CN107733819B - Polarized channel XPD estimation algorithm based on ISLS - Google Patents

Abstract

The invention discloses an ISLS-based polarized channel XPD estimation method. Firstly, a receiving and transmitting model based on a pilot frequency sequence under a dual-polarized channel is established; secondly, a method for estimating the dual-polarization channel XPD at a receiving end is provided. In the method, a scattering factor gamma is introduced on the basis of an LS estimation method at a receiving end, and channel coefficient estimation errors are reduced through continuous iteration, so that compared with an LS algorithm, a more accurate channel coefficient value can be obtained. Then we obtain the autocorrelation matrix of the polarized channel by means of the multiplication and averaging of the polarized channel matrix. Since XPD is a parameter of the autocorrelation matrix of the polarized channel, we can obtain the XPD value of the polarized channel through the autocorrelation matrix of the polarized channel. Finally, theoretical and simulation analysis is carried out, and XPD estimation accuracy can be effectively improved by the method.

Description

An ISLS-based XPD Estimation Algorithm for Polarized Channels

technical field

The invention belongs to the technical field of wireless communication, and relates to a method for estimating XPD at a receiving end, specifically an estimation algorithm for improving XPD estimation performance by using channel statistical information and an iterative manner.

Background technique

Polarization techniques such as polarization diversity, dual-polarization Massive MIMO and polarization modulation have been widely used in wireless communication. However, the complex wireless channel characteristics will produce complex and variable depolarization effects, such as Cross Polarization Discrimination (XPD), which will seriously affect the performance of the polarization technology. The depolarization effect describes the power leakage between the co-polarized channel and the cross-polarized channel in the dual-polarized channel, and the resulting cross-polarized interference will reduce the system data transmission rate and increase the bit error rate. Reduce system performance.

The current research on depolarization XPD mainly focuses on using XPD to improve system performance when XPD is known. Under the dual-polarization channel, the researchers proposed a codebook switching scheme to adapt to the dual-polarization channel environment using the known XPD, which can effectively adapt to the dual-polarization channel and improve the system capacity. In addition, the researchers proposed a compensation method to combat the XPD effect in view of the influence of XPD on polar modulation. This method improves the bit error rate performance of polar modulation under the influence of XPD effect by introducing a compensation factor at the transmitter. However, further research is needed on how to obtain XPD.

SUMMARY OF THE INVENTION

The present invention proposes a method for estimating XPD at the receiving end, which aims to obtain the XPD information of the polarized channel at the receiving end. XPD describes the power leakage between co-polarized and cross-polarized channels in dual-polarized channels. It will change the polarization state of the signal to varying degrees, thereby reducing the system performance of polarization information processing. In order to obtain the XPD value of the polarized channel, the present invention proposes a method for estimating XPD at the receiving end, that is, transmitting a pilot sequence at the transmitting end, and at the receiving end, we introduce a scattering factor γ based on the LS estimation method and Through continuous iteration to reduce the channel coefficient estimation error, we can obtain more accurate channel coefficient values compared to the LS algorithm. Then we obtain the autocorrelation matrix of the polarized channel by multiplying the polarized channel matrix and taking the mean value. Since XPD is a parameter of the autocorrelation matrix of the polarized channel, we can obtain the XPD value of the polarized channel through the autocorrelation matrix of the polarized channel.

The polarization channel XPD estimation algorithm based on iterative scattering factor (ISLS), the specific steps are as follows:

Step 1: Establish a dual-polarization channel model;

Dual-polarized antennas show great advantages in saving antenna distance and improving polarization diversity gain and have been widely used. Therefore, the channel model of the present invention selects a dual-polarization channel model. The dual-polarization channel model is obtained by the product of the space fading matrix and the polar fading matrix Hadamard. Since the pair of horizontally and vertically polarized antennas at the transmitting end and the pair of horizontally and vertically polarized antennas at the receiving end are in the same spatial position, the dual-polarized channel elements experience the same spatial fading.

