JP6949267B2 - Received signal processing device, received signal processing method and optical receiver - Google Patents

Description

The present invention relates to a received signal processing device, a received signal processing method, and an optical receiver that removes phase noise contained in a polarized signal.

The following Patent Document 1 discloses a received signal processing device that compensates for a phase offset of a modulated received signal.
The received signal processing device disclosed in Patent Document 1 uses a Kalman filter to estimate the phase offset of the received signal.

International Publication No. 2015/072515

Since the received signal processing device disclosed in Patent Document 1 includes determination feedback, erroneous propagation of symbol determination may occur.
In the received signal processing device disclosed in Patent Document 1, even if the phase noise which is the phase offset of the received signal changes due to the error propagation of the symbol determination, the Kalman gain of the Kalman filter is not properly updated, so that the received signal is included in the received signal. There is a problem that the phase noise that has been generated may not be removed.

The present invention has been made to solve the above-mentioned problems, and even if the phase noise contained in the received signal changes due to the error propagation of symbol determination, the phase noise can be removed. The purpose is to obtain an apparatus, a received signal processing method and an optical receiver.

The received signal processing device according to the present invention uses a Kalman filter to perform Bayesian estimation of the phase noise contained in the polarization signal indicating the polarization state of the received signal on which the symbol time series is superimposed, and estimates the phase noise. When the phase noise is estimated by the Bayesian estimation unit and the Bayesian estimation unit that removes the phase noise contained in the polarization signal using the values, the estimated values of the phase noises are accumulated and the accumulated estimated values are used. By multiplying the Kalman gain of the Kalman filter by a probability density function calculated based on a certain cumulative phase noise, the Kalman gain is provided with a weight updating unit for updating the Kalman gain to the Bayesian estimation unit.

According to the present invention, when the phase noise is Bayesian estimated by the Bayesian estimation unit, the estimated value of the phase noise is accumulated, and the Kalman gain of the Kalman filter is transferred to the Bayesian estimation unit based on the accumulated phase noise which is the accumulated estimated value. The received signal processing device was configured to include a weight updating unit to be updated. Therefore, the received signal processing device according to the present invention can remove the phase noise even if the phase noise contained in the received signal changes due to the error propagation of the symbol determination.

It is a block diagram which shows the optical transmission apparatus which includes the received signal processing apparatus 43 which concerns on Embodiment 1. FIG. It is a hardware block diagram which shows the hardware of the received signal processing apparatus 43 which concerns on Embodiment 1. FIG. FIG. 5 is a hardware configuration diagram of a computer when the received signal processing device 43 is realized by software, firmware, or the like. It is a flowchart which shows the received signal processing method which is the processing procedure of the received signal processing apparatus 43. It is a block diagram which shows the phase noise compensation part 46 of the received signal processing apparatus 43 which concerns on Embodiment 1. FIG. It is explanatory drawing which shows the probability density function p [φ (k)] calculated by the formula (15), and the probability density function p [φ (k)] calculated by the approximate expression shown in the formula (14). It is explanatory drawing which shows the result of simulating the phase of the polarization signal s hat (k) output from the phase noise compensation unit 46 to the demodulation unit 49. It is explanatory drawing which shows the SNR penalty with respect to the line width symbol rate product when the multi-value modulation signal output from a modulation part 11 is a QPSK signal. It is explanatory drawing which shows the SNR penalty with respect to the line width symbol rate product when the multi-value modulation signal output from a modulation part 11 is a 16-QAM signal. It is explanatory drawing which shows the SNR penalty with respect to the line width symbol rate product when the multi-value modulation signal output from a modulation part 11 is a 64-QAM signal. It is explanatory drawing which shows the SNR penalty with respect to the line width symbol rate product when the multi-value modulation signal output from a modulation part 11 is a 128-QAM signal. It is a block diagram which shows the phase noise compensation part 46 of the received signal processing apparatus 43 which concerns on Embodiment 2. FIG.

Hereinafter, in order to explain the present invention in more detail, a mode for carrying out the present invention will be described with reference to the accompanying drawings.

Embodiment 1.
FIG. 1 is a configuration diagram showing an optical transmission device including a received signal processing device 43 according to the first embodiment.
FIG. 2 is a hardware configuration diagram showing the hardware of the received signal processing device 43 according to the first embodiment.
In FIG. 1, the optical transmission device includes an optical transmitter 1, a transmission line 2, a station light emitting source 3, and an optical receiver 4.
The optical transmitter 1 includes a transmission signal processing unit 10, a transmission light source 14, and a lightning conversion unit 15.
The transmission signal processing unit 10 includes a modulation unit 11, a transmission distortion compensation unit 12, and a digital-to-analog converter (hereinafter, referred to as “D / A converter”) 13.

When the bit time series is input from the outside, the modulation unit 11 multi-values the bit time series and outputs the symbol time series, which is a multi-value modulation signal, to the transmission distortion compensation unit 12.
As the multi-level modulation, QPSK (Quadrature Phase Shift Keying), 16-QAM (Quadrature Amplitude Modulation), 64-QAM, 256-QAM and the like can be considered.
In the optical transmission device shown in FIG. 1, for convenience of explanation, horizontally polarized waves (hereinafter referred to as “X polarized waves”) and vertically polarized waves (hereinafter referred to as “Y polarized waves”) are referred to as bit time series from the outside. Is input to the modulation unit 11.
When the X polarization is input from the outside, the modulation unit 11 multivalues the X polarization and outputs the multivalue modulation signal of the X polarization to the transmission distortion compensation unit 12.
When the Y polarization is input from the outside, the modulation unit 11 multivalues the Y polarization and outputs the Y polarization multivalue modulation signal to the transmission distortion compensation unit 12.

The transmission distortion compensation unit 12 compensates for the distortion of the X-polarized multi-valued modulation signal that is the symbol time series output from the modulation unit 11, and D / D / X-polarized multi-valued modulation signal after the distortion is compensated. Output to A converter 13.
Further, the transmission distortion compensating unit 12 compensates for the distortion of the Y-polarized multi-valued modulation signal, which is the symbol time series output from the modulation unit 11, and after the distortion is compensated, the Y-polarized multi-valued modulation signal is used. Output to the D / A converter 13.
As the symbol time-series distortion compensation processing in the transmission distortion compensation unit 12, a low-pass filtering process for reducing interference between a plurality of symbols can be considered.

The D / A converter 13 converts the X-polarized multi-valued modulation signal output from the transmission distortion compensation unit 12 from a digital signal to an analog signal.
D / A converter 13 outputs an I _X signal in-phase component of the analog signal to the electro-optic conversion unit 15, and outputs a Q _X signal is an orthogonal component of the analog signal to the electro-optic conversion unit 15.
Further, the D / A converter 13 converts the Y-polarized multi-valued modulation signal output from the transmission distortion compensation unit 12 from a digital signal to an analog signal.
_{The D / A converter 13 outputs an I Y} signal, which is an in-phase component of the analog signal, to the lightning conversion unit 15, and outputs a Q _Y signal, which is an orthogonal component of the analog signal, to the lightning conversion unit 15.

The transmission light source 14 generates continuous light and outputs the continuous light to the lightning conversion unit 15.
Optic converter unit 15, by superimposing I _X signal output from the D / A converter 13, Q _X signal, the continuous light output respectively from the transmission light source 14 of the I _Y signal and Q _Y signal, modulated An optical modulation signal, which is an optical signal, is generated, and the optical modulation signal is output to the transmission line 2.
The transmission line 2 is realized by an optical fiber cable.
The optical modulation signal is transmitted to the optical receiver 4 by the transmission line 2.
The local emission source 3 generates locally oscillating light having the same frequency as the continuous light generated by the transmitting light source 14, and outputs the locally oscillating light to the optical receiver 4.

