CN104836774B - A kind of PDL effect compensation methods of high-order continuous polarization modulation - Google Patents

Abstract

The invention discloses a compensation method for the PDL effect in high-order continuous polarization modulation. First, the influence of the PDL effect on the high-order continuous polarization modulation signal is analyzed. Secondly, a method to eliminate the PDL effect by using pre-compensation is proposed. In this method, since the division of the decision area at the receiving end is closely related to the polarization angle of the received polarization state, in order to obtain the optimal compensation effect, an optimal pre-compensation with the maximum polarization angle as the decision criterion is designed factor. Finally, the theoretical and simulation analysis shows that this method can effectively improve the bit error performance of high-order continuous polarization modulation affected by the PDL effect, and then improve the spectral efficiency of high-order continuous polarization modulation.

Description

A PDL Effect Compensation Method for High-Order Continuous Polarization Modulation

technical field

The invention belongs to the technical field of wireless communication, is a method for combating PDL effect based on pre-compensation, and in particular relates to a PDL effect compensation method for high-order continuous polarization modulation.

Background technique

In a wireless communication system, the complexity of the wireless signal propagation environment itself leads to very complex wireless channel characteristics. However, complex wireless channel characteristics will produce complex and changeable depolarization effects, such as polarization mode dispersion (Polarization Mode Dispersion: PMD) polarization dependent loss (Polarization Dependent Loss: PDL) effect, which will seriously affect The polarization state of the transmitted signal. Under single-carrier conditions, the power attenuation characteristic shown on the channel depolarization characteristic is called polarization-dependent attenuation PDL. The researchers found that after the high-order continuous polarization modulation in the single-carrier scenario is affected by PDL, the polarization state will rotate and shrink or spread before the signal reaches the receiver, so that the constellation structure of the high-order continuous polarization modulation MCPM Distortion occurs, thereby reducing the data rate correctly received by the receiving end, and finally leading to the deterioration of the performance of high-order continuous polar modulation MCPM.

In high-order discontinuous polarization modulation, the researchers proposed an algorithm based on pre-compensation to combat the PDL effect. DongWei et al. (Dong Wei, Chunyan Feng, Caili Guo and Fangfang Liu, "A power amplifier energy efficient polarization modulation scheme based on the optimal pre-compensation," IEEE Communications Letters, 2013:513-516) pointed out that the larger the pre-compensation factor ε , the greater the distance between the constellation points of the polarization state of the signal at the receiving end, the smaller the distortion of the constellation structure, and the compensated polarization state will suffer from more serious power attenuation, which makes it impossible to take both power attenuation and The constellation is distorted, and the reduction of the constellation distortion will definitely bring serious power attenuation. In addition, based on channel changes, an adaptive method is used to select the modulation order of polar modulation to effectively counteract the influence of the PDL effect, so the modulation order changes with channel conditions.

Contents of the invention

The invention provides a precompensation method based on the high-order continuous polarization modulation technology of the PDL depolarization channel, aiming at reducing the influence of the PDL effect on the MCPM.

According to the mechanism of continuous polarization state realization of high-order continuous polarization modulation, that is, under the condition of a certain phase difference, the continuous polarization state is realized through the continuous amplitude ratio, that is, the polarization angle, and the polarization vector is on the same Poincaré sphere. The great circle rotates continuously. Due to the PDL effect of the wireless channel, the polarization state of MCPM will have different degrees of attenuation in the interval of sending symbols. Starting from reducing the impact of the PDL effect on MCPM, the present invention proposes a method based on pre-compensation to combat the PDL effect, that is, to obtain the optimal compensation factor based on the criterion of maximizing the polarization angle, and to ensure a larger decision area at the receiving end , thereby effectively reducing the impact of the PDL effect on the bit error rate.

A PDL effect compensation method for high-order continuous polarization modulation according to the present invention: at the transmitting end, the difference degree of the channel matrix eigenvalue is reduced by pre-compensating the continuous polarization state of the transmitted MCPM signal, so that the receiving end The distance between the constellation points of the polarization state of the signal is increased, the distortion of the constellation structure is reduced, and the performance of the MCPM is improved.

