Abstract
Long-haul optical communications based on nonlinear Fourier Transform have gained attention recently as a new communication strategy that inherently embrace the nonlinear nature of the optical fiber. For communications using discrete eigenvalues
${\boldsymbol{\lambda }} \in {\mathbb{C}^ + }$
, information are encoded and decoded in the spectral amplitudes
${\boldsymbol{q}}({\boldsymbol{\lambda }}) = {\boldsymbol{b}}({\boldsymbol{\lambda }})/({\frac{{{\boldsymbol{da}}({\boldsymbol{\lambda }})}}{{{\boldsymbol{d\lambda }}}}})$
at the root
${{\boldsymbol{\lambda }}_{{\rm{rt}}}}$
where
${\boldsymbol{a}}({{{\boldsymbol{\lambda }}_{{\rm{rt}}}}}) = 0$
. In this paper, we propose two alternative decoding methods using
${\boldsymbol{a}}({\boldsymbol{\lambda }})$
and
${\boldsymbol{b}}({\boldsymbol{\lambda }})$
instead of
${\boldsymbol{q}}({\boldsymbol{\lambda }})$
as decision metrics. For discrete eigenvalue modulation systems, we show that symbol decisions using
${\boldsymbol{a}}({\boldsymbol{\lambda }})$
at a prescribed set of
${\boldsymbol{\lambda }}$
values perform similarly to conventional methods using
${\boldsymbol{q}}({\boldsymbol{\lambda }})$
but avoid root searching, and, thus, significantly reduce computational complexity. For systems with phase and amplitude modulation on a given discrete eigenvalue, we propose to use
${\boldsymbol{b}}({\boldsymbol{\lambda }})$
after for symbol detection and show that the noise in
$\frac{{{\boldsymbol{da}}({\boldsymbol{\lambda }})}}{{{\boldsymbol{d\lambda }}}}$
and
${{\boldsymbol{\lambda }}_{{\rm{rt}}}}$
after transmission is all correlated with that in
${\boldsymbol{b}}({{{\boldsymbol{\lambda }}_{{\rm{rt}}}}})$
. A linear minimum mean square error estimator of the noise in
${\boldsymbol{b}}({{{\boldsymbol{\lambda }}_{{\rm{rt}}}}})$
is derived based on such noise correlation and transmission performance is considerably improved for QPSK and 16-quadratic-amplitude modulation systems on discrete eigenvalues.
© 2017 IEEE
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