The optical receiver 4 includes a photoelectric conversion unit 41, an analog-digital converter (hereinafter referred to as “A / D converter”) 42, and a received signal processing device 43.
The photoelectric conversion unit 41 receives the optical modulation signal transmitted by the transmission line 2.
The photoelectric conversion unit 41 uses the local oscillator light output from the local light source 3, the light modulation signal is the received signal, extracts the respective I _X signal, Q _X signal, I _Y signal and Q _Y signal ..
I _X signal extracted by the photoelectric conversion unit 41, Q _X signal includes the noise in each of the I _Y signal and Q _Y signal.
I _X signal extracted by the photoelectric conversion unit 41, in order to distinguish it from I _X signal output from the D / A converter 13, denoted as I X _'signals. Q _X signal extracted by the photoelectric conversion unit 41, in order to distinguish the Q _X signal output from the D / A converter 13 is denoted as Q X _'signals.
I _Y signal extracted by the photoelectric conversion unit 41, in order to distinguish it from I _Y signal outputted from the D / A converter 13, denoted as I Y _'signal. Q _Y signal extracted by the photoelectric conversion unit 41, in order to distinguish the Q _Y signal outputted from the D / A converter 13 is denoted as Q Y _'signal.
The photoelectric conversion unit 41 _'converts the signal into an electric signal, electric I _X is an electrical _signal' I X and outputs a signal to the A / D converter 42.
The photoelectric conversion unit 41 _'converts the signal into an electric signal, electric Q _X is an electrical _signal' Q X and outputs a signal to the A / D converter 42.
The photoelectric conversion unit 41 converts the I _Y'signal into an electric signal, and outputs the electric I _Y'signal, which is an electric signal, to the A / D converter 42.
The photoelectric conversion unit 41 converts the Q _Y'signal into an electric signal, and outputs the electric Q _Y'signal, which is an electric signal, to the A / D converter 42.

A / D converter 42, electric I _X is output from the photoelectric conversion unit 41 _'the signals converted from analog signals to digital signals, digital I _X is a digital _signal' polarization separation of the received signals the signal processing device 43 Output to unit 44.
The A / D converter 42 converts the electric Q _X'signal output from the photoelectric conversion unit 41 from an analog signal to a digital signal, and outputs the digital Q _X'signal, which is a digital signal, to the polarization separation unit 44.
The A / D converter 42 converts the electric I _Y'signal output from the photoelectric conversion unit 41 from an analog signal to a digital signal, and outputs the digital I _Y'signal, which is a digital signal, to the polarization separation unit 44.
The A / D converter 42 converts the electric Q _Y'signal output from the photoelectric conversion unit 41 from an analog signal to a digital signal, and outputs the digital Q _Y'signal, which is a digital signal, to the polarization separation unit 44.

The reception signal processing device 43 includes a polarization separation unit 44, a frequency error compensation unit 45, a phase noise compensation unit 46, and a demodulation unit 49.
The polarization separation unit 44 is realized by, for example, the polarization separation circuit 51 shown in FIG.
Polarization splitter 44 outputs a signal including both digital I _{X 'signal} and the digital Q _X' signals output from the A / D converter 42 into a frequency error compensation unit 45 as X 'polarization signal.
_{The polarization separation unit 44 outputs a signal including both a digital I Y'signal} and a digital Q _Y'signal output from the A / D converter 42 to the frequency error compensation unit 45 as a Y'polarization signal.
Each of the X'polarization signal and the Y'polarization signal indicates the polarization state of the received signal, and the polarization state indicated by the X'polarization signal and the polarization state indicated by the Y'polarization signal are They are orthogonal to each other.
Each of the X'polarization signal and the Y'polarization signal is a frequency that is an error between the frequency of the continuous light output from the transmission light source 14 and the frequency of the locally oscillating light output from the station emission source 3. The error is included.
Further, each of the X'polarized signal and the Y'polarized signal contains phase noise generated by each of the transmission light source 14 and the station light emitting source 3.

The frequency error compensation unit 45 is realized by, for example, the frequency error compensation circuit 52 shown in FIG.
The frequency error compensating unit 45 removes the frequency error included in each of the X'polarization signal and the Y'polarization signal output from the polarization separation unit 44.
The frequency error compensation unit 45 outputs each of the X'polarization signal from which the frequency error has been removed and the Y'polarization signal from which the frequency error has been removed to the phase noise compensation unit 46.

The phase noise compensation unit 46 includes a Bayesian estimation unit 47 and a weight updating unit 48.
The phase noise compensation unit 46 removes the phase noise included in the X'polarization signal output from the frequency error compensation unit 45, and is included in the Y'polarization signal output from the frequency error compensation unit 45. Removes the existing phase noise.

The Bayesian inference unit 47 is realized by, for example, the Bayesian inference circuit 53 shown in FIG.
The Bayesian estimation unit 47 Bayes estimates the phase noise contained in the X'polarization signal output from the frequency error compensation unit 45 using a Kalman filter, and uses the estimated value of the phase noise to perform a frequency error compensation unit. The phase noise included in the X'polarized signal output from 45 is removed.
Further, the Bayesian estimation unit 47 Bayes estimates the phase noise included in the Y'polarized signal signal output from the frequency error compensation unit 45 using a Kalman filter, and uses the estimated value of the phase noise to perform a frequency error. The phase noise included in the Y'polarized signal output from the compensation unit 45 is removed.
The Bayesian inference unit 47 outputs each of the X'polarization signal from which the phase noise has been removed and the Y'polarization signal from which the phase noise has been removed to the demodulation unit 49.

The weight update unit 48 is realized by, for example, the weight update circuit 54 shown in FIG.
When the Bayesian estimation unit 47 Bayesian estimates the phase noise contained in the X'polarized signal signal, the weight updating unit 48 accumulates the estimated value of the phase noise. The weight updating unit 48 causes the Bayes estimation unit 47 to update the Kalman gain of the Kalman filter used for Bayesian estimation of the phase noise included in the X'polarized signal based on the cumulative phase noise which is the accumulated estimated value.
Further, the weight updating unit 48 accumulates the estimated value of the phase noise when the phase noise included in the Y'polarized signal is Bayesian estimated by the Bayesian estimation unit 47. The weight updating unit 48 causes the Bayes estimation unit 47 to update the Kalman gain of the Kalman filter used for Bayesian estimation of the phase noise included in the Y'polarized signal signal based on the cumulative phase noise which is the accumulated estimated value.

The demodulation unit 49 is realized by, for example, the demodulation circuit 55 shown in FIG.
The demodulation unit 49 converts each of the X'polarized signal whose phase noise is removed by the Bayesian inference unit 47 and the Y'polarized signal whose phase noise is removed by the Bayesian inference unit 47 into a bit time series.
The demodulation unit 49 outputs each bit time series to the outside.

In FIG. 1, each of the polarization separation unit 44, the frequency error compensation unit 45, the Bayesian estimation unit 47, the weight update unit 48, and the demodulation unit 49, which are the components of the received signal processing device 43, is dedicated as shown in FIG. It is supposed to be realized by the hardware of. That is, it is assumed that the received signal processing device 43 is realized by the polarization separation circuit 51, the frequency error compensation circuit 52, the Bayesian estimation circuit 53, the weight update circuit 54, and the demodulation circuit 55.
Here, each of the polarization separation circuit 51, the frequency error compensation circuit 52, the Bayes estimation circuit 53, the weight update circuit 54, and the demodulation circuit 55 is, for example, a single circuit, a composite circuit, a programmed processor, or a parallel program. A processor, an ASIC (Application Special Integrated Circuit), an FPGA (Field-Programmable Gate Array), or a combination thereof is applicable.

The components of the received signal processing device 43 are not limited to those realized by dedicated hardware, but the received signal processing device is realized by software, firmware, or a combination of software and firmware. You may.
The software or firmware is stored as a program in the memory of the computer. A computer means hardware that executes a program, and corresponds to, for example, a CPU (Central Processing Unit), a central processing unit, a processing unit, an arithmetic unit, a microprocessor, a microcomputer, a processor, or a DSP (Digital Signal Processor). do.