A PDL effect compensation method for high-order continuous polarization modulation, the specific steps are as follows:

Step 1: Compensating the continuous polarization state output by the polarization state mapping unit;

(1) Since the high-order continuous polarization modulation carries information through the change of the polarization state on a great circle, the unitary matrices U and V obtained after the singular value decomposition of the wireless channel cause the rotation of the continuous polarization state vector It does not affect the demodulation of the high-order continuous polarization modulation signal at the receiving end, and the influence of the unitary matrix on the continuous polarization modulation signal can be ignored, so that the high-order continuous polarization modulation signal received by the receiver can be simplified as:

(2) Compensate the polarization state output by the transmitter polarization state mapping unit, that is, multiply the continuous polarization state at each moment by the pre-compensation matrix and record it as C _P :

Among them, ε(1≤ε≤λ ₁ /λ ₂ ) is defined as the pre-compensation factor;

(3) The influence of the wireless channel on the continuous polarization state of the high-order continuous polarization modulation after precompensation is:

(4) The degree of the wireless channel PDL effect can be changed by adjusting the size of the pre-compensation factor ε. As ε increases, the degree of channel difference will decrease, and the distance between constellations will gradually increase, that is, the distortion will gradually decrease. In order to obtain the best pre-compensation effect, the optimal pre-compensation factor is obtained by maximizing the polarization angle, which can be specifically expressed as:

Step 2: Sampling at the receiving end, and obtaining the corresponding optimal pre-compensation according to the polarization angle of the polarization state obtained by sampling;

(1) The sampling at the receiving end is the sampling at the end of the transmission of the transmitted symbol, and we get:

(2) Calculate and obtain the corresponding optimal pre-compensation ε ^* :

From the above formula, it can be found that as ε increases, the difference between the polarization angle of the polarization state at the sending end and the polarization angle of the polarization state sampled at the receiving end at the end of the parity sequence transmission will become smaller and smaller. Therefore, in the process of selecting the pre-compensation factor, ε can be maximized to obtain the best pre-compensation ε ^* .

Advantages of the present invention:

1. The present invention is based on high-order continuous polarization modulation, the constellation points are always located on the same plane, and the polarization state of the signal is used to carry information.

2. The present invention performs PDL pre-compensation on the continuous polarization state at the transmitting end to reduce constellation distortion;

3. The present invention adopts the selection mechanism of the optimal pre-compensation factor, effectively solving the contradiction between power attenuation and constellation distortion that cannot be optimized at the same time;

4. Compared with the high-order continuous polarization modulation without pre-compensation, the present invention has improved spectrum efficiency and correspondingly reduced bit error performance.

Description of drawings

Fig. 1 is the realization block diagram of pre-compensation among the present invention;

Fig. 2 is the trajectory comparison curve before and after the continuous polarization state is subjected to PDL in the present invention;

Fig. 3 is the bit error rate curve of 2nd order CPM among the present invention;

Fig. 4 is the bit error rate curve of 4th order CPM among the present invention;

Fig. 5 is the spectrum efficiency comparison curve of 2nd-order CPM among the present invention;

Fig. 6 is the spectrum efficiency comparison curve of 4th order CPM among the present invention;

Fig. 7 is a flow chart of the method of the present invention.

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings.

The invention proposes a PDL effect compensation method for high-order continuous polarization modulation.

In a wireless communication system, the complexity of the wireless signal propagation environment itself leads to very complex wireless channel characteristics. However, complex wireless channel characteristics will subsequently produce complex and changeable depolarization effects, such as polarization mode dispersion PMD and polarization-dependent attenuation PDL effects, which will seriously affect the polarization state of the transmitted signal. Under single-carrier conditions, the power attenuation characteristic shown on the channel depolarization characteristic is called polarization-dependent attenuation PDL. After the high-order continuous polarization modulation in the single-carrier scenario is affected by PDL, the polarization state will rotate, shrink or spread before the signal reaches the receiver, which will distort the constellation structure of MCPM, thereby reducing the decoding efficiency of the receiver. Finally, it leads to the deterioration of the performance of high-order continuous polarization modulation MCPM.

The present invention reduces the difference degree of channel matrix eigenvalues by pre-compensating the continuous polarization state of the transmitted MCPM signal at the transmitting end, thereby increasing the constellation point distance of the polarization state of the signal at the receiving end. Since the constellation points of high-order continuous polarization modulation are always on the same plane, the division of the decision domain in the decision process at the receiving end mainly depends on the size of the polarization angle. In order to minimize the influence of the PDL effect on the performance of the MCPM, the present invention proposes to obtain the best pre-compensation factor by optimizing the criterion of maximizing the polarization angle.

