CN114124241A - Polarization demultiplexing method based on Stokes space - Google Patents
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Abstract
The invention provides a polarization demultiplexing method based on Stokes space, which is realized based on a local oscillator CV-QKD system and comprises the following steps: step 1, converting the receiving end electric signal after random deflection interference into a complex form, and calculating a Stokes space vector of the receiving end electric signal; step 2, finding out a clustering point coordinate value of the Stokes space vector through a clustering algorithm; step 3, calculating the phase difference between the polarization rotation angle and the orthogonal polarization state through the coordinates of the clustering points; step 4, calculating a corresponding Jones matrix according to the polarization rotation angle and the orthogonal polarization phase difference; and 5, calculating the receiving end electric signal in the complex form and the Jones matrix to obtain a signal after polarization demultiplexing. The scheme provided by the invention can avoid the performance reduction of the CV-QKD system caused by the polarization crosstalk of the receiving end. Meanwhile, the algorithm has the characteristics of simplicity in implementation, independence of modulation modes, high convergence speed and the like, and the reliability and flexibility of the system can be greatly improved.
Description
Technical Field
The invention relates to the technical field of communication, in particular to a polarization demultiplexing method based on Stokes space.
Background
In recent years, network security accidents often occur and directly threaten the stability of the real world, and the network security becomes a problem to be faced. Although the traditional encryption means and the evolution technology thereof can further strengthen the network security defense line, the vulnerability inevitably occurs and affects the network system. Therefore, a more secure and reliable technique is sought to secure the network. The quantum secret communication provides a potential technical approach for guaranteeing the future network security by using the absolute physical security characteristic of the quantum secret communication. Through decades of development, quantum secure communication has slowly focused on quantum key distribution technology, and meanwhile, in order to improve the compatibility of the quantum key distribution technology and the existing communication system, research emphasis is also on transition from discrete variables to continuous variables.
In order to overcome the challenges of high cost, poor compatibility with the existing communication system and the like of a discrete variable quantum key distribution system, continuous variable Gaussian modulation protocols were proposed by both Grosshans and Grangier as early as 2002. This work demonstrates that the gaussian modulation scheme generated by mature optical communication devices also has security equivalent to a single optical subsystem. In addition, a.levverier et al proposed and demonstrated a continuous variable discrete modulation quantum key distribution protocol in 2009, which further enhanced the compatibility of quantum key distribution systems with optical communication systems. In 2020, Tobias A.Eriksson et al realized 194 wavelength multiplexing continuous variable quantum key distribution systems by using wavelength division multiplexing systems, and realized a transmission system for safely transmitting 25-km standard single mode fiber at a rate of 172.6-Mbit/s by using 500-MBaud QPSK signal experiments. In the same year, at the fiber optic communications convention (OFC' 2020) held in san Diego, USA,
the experiments of the people prove thatThe transmission performance of quantum signals under the condition of classical optical signal common-fiber transmission. In summary, the quantum key distribution technology has become more and more practical in this short time of less than 20 years. In the present stage, the CV-QKD system mainly comprises a channel associated local oscillator and a local oscillator, and the local oscillator CV-QKD system becomes a research hotspot in recent years due to the characteristics of higher safety, higher potential lifting rate and the like. In a local oscillator CV-QKD system, a reference light method is often adopted in order to compensate for the frequency offset of a laser, phase noise, and the influence of an optical fiber link on a signal. In most cases, the beam combination and beam splitting of the reference light and the quantum signal light are realized in a polarization multiplexing mode. Based on this system characteristic, the performance of polarization demultiplexing is directly related to the stability and effectiveness of the CV-QKD system. In the CV-QKD system, polarization demultiplexing has two main methods, optical and electrical. The optical method mainly comprises the steps of monitoring the polarization state of an input signal and adjusting an electric control polarization controller to ensure that the polarization state of an output signal is determined, namely the common polarization deviation corrector. The electrical method is to receive the signals of the I path and the Q path of two orthogonal polarization state signals through a polarization diversity receiver and realize polarization demultiplexing by using a digital signal processing algorithm.
