CN106330810A - XPD compensation method for improving polarization modulation bit error rate performance - Google Patents

Abstract

The present invention discloses an XPD compensation method for improving polarization modulation bit error rate performance. Firstly, a system model of anti-XPD effect under polarization modulation is established, and the effect of XPD effect on polarization modulation is analyzed. Secondly, a method of compensating a signal at the receiving end against XPD effect is proposed. In this method, channel state information needs to be available, and channel state information is estimated, and a compensation factor is calculated using the estimated channel state information, and the signal is compensated at the receiving end. Finally, theoretical and simulation analysis is obtained. The method can effectively improve the bit error rate performance of polarization modulation affected by the XPD effect.

Description

A kind of XPD compensation method promoting polarization modulation bit error rate performance

Technical field

The invention belongs to wireless communication technology field, be a kind of method of antagonism XPD effect compensated at receiving terminal, Particularly relate to a kind of XPD compensation method promoting polarization modulation bit error rate performance.

Background technology

Polarization modulation, as a kind of novel modulation technique, i.e. utilizes the polarized state carrying information of signal, at channel radio Letter has obtained in-depth study.But the characteristics of radio channels of complexity will produce depolarisation effect complicated and changeable, as intersected Polarization discrimination (Cross Polarization Discrimination:XPD), will have a strong impact on the polarization shape launching signal State.What depolarisation effect XPD described is the Power leakage under dual polarization channel between co-polarization channel and cross polarization channel, by This cross polarization interference caused will seriously change Amplitude Ratio and the phase contrast of the polarized state component receiving signal so that receives End cannot correctly demodulate, and affects polarization modulation performance.

Research currently for depolarisation effect XPD is primarily upon XPD in terms of polarity diversity and pole division multiple access technology Impact.Under polarization MIMO-OFDM system, researcher is by introducing zero forcing algorithm (MIMO-ZF) and the ZF string of mimo channel Row interference cancellation algorithm (ZF-SIC) resists the cross polarization interference between the two paths of signals that XPD brings, thus improves polarization Diversity gain.Multiple access is divided to access (Polarization additionally, researcher proposes a kind of pole under wireless polarization fading channel Division Multiple Access:PDMA) technology, this technology can obtain at receiving terminal by adjusting transmitting polarized signal XPD on each subcarrier, and utilize XPD realize polarization filtering detection obtain desired transmitting signal.But, XPD is to letter Number the impact of polarization modulation of polarized state carrying information require further study.

Summary of the invention

The present invention proposes the compensation method resisting XPD effect in a kind of polarization modulation, it is therefore an objective to promote XPD effects Under polarization modulation bit error rate performance.

XPD can make to occur alternating power leakage to interfere between the polarized state of a certain polarized signal two-way component, The serious Amplitude Ratio changing the polarized state component receiving signal and phase contrast so that receiving terminal cannot correctly demodulate, and affects pole Change modulating performance.From reducing the impact on polarization modulation performance of the XPD effect, the present invention proposes a kind of lifting polarization modulation The XPD compensation method of bit error rate performance, i.e. by analyzing the XPD impact on polar-modulated signal polarized state, utilizes channel shape State information is calculated compensating factor, and compensate in receiving terminal docking collection of letters polarized state, reduces and is brought by XPD Alternating power leaks, and then reduces the constellation distortion of polarization modulation, promotes the bit error rate performance of polarization modulation.

A kind of XPD compensation method promoting polarization modulation bit error rate performance, specifically comprises the following steps that

Step one: set up the system model resisting XPD effect in polarization modulation, analyzes the XPD effect shadow to polarization modulation Ring；

Owing to polarization modulation is the polarized state attribute carrying information utilizing signal, and the depolarisation effect in wireless channel The alternating power leakage that XPD brings can change the polarized state of signal.Therefore it is right to have initially set up in the present invention in polarization modulation The system model of anti-XPD.After double polarization transmission channel, polarized signal can be affected by noise and depolarisation effect XPD. Amplitude Ratio and the phase contrast of the polarized state of receiving end signal change, and show each on Poincare (Poincare) ball and connect The distribution receiving polarized state is a uncertain annulus, i.e. polarized state spreads, thus affects the performance of polarization modulation.