The PDL effect compensation method of high-order continuous polarization modulation proposed by the present invention includes pre-compensation, maximum polarization angle and spectrum efficiency analysis, etc. The specific steps are as follows:

Step 1: Assume that the channel information can be completely obtained at the transmitting end, and the channel information remains unchanged in each transmission symbol interval. According to the channel information obtained by the transmitting end, the continuous polarization state output by the polarization state mapping unit can be compensated;

The block diagram of pre-compensation implementation is shown in Figure 1, s _I is the channel information obtained by the transmitter, It is a sequence of binary numbers, and the precompensation block diagram mainly includes two modules, that is, the precompensation unit and the continuous polarization state control unit.

(1) Since the high-order continuous polarization modulation carries information through the change of the polarization state on a great circle, the unitary matrices U and V obtained after the singular value decomposition of the wireless channel cause the rotation of the continuous polarization state vector It does not affect the demodulation of the high-order continuous polarization modulation signal at the receiving end, and the influence of the unitary matrix on the continuous polarization modulation signal can be ignored, so that the high-order continuous polarization modulation signal received by the receiver can be simplified as:

(2) According to the influence of the wireless channel PDL effect on the polarization state of the receiving end of the high-order continuous polarization modulation and the channel information obtained at the transmitting end, the polarization state output by the polarization state mapping unit of the transmitter is compensated, namely The continuous polarization state at each moment is multiplied by the precompensation matrix and recorded as C _P :

Among them, ε(1≤ε≤λ ₁ /λ ₂ ) is defined as the pre-compensation factor;

(3) The influence of the wireless channel on the continuous polarization state of the high-order continuous polarization modulation after precompensation is:

ρ'(t)＝λ ₁ cos ² γ(t)+ελ ₂ sin ² γ(t) (5)

It can be seen from the above analysis that the degree of the PDL effect of the wireless channel can be changed by adjusting the size of the pre-compensation factor ε. As ε increases, the degree of channel difference will decrease, and the distance between constellations will gradually increase, that is, the distortion will gradually decrease; when ε=λ ₁ /λ ₂ , the channel PDL effect will completely disappear.

(4) In order to obtain the best pre-compensation effect, it is necessary to design a reasonable pre-compensation factor ε. Here, according to the characteristics of high-order continuous polarization modulation, an innovative method is proposed to obtain the optimal pre-compensation factor by maximizing the polarization angle , which can be specifically expressed as:

The specific analysis is as follows. First, the polarization vector of high-order continuous polarization modulation runs along a specific great circle trajectory, and the constellation points are always located on the same great circle. After analysis, it can be found that the PDL effect will only affect the amplitude of the polarization state , fundamentally affects the polarization angle of the polarization state. After the continuous polarization state is affected by PDL, the continuity of the polarization state is not destroyed, and the polarization state always rotates on the Poincaré sphere along a continuous trajectory in each transmission interval of the transmitted signal. Compared with high-order discontinuous polarization modulation, the constellation points of high-order continuous polarization modulation are always located on the same plane, and the division of the judgment domain in the judgment process of the receiving end mainly depends on the size of the polarization angle; within a certain power attenuation limit , minimize the influence of the PDL effect on the polarization angle, and the sequence of the transmitted signal can be fully recovered at the receiving end. Therefore, according to the above analysis, the present invention proposes to obtain the optimal pre-compensation factor by optimizing the criterion of maximizing the polarization angle.

Step 2: Sampling at the receiving end, and obtaining the corresponding optimal pre-compensation according to the polarization angle of the polarization state obtained by sampling;

(1) The polarization state of the high-order continuous polarization modulation is always continuous within the symbol interval of the transmission signal transmission, and the demodulation scheme at the receiving end is to decode the transmission sequence according to the change of the polarization state of the odd and even samples respectively, so In the process of designing and selecting pre-compensation, in order to simplify the analysis, it is assumed that the sampling at the receiving end is just at the end of the transmission of the transmitted symbol, so that:

(2) Under certain conditions of PDL and modulation technology M, if the polarization angle of the polarization state of the transmitting end is recorded as 2γ(t), the standard sample point is obtained by sampling the polarization state at the end of the parity symbol transmission, and the signal passes through After the influence of the PDL effect, the polarization angle of the polarization state obtained by sampling at the receiving end at the transmission time of the odd and even symbols is expressed as:

After introducing the precompensation matrix, the polarization angle of the polarization state at the receiving end becomes:

(3) According to the above analysis, the corresponding optimal pre-compensation ε* can be calculated:

That is, the polarization angle of the polarization state of the sending end is compared with the polarization state angle obtained by sampling the polarization state at the end of the odd-even sequence transmission at the receiving end, and the minimum value of the difference between the two is obtained after pre-compensation; through the above formula, it can be found that , as ε increases, the difference between the two will become smaller and smaller; at the same time, it can be seen that the size of ε is linearly related to the polarization angle of the receiving end, that is, the larger ε is, the larger the polarization angle of the receiving end will be . Therefore, ε can be maximized as far as possible in the selection process.

