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Ultrafast and low overhead training symbol based channel estimation in coherent M-QAM single-carrier transmission systems

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Abstract

We propose a training symbol based channel estimation (TS-EST) algorithm that estimates the 2 × 2 Jones channel matrix. The estimated matrix entries are then used as the initial center taps of the 2 × 2 butterfly equalizer. Employing very few training symbols for TS-EST, ultrafast polarization tracking is achieved and tap update can be initially pursued using the decision-directed least mean squares (DD-LMS) algorithm to mitigate residual intersymbol interference (ISI). We experimentally verify the proposed TS-EST algorithm for 112 Gbps PDM-QPSK and 224 Gbps PDM-16QAM systems using 10 and 40 training symbols for TS-EST, respectively. Steady-state and transient bit error rates (BERs) achieved using the TS-EST algorithm are compared to those obtained using the constant modulus algorithm (CMA) and the training symbol least mean squares (TS-LMS) algorithm and results show that the proposed TS-EST algorithm provides the same steady-state BER with a superior convergence speed. Also, the tolerance of the proposed TS-EST algorithm to laser phase noise and fiber nonlinearity is experimentally verified. Finally, we show by simulation that the superior tracking speed of the TS-EST algorithm allows not only for initial polarization tracking but also for tracking fast polarization transients if four training symbols are periodically sent during steady-state operation with an overhead as low as 0.57%.

©2012 Optical Society of America

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Figures (5)

Fig. 1
Fig. 1 (a) Experimental setup (PBS: Polarization Beam Splitter, PBC: Polarization Beam Combiner, VOA: Variable Optical Attenuator, SW: Optical Switch, ODL: Optical Delay Line, PC: Polarization Controller), (b) Training symbols and framing synchronization header.
Fig. 2
Fig. 2 (a) Steady-state BER versus distance for all algorithms for both PDM-QPSK and PDM-16QAM, (b) Constellations after 320 km transmission for both PDM-QPSK and PDM-16QAM obtained by merely applying the inverse Jones matrix obtained by TS-EST, (c) Constellations of the same case in (d) after the butterfly filter updated using DD-LMS and carrier recovery using DD-PLL.
Fig. 3
Fig. 3 Transient BER for all algorithms for (a) PDM-QPSK, (b) PDM-16QAM.
Fig. 4
Fig. 4 BER for the TS-EST algorithm for PDM-QPSK in both high phase noise and high launch power scenarios for: (a) steady-state, (b) transient cases.
Fig. 5
Fig. 5 (a) Periodic training symbols for SOP tracking, (b) Steady-state BER versus SOP angular frequency for different algorithms for 14 Gbaud PDM-16QAM, (c) Steady-state BER versus SOP angular frequency for different algorithms for 28 Gbaud PDM-16QAM.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

R=[ a b b * a * ]
a= e jδ cosθ, b= e jφ sinθ
S rx [n]= e jψ[n] R S tx [n]= e jψ[n] [ a s tx x [n]+b s tx y [n] b * s tx x [n]+ a * s tx y [n] ]
ψ[ n ]=2πΔfT+ ψ pn [n]
T rx [k]=c e j( ξ+ψ[k] ) [ a+b b * + a * ] , T rx [k+1]=c e j( ξ+ψ[k+1] ) [ ab b * a * ]
| a | 0.5( 1+ 1 N Re{ i=0 N/2 1 ( T rx x [2i] T rx x * [2i+1]... T rx y [2i] T rx y * [2i+1] ) } )
| b | 1 | a | 2
arg{ a }+arg{ b }=arg{ i=0 N/21 ( T rx x [2i] T rx y * [2i+1]+... T rx y * [2i] T rx y [2i+1] ) }
R 1 =[ | a | | b | e j(arg{ a }+arg{ b }) | b | e j(arg{ a }+arg{ b }) | a | ]
R=[ cosωt sinωt sinωt cosωt ]
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