FIG. 3 is a hardware configuration diagram of a computer when the received signal processing device 43 is realized by software, firmware, or the like.
When the received signal processing device 43 is realized by software, firmware, or the like, the computer is made to execute the processing procedures of the polarization separation unit 44, the frequency error compensation unit 45, the Bayes estimation unit 47, the weight update unit 48, and the demodulation unit 49. The program for this is stored in the memory 61. Then, the processor 62 of the computer executes the program stored in the memory 61.
FIG. 4 is a flowchart showing a received signal processing method which is a processing procedure of the received signal processing device 43.
Further, FIG. 2 shows an example in which each of the components of the received signal processing device 43 is realized by dedicated hardware, and FIG. 3 shows an example in which the received signal processing device 43 is realized by software, firmware, or the like. ing. However, this is only an example, and some components in the received signal processing device 43 may be realized by dedicated hardware, and the remaining components may be realized by software, firmware, or the like.

FIG. 5 is a configuration diagram showing a phase noise compensating unit 46 of the received signal processing device 43 according to the first embodiment.
The phase noise compensating unit 46 has a configuration for removing the phase noise θ (k) included in the X'polarized signal and removes the phase noise θ (k) contained in the Y'polarized signal. The configuration for this is the same, and the phase noise compensation unit 46 has both configurations.
The configuration diagram shown in FIG. 5 shows a configuration for removing the phase noise θ (k) included in the X'polarized signal, or a phase noise θ (k) included in the Y'polarized signal. The configuration for removal is shown.
Hereinafter, for convenience of explanation, each of the X'polarization signal and the Y'polarization signal output from the frequency error compensation unit 45 will be described as the polarization signal r (k).
In FIG. 5, the multiplier 71 has a polarization signal r (k) output from the frequency error compensation unit 45 and a complex conjugate value exp [−j · θ hat (k | k−) output from the complex conjugate arithmetic unit 80. 1)] and. k is a sample number of a received signal which is an optical modulation signal received by the optical receiver 4.
_{The multiplier 71 outputs the multiplication result m 1} (k) of the polarization signal r (k) and the complex conjugate value exp [−j · θ hat (k | k-1)] to the determination unit 72.
In the text of the specification, the symbol "^" cannot be added above the character θ due to the electronic application, so it is written as "θ hat".

The determination unit 72 performs symbol determination processing on _{the multiplication result m 1 (k) output from the multiplier 71.}
The determination unit 72 outputs the determination symbol d (k) indicating the determination result of the symbol determination process to the multiplier 73 and the Kalman gain update unit 75, respectively.
The multiplier 73 multiplies the determination symbol d (k) output from the determination unit 72 with the exponential value exp [j · θ hat (k | k-1)] output from the exponentiation unit 79.
_{The multiplier 73 outputs the multiplication result m 2} (k) of the determination symbol d (k) and the exponentiation value exp [j · θ hat (k | k-1)] to the subtractor 74.

The subtractor 74 subtracts the multiplication result m ₂ (k) output from the multiplier 73 from the polarization signal r (k) to obtain the polarization signal r (k) and the multiplication result m ₂ (k). The innovation variable e (k), which is the error of, is calculated.
The subtractor 74 outputs the calculated innovation variable e (k) to the Kalman gain update unit 75.

The Kalman gain update unit 75 uses the determination symbol d (k) output from the determination unit 72, the error covariance P (k | k-1), and the state noise covariance R to use the Kalman gain G (k) of the Kalman filter. ) Is calculated. The covariance R of the state noise is a fixed value and is stored in the internal memory of the Kalman gain update unit 75. The covariance R of the state noise may be given to the Kalman gain update unit 75 from the outside of the optical receiver 4 shown in FIG. The details of the error covariance P (k | k-1) will be described later.
The Kalman gain update unit 75 updates the Kalman gain G (k) by multiplying the Kalman gain G (k) of the Kalman filter by the probability density function p [φ (k)] output from the probability density function calculation unit 93. do.
The Kalman gain update unit 75 multiplies the updated Kalman gain G'(k) by the innovation variable e (k) output from the subtractor 74, and the updated Kalman gain G'(k) and the innovation variable e. The multiplication result m ₃ (k) with (k) is output to the adder 76.

The adder 76 adds the pre-estimated value θ hat (k | k-1) of the phase noise output from the delay unit 78 and the multiplication result m ₃ (k) output from the Kalman gain update unit 75. , Calculate the ex post facto estimated value θ hat (k | k) of the phase noise.
The pre-estimated value θ hat (k | k-1) of the phase noise corresponds to the prior probability of the phase noise at the time when the sample number is k, which is predicted when the sample number is (k-1).
The ex post facto estimated value θ hat (k | k) of the phase noise is an estimated value of the phase noise at the time when the sample number is k.
The adder 76 outputs the calculated ex post facto estimated value θ hat (k | k) of the phase noise to the exponentiation 77 and the sum total 91, respectively.

The exponentiation 77 performs exponentiation of phase noise output from the adder 76 with respect to the ex post facto estimated value θ hat (k | k), where the number of napiers is e and the exponentiation is j.
The exponentiation 77 outputs the exponential value exp [j · θ hat (k | k)], which is the operation result of the exponentiation, to the complex conjugate arithmetic unit 81.
Further, the power calculator 77 outputs the ex post facto estimated value θ hat (k | k) of the phase noise output from the adder 76 to the delay unit 78.

The delay unit 78 holds the ex post facto estimated value θ hat (k | k) of the phase noise output from the exponentiation 77 for only one sample time.
The delay unit 78 uses the ex post facto estimated value θ hat (k | k) of the phase noise held for one sample time as the pre-estimated value θ hat (k | k-1) of the phase noise of the adder 76 and the power calculator 79. Output to each.
The power calculator 79 performs a power calculation with a napier number of e and a power exponent of j with respect to the pre-estimated value θ hat (k | k-1) of the phase noise output from the delay unit 78.
The power calculator 79 outputs the power calculation value exp [j · θ hat (k | k-1)], which is the calculation result of the power calculation, to the multiplier 73 and the complex conjugate calculator 80, respectively.

The complex conjugate arithmetic unit 80 performs the complex conjugate operation on the exponentiation value exp [j · θ hat (k | k-1)] output from the power arithmetic unit 79, and the complex conjugate value which is the operation result of the complex conjugate. The exp [−j · θ hat (k | k-1)] is output to the multiplier 71.
The complex conjugate arithmetic unit 81 performs a complex conjugate operation on the exponentiation value exp [j · θ hat (k | k)] output from the exponentiation 77, and performs a complex conjugate operation on the exponentiation value exp [j · θ hat (k | k)]. −j · θ hat (k | k)] is output to the multiplier 82.

The multiplier 82 multiplies the polarization signal r (k) output from the frequency error compensation unit 45 with the complex conjugate value exp [−j · θ hat (k | k)] output from the complex conjugate arithmetic unit 81. do.
The multiplier 82 is a multiplication result of the polarization signal r (k) and the complex conjugate value exp [−j · θ hat (k | k)] r (k) · exp [−j · θ hat (k | k). ] Is output to the demodulation unit 49 as a polarization signal s hat (k) from which the phase noise has been removed.

The cumulative phase noise calculation unit 90 includes a total calculation unit 91 and an average calculation unit 92.
When the phase noise θ hat (k) is Bayesian estimated by the Bayesian estimation unit 47, the cumulative phase noise calculation unit 90 accumulates the estimated values of the phase noise θ hat (k), thereby accumulating the cumulative estimated values. Calculate the phase noise φ (k).
The cumulative phase noise calculation unit 90 outputs the calculated cumulative phase noise φ (k) to the probability density function calculation unit 93.

