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

Polarized channel XPD estimation algorithm based on ISLS Download PDF

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CN107733819B
CN107733819B CN201710822733.7A CN201710822733A CN107733819B CN 107733819 B CN107733819 B CN 107733819B CN 201710822733 A CN201710822733 A CN 201710822733A CN 107733819 B CN107733819 B CN 107733819B
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CN107733819A (en
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刘芳芳
王炳程
冯春燕
赵殊伦
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Beijing University of Posts and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/0204—Channel estimation of multiple channels
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/002—Reducing depolarization effects
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/10—Polarisation diversity; Directional diversity

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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

Polarized channel XPD estimation algorithm based on ISLS
Technical Field
The invention belongs to the technical field of wireless communication, and relates to a method for estimating XPD (X-ray diffraction) at a receiving end, in particular to an estimation method for improving XPD estimation performance by utilizing channel statistical information and an iteration mode.
Background
Polarization techniques, such as polarization diversity, dual-polarization Massive MIMO, and polarization modulation, have been widely used in wireless communications. However, the complex wireless channel characteristics will generate 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 power leakage between a co-polarized channel and a cross-polarized channel under a dual-polarized channel, and cross-polarized interference caused by the power leakage can reduce the data transmission rate of the system, improve the bit error rate and seriously reduce the system performance.
Currently, research aiming at depolarization effect XPD mainly focuses on improving system performance by using XPD under the condition that XPD is known. Under the dual-polarization channel, researchers provide a codebook switching scheme to adapt to the dual-polarization channel environment by using the known XPD, and the scheme can effectively adapt to the dual-polarization channel so as to improve the system capacity. In addition, a researcher provides a compensation method for resisting XPD effect aiming at the influence of XPD on polarization modulation, and the method improves the error rate performance of polarization modulation under the influence of XPD effect by introducing a compensation factor into a transmitting terminal. However, further investigation is required on how to obtain XPD.
Disclosure of Invention
The invention provides a method for estimating XPD at a receiving end, aiming at obtaining XPD information of a polarization channel at the receiving end. XPD describes the power leakage between co-polarized and cross-polarized channels under dual-polarized channels. It changes the polarization state of the signal to varying degrees, thereby degrading the system performance of polarization information processing. In order to obtain an XPD value of a polarization channel, the invention provides a method for estimating the XPD value at a receiving end, namely, a pilot frequency sequence is transmitted at a transmitting end, a scattering factor gamma is introduced at the receiving end on the basis of an LS estimation method, 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.
The polarized channel XPD estimation algorithm based on iterative scattering factors (ISLS) specifically comprises the following steps:
the method comprises the following steps: establishing a dual-polarization channel model;
the dual-polarized antenna has great advantages in saving antenna distance and improving polarization diversity gain and is widely applied. The channel model of the present invention therefore selects a dual polarization channel model. The dual-polarization channel model is obtained by the product of a space fading matrix and a polarization fading matrix Hadamard. Because the horizontal and vertical polarized antenna pairs at the transmitting end and the horizontal and vertical polarized antenna pairs at the receiving end are all in the same spatial position, the dual-polarized channel elements experience the same spatial fading.
Step two: obtaining a polarization channel coefficient by using an ISLS estimation method;
in order to obtain more accurate channel coefficients, the invention introduces a scattering coefficient gamma on the basis of an LS estimation method to reduce the estimation error of the channel coefficients by minimizing the mean square error, and in order to further reduce the estimation error of the channel coefficients and improve the estimation performance, the invention introduces an iterative method, and the estimation error can be continuously reduced and tends to be stable along with the increase of the iteration times.
Step three: obtaining a polarization channel autocorrelation matrix by using a channel coefficient;
if the estimation is performed by directly using the calculation formula of the XPD, the estimation performance of the algorithm is poor due to the existence of the estimation error of the numerator denominator, so the XPD value of the channel is estimated by estimating the polarization correlation matrix of the channel. We can obtain the polar channel correlation matrix of the channel by multiplying the channel matrix and its conjugate transpose and averaging.