There are various drawbacks to the optical method. Firstly, an optical deviation corrector is added, and the system cost is increased. Secondly, the loss of the receiving end is increased, which is equivalent to reducing the transmission distance with the same loss. In addition, when the change speed of the link polarization state is high, the optical deviation corrector cannot respond in time, and the system performance is directly influenced. The digital signal processing algorithm for polarization demultiplexing mainly comprises a Constant Modulus Algorithm (CMA), a Kalman filter and a polarization demultiplexing algorithm based on Stokes space. The first two algorithms adopt a balanced filtering mode to realize tracking and demultiplexing of polarization, and the algorithm complexity is relatively high. The Stokes algorithm tracks the rotation angle of the polarization state in Stokes space by converting the signal into Stokes space to implement polarization demultiplexing. In the CV-QKD system, reference light is stronger than quantum signal light, so that only one clustering point is represented in a Stokes space, thereby easily finding a polarization rotation angle, and the algorithm complexity is relatively simple. Therefore, the polarization demultiplexing algorithm based on the Stokes space in the local oscillator CV-QKD system has high practical value.
Disclosure of Invention
Aiming at the problem of performance deterioration caused by random disturbance of the polarization state of a transmission link in a polarization multiplexing local oscillator CV-QKD system, a polarization demultiplexing method based on Stokes space is provided, the problem of performance reduction of the CV-QKD system caused by polarization crosstalk can be effectively avoided through the method, and the stability and flexibility of the system are further improved.
The technical scheme adopted by the invention is as follows: a polarization demultiplexing method based on Stokes space is realized on the basis of a local oscillator CV-QKD system, a strong light signal is adopted in the CV-QKD system as a reference light and a quantum signal to be respectively loaded on different polarization states of an optical carrier, the quantum signal has weak light intensity, the signal only shows a concentrated clustering point in the Stokes space, and the polarization demultiplexing process is as follows: the method comprises the following steps:
step 2, finding out the coordinate value of the clustering point of the Stokes space vector through a clustering algorithm;
step 4, calculating a corresponding Jones matrix according to the polarization rotation angle and the orthogonal polarization phase difference;
and 5, calculating the receiving end electric signal in the complex form and the Jones matrix to obtain a signal after polarization demultiplexing.
Further, the Stokes space vector calculation method comprises the following steps:
wherein ,EX and EYIs in the form of complex electric field of input signal at receiving end, and represents conjugateAnd j represents an imaginary number.
Further, the method for calculating the phase difference between the orthogonal polarization states comprises the following steps:
if it is
Order to
If it is
Order to
wherein ,
is a phase difference of orthogonal polarization states, [ S ]1(i)；S2(i)；S3(i)]TIs the coordinate value of the clustering point.
Further, the polarization rotation angle calculation method comprises the following steps:
if so
And S3(i)>0，
Or
And S2(i)>0，
Or
And S3(i) Less than or equal to 0, make
If it is not
And S3(i)≤0，
Or
And S2(i)≤0，
Or
And S3(i)>0, order
If α (i) - α (i-1) > pi, let α (i) ═ α (i) -pi; if α (i) - α (i-1) < -pi, let α (i) ═ α (i) + pi;
where α (i) is the polarization rotation angle.
Further, the Jones matrix is:
wherein J is a Jones matrix.
Further, the calculation method of the signal after polarization demultiplexing is as follows:
[Eoutx(i)；Eouty(i)]T＝J·[Ex(i)；Ey(i)]T
wherein ,[Eoutx(i)；Eouty(i)]TFor the demultiplexed signal, [ Ex(i)；Ey(i)]TIs a complex electric field form of the input signal at the receiving end.
Further, the clustering algorithm adopts K-means.
Compared with the prior art, the beneficial effects of adopting the technical scheme are as follows:
1) compared with an optical polarization tracking scheme, the invention adopts a digital signal processing technology to realize polarization demultiplexing and improves the flexibility and reliability of the CV-QKD system.
