US 7,444,082 B2 · Polarisation mode dispersion compensator using a mean square error technique

Abstract

A method for the adaptive adjustment of a PMD compensator in optical fiber communication systems comprises the steps of taking the signal at the compensator output and extracting the components y1(t) and y2(t) on the two orthogonal polarizations, computing the signal y(t)=[y1(t)]2+[y2(t)]2, sampling the signal y(t) at instants tk=kT with T=symbol interval to obtain samples y(tk), computing the mean square error e(k)=y(tk)−u(k) with u(k) equal to the symbol transmitted, and adjusting the parameters of the compensator to seek to minimize e(k). A PMD compensator in accordance with the method comprises an adjustment system which comprises in turn a photodetecor (17) which takes the components y1(t) and y2(t) on the two orthogonal polarizations from the signal at the compensator output, a sampler (19) which samples at instants tk=kT with T=symbol interval, the signal y(t)=[y1(t)]2+[y2(t)]2 at the output of the photodetector (17) to obtain samples y(tk), a circuit (18, 20) for computation of the mean square error e(k)=y(tk)−u(k) with u(k) equal to the symbol transmitted, and a regulator (15, 16) which regulates the parameters of the compensator to seek to minimize e(k).

Method for the adaptive adjustment of a PMD compensator in optical fiber communication systems with the compensator comprising a cascade of adjustable optical devices over which passes an optical signal to be compensated comprising the steps of:

a. extracting the y1(t) and y2(t) on the two orthogonal polarizations of the signal at the compensator output,
b. obtaining the signal y(t)=|y1(t)|2+|y2(t)|2;
c. sampling the signal y(t) at instants tk=kT with T=symbol interval to obtain samples y(tk),
d. computing the mean square value of the error e(k)=y(tk)−u(k) with u(k) equal to the symbol transmitted or with u(k) replaced by a decision û(k) on the transmitted symbol u(k), and
e. producing control signals for parameters of at least some of said adjustable optical devices to tend toward minimization of the mean square value of e(k),
in which said parameters being consolidated in a vector θ and a function F(θ)=e(k) being defined the parameters are adjusted to tend to minimize the mean value of F2(θ),
in which the vector θ of the parameters is updated by adding a new vector with the norm proportionate to the norm of the gradient of F2(θ) and with opposite direction, all its components have their sign changed so that the updating rule is:
θ[(n+1)L]=θ(nL)−γ∇E{F2(θ)}|θ=θ(nL)=θ(nL)−2γF(θ)∇E{F(θ)}|θ=θ(nL) (9)
so that movement is towards a relative minimum of the function F2(θ),
in which in the error F(θ)=e(k) the transmitted information symbol u(nL) is substituted with the corresponding decision û(nL) so as to substitute the error e(k) with the estimated error ê(k) defined as ê(k)=y(tk)−û(k),
in which G[θ(nL)]=E{ê2(nL)} is defined so that the updating rule (9) becomes:
θ[(n+1)L]=θ(nL)−γ∇G(θ)|θ=θ(nL) (14),
and in which the partial derivatives of G(θ) for θ=θ(tn) are computed by the following five-step procedure:
Step 1. Find the value of G[θ(nL)]=G[φ1(nL),φ2(nL),θ1(nL),θ2(nL)] at iteration n;
to do this, in the time interval (nLT, nLT+LT/5) an estimate of G[θ(nL)] is computed by averaging the L/5 values of the estimated square error,
G
⁡
[
θ
⁡
(
nL
)
]
=
∑
i
=
0
L
/
5
-
1
⁢
⁢
e
^
⁡
(
nL
+
i
)
L
/
5
(
15
)
Step 2. Find the partial derivative:
∂
G
⁡
(
θ
)
∂
φ
1
⁢
❘
θ
=
θ
⁡
(
nL
)
at iteration n;
to do this, parameter φ1 is set at φ1(nL)+Δ while the other parameters are left unchanged;
the corresponding value of G(θ), G[φ1(nL)+Δ,φ2(nL), θ1(nL), θ2(nL)] is computed as in step 1 but in the time interval (nLT+LT/5, nLT+2LT/5);
the estimate of the partial derivative of G(θ) with respect to φ1 is computed as:
∂
G
⁡
(
θ
)
∂
φ
1
⁢
❘
θ
=
θ
⁡
(
nL
)
⁢
≅
G
⁡
[
φ
1
⁡
(
nL
)
,
+
Δ
,
φ
2
⁡
(
nL
)
,
θ
1
⁡
(
nL
)
,
θ
2
⁡
(
nL
)
]
-
G
⁡
[
φ
1
⁡
(
nL
)
,
φ
2
⁡
(
nL
)
,
θ
1
⁡
(
nL
)
,
θ
2
⁡
(
nL
)
]
Δ
(
16
)
Step 3. Find the partial derivative:
∂
G
⁡
(
θ
)
∂
φ
2
⁢
❘
θ
=
θ
⁡
(
nL
)
at iteration n;
to do this the parameter φ2 is set at φ2(nL)+Δ while the other parameters are left unchanged;
the corresponding value of G(θ), G[φ1(nL), φ2(nL)+Δ,θ1(nL), θ2(nL)], is computed as in step 1 but in the time interval (nLT+2LT/5, nLT+3LT/5);
the estimate of the partial derivative of G(θ) with respect to φ2 is computed as:
∂
G
⁡
(
θ
)
∂
φ
2
⁢
❘
θ
=
θ
⁡
(
nL
)
⁢
≅
G
⁡
[
φ
1
⁡
(
nL
)
,
φ
2
⁡
(
nL
)
+
Δ
,
θ
1
⁡
(
nL
)
,
θ
2
⁡
(
nL
)
]
-
G
⁡
[
φ
1
⁡
(
nL
)
,
φ
2
⁡
(
nL
)
,
θ
1
⁡
(
nL
)
,
θ
2
⁡
(
nL
)
]
Δ
(
17
)
Step 4. Find the partial derivative:
∂
G
⁡
(
θ
)
∂
θ
1
⁢
❘
θ
=
θ
⁡
(
nL
)
at iteration n;
to do this, parameter θ1 is set at θ1(nL)+Δ while the other parameters are left unchanged;
the corresponding value of G(θ), G[φ1(nL),φ2(nL), θ1(nL)+Δ,θ2(nL)], is computed as in Step 1 but in the time interval (nLT+3LT/5, nLT=4LT/5);
the estimate of the partial derivative of G(θ) with respect to θ1 is computed as:
∂
G
⁡
(
θ
)
∂
θ
1
⁢
❘
θ
=
θ
⁡
(
nL
)
⁢
≅
G
⁡
[
φ
1
⁡
(
nL
)
,
φ
2
⁡
(
nL
)
,
θ
1
⁡
(
nL
)
+
Δ
,
θ
2
⁡
(
nL
)
]
-
G
⁡
[
ϕ
1
⁡
(
nL
)
,
φ
2
⁡
(
nL
)
,
θ
1
⁡
(
nL
)
,
θ
2
⁡
(
nL
)
]
Δ
(
13
)
Step 5. Find the partial derivative:
∂
G
⁡
(
θ
)
∂
θ
2
⁢
❘
θ
=
θ
⁡
(
nL
)
at iteration n;
to do this the parameter θ2 is set at θ2(nL)+Δ while the other parameters are left unchanged;
the corresponding value of G(θ), G[φ1(nL),φ2(nL),θ1(nL),θ2(nL)+Δ], is computed as in Step 1 but in the time interval (nLT+4LT/5, (n+1)LT);
the estimate of the partial derivative of G(θ) with respect to θ2 is computed as:
∂
G
⁡
(
θ
)
∂
θ
2
⁢
❘
θ
=
θ
⁡
(
nL
)
⁢
≅
G
⁡
[
φ
1
⁡
(
nL
)
,
φ
2
⁡
(
nL
)
,
θ
1
⁡
(
nL
)
,
θ
2
⁡
(
nL
)
+
Δ
]
-
G
⁡
[
φ
1
⁡
(
nL
)
,
φ
2
⁡
(
nL
)
,
θ
1
⁡
(
nL
)
,
θ
2
⁡
(
nL
)
]
Δ
.
(
14
)

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Polarisation mode dispersion compensator using a mean square error technique

Life of this patent

Polarisation mode dispersion compensator using a mean square error technique

Life of this patent

Abstract

Claims12