Step 2: use the ISLS estimation method to obtain the polarization channel coefficient;

In order to obtain a more accurate channel coefficient, the present invention introduces the scattering coefficient γ on the basis of the LS estimation method to reduce the estimation error of the channel coefficient by minimizing the mean square error. In order to further reduce the estimation error of the channel coefficient and improve the estimation performance, this The method of introducing iteration is invented. With the increase of the number of iterations, the estimation error will continue to decrease and become stable.

Step 3: Obtain the polarization channel autocorrelation matrix by using the channel coefficients;

If the calculation formula of XPD is directly used for estimation, the estimation performance of the algorithm will be poor due to the estimation error of the numerator and denominator. Therefore, we estimate the XPD value of the channel by estimating the polarization correlation matrix of the channel. We can obtain the polarization channel correlation matrix of the channel by multiplying the channel matrix and its conjugate transpose and averaging.

Step 4: use the polarization channel correlation matrix to obtain the XPD value;

Since XPD is a parameter of the polarization channel correlation matrix, we can obtain the XPD value of the channel after obtaining the polarization correlation matrix.

Advantages of the present invention:

1. The present invention can obtain accurate channel coefficient estimation by introducing the scattering factor γ and the iterative method;

2. The present invention obtains the XPD value by estimating the autocorrelation matrix of the polarized channel, which can avoid the poor XPD estimation performance caused by the estimation error of the numerator and denominator in the XPD calculation formula;

3. Compared with LS, the present invention has better estimation performance, and with the deepening of iteration, the estimation performance is close to MMSE;

Description of drawings

1 is a performance diagram illustrating channel coefficient estimation performance of LS, MMSE and ISLS only through one iteration in the present invention;

Fig. 2 is the performance figure that illustrates LS, MMSE and ISLS that only pass through one iteration to XPD estimation performance in the present invention;

FIG. 3 is a graph illustrating the performance of the ISLS algorithm for channel coefficient estimation under different iterations in the present invention;

4 is a graph illustrating the performance of the ISLS algorithm for XPD estimation under different iterations in the present invention;

Figure 5 is a flow chart of the method of the present invention.

Detailed ways

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

The present invention proposes a method for estimating XPD at the receiving end.

In wireless communication systems, due to the complexity of the wireless environment, polarization technologies such as polarization diversity, dual-polarization MassiveMIMO and polarization modulation are susceptible to the channel depolarization effect XPD, such as data rate reduction and bit error rate improvement. , which greatly reduces system performance.

The present invention proposes an ISLS-based polarization channel XPD estimation algorithm, that is, a pilot sequence is transmitted at the transmitting end, and a scattering factor γ is introduced at the receiving end based on the LS estimation method and iteratively reduces the channel coefficient estimation error. Then we obtain the autocorrelation matrix of the channel by multiplying the channel matrix and taking the mean value. Since XPD is a parameter of the channel autocorrelation matrix, we can obtain the XPD value of the channel through the channel autocorrelation matrix

The ISLS-based polarization channel XPD estimation algorithm proposed by the present invention includes acquisition of channel coefficients, acquisition of polarization correlation matrix, acquisition of XPD and analysis of estimation performance, etc. The specific steps are as follows:

Step 1: Establish a dual-polarization channel model;

In this system, we consider co-locating dual-polarized 2*2 Rayleigh fading channels, and the length of the transmitted signal is T, then the received signal can be expressed as:

Y=HP+N (1)

In the formula, H represents a 2*2 dual-polarized channel matrix, P represents a 2*T transmit symbol matrix, Y represents a 2*T receive symbol matrix, and N represents a 2*T dimension that obeys iid.N( 0,σ ² ) complex noise matrix.

Since the horizontally and vertically polarized antenna pairs at the transmitting end and the horizontally and vertically polarized antenna pairs at the receiving end are in the same spatial position, the co-positioned polarized MIMO channel elements experience the same spatial fading, so the dual-polarized TITO channel matrix can be expressed as for:

表征了极化衰落。where g represents spatial fading, modeled as a complex cyclic symmetric Gaussian variable,

Polarization fading is characterized.