The summation unit 91 holds the post-estimation value θ hat (k | k) of the phase noise output from the adder 76 for one sample time, and holds the post-estimation value θ hat (k) of the phase noise for only one sample time. Let | k) be the pre-estimated value θ hat (k | k-1) of the phase noise.
The summation unit 91 performs a power calculation with a napier number of e and a power exponent of j with respect to the pre-estimated value θ hat (k | k-1) of the phase noise.
The sum total calculator 91 calculates the sum of the exponential value exp [j · θ hat (k | k−i)], which is the result of the exponentiation of the sample numbers (k−N) to (k-1). do. i = 1, ..., N. N is an integer greater than or equal to 2.
The sum total calculator 91 outputs the calculated sum to the average calculator 92.

The average calculator 92 calculates the average value of the exponential value exp [j · θ hat (k | k−i)] by dividing the sum output from the sum calculator 91 by N.
The average calculator 92 outputs the calculated average value to the probability density function calculation unit 93 as cumulative phase noise φ (k).
The probability density function calculation unit 93 calculates the probability density function p [φ (k)] of the cumulative phase noise φ (k) output from the average calculator 92.
The probability density function calculation unit 93 outputs the calculated probability density function p [φ (k)] to the Kalman gain update unit 75.

Next, the operation of the optical transmission device shown in FIG. 1 will be described.
When the X polarization is input from the outside, the modulation unit 11 multivalues the X polarization and outputs the multivalue modulation signal of the X polarization to the transmission distortion compensation unit 12.
Further, when the Y polarization is input from the outside, the modulation unit 11 multivalues the Y polarization and outputs the Y polarization multivalue modulation signal to the transmission distortion compensation unit 12.
In the optical transmission device shown in FIG. 1, X-polarized light and Y-polarized wave are input to the modulation unit 11 from the outside. However, this is only an example, and one polarization may be input to the modulation unit 11 from the outside.

When the transmission distortion compensating unit 12 receives the X-polarized multi-valued modulation signal from the modulation unit 11, the transmission distortion compensating unit 12 compensates for the distortion of the X-polarized multi-valued modulation signal, and after compensating for the distortion, the X-polarized multi-valued modulation. The signal is output to the D / A converter 13.
Further, when the transmission distortion compensating unit 12 receives the Y-polarized multi-valued modulation signal from the modulation unit 11, the transmission distortion compensating unit 12 compensates for the distortion of the Y-polarized multi-valued modulation signal, and after compensating for the distortion, the Y-polarized multi-valued modulation signal is multi-valued. The value modulation signal is output to the D / A converter 13.

When the D / A converter 13 receives the X polarization multi-value modulation signal after distortion compensation from the transmission distortion compensation unit 12, the X polarization multi-value modulation signal after distortion compensation is digitally signaled. To convert to an analog signal.
D / A converter 13 outputs an I _X signal in-phase component of the analog signal to electro-optic conversion unit 15, and outputs a Q _X signal is an orthogonal component of the analog signal to electro-optic conversion unit 15.
Further, when the D / A converter 13 receives the Y polarization multi-value modulation signal after distortion compensation from the transmission distortion compensation unit 12, the Y polarization multi-value modulation signal after distortion compensation is received. Converts a digital signal to an analog signal.
_{The D / A converter 13 outputs an I Y} signal, which is an in-phase component of the analog signal, to the lightning conversion unit 15, and outputs a Q _Y signal, which is an orthogonal component of the analog signal, to the lightning conversion unit 15.

The transmission light source 14 generates continuous light and outputs the continuous light to the lightning conversion unit 15.
Optic converter section 15, the light modulation by superimposing I _X signal output from the D / A converter 13, Q _X signal, the continuous light output respectively from the transmission light source 14 of the I _Y signal and Q _Y signal Generate a signal.
The lightning conversion unit 15 outputs the generated light modulation signal to the transmission line 2.
The optical modulation signal is transmitted to the photoelectric conversion unit 41 of the optical receiver 4 by the transmission line 2.
In the transmission line 2, for example, additive white Gaussian noise (AWGN) may be added to the optical modulation signal.
The local emission source 3 generates locally oscillating light and outputs the locally oscillating light to the photoelectric conversion unit 41.

The photoelectric conversion unit 41 uses the local oscillator light output from the local light source 3, a modulated optical signal transmitted by the transmission path 2, I X _'signal, Q _X' signal, I Y _'signal and Q _Y 'Extract each of the signals.
The photoelectric conversion unit 41, the extracted I _{X 'the} signal is converted into an electrical signal, the electrical I _X is an electrical _signal' outputs a signal to the A / D converter 42.
The photoelectric conversion unit 41, the extracted Q _{X 'the} signal is converted into an electric signal, electric Q _X is an electrical _signal' outputs a signal to the A / D converter 42.
The photoelectric conversion unit 41 converts the extracted I _Y'signal into an electric signal, and outputs the electric I _Y'signal, which is an electric signal, to the A / D converter 42.
The photoelectric conversion unit 41 converts the extracted Q _Y'signal into an electric signal, and outputs the electric Q _Y'signal, which is an electric signal, to the A / D converter 42.

A / D converter 42, _'receives the signal, electrical I _X' electrical I _X from the photoelectric conversion unit 41 a signal from an analog signal to a digital signal, the polarization separating digital I _{X 'signal} is a digital signal Output to unit 44.
A / D converter 42, _'receives the signal, electrical Q _X' electrical Q _X from the photoelectric conversion unit 41 a signal from an analog signal to a digital signal, the polarization separating digital Q _{X 'signal} is a digital signal Output to unit 44.
_{When the A / D converter 42 receives an electric I Y'signal} from the photoelectric conversion unit 41, the A / D converter 42 converts the electric I _Y'signal from an analog signal to a digital signal, and polarization-separates the _{digital I Y'signal, which is a digital signal.} Output to unit 44.
_{When the A / D converter 42 receives the electric Q Y'signal} from the photoelectric conversion unit 41, the A / D converter 42 converts the electric Q _Y'signal from an analog signal to a digital signal, and polarization-separates the _{digital Q Y'signal which is a digital signal.} Output to unit 44.

Polarization separating section 44, A / receives the digital I _{X 'signal} and the digital Q _X' signals from D converter 42, signals X 'polarization, including both digital I _X' signal and the digital Q _{X 'signal} It is output as a signal to the frequency error compensation unit 45 (step ST1 in FIG. 4).
Polarization separating section 44, A / the D converter 42 receives the digital I _{Y 'signal} and the digital Q _Y' signals, digital I _{Y 'signal} and the digital Q _Y' signal Y 'polarization including both signal It is output as a signal to the frequency error compensation unit 45 (step ST1 in FIG. 4).
Each of the X'polarization signal and the Y'polarization signal is a frequency that is an error between the frequency of the continuous light output from the transmission light source 14 and the frequency of the locally oscillating light output from the station emission source 3. The error Δf is included.
Further, each of the X'polarization signal and the Y'polarization signal includes a phase noise θ (k) which is the sum of the phase noises generated by the transmission light source 14 and the station light emitting source 3.

When the frequency error compensating unit 45 receives each of the X'polarization signal and the Y'polarization signal from the polarization separation unit 44, the frequency error compensation unit 45 includes the frequency error included in each of the X'polarization signal and the Y'polarization signal. Δf is removed (step ST2 in FIG. 4).
Since the process itself for removing the frequency error Δf included in the polarization signal is a known technique, detailed description thereof will be omitted. For example, the following Non-Patent Document 1 discloses a process for removing the frequency error Δf included in the polarization signal.
[Non-Patent Document 1]
A. Leven et al., “Frequency Estimation in Intradyne Reception” IEEE Photon. Technol. Lett., Vol. 19, No. 6, pp. 366-368, (2007).
The frequency error compensation unit 45 outputs each of the X'polarization signal from which the frequency error Δf has been removed and the Y'polarization signal from which the frequency error Δf has been removed to the phase noise compensation unit 46.

