Abstract

Self-coherent detection with interferometric field reconstruction aims at retrieving the complex-valued optical field (amplitude and phase) by digitally processing delay interferometer (DI) measurements, in order to realize a differential direct detection receiver with capabilities akin to that of a fully coherent receiver with polarization multiplexing, albeit without requiring a local oscillator laser in the receiver. Here we introduce a novel digital recursive algorithm capable of accurately reconstructing the optical complex field (both amplitude and phase) solely from the quadrature DI outputs, eliminating the AM photo-detector branch. We analyze a key impairment namely the accumulation of errors and fluctuations in the reconstructed amplitude and phase due to ADC quantization noise, recirculating in the recursion. We introduce signal processing measures to effectively mitigate this noise impairment leading to a potentially practical self-coherent receiver, demonstrated in this paper for a single polarization. We also investigate the range of applicability of self-coherent detection concluding that it is most suitable to relatively low baud-rate systems such as passive optical networks, for which application the self-coherent receiver outperforms the coherent homodyne receiver due to its improved laser noise tolerance, obtained due to the removal of the optical local oscillator.

© 2012 OSA

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References

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  1. N. Kikuchi, K. Mandai, S. Sasaki, and K. Sekine, “Proposal and First Experimental Demonstration of Digital Incoherent Optical Field Detector for Chromatic Dispersion Compensation,” in ECOC’05 European Conference of Optical Communication, PDP Th. 4.4.4 (2005).
  2. J. Zhao, M. E. McCarthy, and A. D. Ellis, “Electronic dispersion compensation using full optical-field reconstruction in 10Gbit/s OOK based systems,” Opt. Express16(20), 15353–15365 (2008).
    [CrossRef] [PubMed]
  3. X. Liu, S. Chandrasekhar, and A. Leven, “Digital self-coherent detection,” Opt. Express16(2), 792–803 (2008).
    [CrossRef] [PubMed]
  4. N. Kikuchi and S. Sasaki, “Highly Sensitive Optical Multilevel Transmission of Arbitrary Quadrature-Amplitude Modulation (QAM) Signals With Direct Detection,” J. Lightwave Technol.28(1), 123–130 (2010).
    [CrossRef]
  5. Y. Takushima, H. Y. Choi, and Y. C. Chung, “Transmission of 108-Gb/s PDM 16ADPSK signal on 25-GHz grid using non-coherent receivers,” Opt. Express17(16), 13458–13466 (2009).
    [CrossRef] [PubMed]
  6. J. Li, R. Schmogrow, D. Hillerkuss, M. Lauermann, M. Winter, K. Worms, C. Schubert, C. Koos, W. Freude, and J. Leuthold, “Self-Coherent Receiver for PolMUX Coherent Signals, ” in OFC/NFOEC’11 Conference on Optical Fiber Communication, OWV5 (2011).
  7. S. Kumar, Impact of Nonlinearities on Fiber Optic Communications (Springer, 2011).
  8. N. Sigron, I. Tselniker, and M. Nazarathy, “Carrier phase estimation for optically coherent QPSK based on Wiener-optimal and adaptive Multi-Symbol Delay Detection (MSDD),” Opt. Express20(3), 1981–2003 (2012).
    [CrossRef] [PubMed]
  9. I. Tselniker, N. Sigron, and M. Nazarathy, “Joint phase noise and frequency offset estimation and mitigation for optically coherent QAM based on adaptive multi-symbol delay detection (MSDD),” Opt. Express20(10), 10944–10962 (2012).
    [CrossRef] [PubMed]
  10. M. Nazarathy, Y. Yadin, M. Orenstein, Y. K. Lize, L. Christen, and A. E. Willner, “Enhanced Self-Coherent Optical Decision-Feedback-Aided Detection of Multi-Symbol M-DPSK/PolSK in particular 8-DPSK/BPolSK at 40 Gbps,” in OFC/NFOEC’07 Conference on Optical Fiber Communication (2007).
  11. S. Zhang, P. Y. Kam, C. Yu, and J. Chen, “Decision-Aided Carrier Phase Estimation for Coherent Optical Communications,” J. Lightwave Technol.28(11), 1597–1607 (2010).
    [CrossRef]
  12. H. Sun and W. K. Tsan, “Clock recovery and jitter sources in coherent transmission, paper OTh4C.2,” in OFC/NFOEC’ Conference on Optical Fiber Communication, OTh4C.2 (2012).