2) Compared with the scheme of polarization demultiplexing by adopting an equilibrium filtering algorithm, the method has the advantages of low algorithm complexity and high convergence speed.
3) And the method is not influenced by carrier frequency offset and phase noise.
4) The low-speed analog-to-digital converter can be used for acquiring data and realizing polarization tracking, and hardware implementation is easy.
Drawings
FIG. 1 shows the structure of the transmitting end of the CV-QKD system in the present invention.
FIG. 2 shows a polarization diversity receiving structure of the CV-QKD system in the present invention.
FIG. 3 is a schematic diagram of polarization state rotation of signals in Stokes space according to the present invention.
Fig. 4 is a flow chart of digital signal processing at the receiving end in the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The invention provides a polarization demultiplexing method based on a Stokes space, which is realized based on a CV-QKD system and a local oscillator CV-QKD system, wherein a strong light signal is adopted in the CV-QKD system as a reference light and a quantum signal to be respectively loaded on different polarization states of an optical carrier, the light intensity of the quantum signal is weak, the signal only shows one concentrated clustering point in the Stokes space, and the structure of the system is firstly explained in the embodiment.
As shown in fig. 1, which is a transmitting end structure of the CV-QKD system provided in this embodiment, after an optical carrier is emitted by a laser at a transmitting end, an optical signal is split into two paths by a beam splitter. One path generates reference light, the reference light is not limited to the additional time division multiplexing and frequency division multiplexing, and the optical power and the polarization state of the path of optical signal are respectively controlled by the optical attenuator 1 and the polarization controller 1, so that the optical power of the reference light is in a reasonable range and the polarization state is aligned with the main axis of the polarization beam combiner. Similarly, the other optical signal loads the key to be transmitted, where the adopted modulation mode may be gaussian modulation, discrete modulation, and the like, and the quantity is obtained through the optical attenuator 2 and the polarization controller 2A sub-optical signal. Finally, the two optical signals are synthesized by a polarization beam combiner to obtain a multiplexing signal
In order to obtain complete phase and amplitude information on two orthogonal polarization multiplexed signals, the CV-QKD system polarization diversity reception architecture shown in fig. 2 is employed in the present embodiment. The optical signal is transmitted and enters a receiver, and is first divided into two polarization directions by a polarization beam splitter 1(PBS 1). Meanwhile, optical signals output by the local oscillator laser are input into the PBS2 in a mode of forming an included angle of 45 degrees with the main shaft of the PBS2 and are equally divided into two local oscillator optical signals. The optical signals output by the two PBSs interfere in the polarization maintaining couplers 1 and 2, respectively, and are input to the balanced detectors 1 and 2, respectively, for detection. Finally, electrical signals 1 and 2 are obtained, respectively. The scheme acquires the phase and amplitude information of the signal by detecting the intermediate frequency signal and utilizing a digital IQ demodulation mode. Compared with a mode of detecting a baseband signal by adopting a 90-degree mixer, the scheme can reduce the loss of a receiving end and further equivalently improve the transmission distance. Of course, in another embodiment, the polarization demultiplexing method proposed by the present invention can also be adopted in a polarization diversity system that uses a 90-degree mixer for baseband signal detection.