Step 2: estimate channel condition information, utilizes the channel condition information estimating to obtain to be calculated compensation The factor, and at receiving terminal, signal is compensated；

For simplifying the analysis, the present invention uses the most frequently used channel estimation methods, i.e. based on pilot tone channel estimation method Channel condition information is estimated.Estimate ideally at channel, it is assumed that channel in each sends mark space Information keeps constant, is calculated compensating factor.Then at receiving terminal, signal is processed, i.e. to each reception signal Polarized state be multiplied by compensating factor, thus resist the alternating power between the two paths of signals component that depolarisation effect XPD brings Decay, promotes the bit error rate performance of polarization modulation.

Advantages of the present invention:

1, this invention takes novel polar modulation technology, i.e. utilize the polarized state carrying information of signal；

2, channel condition information is estimated by the present invention by channel estimation method, utilizes channel condition information to be mended Repay the factor；

3, the polarizations state by XPD effects is compensated by the present invention at receiving terminal, reduces constellation distortion；

4, before the present invention compares compensation, the bit error rate performance of polarization modulation has the biggest lifting.

Accompanying drawing explanation

Fig. 1 be in the present invention in polarization modulation XPD backoff algorithm realize block diagram；

Fig. 2 is the track correlation curve before and after polarized state is affected by XPD in the present invention；

Fig. 3 is polarized state distribution on Poincare ball before and after compensation in second order polarization modulation (2PM) in the present invention Figure；

Fig. 4 be the present invention compensates before and after the bit error rate correlation curve of 2PM；

Fig. 5 is the method flow diagram of the present invention.

Detailed description of the invention

Below in conjunction with accompanying drawing, the present invention is described in further detail.

The present invention proposes a kind of XPD compensation method promoting polarization modulation bit error rate performance.

In a wireless communication system, the complexity of radio signal propagation environment itself, result in characteristics of radio channels very Complicated.But, complicated characteristics of radio channels will produce depolarisation effect complicated and changeable thereupon, as cross polarization differentiates Degree XPD, will have a strong impact on the polarized state launching signal.What depolarisation effect XPD described is co-polarization letter under dual polarization channel Power leakage between road and cross polarization channel, the cross polarization interference thereby resulted in receives the polarization of signal by seriously changing The Amplitude Ratio of state component and phase contrast so that receiving terminal cannot correctly demodulate, affect polarization modulation performance.

The present invention proposes a kind of XPD compensation method promoting polarization modulation bit error rate performance, i.e. by analyzing XPD to pole Change the impact of modulated signal polarized state, utilize channel condition information to be calculated compensating factor, and collect mail in receiving terminal docking Number polarized state compensates, thus promotes the bit error rate performance of polarization modulation.

The XPD compensation method of the lifting polarization modulation bit error rate performance that the present invention proposes, including the XPD shadow to polarized state Ring analysis, the calculating of compensating factor and error rate analyzer etc., specifically comprise the following steps that

Step one: set up the system model resisting XPD effect in polarization modulation, analyzes the XPD effect shadow to polarization modulation Ring；

In this system model, first transmitting information I is carried out source coding and channel coding and obtain binary digit sequence RowIt is mapped to M rank polarized state constellation by polarized statePolarized statePole can be used Change phase place and describe son (δ_i,φ_i) represent, δ_i∈[0,π/2],φ_i∈[0,2π].Then obtained by polarized state control unit Polarized signal, and by pair of orthogonal dual polarized antenna, polarized signal launched polarized state and modulate.

(1) receive polarized signal can be expressed as:

R=H (t) E+w (t) (1)

Wherein, E and w (t) represents the white Gaussian noise sent in polarized signal and channel of 2 × 1 respectively.H (t) represents 2 The dual polarization channel matrix of × 2.

Send polarized signal and can be decomposed into the most orthogonal two polarization components, be broken down into horizontal and vertical here Orthogonally polarized component, can be expressed as:

$E=\left[\begin{array}{c}{E}_i^H\\ E_i^V\end{array}\right]=\left[\begin{array}{c}{\mathrm{cos\δ}}_i\\ {\mathrm{sin\δ}}_i\·e^{{\mathrm{j\φ}}_i}\end{array}\right]---\left(2\right)$

Wherein, δ_iAnd φ_iRepresent the Amplitude Ratio between polarized signal two component and phase contrast respectively.