2012

2010

2009

2008

Chandrasekhar, S.

Chen, J.

Choi, H. Y.

Chung, Y. C.

Ellis, A. D.

Kam, P. Y.

Kikuchi, N.

Leven, A.

Liu, X.

McCarthy, M. E.

Nazarathy, M.

Sasaki, S.

Sigron, N.

Takushima, Y.

Tselniker, I.

Yu, C.

Zhang, S.

Zhao, J.

J. Lightwave Technol.

Opt. Express

Other

M. Nazarathy, Y. Yadin, M. Orenstein, Y. K. Lize, L. Christen, and A. E. Willner, “Enhanced Self-Coherent Optical Decision-Feedback-Aided Detection of Multi-Symbol M-DPSK/PolSK in particular 8-DPSK/BPolSK at 40 Gbps,” in OFC/NFOEC’07 Conference on Optical Fiber Communication (2007).

J. Li, R. Schmogrow, D. Hillerkuss, M. Lauermann, M. Winter, K. Worms, C. Schubert, C. Koos, W. Freude, and J. Leuthold, “Self-Coherent Receiver for PolMUX Coherent Signals, ” in OFC/NFOEC’11 Conference on Optical Fiber Communication, OWV5 (2011).

S. Kumar, Impact of Nonlinearities on Fiber Optic Communications (Springer, 2011).

H. Sun and W. K. Tsan, “Clock recovery and jitter sources in coherent transmission, paper OTh4C.2,” in OFC/NFOEC’ Conference on Optical Fiber Communication, OTh4C.2 (2012).

N. Kikuchi, K. Mandai, S. Sasaki, and K. Sekine, “Proposal and First Experimental Demonstration of Digital Incoherent Optical Field Detector for Chromatic Dispersion Compensation,” in ECOC’05 European Conference of Optical Communication, PDP Th. 4.4.4 (2005).

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Figures (8)

Fig. 1
Fig. 1

SC receiver front-end alternatives. (a): An IQ DI realization consisting of a pair of delay interferometers in quadrature. (b): An equivalent 90 deg hybrid-based realization of the IQ DI.

Fig. 2
Fig. 2

The field reconstruction algorithm embedded in a schematic of a self-coherent receiver.

Fig. 3
Fig. 3

Scalar (single-polarization) link. (a): Single channel 16-QAM transmitter with modulus preserving differential precoding [8] (b): Simple additive white Gaussian (ASE) noise and laser phase noise channel model. (c): SC single-polarization receiver using and DIs with half baud-interval delay and 2x oversampled ADC. (d): Comparable fully-coherent receiver. For coherent detection the channel model is modified by doubling the effective linewidth (making the substitution Δν2Δν ) to account for the combined effect of transmit laser and OLO laser.

Fig. 4
Fig. 4

Multi-Symbol Delay Detection (MSDD) Carrier Recovery system, incorporating a modified adaptive NLMS AGC algorithm. This system resembles the U-notU MSDD disclosed in [9] but differs from it in using a more rapidly converging Normalized LMS (NLM) rather than an LMS MSDD algorithm.

Fig. 5
Fig. 5

Block diagram of simulated field reconstruction post-detection noise impairment and its mitigation through oversampling and bandlimiting. (a): Transmitter model. (b): Receiver model. The switch SW has two positions corresponding to either using the band-limiting filter or not using it.

Fig. 6
Fig. 6

Magnitude and phase errors time evolution for the SC receiver front end of Fig. 5, plotted over ten cycles of 20 training symbols with C-AGC tracking, followed by 180 info symbols, with the C-AGC frozen to the last value attained at the end of the preceding training sequence. The yellow square wave is an indicator of the data-aided mode – it is “on” during the 20 symbols long training sequences, while it is “off” during the 180 symbols long operating intervals during which the FR module reconstructs the received field. (a,b): Respective relative magnitude and phase errors for B = 12 bits ADC. (c,d): Respective relative magnitude and phase errors for B = 13 bits ADC. (e,f): Respective relative magnitude and phase errors for B = 14 bits ADC. In all phase error plots, (b,d,f), the “wildest” curve (red) is the total received phase noise of a reference coherent system, due to the combined effect of the transmitter and receiver OLO lasers. It is apparent that the phase wander induced by the ADC noise is substantially smaller than that due to the laser phase noise.