When the Bayesian estimation unit 47 of the phase noise compensation unit 46 receives the X'polarization signal from the frequency error compensation unit 45, the Bayesian estimation unit 47 uses a Kalman filter to Bayes the phase noise θ (k) included in the X'polarization signal. presume. The Bayesian estimation unit 47 uses the estimated value of the phase noise θ (k) to remove the phase noise θ (k) included in the X'polarized signal (step ST3 in FIG. 4).
Further, when the Bayesian estimation unit 47 receives the Y'polarization signal from the frequency error compensation unit 45, the Bayesian estimation unit 47 Bayesian estimates the phase noise θ (k) included in the Y'polarization signal using the Kalman filter. The Bayesian estimation unit 47 uses the estimated value of the phase noise θ (k) to remove the phase noise θ (k) included in the Y'polarized signal (step ST3 in FIG. 4).
Hereinafter, the process of removing the phase noise θ (k) by the Bayesian estimation unit 47 will be specifically described assuming that each of the X'polarization signal and the Y'polarization signal is represented by the polarization signal r (k). do.

式（１）において、ｎ（ｋ）は、状態雑音であり、状態雑音ｎ（ｋ）は、位相雑音θ（ｋ）と異なる雑音である。
式（２）において、ｗ（ｋ）は、観測雑音である。観測雑音ｗ（ｋ）は、位相雑音θ（ｋ）に含まれている。First, the polarization signal r (k) output from the frequency error compensation unit 45 has a phase noise θ (k) and a determination symbol d (k) obtained by the determination unit 72, as shown in the following equation (1). ) And.

In the equation (1), n (k) is a state noise, and the state noise n (k) is a noise different from the phase noise θ (k).
In equation (2), w (k) is the observed noise. The observed noise w (k) is included in the phase noise θ (k).

乗算器７１は、偏波信号ｒ（ｋ）と複素共役値ｅｘｐ［−ｊ・θハット（ｋ｜ｋ−１）］との乗算結果ｍ_１（ｋ）を判定部７２に出力する。When the multiplier 71 receives the polarization signal r (k) from the frequency error compensation unit 45, it is output from the polarization signal r (k) and the complex conjugate arithmetic unit 80 as shown in the following equation (3). Multiply with the complex conjugate value exp [−j · θ hat (k | k-1)].

_{The multiplier 71 outputs the multiplication result m 1} (k) of the polarization signal r (k) and the complex conjugate value exp [−j · θ hat (k | k-1)] to the determination unit 72.

Determining unit 72, the multiplication result _m 1 receives a (k) from the multiplier 71, to implement the symbol determination process for the multiplication result _m 1 (k).
The determination unit 72 outputs the determination symbol d (k) indicating the determination result of the symbol determination process to the multiplier 73 and the Kalman gain update unit 75, respectively.
For example, when each of the X-polarized multi-value modulation signal and the Y-polarized multi-value modulation signal is a QPSK signal, the determination unit 72 determines the four symbols “11”, “01”, “00” in the QPSK signal. , “10” and the multiplication result m ₁ (k) are calculated as Euclidean distances.
The determination unit 72 determines the symbol having the smallest Euclidean distance from the _{multiplication result m 1} (k) among the four symbols “11”, “01”, “00”, and “10” in the QPSK signal, as the determination symbol d (k). ).

乗算器７３は、判定シンボルｄ（ｋ）と冪演算値ｅｘｐ［ｊ・θハット（ｋ｜ｋ−１）］との乗算結果ｍ_２（ｋ）を減算器７４に出力する。When the multiplier 73 receives the determination symbol d (k) from the determination unit 72, the determination symbol d (k) and the exponentiation value exp [output from the exponentiation unit 79] are shown in the following equation (4). j · θ hat (k | k-1)] and.

_{The multiplier 73 outputs the multiplication result m 2} (k) of the determination symbol d (k) and the exponentiation value exp [j · θ hat (k | k-1)] to the subtractor 74.

減算器７４は、算出したイノベーション変数ｅ（ｋ）をカルマンゲイン更新部７５に出力する。Subtractor 74, the multiplication result _m 2 undergo (k) from the multiplier 73, as shown in the following equation (5), subtracting the multiplication result _m 2 (k) from the polarization signal r (k) Then, the innovation variable e (k) is calculated.

The subtractor 74 outputs the calculated innovation variable e (k) to the Kalman gain update unit 75.

式（６）において、Ｑは、観測雑音ｗ（ｋ）の共分散であり、固定値である。観測雑音ｗ（ｋ）の共分散Ｑは、例えば、カルマンゲイン更新部７５の内部メモリに格納されている。観測雑音ｗ（ｋ）の共分散Ｑは、図１に示す光受信器４の外部からカルマンゲイン更新部７５に与えられるものであってもよい。The internal memory of the Kalman gain update unit 75 holds the error covariance P (k-1 | k-1) related to the post-estimation value θ hat (k-1 | k-1) of the phase noise one sample before. There is.
The Kalman gain update unit 75 relates to the pre-estimated value θ hat (k | k-1) of the phase noise by substituting the error covariance P (k-1 | k-1) into the following equation (6). The error covariance P (k | k-1) is calculated.

In equation (6), Q is the covariance of the observed noise w (k) and is a fixed value. The covariance Q of the observed noise w (k) is stored in, for example, the internal memory of the Kalman gain update unit 75. The covariance Q of the observed noise w (k) may be given to the Kalman gain update unit 75 from the outside of the optical receiver 4 shown in FIG.

式（７）において、＊は、共役を示す数学記号である。
カルマンゲイン更新部７５は、１サンプル後において、カルマンゲインＧ（ｋ）を算出できるようにするため、算出した誤差共分散Ｐ（ｋ｜ｋ−１）を以下の式（８）に代入することで、誤差共分散Ｐ（ｋ｜ｋ）を算出する。

カルマンゲイン更新部７５の内部メモリは、誤差共分散Ｐ（ｋ｜ｋ）を、１サンプル前の誤差共分散Ｐ（ｋ−１｜ｋ−１）として保持する。The Kalman gain update unit 75 sets the calculated error covariance P (k | k-1), the determination symbol d (k) output from the determination unit 72, and the covariance R of the state noise n (k) as follows. By substituting into equation (7), the Kalman gain G (k) of the Kalman filter is calculated.

In equation (7), * is a mathematical symbol indicating conjugation.
The Kalman gain update unit 75 substitutes the calculated error covariance P (k | k-1) into the following equation (8) so that the Kalman gain G (k) can be calculated after one sample. Then, the error covariance P (k | k) is calculated.

The internal memory of the Kalman gain update unit 75 holds the error covariance P (k | k) as the error covariance P (k-1 | k-1) one sample before.

カルマンゲイン更新部７５は、以下の式（１０）に示すように、更新後のカルマンゲインＧ’（ｋ）と減算器７４から出力されたイノベーション変数ｅ（ｋ）とを乗算する。

カルマンゲイン更新部７５は、更新後のカルマンゲインＧ’（ｋ）とイノベーション変数ｅ（ｋ）との乗算結果ｍ_３（ｋ）を加算器７６に出力する。When the Kalman gain update unit 75 receives the probability density function p [φ (k)] from the probability density function calculation unit 93, the probability density is added to the calculated Kalman gain G (k) as shown in the following equation (9). The Kalman gain G (k) is updated by multiplying the function p [φ (k)].

The Kalman gain update unit 75 multiplies the updated Kalman gain G'(k) by the innovation variable e (k) output from the subtractor 74, as shown in the following equation (10).

_{The Kalman gain update unit 75 outputs the multiplication result m 3} (k) of the updated Kalman gain G'(k) and the innovation variable e (k) to the adder 76.