Step four: obtaining an XPD value by utilizing a polarization channel correlation matrix;
since XPD is a parameter of the polarization channel correlation matrix, we can obtain the XPD value of the channel by obtaining the polarization correlation matrix.
The invention has the advantages that:
1. the invention can obtain accurate channel coefficient estimation by introducing a scattering factor gamma and an iteration method;
2. the method obtains the XPD value by estimating the autocorrelation matrix of the polarization channel, and can avoid the poor XPD estimation performance caused by the estimation error of the numerator denominator in an XPD calculation formula;
3. compared with LS, the method has better estimation performance, and the estimation performance approaches MMSE along with the deepening of iteration;
drawings
FIG. 1 is a graph illustrating LS, MMSE and ISLS channel coefficient estimation performance for only one iteration in the present invention;
FIG. 2 is a graph illustrating LS, MMSE and ISLS versus XPD estimation performance for only one iteration in the present invention;
FIG. 3 is a diagram illustrating the performance of ISLS algorithm on channel coefficient estimation under different iterations in the present invention;
FIG. 4 is a graph illustrating performance of ISLS algorithm on XPD estimation for different iterations according to the present invention;
fig. 5 is a flow chart of a method of the present invention.
Detailed Description
The present invention will be described in further detail below with reference to the accompanying drawings.
The invention provides a method for estimating XPD at a receiving end.
In a wireless communication system, due to the complexity of a wireless environment, polarization technologies such as polarization diversity, dual polarization MassiveMIMO and polarization modulation are easily affected by a channel depolarization effect XPD, such as data rate reduction, error rate improvement and great reduction of system performance.
The invention provides an ISLS-based polarized channel XPD estimation algorithm, namely a pilot frequency sequence is transmitted at a transmitting end, and a scattering factor gamma is introduced on a receiving end on the basis of an LS estimation method and is iterated continuously to reduce channel coefficient estimation errors. We then obtain the autocorrelation matrix of the channel by averaging through channel matrix multiplication. 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 polarized channel XPD estimation algorithm based on ISLS comprises the steps of channel coefficient acquisition, polarization correlation matrix acquisition, XPD acquisition, estimation performance analysis and the like, and specifically comprises the following steps:
the method comprises the following steps: establishing a dual-polarization channel model;
in the system, we consider co-located dual-polarization 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 transmit symbol matrix with a dimension of 2 × T, Y represents a receive symbol matrix with a dimension of 2 × T, and N represents compliance id.n (0, σ) with a dimension of 2 × T2) A complex noise matrix.
Since the horizontal and vertical polarized antenna pairs at the transmitting end and the horizontal and vertical polarized antenna pairs at the receiving end are all in the same spatial position, the co-located polarized MIMO channel elements experience the same spatial fading, so the dual-polarized TITO channel matrix can be expressed as:
Figure BDA0001406712260000031
in the formula, g represents spatial fading and is modeled as a complex-cycle symmetric Gaussian variable,
Figure BDA0001406712260000032
polarization fading is characterized.
Defining polarization fading
Figure BDA0001406712260000033
Comprises the following steps:
Figure BDA0001406712260000041
in the formula (I), the compound is shown in the specification,
Figure BDA0001406712260000042
is a 2 × 2 matrix, the four elements of which are independent circularly symmetric complex exponentials of unit amplitude
Figure BDA0001406712260000043
Angle phikObey a uniform distribution over 0,2 pi). (.)HThe result is expressed as the hermite transpose,
Figure BDA0001406712260000044
also from RpIs decomposed to obtain RpComprises the following steps:
Figure BDA0001406712260000045
● mu and chi respectively represent the reciprocal of the main polarization ratio and the cross polarization ratio, i.e., mu-E { | hhh|2/h|vv|2}，χ＝E{|hhv|2/|hvv|2Is subject to a lognormal distribution [15 ]]；
● sigma denotes the reception polarization correlation coefficient for vertical or horizontal polarization antenna transmission and vertical and horizontal polarization antenna reception, i.e.