Fig. 7
Fig. 7

Bit Error Ratio (BER) vs. Optical Signal to Noise Ratio (OSNR) performance of a scalar (single) polarization SC Rx with optical amplification, vs. a fully coherent receiver, for 0 KHz, 100 KHz and 200 KHz laser linewidth (LW) and for 100 MBd and 200 MBd baud rates. (top to bottom): various numbers of bits in the ADC, as listed in the header of each plot.

Fig. 8
Fig. 8

Field reconstruction algorithm with evasion of the divisive-exception.

Equations (35)

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I(t)=Re{ ρ ˜ (t) ρ ˜ * (t τ DI ) }=ρ(t)ρ(t τ DI )cos[ ρ ˜ k ρ ˜ (t τ DI ) ] Q(t)=Im{ ρ ˜ (t) ρ ˜ * (t τ DI ) }=ρ(t)ρ(t τ DI )sin[ ρ ˜ k ρ ˜ (t τ DI ) ]
q ˜ (t)=I(t)+jQ(t)= ρ ˜ (t) ρ ˜ * (t τ DI )
q ˜ k q ˜ (k τ DI )= ρ ˜ (k τ DI ) ρ ˜ * ((k1) τ DI )
q ˜ k = ρ ˜ k ρ ˜ k1 *
I k =Re ρ ˜ k ρ ˜ k1 * = ρ k ρ k1 cos( ρ ˜ k ρ ˜ k1 ) Q k =Im ρ ˜ k ρ ˜ k1 * = ρ k ρ k1 sin( ρ ˜ k ρ ˜ k1 ).
q ˜ k = I k +j Q k =Re{ ρ ˜ k ρ ˜ k1 * }+jIm{ ρ ˜ k ρ ˜ k1 * }= ρ ˜ k ρ ˜ k1 * = ρ k ρ k1 e j( ρ ˜ k ρ ˜ k1 )
q k = I k 2 + Q k 2 = ρ k ρ k1 , q ˜ k =arctan Q k I k = ρ ˜ k ρ ˜ k1
ρ ˜ ^ k = q ˜ k + ρ ˜ ^ k1 = k =0 k q ˜ k
ρ ˜ ^ k = P k exp{ j k =0 k arctan( Q k / I k ) }
ρ ^ k ρ k ρ k1 q k = ( I k 2 + Q k 2 ) 1/4
ρ ˜ ^ k = q ˜ k / ρ ˜ ^ k1 * witharbitraryinitialcondition ρ ˜ ^ 0
ρ ˜ ^ 1 = q ˜ 1 ρ ˜ ^ 0 * ; ρ ˜ ^ 2 = q ˜ 2 ρ ˜ ^ 1 * ; ρ ˜ ^ 3 = q ˜ 3 ρ ˜ ^ 2 * ..... ρ ˜ ^ k = q ˜ k ρ ˜ ^ k1 * ....
k=1,2,3,4,...:k=1: ρ ˜ ^ 1 = q ˜ 1 ρ ˜ ^ 0 * = ρ ˜ 1 ρ ˜ 0 * g ˜ 0 * ρ ˜ 0 * = ρ ˜ 1 / g ˜ 0 *
k=2: ρ ˜ ^ 2 = q ˜ 2 ρ ˜ ^ 1 * = ρ ˜ 2 ρ ˜ 1 * ( ρ ˜ 1 / g ˜ 0 * ) * = ρ ˜ 2 ρ ˜ 1 * ρ ˜ 1 * / g ˜ 0 = ρ ˜ 2 g ˜ 0
k=3: ρ ˜ ^ 3 = q ˜ 3 ρ ˜ ^ 2 * = ρ ˜ 3 ρ ˜ 2 * ( ρ ˜ 2 g ˜ 0 ) * = ρ ˜ 3 ρ ˜ 2 * ρ ˜ 2 * g ˜ 0 * = ρ ˜ 3 / g ˜ 0 *