加算器７６は、算出した位相雑音の事後推定値θハット（ｋ｜ｋ）を冪演算器７７及び総和演算器９１のそれぞれに出力する。 _{When the adder 76 receives the multiplication result m 3} (k) from the Kalman gain update unit 75, the adder 76 receives the pre-estimated value θ hat (k) of the phase noise output from the delay unit 78 as shown in the following equation (11). By adding | k-1) and the multiplication result m ₃ (k), the ex post facto estimated value θ hat (k | k) of the phase noise is calculated.

The adder 76 outputs the calculated ex post facto estimated value θ hat (k | k) of the phase noise to the exponentiation 77 and the sum total 91, respectively.

When the exponentiation 77 receives the ex post facto estimation value θ hat (k | k) of the phase noise from the adder 76, the Napier number is e with respect to the ex post facto estimation value θ hat (k | k) of the phase noise. Performs a power calculation with a power index of j.
The exponentiation 77 outputs the exponential value exp [j · θ hat (k | k)], which is the operation result of the exponentiation, to the complex conjugate arithmetic unit 81.
Further, the power calculator 77 outputs the ex post facto estimated value θ hat (k | k) of the phase noise output from the adder 76 to the delay unit 78.

When the delay unit 78 receives the post-estimation value θ hat (k | k) of the phase noise from the exponentiation 77, the delay unit 78 holds the post-estimation value θ hat (k | k) of the phase noise for only one sample time.
The delay unit 78 uses the ex post facto estimated value θ hat (k | k) of the phase noise held for one sample time as the pre-estimated value θ hat (k | k-1) of the phase noise of the adder 76 and the power calculator 79. Output to each.

When the exponentiation 79 receives the phase noise pre-estimated value θ hat (k | k-1) from the delay unit 78, the power arithmetic unit 79 has a number of Napiers with respect to the phase noise pre-estimated value θ hat (k | k-1). Is e, and the exponentiation is j.
The power calculator 79 outputs the power calculation value exp [j · θ hat (k | k-1)], which is the calculation result of the power calculation, to the multiplier 73 and the complex conjugate calculator 80, respectively.

When the complex conjugate arithmetic unit 80 receives the exponentiation value exp [j · θ hat (k | k-1)] from the exponentiation 79, the exponentiation value exp [j · θ hat (k | k-1)] Performs a complex conjugate operation on.
The complex conjugate arithmetic unit 80 outputs the complex conjugate value exp [−j · θ hat (k | k-1)], which is the calculation result of the complex conjugate, to the multiplier 71.

When the complex conjugate arithmetic unit 81 receives the exponentiation value exp [j · θ hat (k | k)] from the exponentiation 79, the complex conjugate arithmetic with respect to the exponential exponential value exp [j · θ hat (k | k)] To carry out.
The complex conjugate arithmetic unit 81 outputs the complex conjugate value exp [−j · θ hat (k | k)], which is the operation result of the complex conjugate operation, to the multiplier 82.

乗算器８２は、偏波信号ｒ（ｋ）と複素共役値ｅｘｐ［−ｊ・θハット（ｋ｜ｋ）］との乗算結果ｒ（ｋ）・ｅｘｐ［−ｊ・θハット（ｋ｜ｋ）］を、位相雑音を除去した偏波信号ｓハット（ｋ）として復調部４９に出力する。When the multiplier 82 receives the complex conjugate value exp [−j · θ hat (k | k)] from the complex conjugate arithmetic unit 81, it is output from the frequency error compensation unit 45 as shown in the following equation (12). The polarization signal r (k) is multiplied by the complex conjugate value exp [−j · θ hat (k | k)].

The multiplier 82 is a multiplication result of the polarization signal r (k) and the complex conjugate value exp [−j · θ hat (k | k)] r (k) · exp [−j · θ hat (k | k). ] Is output to the demodulation unit 49 as a polarization signal s hat (k) from which the phase noise has been removed.

The demodulation unit 49 converts each of the polarization signal X from which the phase noise has been removed by the Bayesian estimation unit 47 and the polarization signal Y from which the phase noise has been removed by the Bayes estimation unit 47 into a bit time series.
The demodulation unit 49 outputs each bit time series to the outside.
For example, when each of the X-polarized multi-value modulation signal and the Y-polarized multi-value modulation signal is a QPSK signal, the demodulation unit 49 uses the four symbols “11”, “01”, and “00” in the QPSK signal. , “10” and the polarization signal s hat (k) are calculated as Euclidean distances.
The demodulation unit 49 uses the symbol having the smallest Euclidean distance from the polarization signal s hat (k) among the four symbols "11", "01", "00", and "10" in the QPSK signal as a bit time series. Output to the outside.

When the Bayesian estimation unit 47 Bayesian estimates the phase noise θ hat (k) included in the X'polarization signal represented by the polarization signal r (k), the weight update unit 48 Bayesian estimates the phase noise θ. Accumulate hats (k). The weight update unit 48 calculates the probability density function p [φ (k)] of the cumulative phase noise φ (k), which is the cumulative estimated value.
The weight update unit 48 updates the Kalman gain G (k) of the Kalman filter used for Bayesian estimation of the phase noise included in the X'polarized signal based on the probability density function p [φ (k)]. The unit 75 is updated (step ST4 in FIG. 4).
Further, when the Bayesian estimation unit 47 Bayesian estimates the phase noise θ hat (k) included in the Y'polarization signal represented by the polarization signal r (k), the weight update unit 48 has a phase. Accumulate the estimated values of the noise θ hat (k). The weight update unit 48 calculates the probability density function p [φ (k)] of the cumulative phase noise φ (k), which is the cumulative estimated value.
The weight update unit 48 updates the Kalman gain G (k) of the Kalman filter used for Bayesian estimation of the phase noise included in the Y'polarized signal based on the probability density function p [φ (k)]. The unit 75 is updated (step ST4 in FIG. 4).
When the Kalman gain update unit 75 updates the Kalman gain G (k), the accuracy of removing the phase noise θ hat (k) in the Bayesian estimation unit 47 is improved.
Hereinafter, the calculation process of the probability density function p [φ (k)] by the weight updating unit 48 will be specifically described.

Upon receiving the post-estimation value θ hat (k | k) of the phase noise from the adder 76, the summation unit 91 holds the post-estimation value θ hat (k | k) of the phase noise for only one sample time.
The sum total calculator 91 sets the ex post facto estimated value θ hat (k | k) of the phase noise held for one sample time as the pre-estimated value θ hat (k | k-1) of the phase noise.
The summation unit 91 performs a power calculation with a napier number of e and a power exponent of j with respect to the pre-estimated value θ hat (k | k-1) of the phase noise.
The sum total calculator 91 calculates the sum of the exponential value exp [j · θ hat (k | k−i)], which is the result of the exponentiation of the sample numbers (k−N) to (k-1). do. i = 1, ..., N. N is an integer greater than or equal to 2.
The sum total calculator 91 outputs the calculated sum to the average calculator 92.

平均演算器９２は、算出した平均値を、累積位相雑音φ（ｋ）として確率密度関数算出部９３に出力する。When the average calculator 92 receives the sum from the sum calculator 91, the sum is divided by N as shown in the following equation (13), so that the exponentiation value exp [j] calculated by the sum calculator 91 is calculated. -Calculate the average value of the absolute values of θ hat (k | ki)].

The average calculator 92 outputs the calculated average value to the probability density function calculation unit 93 as cumulative phase noise φ (k).

式（１４）において、ｍｉｎ｛ｘ，ｙ｝は、ｘとｙのうち、小さい方を選択する旨を示す数学記号である。
確率密度関数算出部９３は、算出した確率密度関数ｐ［φ（ｋ）］をカルマンゲイン更新部７５に出力する。When the probability density function calculation unit 93 receives the cumulative phase noise φ (k) from the average calculator 92, the probability density function calculation unit 93 substitutes the cumulative phase noise φ (k) into the approximate expression shown in the following equation (14). Calculate the density function p [φ (k)].