Fig. 3 is a schematic diagram illustrating the rotation of the polarization state of the signal in the Stokes space in this embodiment, and under a normal condition, if the polarization main axis of the signal at the transmitting end is aligned with the polarization main axis at the receiving end, the reference optical signal and the quantum optical signal can be completely distinguished theoretically. However, polarization disturbance exists in the transmission process, and the main axes of the transceiving ends are difficult to maintain the alignment relationship. The polarization change relationship between the transmitting end and the receiving end can be generally expressed by a Jones matrix as shown in formula (1):
wherein, α and
respectively representing the polarization rotation angle and the phase difference between the X polarization state and the Y polarization state, and the tracking precision of the polarization rotation angle and the phase difference is mainly determined by the intensity ratio of the reference light and the quantum signal light. Obviously, to demultiplex the signal at the receiving end, the sum of α needs to be known
These two values. Thus, Stokes space is introduced to obtain alpha and
firstly, the Jones vector needs to be converted into the Stokes vector, and for the transmitting end signal, the conversion is as shown in formula (2):
wherein ,[Stx1；Stx2；Stx3]TFor the sender Stokes vector, "+" indicates a conjugate, and j indicates an imaginary number. In general, the Stokes vector is normalized by the total power. Since the reference light is much stronger than the optical power of the quantum signal light, the distribution of the transmitting-end signal in the Stokes space finally appears as [ 1; 0; 0]TThis point. According to the transformation relation between the Jones matrix and the Muller matrix, the change relation of polarization in Stokes space can be obtained by combining the formula (1) as shown in the formula (3):
wherein ,[Srx1；Srx2；Srx3]TAnd the receiver-side Stokes vector. Therefore, the distribution of the receiving end signal in the Stokes space finally appears as shown in FIG. 3
This point. It is obvious that by finding the clustering point in the Stokes space of the received signal, it is assumed that its value is [ S ]1；S2；S3]TThe sum of α can be obtained by the formula (4)
Fig. 4 is a flowchart of the digital signal processing at the receiving end in the present embodiment. The specific process comprises the following steps:
1) and (4) band-pass filtering. Noise except the intermediate frequency signal can be filtered by a digital band-pass filter;
2) digital IQ demodulation, which respectively obtains phase and amplitude information of two orthogonal polarization signals;
3) polarization demultiplexing;
4) extracting quantum signals on corresponding polarization states;
5) and (4) matched filtering. Under the condition that a transmitting end adopts a root raised cosine filter to perform shaping filtering on a signal, a receiving end adopts a corresponding root raised cosine filter to realize matched filtering and low-pass filtering;
6) and (6) resampling. Resampling the signal to 2 times oversampling;
7) and (5) signal equalization filtering. The method is used for compensating the influence of the link on the signal, residual phase noise and the like;
8) and (6) parameter estimation. Calculating parameters such as over noise, signal-to-noise ratio, bit error rate and the like of a transmission system;
9) and (6) post-processing the data. The method mainly comprises error correction, privacy enhancement and security authentication.
The invention provides a polarization demultiplexing method in Stokes space aiming at the polarization demultiplexing step, which comprises the following specific processes:
Step 2, finding out coordinate value [ S ] of clustering point of Stokes space vector through clustering algorithm1(i)；S2(i)；S3(i)]T；
Step 4, calculating a corresponding Jones matrix according to the polarization rotation angle and the orthogonal polarization phase difference;
and 5, calculating the receiving end electric signal in the complex form and the Jones matrix to obtain a signal after polarization demultiplexing.
Specifically, the Stokes space vector calculation method includes:
wherein ,EX and EYIs a complex electric field form of the input signal at the receiving end.
The method for calculating the phase difference of the orthogonal polarization state comprises the following steps:
if it is
Order to
If it is
Order to
wherein ,
is a phase difference of orthogonal polarization states, [ S ]1(i)；S2(i)；S3(i)]TIs the coordinate value of the clustering point.
The polarization rotation angle calculation method comprises the following steps:
if so
And S3(i)>0，
Or
And S2(i)>0，
Or
And S3(i) Less than or equal to 0, make
If it is not
And S3(i)≤0，
Or
And S2(i)≤0，
Or
And S3(i)>0, order
If α (i) - α (i-1) > pi, let α (i) ═ α (i) -pi; if α (i) - α (i-1) < -pi, let α (i) ═ α (i) + pi;
where α (i) is the polarization rotation angle.
A and
the method has the slow-changing characteristic, and polarization rotation angle and phase difference value jumping caused by calculation errors can be avoided by comparing the difference values of the calculation results of the previous time and the subsequent time.
And obtaining a Jones matrix J according to the polarization rotation angle and the phase difference of the orthogonal polarization state:
the polarization demultiplexed signal can be calculated from the Jones matrix:
[Eoutx(i)；Eouty(i)]T＝J·[EX(i)；EY(i)]T
wherein ,[Eoutx(i)；Eouty(i)]TFor the demultiplexed signal, [ EX(i)；EY(i)]TIs a complex electric field form of the input signal at the receiving end.