k=4: ρ ˜ ^ 3 = q ˜ 3 ρ ˜ ^ 2 * = ρ ˜ 3 ρ ˜ 2 * ( ρ ˜ 2 g ˜ 0 ) * = ρ ˜ 3 ρ ˜ 2 * ρ ˜ 2 * g ˜ 0 * = ρ ˜ 3 / g ˜ 0 * ρ ˜ ^ 4 = q ˜ 4 ρ ˜ ^ 3 * = ρ ˜ 4 ρ ˜ 3 * ( ρ ˜ 3 / g ˜ 0 * ) * = ρ ˜ 4 ρ ˜ 3 * ρ ˜ 3 * / g ˜ 0 = ρ ˜ 4 g ˜ 0
{ ρ ˜ ^ 0 , ρ ˜ ^ 2 , ρ ˜ ^ 4 ,..., ρ ˜ ^ 2 k ,...}= g ˜ 0 { ρ ˜ 0 , ρ ˜ 2 , ρ ˜ 4 ,..., ρ ˜ 2 k ,...} { ρ ˜ ^ 1 , ρ ˜ ^ 3 , ρ ˜ ^ 5 ,..., ρ ˜ ^ 2 k +1 ,...}= g ˜ 1 { ρ ˜ ^ 1 , ρ ˜ ^ 3 , ρ ˜ ^ 5 ,..., ρ ˜ ^ 2 k +1 ,...}where g ˜ 1 1/ g ˜ 0 *
γ 0 g ˜ 0 : ρ ˜ ^ k = ρ ˜ k + γ 0 ,k=0,1,2,3,4,....
ρ ^ k = q k / ρ ^ k1 ; ρ ˜ ^ k = q ˜ k + ρ ˜ ^ k1
q ˜ k = q ˜ k o + n ˜ k q = q ˜ k o ( 1+ n ˜ k q / q ˜ k o )= q ˜ k o ( 1+ η ˜ k q ) ρ ˜ ^ k = ρ ˜ ^ k o + n ˜ k ρ = ρ ˜ ^ k o + n ˜ k ρ = ρ ˜ ^ k o ( 1+ n ˜ k ρ / ρ ˜ ^ k o )= ρ ˜ ^ k o ( 1+ η ˜ k ρ )
η k q n ˜ k q / q ˜ k o =( q ˜ k q ˜ k o )/ q ˜ k o ; η k ρ n ˜ k ρ / ρ ˜ k o =( ρ ˜ k ρ ˜ k o )/ ρ ˜ k o
ρ ^ k | ρ ˜ ^ k |= ρ ^ k o | 1+ η ˜ k ρ |= ρ ^ k o | 1+ η k ρRe +j η k ρIm | ρ ^ k o ( 1+ η k ρRe )
ρ ˜ ^ k ρ ˜ k ρ ˜ k1 * = q ˜ k ρ ˜ ^ k1 * = q ˜ k o ( 1+ η ˜ k q ) ρ ˜ ^ k1 o* ( 1+ η ˜ k1 ρ* ) = ρ ˜ ^ k o ( 1+ η ˜ k q η ˜ k1 ρ* )
η ˜ k ρ = η ˜ k q η ˜ k1 ρ*
η k ρRe = η k qRe η k1 ρRe ; η k ρIm = η k qIm + η k1 ρIm
Z{ η k ρRe }=Z{ η k qRe } z 1 Z{ η k ρRe } Z{ η k ρRe } Z{ η k qRe } = 1 1+ z 1 = z z+1
Z{ η k ρIm }=Z{ η k qIm }+ z 1 Z{ η k ρIm } Z{ η k ρIm } Z{ η k qIm } = 1 1 z 1 = z z1
ρ ˜ ^ k = ρ ˜ ^ k o ( 1+ η k ρ )= ρ ˜ ^ k o ( 1+ η k qRe +j η k qIm ) ρ ˜ ^ k o ( 1+ η k qRe ) e j η k qIm
η k ρIm = k =0 k η k qIm
H Q ( e jω )= z/(z1) | z= e jω = j 2 e jω/2 /sin( ω/2 )
η k ρRe = k =0 k (1) k k η k qRe = (1) k k =0 k (1) k η k qRe
H I ( e jω )= (1) k k =0 k (1) k e jω = z/(z+1) | z= e jω = 1 2 e jω/2 /cos( ω/2 )
ρ ˜ ^ k = ρ ˜ ^ k o ( 1+ η k qRe +j η k qIm ) ρ ˜ ^ k o ( 1+ (1) k k =0 k (1) k η k qRe )exp{ j k =0 k η k qIm }
A ˜ k = s ˜ k A ˜ k1 /| A ˜ k1 |
ε k ρ | ρ ˜ ^ k || ρ ˜ k |; ε k ϕ ρ ˜ ^ k ρ ˜ k

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