As a example by second order polarization modulation, it is assumed that send two kinds of polarized states corresponding to signal after second order polarization modulation respectively For horizontal polarization state and vertical polarization state, even in formula (2):

${\mathrm{\δ}}_i=\left\{\begin{array}{cc}0,& i=1\\ \mathrm{\π}/2,& i=2\end{array}\right.---\left(3\right)$

After double polarization transmission channel, polarized signal can be affected by noise and depolarisation effect XPD.Dual polarization is believed Road matrix can be expressed as:

$H\left(t\right)=\left[\begin{array}{cc}{H}_{HH}\left(t\right)& H_{HV}\left(t\right)\\ H_{VH}\left(t\right)& H_{VV}\left(t\right)\end{array}\right]---\left(4\right)$

Wherein, H_XYT () represents the channel gain between receiving terminal polarization components X and transmitting terminal polarization components Y.

In view of the depolarisation effect XPD of channel, its channel condition meets:

$\left\{\begin{array}{c}E\[{\left|H_{HH}\right|}^2\]=E\[{\left|H_{VV}\right|}^2\]=1\\ E\[{\left|H_{HV}\right|}^2\]=E\[{\left|H_{VH}\right|}^2\]=\mathrm{\χ},0\≤\mathrm{\χ}1\end{array}\right.---\left(5\right)$

Wherein χ is the inverse of XPD, and usual XPD is defined as:

$XPD=\frac{1}{\mathrm{\χ}}=\frac{E\[H_{HH}\·H_{HH}^{*}\]}{E\[H_{VH}\·H_{VH}^{*}\]}=\frac{E\[H_{VV}\·H_{VV}^{*}\]}{E\[H_{HV}\·H_{HV}^{*}\]}---\left(6\right)$

After wireless channel, receive polarized signal and be expressed as:

$\begin{array}{c}\left[\begin{array}{c}{R}_i^H\\ R_i^V\end{array}\right]=H\left(t\right)\left[\begin{array}{c}{E}_i^H\\ E_i^V\end{array}\right]+w\left(t\right)\\ =\left[\begin{array}{c}{E}_i^H{H}_{HH}\left(t\right)+E_i^V{H}_{HV}\left(t\right)\\ E_i^H{H}_{VH}\left(t\right)+E_i^V{H}_{VV}\left(t\right)\end{array}\right]+w\left(t\right)\end{array}---\left(7\right)$

According to formula (2) and formula (3), receiving polarized signal can be with abbreviation:

$\left\{\begin{array}{c}\left[\begin{array}{c}{R}_1^H\\ R_1^V\end{array}\right]=\left[\begin{array}{c}{H}_{HH}\\ H_{VH}\end{array}\right]+w\left(t\right)\\ \left[\begin{array}{c}{R}_2^H\\ R_2^V\end{array}\right]=\left[\begin{array}{c}{H}_{HV}\\ H_{VV}\end{array}\right]+w\left(t\right)\end{array}\right.---\left(8\right)$

(2) in order to observe the XPD impact on polarizations state intuitively, calculate here according to formula (2) and formula (3) The form of expression of the stokes vector parameters launched and receive polarized signal is as follows.

The stokes vector parameters sending polarized signal is:

$\left\{\begin{array}{c}{g}_i^0={\left|E_i^H\right|}^2+{\left|E_i^V\right|}^2\\ g_i^1={\left|E_i^H\right|}^2-{\left|E_i^V\right|}^2\\ g_i^2=2\left|E_i^H\right|\·\left|E_i^V\right|\·{\mathrm{cos\φ}}_i\\ g_i^3=2\left|E_i^H\right|\·\left|E_i^V\right|\·{\mathrm{sin\φ}}_i\end{array}\right.---\left(9\right)$

The stokes vector parameters receiving polarized signal is:

$\left\{\begin{array}{c}{g}_i^{r0}=(1+\mathrm{\χ})({\left|E_i^H\right|}^2+{\left|E_i^V\right|}^2)=1+\mathrm{\χ}\\ g_i^{r1}=(1-\mathrm{\χ})({\left|E_i^H\right|}^2-{\left|E_i^V\right|}^2)/(1+\mathrm{\χ})\\ g_i^{r2}=2\left|R_i^H\right|\·\left|R_i^V\right|\·{\mathrm{cos\φ}}_i^{\′}/(1+\mathrm{\χ})\\ g_i^{r3}=2\left|R_i^H\right|\·\left|R_i^V\right|\·{\mathrm{sin\φ}}_i^{\′}/(1+\mathrm{\χ})\end{array}\right.---\left(10\right)$

Wherein φ_iWith φ '_iRepresent transmitting terminal and the phase contrast of receiving end signal polarized state two-way component respectively.Need note Meaning,WithRepresent is the power summation of signal two-way component.Under spheric coordinate system, the stokes vector of signal The polarized state of parameter and signal is relation one to one.OrRepresent is on Poincare ball The coordinate of certain point.

Stokes vector parameters according to transmitting terminal and receiving end signal is it is found that signal is by depolarisation effect XPD After impact, Amplitude Ratio and the phase contrast of the polarized state of polar-modulated signal change, and show each on Poincare ball The distribution receiving polarized state is a uncertain annulus, i.e. polarized state spreads, thus affects the property of polarization modulation Energy.

Additionally, ignore effect of noise, formula (8) can be calculated the corresponding power receiving signal is:

$\{\begin{array}{c}{P}_1^{\′}=E\[{\left|H_{HH}\right|}^2\]+E\[{\left|H_{VH}\right|}^2\]=1+\mathrm{\χ}\\ P_2^{\′}=E\[{\left|H_{HV}\right|}^2\]+E\[{\left|H_{VV}\right|}^2\]=\mathrm{\χ}+1\end{array}---\left(11\right)$

Then general power P' of the receiving terminal useful signal after normalization_RFor:

${P^{\′}}_R=\frac{1}{1+\mathrm{\χ}}---\left(12\right)$

By formula (12) it is found that depolarisation effect XPD also can reduce receiving terminal available signal power, i.e. by cross-pole Changing Power leakage causes system received signal to noise ratio to decline, and reduces the performance of polarization modulation.

Step 2: estimate channel condition information, utilizes the channel condition information estimating to obtain to be calculated compensation The factor, and at receiving terminal, signal is compensated；

(1) for simplifying the analysis, the present invention uses the most frequently used channel estimation methods, and i.e. based on pilot tone channel is estimated to calculate Channel condition information is estimated by method.Estimate ideally at channel, it is assumed that believe in each sends mark space Road information keeps constant, is calculated compensating factor W:

$W=\frac{1}{1-\mathrm{\χ}}\left[\begin{array}{cc}1& -\sqrt{\mathrm{\χ}}\\ -\sqrt{\mathrm{\χ}}& 1\end{array}\right]---\left(13\right)$

(2) at receiving terminal, signal is processed, i.e. the polarized state of each reception signal is multiplied by compensating factor W, receives polarized signal (ignoring effect of noise), can be expressed as after being compensated:

$\begin{array}{c}\left[\begin{array}{c}{R}_i^{H\′}\\ R_i^{V\′}\end{array}\right]=W\·\left(H\right(t)\·\left[\begin{array}{c}{E}_i^H\\ E_i^V\end{array}\right])\\ =\frac{1}{1-\mathrm{\χ}}\left[\begin{array}{cc}1& -\sqrt{\mathrm{\χ}}\\ -\sqrt{\mathrm{\χ}}& 1\end{array}\right]\·\left[\begin{array}{c}{E}_i^H{H}_{HH}+E_i^V{H}_{HV}\\ E_i^H{H}_{VH}+E_i^V{H}_{VV}\end{array}\right]\\ =\frac{1}{1-\mathrm{\χ}}\left[\begin{array}{c}{E}_i^H(H_{HH}-\sqrt{\mathrm{\χ}}{H}_{VH})+E_i^V(H_{HV}-\sqrt{\mathrm{\χ}}{H}_{VV})\\ E_i^V(H_{VV}-\sqrt{\mathrm{\χ}}{H}_{HV})+E_i^H(H_{VH}-\sqrt{\mathrm{\χ}}{H}_{HH})\end{array}\right]\end{array}---\left(14\right)$

