw. 4(4) 296-303 (2012)
Gal Shulkind and Moshe Nazarathy
Opt. Express 20(27) 29035-29062 (2012)
Fan Zhang, Chuanchuan Yang, Xi Fang, Tingting Zhang, and Zhangyuan Chen
Opt. Express 21(5) 6115-6130 (2013)
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Opt. Express 21(11) 13145-13161 (2013)
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(a) DFT-S OFDM link with (de)spreading pre(post)-processing. M sub-single-carriers are transmitted over M FDM sub-bands per channel (b). Tx signal flow for a single sub-band.
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Cyclically extended Single-Carrier Tx (a) obtained as a special case of DFT-S with M = 1 SSC sub-band. (b) resulting CE-SC block diagram. The Tx is just a single-carrier one with added CP; the Rx drops the CP and performs DFT-based FD one-tap per tone equalization.
Numeric simulation of the received FWM NLI MER over a 16-QAM DFT-S OFDM optically amplified fiber link, for an SSF transmission experiment with the following parameters:
38400 data-symbols were used to gather the statistics (and we have verified that the MER converged to steady values).
PAPR of the transmitted DFT-S OFDM signal, parameterized by the number of SSC sub-bands. Other parameters: RRC Tx filter with parameter alpha = 0.1; 4x upsampling; QAM16 constellation; main FFT size MN = 128. The abbreviations anlg = analog and dig = digital refer to the PAPR type.
Numeric simulation of the received FWM NLI MER over a 16-QAM DFT-S OFDM optically amplified fiber link. The two curves present Monte Carlo simulations respectively based on the SSF and third-order Volterra series models with the following parameters:
Notice that the worst case deviation of the Volterra-based trilinear model is bounded by 0.4 dB. 38400 data-symbols were used to gather the statistics (and we have verified that the MER converged to steady values).
Numeric Monte Carlo simulation of the PDF of the modulus (magnitude) and angle of the output samples of a 16-QAM DFT-S transmitter, parameterized by the number N (64,128,256) of tones per sub-band. The empirical histograms track the respective theoretical PDFs which are Rayleigh for the modulus and uniform over
for the phase. The plot pertains to the tone indexed i = 1.
(a) Averaged (over all tones) NLI MER vs. the number of sub-bands for a 16-PSK DFT-S OFDM channel over an optically amplified fiber link with the following parameters: Three curves are shown. The analytic curve accurately tracks the Monte-Carlo trilinear Volterra series simulation while the SSF slightly deviates away for the high plotted range of M values. (b) Averaged NLI MER vs. sub-bands, for 16-QAM vs. 16-PSK, over a link with:
NLI MER averaged (over all tones) vs. the number of unitary-spread sub-bands over an optically amplified fiber link with the following parameters:
(a) 16-QAM MC-SSF simulation over
comparing WAV-S vs. DTF-S OFDM NL performance for MN = 128 tones (also vs. CE-SC and plain OFDM discrete-points). Plain OFDM NL performance is exceeded with both DFT-S and WAV-S systems, but only DFT-S exceeds the single-carrier (CE-SC) performance. (b) 16-PSK channel over
with MN = 32 tones simulated analytically and also with MC trilinear Volterra series. The analytic WAV-S curve accurately tracks the MC-Trilinear simulation and indicates improved performance relative to plain OFDM, but worse performance relative to single-carrier. The DFT spread performance at its optimized peak (occurring for M = 2 sub-bands) exceeds the performance of all other systems (but requires higher complexity)
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