In the equation (14), min {x, y} is a mathematical symbol indicating that the smaller of x and y is selected.
The probability density function calculation unit 93 outputs the calculated probability density function p [φ (k)] to the Kalman gain update unit 75.

Since the probability density function p [φ (k)] is expressed by the following equation (15), it can also be calculated from the probability density function p [φ (k-1)] one sample before. .. However, in the received signal processing device shown in FIG. 1, in order to reduce the calculation load of the probability density function p [φ (k)], the probability density function calculation unit 93 uses the approximate expression shown in the equation (14) to reduce the probability density. The function p [φ (k)] is calculated.

FIG. 6 shows an explanation showing the probability density function p [φ (k)] calculated by the equation (15) and the probability density function p [φ (k)] calculated by the approximate equation shown in the equation (14). It is a figure.
FIG. 6 shows the probability density function p [φ (k)] when N = 20. The horizontal axis of FIG. 6 shows the normalized cumulative phase noise φ (k), and the vertical axis of FIG. 6 shows the probability density.
The error between the probability density function p [φ (k)] calculated by the equation (15) and the probability density function p [φ (k)] calculated by the approximate equation shown in the equation (14) is shown in FIG. As shown, there is little and the error has little effect on updating the Kalman gain G (k).

As described above, the Kalman gain update unit 75 multiplies the Kalman gain G (k) of the Kalman filter by multiplying the probability density function p [φ (k)] output from the probability density function calculation unit 93 by the Kalman gain G. Update (k).
When the determination symbol d (k) output from the determination unit 72 to the multiplier 73 is erroneous due to the influence of the phase noise θ hat (k), the absolute value of the innovation variable e (k) becomes large.
As the absolute value of the innovation variable e (k) increases, the cumulative phase noise φ (k) calculated by the cumulative phase noise calculation unit 90 decreases, and the probability density function p calculated by the probability density function calculation unit 93. [Φ (k)] becomes smaller.
As the probability density function p [φ (k)] becomes smaller, the Kalman gain G'(k) updated by the Kalman gain update unit 75 becomes smaller.
As the updated Kalman gain G'(k) becomes smaller, the weight of the term of the innovation variable e (k) becomes smaller in the ex post facto estimation value θ hat (k | k) of the phase noise shown in the equation (11). .. Therefore, the error propagation of the symbol determination due to the influence of the phase noise θ hat (k) is suppressed.

FIG. 7 is an explanatory diagram showing the result of simulating the phase of the polarization signal s hat (k) output from the phase noise compensation unit 46 to the demodulation unit 49.
In the phase simulation of the polarization signal s hat (k), the modulation unit 11 outputs a 256-QAM signal having ^{a line width symbol rate product of 1 × 10 −5 as a multi-level modulation signal.} Further, in the phase simulation of the polarization signal s hat (k), it is assumed that the signal-to-noise ratio (SNR: Signal-to-Noise Ratio) of the 256-QAM signal received by the optical receiver 4 is 27 dB. ..
In FIG. 7, the solid line shows the phase of the polarization signal s hat (k) output from the phase noise compensation unit 46 shown in FIG. 1 to the demodulation unit 49.
The alternate long and short dash line indicates the phase of the polarization signal s hat (k) output to the demodulation unit 49 from the phase noise compensation unit having only the Bayesian estimation unit 47 without the weight update unit 48.
The dotted line is the true value of the phase of the polarization signal s hat (k).

As shown in FIG. 7, the phase of the polarization signal s hat (k) output from the phase noise compensation unit not provided with the weight update unit 48 to the demodulation unit 49 is, for example, when the sample number is around 700 and the phase is It is very different from the true value.
Therefore, in an optical receiver having a phase noise compensating unit having only the Bayesian inference unit 47 without the weight updating unit 48, erroneous propagation of symbol determination occurs due to the influence of the phase noise θ hat (k). ..
As shown in FIG. 7, the phase of the polarization signal s hat (k) output from the phase noise compensating unit 46 to the demodulation unit 49 shown in FIG. 1 is substantially the same as the true value of the phase.
Therefore, in the optical receiver 4 shown in FIG. 1, erroneous propagation of symbol determination due to the influence of phase noise hardly occurs.

FIG. 8 is an explanatory diagram showing an SNR penalty for the line width symbol rate product when the multi-value modulation signal output from the modulation unit 11 is a QPSK signal.
FIG. 9 is an explanatory diagram showing an SNR penalty for the line width symbol rate product when the multi-level modulation signal output from the modulation unit 11 is a 16-QAM signal.
FIG. 10 is an explanatory diagram showing an SNR penalty for the line width symbol rate product when the multi-level modulation signal output from the modulation unit 11 is a 64-QAM signal.
FIG. 11 is an explanatory diagram showing an SNR penalty for the line width symbol rate product when the multi-level modulation signal output from the modulation unit 11 is a 128-QAM signal.
8 to 10, the solid line shows the SNR penalty of the optical receiver 4 shown in FIG. 1, and the alternate long and short dash line has a phase noise compensation unit having only the Bayesian estimation unit 47 without the weight update unit 48. Shows the SNR penalty for optical receivers with.
The dotted line shows the SNR penalty of the optical receiver (see Non-Patent Document 2) that estimates the phase noise by performing a blind phase search (BPS) algorithm instead of using a Kalman filter. There is.
The SNR penalty is an index indicating that the smaller the SNR is, the better the SNR is.
[Non-Patent Document 2]
T. Pfau et al., “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightw. Technol., Vol. 27, no. 8, pp. 989-999, (2009) ..

As shown in FIGS. 8 to 11, the SNR penalty of the optical receiver 4 shown in FIG. 1 is a Bayesian estimation unit without the weight update unit 48, regardless of the multi-valued modulation signal output from the modulation unit 11. It is smaller than the SNR penalty of an optical receiver having a phase noise compensator with only 47.
Further, the SNR penalty of the optical receiver 4 shown in FIG. 1 is smaller than the SNR penalty of the optical receiver estimating the phase noise by executing the BPS algorithm as shown in FIGS. 8 to 11. It has become.

In the above-described first embodiment, when the phase noise is Bayesian-estimated by the Bayesian estimation unit 47, the estimated values of the phase noise are accumulated, and the Kalman gain of the Kalman filter is Bayesed based on the accumulated phase noise which is the accumulated estimated value. The received signal processing device 43 is configured to include a weight updating unit 48 to be updated by the estimation unit 47. Therefore, the received signal processing device 43 can remove the phase noise even if the phase noise included in the received signal changes due to the error propagation of the symbol determination.

Embodiment 2.
In the second embodiment, the accumulated phase accumulation phase noise accumulated by the noise calculation unit 90 phi (k) with a threshold value phi _th unit step function returns a value corresponding to the comparison result between _{U [φ (k) -φ th} ] The received signal processing device 43 including the probability density function calculation unit 94 that calculates the probability density function p [φ (k)] will be described.

The configuration diagram showing the optical transmission device including the received signal processing device 43 according to the second embodiment is the same as that of the first embodiment.
FIG. 12 is a configuration diagram showing a phase noise compensating unit 46 of the received signal processing device 43 according to the second embodiment. In FIG. 12, the same reference numerals as those in FIG. 5 indicate the same or corresponding parts, and thus the description thereof will be omitted.
The probability density function calculating section 94, the average calculator cumulative phase noise output from the 92 phi (k) with a threshold value phi _th unit step function returns a value corresponding to the comparison result between _{U [φ (k) -φ th} ] Is calculated as the probability density function p [φ (k)] of the cumulative phase noise φ (k).
The probability density function calculation unit 94 outputs the calculated probability density function p [φ (k)] to the Kalman gain update unit 75.
The internal memory of the probability density function calculation unit 94 stores _{the threshold value φth.} However, this is only an example, the threshold phi _th may be those given in the probability density function calculating section 94 from the outside of the optical receiver 4 shown in FIG.