为：define polarization fading

for:

是一个2×2矩阵，它的四个元素均是单位幅值的独立循环对称复指数

角度φ_k在[0,2π)上服从均匀分布。(·)^H表示厄米特转置，

同样由R_p的cholesky分解得到，其中R_p为：In the formula,

is a 2 × 2 matrix whose four elements are independent cyclic symmetric complex exponents of unit magnitude

The angle φ _k is uniformly distributed on [0,2π). ( ) ^H stands for Hermitian transpose,

It is also obtained by the cholesky decomposition of R _p , where R _p is:

μ and χ represent the reciprocal of the main polarization ratio and the cross polarization ratio, respectively, that is, μ=E{|h _hh | ² /h| _vv | ² }, χ=E{|h _hv | ² /|h _vv | ² }, obeying the log-normal distribution [15];

θ表示垂直与水平极化天线发射，垂直或水平极化天线接收的发射极化相关系数，即

发送和接收极化相关统称为交叉极化相关；σ represents the vertical or horizontal polarized antenna transmit, the vertical and horizontal polarized antenna receive the received polarization correlation coefficient, namely

θ represents the correlation coefficient between the vertical and horizontal polarized antennas, and the transmit polarization correlation coefficient received by the vertical or horizontal polarized antennas, namely

Transmit and receive polarization correlations are collectively referred to as cross-polarization correlations;

δ₂表示垂直极化天线发送水平极化天线接收信道与水平极化天线发送垂直极化天线接收信道间的反极化相关系数，即

δ ₁ represents the main polarization correlation coefficient between the vertical polarization antenna transmitting the vertical polarization antenna receiving channel and the horizontal polarization antenna transmitting the horizontal polarization antenna receiving channel, namely

δ ₂ represents the anti-polarization correlation coefficient between the receiving channel of the horizontally polarized antenna and the receiving channel of the horizontally polarized antenna, that is,

Step 2: Use ISLS estimation method to obtain channel coefficients;

Before the algorithm is used, we first use the LS method to obtain the channel matrix H _LS and the mean square error J _LS . The specific expression is:

H _LS = YP ⁺ (5)

表示信道的噪声功率，r表示信道的行数，tr{·}表示矩阵的迹。where P represents the pilot signal, P _⁺ =P ^H (PP ^H ) ^-1 is the generalized inverse of P, ( ) ^-1 is the inverse operation of the matrix,

represents the noise power of the channel, r represents the number of rows of the channel, and tr{·} represents the trace of the matrix.

作为迭代的初始值。Then rewrite H _LS and J _LS as:

as the initial value of the iteration.

(k＝0,1,2,…，n)为第k次迭代后的信道矩阵估计值，

是第k次迭代后的均方误差，γ_k表示第k次迭代后的散射因子。为了获得

可以通过如下计算过程：Assume

(k=0,1,2,...,n) is the estimated value of the channel matrix after the kth iteration,

is the mean square error after the _kth iteration, and γk represents the scattering factor after the kth iteration. in order to achieve

It can be calculated as follows:

We express the estimation error of the channel coefficients as follows:

where R _H =E{H ^H H} is the autocorrelation matrix of the channel.

In order to obtain the minimum value of equation (7), by derivation of both sides of it, we can get:

Bringing γ _k into Equation (7), the mean square error can be obtained as:

At the same time, we can get the channel estimation matrix as:

为算法的最终输出值，通过递推我们可以得到：Obviously, this is a recursive formula, let

For the final output value of the algorithm, by recursion we can get:

和每一次迭代过程的散射系数γ_k，我们就可以获得算法的最终输出值

So just know the initial estimate of the channel

and the scattering coefficient γ _k of each iteration process, we can obtain the final output value of the algorithm

Step 3: Obtain the polarization channel autocorrelation matrix by using the channel coefficients;

XPD describes the power leakage between the co-polarized channel and the cross-polarized channel in a dual-polarized channel, which can be expressed as:

It can be seen from the formula that in order to obtain the XPD value of the channel, the coefficient of the channel must be obtained first. However, due to the estimation error of the channel coefficients h _vv and h _hv obtained by channel estimation, their division makes the estimation performance of the estimation algorithm poor. In order to better estimate the XPD value of the channel, here we obtain the XPD value by estimating χ in the polarization correlation matrix R _p (χ ⁻¹ =XPD).