Step 3: Simulation results and spectrum performance and bit error rate performance analysis;

Relevant instructions on the spectrum performance of the algorithm of the present invention:

The spectral efficiency of MCPM is related to the transmission rate of the signal and the bandwidth of the intermediate frequency. Here, after considering the channel PDL effect, the signal rate is now defined as the correct symbol sequence received by the receiving end, and the spectral efficiency can be defined as:

Among them, R _e is the original transmission data rate, W is the bandwidth of the IF filter at the receiving end, and the size of W is determined by ξ;

ξ is defined as:

In the formula, G(f) represents the power spectral density of the transmitted signal, and ξ is defined as the ratio of the received effective power to the total power, that is, the power utilization ratio. For different modulation systems, due to the difference in signal power spectral density, the system bandwidth required to achieve the same power utilization is different, so the spectral efficiency is also different.

It should be noted that in the process of analyzing the spectral efficiency under the influence of the PDL effect, it is assumed that the influence of the channel on the amplitude of the power spectrum of the MCPM signal is negligible, and only the influence of the channel on the data rate of the transmitted information is considered here. It can be obtained from the above formula that under the condition of a certain IF bandwidth, that is, under the condition of the power utilization rate of the signal, the lower the correctly received data rate, the lower the spectral efficiency of the signal, which means that the bit error rate of MCPM The larger it is, the lower its spectral efficiency will be.

Simulation results:

The simulation condition is that the channel PDL value is 1.2589dB, and 1>λ ₁ ≥λ ₂ >0. During the simulation process, it is also assumed that λ ₂ =λ ₁ /PDL, the bit rate of information transmission R _b =1kbit, and the bit rate of each bit of information Symbol interval T _b =1 ms.

First of all, as shown in Figure 2, the trajectory of the continuous polarization vector z(t) of the high-order continuous polarization modulation MCPM before and after being affected by the channel PDL effect is compared; secondly, the present invention sets three kinds of simulation environments, and in turn only considers AWGN channel, PDL channel affected by channel PDL effect and precompensated.

Figure 5 and Figure 6 show the spectrum efficiency comparison curves before and after channel PDL influence. Wherein, FIG. 5 is a comparison curve of spectral efficiency of second-order continuous polarization modulation, and FIG. 6 is a comparison curve of spectral efficiency of fourth-order continuous polarization modulation. From these two comparison figures, it can be seen that the spectral efficiency of the second-order continuous polarization modulation not affected by the channel PDL effect is the highest, the spectral efficiency after precompensation is second, and the spectral efficiency of uncompensated is the worst. This difference is similar to that of The bit error rate performance is related. The reason for the above changes is affected by the channel PDL effect. The uncompensated bit error rate is the worst, which means that the receiving end receives less effective information, making its spectral efficiency the worst. , the other two curves can be obtained in the same way. The variation of the spectral efficiency of the fourth-order continuous polarization modulation is similar to that of the second-order continuous polarization modulation. And, at the same time, it can be found that with the increase of E _b /N ₀ , the spectral efficiency will become larger and larger, because the larger the E _b /N ₀ is, the smaller the bit error rate of the signal is, and the correctly received symbol sequence The more , the spectral efficiency will increase accordingly; in addition, in the case of the same E _b /N ₀ , the spectral efficiency of the fourth-order continuous polarization modulation is twice that of the second-order continuous polarization modulation. When sending the same rate information When , using a higher order can improve the spectral efficiency, which is consistent with the existing theory.

Relevant explanations about the bit error rate performance of the method of the present invention:

Due to the effect of the channel PDL effect, the polarization state of the receiving end will shrink and rotate in different degrees, and its decision domain will be reduced, which will increase the bit error rate of MCPM. Next, analyze the impact of the bit error rate of MCPM on the PDL effect .

