## Abstract

Abstract: We experimentally demonstrate the simultaneous detection of 10-Gbit/s quadrature phase shift keying (QPSK) × 2-channel Fourier-encoded synchronous optical code division multiplexing (FE-SOCDM) signals using a digital coherent receiver, for the first time. First, we analytically verify that simultaneous detection can be achieved with an *N*-point discrete Fourier transform (DFT) using digital signal processing (DSP) because the *N*-channel Fourier encoding corresponds to an *N* × *N* inverse DFT, then the operation is experimentally confirmed. Simultaneous detection of 10-Gbit/s QPSK × 2-channel FE-SOCDM signals is evaluated. The proposed scheme dramatically expands the capability of OCDM systems.

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Opt. Express **23**(25) 32054-32062 (2015)

### Equations (8)

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(1)
$${s}_{n}={E}_{n}{e}^{j{\theta}_{n}}\text{}n=1,2,3,\cdots ,N$$
(2)
$${F}_{N}=\left[\mathrm{exp}\left(j\frac{2\pi \left(n-1\right)\left(k-1\right)}{N}\right)\right]\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}n,k=1,2,\mathrm{...},N.$$
(3)
$${F}_{4}=\left[\begin{array}{cccc}{e}^{j0}& {e}^{j0}& {e}^{j0}& {e}^{j0}\\ {e}^{j0}& {e}^{j\frac{\pi}{2}}& {e}^{j\pi}& {e}^{j\frac{3\pi}{2}}\\ {e}^{j0}& {e}^{j\pi}& {e}^{j2\pi}& {e}^{j3\pi}\\ {e}^{j0}& {e}^{j\frac{3\pi}{2}}& {e}^{j3\pi}& {e}^{j\frac{9\pi}{2}}\end{array}\right]=\left[\begin{array}{cccc}+1& +1& +1& +1\\ +1& +j& -1& -j\\ +1& -1& +1& -1\\ +1& -j& -1& +j\end{array}\right]=\left[\begin{array}{c}{c}_{1}\\ {c}_{2}\\ {c}_{3}\\ {c}_{4}\end{array}\right]$$
(4)
$${g}_{n}={s}_{n}\left[\begin{array}{cccc}{e}^{j0}& {e}^{j\frac{\pi \left(n-1\right)}{2}}& {e}^{j\pi \left(n-1\right)}& {e}^{j\frac{3\pi \left(n-1\right)}{2}}\end{array}\right]\text{}n=1,2,3,4.$$
(5)
$$x={g}_{1}+{g}_{2}+{g}_{3}+{g}_{4}={s}^{T}{F}_{4}\text{}\text{where}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}s=\left[\begin{array}{c}{s}_{1}\\ {s}_{2}\\ {s}_{3}\\ {s}_{4}\end{array}\right].$$
(6)
$$y=D{s}^{T}{F}_{4}.$$
(7)
$${y}^{T}={F}_{4}s{D}^{T}.$$
(8)
$$r={F}_{4}^{-1}{F}_{4}s{D}^{T}=s{D}^{T}.$$