According to formula (2), the acquisition process of the polarization correlation matrix R _p is as follows:

Step 4: use the polarization channel correlation matrix to obtain the XPD value;

After obtaining the autocorrelation matrix of the channel, we can obtain the XPD value of the channel by formula (4).

Step 5: XPD estimation performance analysis and simulation results based on ISLS;

About the relevant description of the XPD estimation performance based on ISLS in the method of the present invention:

It can be seen from equation (13) that in order to obtain a higher-precision XPD estimation value, a higher-precision channel coefficient must be obtained. The estimation performance of the whole estimation algorithm depends on the accuracy of the estimation of the channel coefficients. In the following, the estimation performance of the algorithm for XPD is analyzed by comparing the estimation errors of the channel coefficients between the proposed algorithm and the LS algorithm.

It can be seen from equation (6) that the estimation error of the LS algorithm for the channel coefficient is:

It can be seen from equation (9) that the estimation error of the channel coefficients after the k-th iteration of the proposed algorithm is:

和tr{R_H}都是大于0的数，所以可以得到

即每次迭代后的估计精度都会优于上一次的估计精度。由于

结合(17)可知，所提算法对信道系数的估计误差要优于LS的估计误差，并且会随着迭代的增加不断减少，最后会慢慢收敛。because

and tr{R _H } are both numbers greater than 0, so we can get

That is, the estimation accuracy after each iteration will be better than the previous estimation accuracy. because

Combined with (17), it can be seen that the estimation error of the proposed algorithm for the channel coefficient is better than that of LS, and it will continue to decrease with the increase of iterations, and will eventually converge slowly.

Simulation results:

The system adopts a dual-polarized antenna with 2 transmissions and 2 receptions. The channel uses the dual-polarized Rayleigh fading channel of equation (2), and the polarization correlation matrix is set as: θ=σ=0, δ ₁ =δ ₂ = |1|, μ=0.1, χ=0.001. The transmit pilot shape adopts block pilot, the pilot power is |P|=1, and the pilot expression is:

where p represents the pilot power, N represents the number of rows of the training sequence, t represents the number of columns of the training sequence, W _N =e ^j2π/N

Fig. 1, Fig. 2 represent respectively LS, ISLS ₁ (that is, ISLS algorithm only performs one iteration and MMSE three algorithms under different signal-to-noise ratio conditions of channel coefficient and XPD estimation error curve. As the signal-to-noise ratio continues to increase, because the influence of noise on the signal continues to decrease, the estimation errors of the three algorithms also continue to decrease. In the case of high SNR, the estimation performance of the three algorithms tends to be the same, This is because under the condition of high signal-to-noise ratio, the gain brought by using the statistical characteristics of the channel is limited compared to the gain brought by the condition of low signal-to-noise ratio, and even if the statistical characteristics of the channel are not used, a better Performance. Under the condition of low signal-to-noise ratio, due to the relatively large influence of noise, the LS algorithm does not consider the statistical characteristics of the channel, so its estimation performance is poor. MMSE utilizes the two channel prior information of the channel autocorrelation matrix and the noise power. , its estimation performance is better. ISLS ₁ adds a scattering factor on the basis of LS, and considers the statistical characteristics of the channel while maintaining low complexity, so its performance will be better than LS estimation. From Figure 1 and Figure 2 It can also be seen that, when estimating XPD, it tends to converge only under the condition of higher signal-to-noise ratio than the estimation of channel coefficients.

FIG. 3 and FIG. 4 respectively show the channel coefficient and XPD estimation error curves of the MMSE estimation algorithm under different SNR conditions and the ISLS estimation algorithm under different iteration times. It can be seen that as the signal-to-noise ratio continues to increase, due to the decreasing influence of noise on the signal, their estimation errors continue to decrease and eventually tend to be the same. Under the condition of low signal-to-noise ratio, MMSE has good estimation performance. With the continuous increase of the number of iterations of ISLS, the estimation error will decrease accordingly and eventually converge to MMSE. This is also the same as our analysis above, with each iteration, the estimation accuracy of ISLS increases. At the same time, it can be seen that with the continuous increase of the number of iterations, the performance improvement of the ISLS estimation algorithm will gradually decrease accordingly, resulting in the improvement brought by the iteration will gradually decrease, and eventually tend to converge.