Next, the operation of the optical transmission device will be described.
Since the parts other than the probability density function calculation unit 94 are the same as those of the optical transmission device shown in FIG. 1, only the operation of the probability density function calculation unit 94 will be described here.
When the probability density function calculation unit 94 receives the cumulative phase noise φ (k) from the averaging calculator 92, the probability density function calculation unit 94 _{substitutes the cumulative phase noise φ (k) and the threshold value φth} into the following equation (16). The unit step function U [φ (k) −φ _th ] is calculated.

When the probability density function calculation unit 94 calculates the unit step function U [φ (k) −φ _th ], the unit step function U [φ (k) −φ _th ] is set as the probability density function p [φ (k)]. Output to the Kalman gain update unit 75.

When the Kalman gain update unit 75 receives the probability density function p [φ (k)] from the probability density function calculation unit 94, the Kalman gain update unit 75 multiplies the probability density function p [φ (k)] by the Kalman gain G (k) of the Kalman filter. By doing so, the Kalman gain G (k) is updated.
When the determination symbol d (k) output from the determination unit 72 to the multiplier 73 is erroneous due to the influence of the phase noise θ hat (k), the absolute value of the innovation variable e (k) becomes large.
As the absolute value of the innovation variable e (k) increases, the cumulative phase noise φ (k) calculated by the cumulative phase noise calculation unit 90 decreases, and the probability density function p calculated by the probability density function calculation unit 94. The probability that [φ (k)] becomes zero increases.
When the probability density function p [φ (k)] becomes zero, the term of the innovation variable e (k) disappears in the ex post facto estimated value θ hat (k | k) of the phase noise shown in the equation (11). Therefore, the error propagation of the symbol determination due to the influence of the phase noise θ hat (k) is suppressed.

In the second above embodiment, the cumulative phase accumulation phase noise accumulated by the noise calculation unit 90 phi (k) a unit step function returns a value corresponding to a result of comparison between the threshold value _{φ th U [φ (k)} -φ _The received signal processing device 43 is configured to include a probability density function calculation unit 94 that calculates th] as a probability density function p [φ (k)]. Therefore, the received signal processing device 43 can remove the phase noise even if the phase noise contained in the received signal changes, as in the first embodiment, and has a higher probability than the first embodiment. The calculation load of the density function p [φ (k)] can be reduced.

In the present invention, within the scope of the invention, it is possible to freely combine each embodiment, modify any component of each embodiment, or omit any component in each embodiment. ..

The present invention is suitable for a received signal processing device, a received signal processing method, and an optical receiver that removes phase noise contained in a polarized signal.

1 Optical transmitter, 2 transmission path, 3 station light emitting source, 4 optical receiver, 10 transmission signal processing unit, 11 modulator, 12 transmission distortion compensation unit, 13 D / A converter, 14 transmission light source, 15 lightning converter , 41 photoelectric conversion unit, 42 A / D converter, 43 reception signal processing device, 44 polarization separation unit, 45 frequency error compensation unit, 46 phase noise compensation unit, 47 bays estimation unit, 48 weight update unit, 49 demodulation unit. , 51 polarization separation circuit, 52 frequency error compensation circuit, 53 Bayes estimation circuit, 54 weight update circuit, 55 demodulation circuit, 61 memory, 62 processor, 71 multiplier, 72 judgment unit, 73 multiplier, 74 subtractor, 75 Kalman gain updater, 76 adder, 77 adder, 78 delay, 79 冪 math, 80 complex conjugate math, 81 complex conjugation, 82 multiplier, 90 cumulative phase noise math, 91 total math , 92 Average calculator, 93,94 Probability density function calculation unit.

Claims (8)

The Kalman filter is used to Bayesi estimate the phase noise contained in the polarization signal indicating the polarization state of the received signal on which the symbol time series is superimposed, and the polarization signal is estimated using the estimated value of the phase noise. Bayesian estimation unit that removes the phase noise contained in
When the phase noise is Bayesian estimated by the Bayesian inference unit, the estimated values of the phase noises are accumulated, and the probability density function calculated based on the accumulated estimated values, which is the accumulated phase noises, is multiplied by the Kalman gain of the Kalman filter. A received signal processing device including a weight updating unit that causes the Bayesian estimation unit to update the Kalman gain. The received signal processing device according to claim 1, further comprising a demodulation unit that converts a polarized signal from which phase noise has been removed by the Bayesian estimation unit into a bit time series. The weight update unit
When the phase noise is Bayesian estimated by the Bayesian estimation unit, the cumulative phase noise calculation unit that calculates the cumulative phase noise by accumulating the estimated values of the phase noise, and the cumulative phase noise calculation unit.
It is provided with a probability density function calculation unit for calculating the probability density function of the cumulative phase noise calculated by the cumulative phase noise calculation unit.
The Bayesian inference unit
The reception according to claim 1, further comprising a Kalman gain update unit that updates the Kalman gain by multiplying the Kalman gain of the Kalman filter by the probability density function calculated by the probability density function calculation unit. Signal processing device. The probability density function calculation unit
By substituting φ (k), which is the cumulative phase noise calculated by the cumulative phase noise calculation unit, into the following approximate expression, the probability density function p [φ (k)] is calculated. The received signal processing device according to claim 3.
[Approximate formula]

In the approximate expression, k is a sample number of the received signal. min {x, y} is a mathematical symbol indicating that the smaller of x and y is selected. The weight update unit
When the phase noise is Bayesian estimated by the Bayesian estimation unit, the cumulative phase noise calculation unit that calculates the cumulative phase noise by accumulating the estimated values of the phase noise, and the cumulative phase noise calculation unit.
It is provided with a probability density function calculation unit that calculates a unit step function that returns a value corresponding to a comparison result between the cumulative phase noise calculated by the cumulative phase noise calculation unit and a threshold value as a probability density function of the cumulative phase noise.
The Bayesian inference unit
The reception according to claim 1, further comprising a Kalman gain update unit that updates the Kalman gain by multiplying the Kalman gain of the Kalman filter by the probability density function calculated by the probability density function calculation unit. Signal processing device. The probability density function calculation unit
By substituting φ (k), which is the cumulative phase noise calculated by the cumulative phase noise calculation unit, and φ _th , which is the threshold value, into the following calculation formula, U [φ (k), which is the unit step function, is used. The received signal processing apparatus according to claim 5, wherein −φ _{th] is calculated.}
[Calculation formula]

In the calculation formula, k is a sample number of the received signal. The Bayesian estimation unit Bayes estimates the phase noise contained in the polarization signal indicating the polarization state of the received signal on which the symbol time series is superimposed by using the Kalman filter, and uses the estimated value of the phase noise. , The phase noise contained in the polarization signal is removed,
When the weight update unit Bayesian estimates the phase noise by the Bayesian estimation unit, the weight update unit accumulates the estimated values of the phase noise, and the Kalman filter calculates a probability density function based on the accumulated phase noise which is the accumulated estimated value. A received signal processing method for causing the Bayesian inference unit to update the Kalman gain by multiplying the Kalman gain of. A photoelectric conversion unit that converts a received signal on which a symbol time series is superimposed from an optical signal to an electrical signal,
An analog-to-digital converter that converts the electrical signal from an analog signal to a digital signal,
The Kalman filter is used to Bayesi estimate the phase noise contained in the polarization signal indicating the polarization state of the digital signal, and the estimated value of the phase noise is used to estimate the phase noise contained in the polarization signal. Bayesian estimation unit to remove
When the phase noise is Bayesian estimated by the Bayesian inference unit, the estimated values of the phase noise are accumulated, and the probability density function calculated based on the accumulated estimated value is multiplied by the Kalman gain of the Kalman filter. By doing so, the weight update unit that causes the Bayesian estimation unit to update the Kalman gain, and
An optical receiver including a demodulation unit that converts a polarized signal from which phase noise has been removed by the Bayesian estimation unit into a bit time series.

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