The condition met according to channel when considering depolarisation effect XPD in formula (4) and formula (5) and the definition of XPD, Above formula can be with abbreviation:

$\left[\begin{array}{c}{R}_i^{H\′}\\ R_i^{V\′}\end{array}\right]=\left[\begin{array}{c}{E}_i^H\·H_{HH}\\ E_i^V\·H_{VV}\end{array}\right]---\left(15\right)$

The power receiving signal two-way component after then can being calculated compensation is respectively as follows:

$\left\{\begin{array}{c}{P}_i^{H\′\′}={\left|E_i^H\right|}^2\\ P_i^{V\′\′}={\left|E_i^V\right|}^2\end{array}\right.---\left(16\right)$

Thus it is found that this backoff algorithm can be effective against two paths of signals component that depolarisation effect XPD brings it Between alternating power decay, and the polarized state receiving signal after being compensated according to formula (15), according to polarized state Mapping ruler carry out inverse mapping and obtain Serial No., and obtain transmitting information through decoding.

Step 3: the Analysis on BER Performance of polarization modulation and simulation result；

About the related description of polarization modulation bit error rate performance in the inventive method:

For the depolarisation effect XPD impact on polarization modulation, the present invention proposes a kind of backoff algorithm at receiving terminal to letter Number polarized state compensates.Next the concrete analysis XPD effect impact on the bit error rate performance of 2PM.

The receiving terminal useful signal general power obtained according to formula (12), can be calculated the received signal to noise ratio before compensation For:

$RSNR={P_R}^{\′}/N_0=\frac{1}{1+\mathrm{\χ}}/N_0---\left(17\right)$

According to the power of receiving terminal useful signal two-way component after the compensation that formula (16) obtains, benefit can be calculated Received signal to noise ratio after repaying is:

RSNR'=(P_i ^H”+P_i ^R”)/N₀=1/N₀ (18)

The error-rate expression of polarization modulation is:

$SER=1/M_P\underset{i=1}{\overset{M_P}{\Σ}}{P}_e^i---\left(19\right)$

Wherein M_pFor the order of modulation of polarization modulation,For the SER function about polarization modulation each reception constellation point, when M_PWhen=2:

Wherein θ₀For the half of adjacent constellation point distance, (θ t) is α (θ, t)=2arccos (tan θ/tant) to function alpha. t_i,It is respectively longitude and the latitude of polarized state, the geometric description subrepresentation of available polarized state.And about the associating of RSNR Probability-distribution functionCan be described as:

Simulation result:

Emulation use modulation system be second order polarization modulation, in simulations, usual depolarisation effect XPD value take 5～ 15dB, XPD=1/ χ and 0≤χ≤1.For simplifying the analysis, the bit rate R of information transmission_b=1kbit, the code of every bit information Unit interval T_b=1ms, signal to noise ratio is in the range of 0～20dB.

First, as in figure 2 it is shown, compared for a certain particular polarization state by channel depolarisation effect XPD shadow in various degree Track on Poincare ball before and after sound；

From Fig. 2 (a) and (b) it can be seen that send a certain particular polarization state as shown in point red figure, gone by channel After polarity effect XPD affects in various degree, receive the distribution on Poincare ball of the polarizations state such as figure in black annulus Shown in.Owing in channel, depolarisation effect XPD is the statistical value weighing dual polarization channel build-in attribute, therefore signal in figure Polarized state is after being affected by XPD, and the polarized state receiving signal is distributed as Channel cyclical repeatedly on Poincare ball The result that statistics obtains.The stokes vector parameters receiving polarized signal it is calculated, at Poincare ball according to formula (10) On show as being centered around and send the annulus of different radii around polarized state.Along with XPD influence degree in the increase i.e. channel of XPD Weakening, the radius of this annulus reduces, and shows as towards sending the point of polarized state to contract in figure.

Secondly, the present invention arranges three kinds of simulated environment, be followed successively by only consider awgn channel, by channel XPD effects and At receiving terminal signal compensated these three situation, and analyze successively receive polarizations state on Poincare ball point Cloth situation and the bit error rate performance of polarization modulation.As a example by second order polarization modulation, assume that transmitting terminal sends one in simulations The binary sequence of a length of num=100000, should obtain two kinds of polarized states of horizontal vertical by polarized state mapping pair, take N=200 i.e. Channel cyclical 200 times.