When the phase difference is constant, the polarization state is located on a constant great circle, and the distribution of the received signal polarization vector Z` on the Poincaré sphere is represented by three parameters (ρ, θ, φ), where ρ represents the received polarization state The distance from the center of the sphere, (θ,φ) is the polarization phase descriptor, where the distribution function of θ is expressed as follows:

where _Eb is the energy per bit of information, β spectral efficiency, _N0 is the power spectral density of Gaussian white noise, - signal-to-noise ratio per bit of signal, t is the distribution function variable.

The expression of bit error rate:

In the formula, n=2, θ ₁ =π/2, the size of θ ₀ depends on the modulation order used, and according to the division of the maximum likelihood decision area, θ ₀ =π/M. l is the distribution function variable, the bit error rate expression of continuous polarization modulation:

The high-order continuous polarization modulation MCPM is affected by the PDL effect, and its amplitude ratio changes from tanγ(t) to If it is assumed that the power of the transmitted signal is 1, that is, the polarization state changes continuously along the selected great circle on the unit Poincaré sphere. After the channel PDL effect acts, the polarization state at different moments changes to different degrees. The energy of the polarization state decays from unit 1 to ρ(t); the polarization states at different moments are still located on the same spherical surface, so the formula (14) still satisfies n=2, θ _{1 =} π/2, however, it is believed that Due to the influence of the PDL effect of the channel, the size of the decision area is no longer equal to M parts, that is, θ ₀ ≠ π/M, but the size of θ ₀ needs to be calculated at each sampling time according to different modulation orders M. Take M=2 or 2CPM as an example,

When M=2, the polarization angle of the polarization state obtained by sampling the end moment of each symbol at the transmitting end is expressed as follows:

where n∈(0,1,2,...,M/2). The phase descriptor of Jones vector, γ(t) is:

Similarly, the phase descriptor of its Jones vector, γ'(t), is:

Calculated by the above formula,

And from the definition of SNR, it can be obtained that the receiving SNR of MCPM at the receiving end is affected by PDL:

Substituting equations (20) and (21) into equation (15) can obtain the bit error rate of 2CPM affected by the PDL effect.

After precompensating the channel, the polarization angle at the receiving end is a function of ε:

Then you can get:

Signal-to-noise ratio at the receiver:

Wherein, ρ"(t)=λ ₁ cos ² γ(t)+ελ ₂ sin ² γ(t).

It can be found that with the increase of ε, the polarization angle 2γ”(t), the decision angle θ ₀ and the energy of the received signal will all increase; similarly, substituting Equation (23) into Equation (14) can obtain the predicted Bit error rate expression of MCPM after compensation.Compare the relation of polarization angle 2γ (t) and decision angle θ ₀ , both satisfy:

2θ ₀ =Δ2γ(t) (25)

The larger the polarization angle, the larger the decision angle, and the better the bit error performance of MCPM, which is consistent with the above-mentioned analysis of the influence of PDL on MCPM. At the same time, in the process of solving the bit error rate after the PDL effect, it is important to calculate the size of θ _0. The polarization angles of the polarization states at different sampling moments at the receiving end are different, so that when calculating the bit error rate each time In the process, the polarization angle at the sampling time needs to be solved separately, and then according to the relationship between the polarization angle and the decision angle, the polarization angle at different times is calculated separately to obtain the size of the decision domain, and finally the bit error rate of MCPM is obtained.

Simulation results:

Three simulation environments are set up, which are only considering the AWGN channel, the PDL channel affected by the channel PDL effect and the pre-compensated PDL channel. In the above three environments, the continuous polarization modulation and discontinuous polarization modulation with different modulation orders under different conditions are simulated The bit error rate performance of the modulation.

For different modulation orders, the results affected by the channel PDL effect are different. Figure 3 and Figure 4 respectively show the errors of the second-order advanced continuous polarization modulation and the fourth-order high-order continuous polarization modulation before and after the channel PDL effect. Bit rate comparison curve, and at the same time compared with the bit error rate under the condition of only Gaussian white noise channel. It can be seen from the figure that after the pre-compensation technology is adopted, the bit error rate performance is between the case of only considering the Gaussian white noise channel and the uncompensated PDL effect, that is, the high-order continuous polarity under the condition of only considering Gaussian white noise The best performance of CPM is the best, and then the performance of precompensating high-order CPM at the sending end by selecting the best precompensation factor after being affected by the PDL effect is second, and the performance of high-order CPM without precompensation Worst in comparison. This is because in the process of performing the pre-compensation algorithm, the size of the optimal factor determines the quality of its compensation performance. In practice, it is impossible to achieve the performance before it is not affected, so its performance is not as good as only considering Gaussian Bit Error Rate Performance of Higher Order Continuous Polar Modulation in White Noise Channel.