In this embodiment, the clustering algorithm preferably uses K-means.
The polarization demultiplexing method provided by the invention avoids the calculation ambiguity in the calculation of the polarization rotation angle alpha by classifying and distinguishing all parameters; the pure digital signal processing mode is adopted to realize polarization demultiplexing between the reference light signal and the quantum signal light in the CV-QKD system, and is irrelevant to the modulation mode of the quantum signal.
The invention is not limited to the foregoing embodiments. The invention extends to any novel feature or any novel combination of features disclosed in this specification and any novel method or process steps or any novel combination of features disclosed. Those skilled in the art to which the invention pertains will appreciate that insubstantial changes or modifications can be made without departing from the spirit of the invention as defined by the appended claims.
All of the features disclosed in this specification, or all of the steps in any method or process so disclosed, may be combined in any combination, except combinations of features and/or steps that are mutually exclusive.
Any feature disclosed in this specification may be replaced by alternative features serving equivalent or similar purposes, unless expressly stated otherwise. That is, unless expressly stated otherwise, each feature is only an example of a generic series of equivalent or similar features.
Claims (7)
1. The polarization demultiplexing method based on the Stokes space is characterized in that the polarization demultiplexing method is realized based on a local oscillator CV-QKD system, a strong light signal is adopted in the CV-QKD system as a reference light and a quantum signal to be respectively loaded on different polarization states of an optical carrier, the light intensity of the quantum signal is weak, the signal only shows a concentrated clustering point in the Stokes space, and the polarization demultiplexing process is as follows:
step 1, converting the receiving end electric signal after random deflection interference into a complex form, and calculating a Stokes space vector of the receiving end electric signal;
step 2, searching a clustering point coordinate value of the Stokes space vector calculated in the step 1 by taking a clustering point as a target through a clustering algorithm;
step 3, directly calculating the phase difference between the polarization rotation angle and the orthogonal polarization state through the coordinate values of the clustering points;
step 4, calculating a corresponding Jones matrix according to the polarization rotation angle and the orthogonal polarization phase difference;
and 5, calculating the receiving end electric signal in the complex form and the Jones matrix to obtain a signal after polarization demultiplexing.
2. The Stokes space-based polarization demultiplexing method according to claim 1, wherein said Stokes space vector calculation method is:
wherein ,EX and EYIs a complex electric field form of the input signal at the receiving end, "+" indicates conjugation, and j indicates an imaginary number.
3. The Stokes space-based polarization demultiplexing method according to claim 2, wherein the orthogonal polarization state phase difference calculation method is:
if it is
Order to
If it is
Order to
wherein ,
is a phase difference of orthogonal polarization states, [ S ]1(i)；S2(i)；S3(i)]TIs the coordinate value of the clustering point.
4. The Stokes space-based polarization demultiplexing method according to claim 3, wherein the polarization rotation angle calculation method is:
if so
And S3(i)>0，
Or
And S2(i)>0，
Or
And S3(i) Less than or equal to 0, make
If it is not
And S3(i)≤0，
Or
And S2(i)≤0，
Or
And S3(i)>0, order
If α (i) - α (i-1) > pi, let α (i) ═ α (i) -pi; if α (i) - α (i-1) < -pi, let α (i) ═ α (i) + pi;
where α (i) is the polarization rotation angle.
5. The Stokes space-based polarization demultiplexing method according to claim 4, wherein the Jones matrix is:
wherein J is a Jones matrix.
6. The Stokes space-based polarization demultiplexing method according to claim 5, wherein the calculation method of the polarization demultiplexed signals is:
[Eoutx(i)；Eouty(i)]T＝J·[EX(i)；EY(i)]T
wherein ,[Eoutx(i)；Eouty(i)]TFor the demultiplexed signal, [ EX(i)；EY(i)]TIs a complex electric field form of the input signal at the receiving end.
7. The Stokes-space based polarization demultiplexing method according to claim 1, wherein the clustering algorithm employs K-means.
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