It can be seen that the proposed estimation algorithm has good estimation performance for both channel coefficient estimation and XPD estimation, and with the increase of the number of iterations, the estimation performance will get better and better, and finally close to MMSE estimated performance. It is precisely because of the introduction of iteration that the algorithm has great flexibility. In practical situations, we can freely set the number of iterations according to the signal-to-noise ratio of the current channel and the requirements for the estimation error.

Claims (2)

1. A polarized channel XPD estimation method based on iterative scattering factors, characterized in that the channel coefficient estimation accuracy is improved by an iterative manner at the receiving end; First use the LS estimation method to obtain the channel matrix

and mean square error J _LS , the specific expression is:

where P represents the pilot signal, P ⁺ =P ^H (PP ^H ) ^-1 is the generalized inverse of P, Y represents the received signal, ( ) ^-1 is the matrix inversion operation,

represents the noise power of the channel, r represents the number of rows of the channel, tr{·} represents the trace of the matrix, E{·} represents the mean calculation, H represents the channel matrix,

represents the two-norm of the matrix; then rewrite

and J _LS , denoted as:

as the initial value of the iteration; Assume

is the estimated value of the channel matrix after the kth iteration,

is the mean square error after the _kth iteration, γk represents the scattering factor after the kth iteration, in order to obtain

Through the following calculation process: The estimation error of the channel coefficients is expressed in the following form:

where R _H =E{H ^H H} is the autocorrelation matrix of the channel; In order to obtain the minimum value of equation (3), by derivation on both sides of it, we get:

Bringing γ _k into Equation (3), the mean square error is obtained as:

At the same time, the channel estimation matrix is obtained as:

Assume

is the final output value of the algorithm, calculated by recursion:

By obtaining an initial estimate of the channel

and the scattering coefficient γ _k of each iteration process to obtain the final output value of the algorithm

The polarized channel is expressed as:

Among them, _hXY represents the channel element sent by the Y antenna and received by the X antenna; XPD describes the power leakage between the co-polarized channel and the cross-polarized channel in a dual-polarized channel, expressed as:

2. method according to claim 1, is characterized in that, obtains the XPD value of channel by estimating the channel autocorrelation matrix so as to overcome the poor XPD estimation performance due to the estimation error of numerator and denominator in the XPD formula; It can be seen from equation (9) that in order to obtain the XPD value of the channel, the coefficient of the channel must be obtained first; however, due to the estimation error of the channel coefficients h _vv and h _hv obtained by the channel estimation, their division makes the estimation of the estimation algorithm. Poor performance; in order to improve the estimation accuracy of XPD, the XPD value is obtained by estimating χ in the polarization correlation matrix R _p , that is, χ ⁻¹ =XPD; The acquisition process of the polarization correlation matrix R _p is as follows:

Among them, vec( ) represents matrix vectorization, g is a scalar that satisfies the complex Gaussian distribution, and is used to simulate channel fading,

represents the correlation and power imbalance under the influence of the channel depolarization effect, μ and χ represent the main polarization ratio and the cross polarization ratio, respectively, that is, μ=E{|h _hh | ² /|h _vv | ² }, χ =E{|h _hv | ² /|h _vv | ² }, σ represents the vertical or horizontal polarization antenna transmission, the vertical and horizontal polarization antenna receiving polarization correlation coefficient, namely

θ represents the correlation coefficient between the vertical and horizontal polarized antennas, and the transmit polarization correlation coefficient received by the vertical or horizontal polarized antennas, namely

δ ₁ represents the main polarization correlation coefficient between the vertical polarization antenna transmitting the vertical polarization antenna receiving channel and the horizontal polarization antenna transmitting the horizontal polarization antenna receiving channel, namely

δ ₂ represents the anti-polarization correlation coefficient between the receiving channel of the horizontally polarized antenna and the receiving channel of the horizontally polarized antenna, that is,

According to formula (7) (10), it can be calculated,

Thus, XPD=χ ^-1 is calculated, that is, the XPD value of the channel.

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