Claims (2)

1. A PDL effect compensation method of high-order continuous polarization modulation, the specific steps are as follows: Step 1: Compensating the continuous polarization state output by the polarization state mapping unit; Assuming that the channel information can be completely obtained at the transmitting end, and the channel information remains unchanged in each transmission symbol interval, the continuous polarization state output by the polarization state mapping unit is compensated according to the channel information obtained at the transmitting end; (1) The high-order continuous polarization modulation signal received by the receiver is simplified as: in, is the continuous polarization state of the transmitted signal modulated by high-order continuous polarization; x ₁ (t) and x ₂ (t) respectively represent the two components of the continuous polarization state of the transmitted signal, A represents the amplitude of the signal, γ(t ) is the electric field polarization phase descriptor, μ _T (t) represents the unit rectangular function whose duration is T, k represents the kth transmitted symbol, and T _s represents the symbol interval; λ ₁ and λ ₂ are R=H(t) *H(t) The maximum and minimum eigenvalues of ^H , R is the eigenmatrix of the channel matrix H(t), (·) ^H represents the conjugate transpose operation on the matrix: Where: λ ₁ ≥ λ ₂ >0, Tr means the trace of the matrix, Det( ) means the determinant of the matrix; (2) According to the influence of the wireless channel PDL effect on the polarization state of the receiving end of the high-order continuous polarization modulation and the channel information obtained at the transmitting end, the polarization state output by the polarization state mapping unit of the transmitter is compensated, namely The continuous polarization state at each moment is multiplied by the precompensation matrix and recorded as C _P : Among them, ε is the pre-compensation factor, 1≤ε≤λ ₁ /λ ₂ ; (3) The influence of the wireless channel on the continuous polarization state of the high-order continuous polarization modulation after precompensation is: Among them, the matrix Indicates the influence of the precompensated wireless channel on the high-order continuous polarization modulation signal; (4) The optimal precompensation factor is obtained with the criterion of maximizing the polarization angle, specifically expressed as: Step 2: Sampling at the receiving end, and obtaining the corresponding optimal pre-compensation according to the polarization angle of the polarization state obtained by sampling; (1) Assuming that the sampling at the receiving end is the sampling at the end of the transmitted symbol transmission, we get: (2) Calculate and obtain the corresponding optimal pre-compensation ^ε : . 2. According to the PDL effect compensation method of a kind of high-order continuous polarization modulation according to claim 1, the polarization angles of the polarization states at different sampling moments at the receiving end are different, and M=2 or 2CPM is taken as an example for illustration, wherein M represents the modulation order, and CPM represents the continuous polarization modulation method: When M=2, the polarization angle of the polarization state obtained by sampling at the end of each symbol at the transmitting end is expressed as follows: Among them, n∈(0,1,2,...,M/2); After being affected by the channel PDL effect, the polarization angle obtained by sampling the polarization state at the receiving end is: After precompensating the channel, the polarization angle at the receiving end is a function of ε: The transmitter samples at the end of each symbol to obtain the polarization angle of the polarization state, and then calculates the decision angle as follows: And always satisfy θ ₀ = π/2; After being affected by the channel PDL effect, After precompensating the channel, Comparing the relationship between the polarization angle 2γ(t) and the decision angle θ ₀ , the two satisfy: 2θ ₀ =Δ2γ(t) (14) Substitute the θ ₀ calculated after being affected by the channel PDL effect and the θ ₀ calculated after pre-compensating the channel into formula (15), and finally get the bit error rate of 2CPM: In the formula, n=2, f _θ (t) represents the probability density function of the parameter θ of one of the polarization phase descriptors, and f _θ,φ (t,l) represents the joint probability density function of the polarization phase descriptor (θ,φ) , θ ₁ = π/2, the size of θ ₀ depends on the modulation order used, affected by the channel PDL effect, the size of the decision area is no longer equal to M parts, that is, θ ₀ ≠ π/M, but needs According to different modulation orders M, the size of θ ₀ is calculated at each sampling moment, and then the bit error rate is calculated.