Optimized normalized least mean square phase estimation
View Patent ↗Methods and systems for normalized least mean square phase estimation are shown that include receiving optical transmissions that include a modulated signal, determining a step size based on a signal-to-noise ratio (SNR) and a laser linewidth that provides a balance between convergence speed and precision, estimating phase error using the determined step size, derotating the modulated signal to remove the estimated phase error, and demodulating the derotated signal to produce a bitstream.
1. A method, comprising:
receiving optical transmissions that include a modulated signal;
determining a step size based on a signal-to-noise ratio (SNR) and a laser linewidth that provides a balance between convergence speed and precision;
estimating phase error using the determined step size;
derotating the modulated signal to remove the estimated phase error; and
demodulating the derotated signal to produce a bitstream,
wherein the stepsize is determined as
μ
opt
=
ρ
(
1
+
2
ρ
-
1
)
,
where ρ=σ p 2 /σ n 2 , σ n 2 =1/γ, γ is the SNR, and σ p 2 is the laser phase noise variance.
2. The method of claim 1 , wherein the step size is determined analytically and increases as laser phase noise variance and SNR increase.
3. The method of claim 1 , wherein said estimating and derotating are performed in a cascaded fashion, using results from estimation and derotation of previous signals to estimate and derotate a current signal.
4. The method of claim 1 , further comprising updating the step size if the SNR or laser phase error variance change.
5. The method of claim 1 , wherein estimating phase error includes using normalized least-mean square with the determined step size.
6. The method of claim 1 , wherein derotating multiplies the modulated signal by a coefficient
c
(
n
+
1
)
=
c
(
n
)
+
μ
x
(
n
)
2
e
(
n
)
x
*
(
n
)
,
where c(n) is the previous coefficient, μ is the step size, x(n) is the received signal, e(n) is the estimation error defined as the difference between the rotated complex amplitude and the decoded symbol, and x*(n) is the complex conjugate of the received signal.
7. A receiver, comprising:
a detection module configured to estimate the phase error of incoming signals and detect data symbols within an optical beam comprising:
a step size computing module configured to determine a step size based on laser phase variance and signal-to-noise ratio (SNR) that provides a balance between convergence speed and precision; and
a derotator module configured to determine a rotation coefficient using normalized least-mean square and the determined step size and to derotate the incoming signals to compensate for phase error; and
a demodulator configured to extract a bitstream from the data symbols,
wherein the stepsize is determined as
μ
opt
=
ρ
(
1
+
2
ρ
-
1
)
,
where ρ=σ p 2 /σ n 2 , σ n 2 =1/γ, γ is the SNR, and σ p 2 is the laser phase noise variance.
8. The receiver of claim 7 , wherein the step size is determined analytically and increases as laser phase noise variance and SNR increase.
9. The receiver of claim 7 , further comprising additional derotators arranged in a cascaded fashion and configured to use results from previous derotators to estimate and derotate a current signal.
10. The receiver of claim 7 , wherein the step size computing module determines a new step size if the SNR or laser phase error variance change.
11. The receiver of claim 7 , wherein the derotator module is further configured to estimate phase error using normalized least-mean square with the determined step size.
12. The receiver of claim 7 , wherein the rotation coefficient is determined as
c
(
n
+
1
)
=
c
(
n
)
+
μ
x
(
n
)
2
e
(
n
)
x
*
(
n
)
,
where c(n) is the previous coefficient, μ is the step size, x(n) is the received signal, e(n) is the estimation error defined as the difference between the rotated complex amplitude and the decoded symbol, and x*(n) is the complex conjugate of the received signal.
13. A detection module, comprising:
a rotation coefficient module configured to generate a rotation coefficient based on a step size, the complex conjugate of a received signal, and an error signal that represents the difference between a previous received signal and a previous determined symbol;
a rotator configured to rotate a received signal using the rotation coefficient to produce a rotated signal;
a decision module configured to determine a symbol from the rotated signal;
a combiner configured to find the difference between the rotated signal and the determined symbol, producing an error signal; and
a step size computing module configured to determine a step size based on present conditions that provides a balance between convergence speed and precision,
wherein the stepsize is determined as
μ
opt
=
ρ
(
1
+
2
ρ
-
1
)
,
where ρ=σ p 2 /σ n 2 , σ n 2 =1/γ, γ is the SNR, and σ p 2 is the laser phase noise variance.
14. The detection module of claim 13 , wherein the step size is determined based on a laser phase noise variance and a signal-to-noise ratio.
15. The detection module of claim 14 , wherein the step size is determined analytically and increases as laser phase noise variance and SNR increase.
16. The detection module of claim 13 , wherein the op step size computing module determines a new step size if the SNR or laser phase error variance change.
17. The detection module of claim 13 , wherein the rotation coefficient is determined as
c
(
n
+
1
)
=
c
(
n
)
+
μ
x
(
n
)
2
e
(
n
)
x
*
(
n
)
,
where c(n) is the previous coefficient, μ is the step size, x(n) is the received signal, e(n) is the estimation error defined as the difference between the rotated complex amplitude and the decoded symbol, and x*(n) is the complex conjugate of the received signal.