In the case of Fig. 3 and Fig. 4 sets forth XPD=7.5dB, before and after compensating under second order polarization modulation, receive polarizations State distribution on Poincare ball and ber curve, and simultaneously with awgn channel under the conditions of the pole of second order polarization modulation Change distributions and the bit error rate contrasts.From Fig. 3 it is found that encircled portion is signal is followed by the collection of letters through awgn channel The distribution situation of number polarized state；After being affected by channel depolarisation effect XPD, receive polarizations state from sending polarizations The center entirety shift outward of state, i.e. shown in stain part；After signal is compensated by receiving terminal, dividing of polarized state Cloth is as shown in triangular portions, close to the distribution under the conditions of awgn channel.

From Fig. 4 it is found that after signal is compensated by receiving terminal, its bit error rate performance between awgn channel with not When being affected by channel depolarisation effect XPD during compensation between the bit error rate performance of polarization modulation.Along with signal to noise ratio is continuously increased, pole The bit error rate performance changing modulation gradually promotes.Additionally, when error rate BER=10^-5Time, under awgn channel, required signal-to-noise ratio is 13dB, being affected rear required signal-to-noise ratio by XPD is 17dB, and after compensation, required signal-to-noise ratio is 14.5dB.

It can thus be seen that this backoff algorithm contrasts the performance before not compensating the lifting of 2.5dB.But, in reality Compensation be unable to reach unaffected channel circumstance, therefore its performance is always not as only considering that the second order polarization under awgn channel is adjusted The bit error rate performance of system.

Claims (3)

1. the XPD compensation method promoting polarization modulation bit error rate performance, it is characterised in that for depolarisation effect in channel The XPD impact on polarizations state, analyzes the impact that systematic function is caused by XPD effect in polarization modulation；

After polarization modulation, receiving signal can be expressed as:

R=H (t) E+w (t) (1)

Wherein, E and w (t) represents the modulated polarized signal of transmission and the white Gaussian noise vector of 2 × 1 respectively.H (t) represents 2 × 2 Dual polarization channel matrix.

Send polarized signal and can be decomposed into the most orthogonal two polarization components, be just broken down into horizontal and vertical here Hand over polarization components, can be expressed as:

$E=\left[\begin{array}{c}{E}_i^H\\ E_i^V\end{array}\right]=\left[\begin{array}{c}cos{\mathrm{\δ}}_i\\ {\mathrm{sin\δ}}_i\·e^{{\mathrm{j\φ}}_i}\end{array}\right]---\left(2\right)$

Wherein, δ_iAnd φ_iRepresent the Amplitude Ratio between polarized signal two component and phase contrast respectively.

After dual polarization transmission, polarized signal can be affected by noise and depolarisation effect XPD.Receive polarized signal It is expressed as:

$\begin{array}{c}\left[\begin{array}{c}{R}_i^H\\ R_i^V\end{array}\right]=H\left(t\right)\left[\begin{array}{c}{E}_i^H\\ E_i^V\end{array}\right]+w\left(t\right)\\ =\left[\begin{array}{c}{E}_i^H{H}_{HH}\left(t\right)+E_i^V{H}_{HV}\left(t\right)\\ E_i^H{H}_{VH}\left(t\right)+E_i^V{H}_{VV}\left(t\right)\end{array}\right]+w\left(t\right)\end{array}---\left(3\right)$

Wherein, H_XYT () represents the channel gain between receiving terminal polarization components X and transmitting terminal polarization components Y；

A kind of method the most according to claim 1, it is characterised in that XPD compensation method at receiving terminal；

The method utilizes channel to estimate to obtain channel condition information.To simplify the analysis, it is assumed that channel estimates ideal, it is thus achieved that believe completely Channel state information.On this basis, it is assumed that in each sends mark space, channel information keeps constant, is calculated compensation Factor W:

$W=\frac{1}{1-\mathrm{\χ}}\left[\begin{array}{cc}1& -\sqrt{\mathrm{\χ}}\\ -\sqrt{\mathrm{\χ}}& 1\end{array}\right]---\left(4\right)$

Wherein χ is the inverse of XPD, and usual XPD is defined as:

$XPD=\frac{1}{\mathrm{\χ}}=\frac{E\[H_{HH}\·H_{HH}^{*}\]}{E\[H_{VH}\·H_{VH}^{*}\]}=\frac{E\[H_{VV}\·H_{VV}^{*}\]}{E\[H_{HV}\·H_{HV}^{*}\]}---\left(5\right)$

At receiving terminal, signal is processed, i.e. the polarized state of each reception signal is multiplied by compensating factor W, is mended Receive polarized signal (ignoring effect of noise) after repaying, can be expressed as:

$\begin{array}{c}\left[\begin{array}{c}{R}_i^{H^{\′}}\\ R_i^{V^{\′}}\end{array}\right]=W\·\left(H\left(t\right)\·\left[\begin{array}{c}{E}_i^H\\ E_i^V\end{array}\right]\right)\\ =\frac{1}{1-\mathrm{\χ}}\left[\begin{array}{cc}1& -\sqrt{\mathrm{\χ}}\\ -\sqrt{\mathrm{\χ}}& 1\end{array}\right]\·\left[\begin{array}{c}{E}_i^H{H}_{HH}+E_i^V{H}_{HV}\\ E_i^H{H}_{VH}+E_i^V{H}_{VV}\end{array}\right]\\ =\frac{1}{1-\mathrm{\χ}}\left[\begin{array}{c}{E}_i^H(H_{HH}-\sqrt{\mathrm{\χ}}{H}_{VH})+E_i^V(H_{HV}-\sqrt{\mathrm{\χ}}{H}_{VV})\\ E_i^V(H_{VV}-\sqrt{\mathrm{\χ}}{H}_{HV})+E_i^H(H_{VH}-\sqrt{\mathrm{\χ}}{H}_{HH})\end{array}\right]\end{array}---\left(6\right)$

Above formula can be with abbreviation:

$\left[\begin{array}{c}{R}_i^{H^{\′}}\\ R_i^{V^{\′}}\end{array}\right]=\left[\begin{array}{c}{E}_i^H\·H_{HH}\\ E_i^V\·H_{VV}\end{array}\right]---\left(7\right)$

XPD compensation method the most according to claim 2, as a example by second order polarization modulation (2PM), makes a concrete analysis of this compensation side The method impact on polarization modulation bit error rate performance:

As M=2, it is assumed that the two kinds of polarized states sending signal corresponding after second order polarization modulation are respectively horizontal polarization state With vertical polarization state,

Ignore effect of noise, after being affected by channel depolarisation effect XPD, general power P' of receiving terminal useful signal_RFor:

${P^{\′}}_R=\frac{1}{1+\mathrm{\χ}}---\left(8\right)$

After reception polarized signal is compensated, receive the power of signal two-way component after compensation can be calculated respectively For:

$\left\{\begin{array}{c}{P}_i^{H^{\′\′}}=|E_i^H{|}^2\\ P_i^{V^{\′\′}}=|E_i^V{|}^2\end{array}\right.---\left(9\right)$

The receiving terminal useful signal general power obtained according to formula (8), can be calculated the received signal to noise ratio before compensation is:

$RSNR={P_R}^{\′}/N_0=\frac{1}{1+\mathrm{\χ}}/N_0---\left(10\right)$

According to the power of receiving terminal useful signal two-way component after the compensation that formula (9) obtains, after compensation can being calculated Received signal to noise ratio be:

RSNR'=(P_i ^H”+P_i ^R”)/N₀=1/N₀ (11)

The error-rate expression of polarization modulation is:

$SER=1/M_P\underset{i=1}{\overset{M_P}{\Σ}}{P}_e^i---\left(12\right)$

Wherein M_pFor the order of modulation of polarization modulation,For the SER function about polarization modulation each reception constellation point, work as M_P=2 Time:

Wherein θ₀For the half of adjacent constellation point distance, (θ t) is α (θ, t)=2arccos (tan θ/tant) to function alpha.t_i, It is respectively longitude and the latitude of polarized state, the geometric description subrepresentation of available polarized state.And about the joint probability of RSNR Distribution functionCan be described as:

Received signal to noise ratio before and after compensating substitutes into above formula, can be calculated the bit error rate of polarization modulation before and after compensation.