Figure BDA0001406712260000046
Theta denotes the correlation coefficient of the transmission polarization of the vertically and horizontally polarized antennas, i.e. the reception polarization of the vertically or horizontally polarized antennas
Figure BDA0001406712260000048
Transmit and receive polarization correlations are collectively referred to as cross polarization correlations;
●δ1indicating the main polarization correlation coefficient between the vertically polarized antenna receiving channel and the horizontally polarized antenna receiving channel, i.e. transmitting
Figure BDA0001406712260000049
δ2Representing the inverse-polarization correlation coefficient between the vertically-polarized antenna transmitting horizontally-polarized antenna receiving channel and the horizontally-polarized antenna transmitting vertically-polarized antenna receiving channel, i.e.
Figure BDA00014067122600000410
Step two: obtaining a channel coefficient by using an ISLS estimation method;
before the algorithm is used, we first obtain the channel matrix H by using LS methodLSSum mean square error JLS. The specific expression is as follows:
HLS＝YP+(5)
Figure BDA00014067122600000411
wherein P represents a pilot signal, P + ＝PH(PPH)-1Is the generalized inverse of P (.)-1Is the inversion operation of the matrix and is,
Figure BDA0001406712260000051
representing the noise power of the channel, r the number of rows of the channel, and tr {. cndot } the traces of the matrix.
Then rewrite HLSAnd JLSAnd is recorded as:
Figure BDA0001406712260000052
as an initial value for the iteration.
Is provided with
Figure BDA0001406712260000053
(k is 0,1,2, …, n) is the estimated value of the channel matrix after the k iteration,
Figure BDA0001406712260000054
is the mean square error, gamma, after the kth iterationkRepresenting the scattering factor after the k-th iteration. To obtain
Figure BDA0001406712260000055
The calculation process can be as follows:
we express the estimation error of the channel coefficients as follows:
Figure BDA0001406712260000056
wherein R isH＝E{HHH is the autocorrelation matrix of the channel.
To obtain the minimum value of equation (7), by deriving both sides, one can obtain:
Figure BDA0001406712260000057
will gammakWith the equation (7), the mean square error can be obtained as:
Figure BDA0001406712260000058
meanwhile, we can obtain a channel estimation matrix as follows:
Figure BDA0001406712260000059
it is obvious that this is a recursive one, let
Figure BDA00014067122600000510
For the final output value of the algorithm, we can get by recursion:
Figure BDA00014067122600000511
so long as the initial estimate of the channel is known
Figure BDA00014067122600000512
And the scattering coefficient gamma of each iterationkWe can obtain the final output value of the algorithm
Figure BDA00014067122600000513
Step three: obtaining a polarization channel autocorrelation matrix by using a channel coefficient;
XPD describes the power leakage between co-polarized and cross-polarized channels under dual-polarized channels, which can be expressed as:
Figure BDA00014067122600000514
from the equation, it can be seen that to obtain the XPD value of the channel, the coefficients of the channel must be first found. But due to channel coefficients h derived from channel estimationvvAnd hhvThere are estimation errors, which divide up making the estimation performance of the estimation algorithm poor. In order to better estimate the XPD value of the channel, we estimate the polarization correlation matrix RpObtaining XPD value (x) from middle x-1＝XPD)。
Polarization correlation matrix R according to equation (2)pThe acquisition process is as follows:
Figure BDA0001406712260000061
step four: obtaining an XPD value by utilizing a polarization channel correlation matrix;
after obtaining the autocorrelation matrix of the channel, we can obtain the XPD value of the channel by equation (4).
Step five: XPD estimation performance analysis and simulation results based on ISLS;
the method of the invention is characterized by the following steps of XPD estimation performance correlation explanation based on ISLS:
as can be seen from equation (13), in order to obtain an XPD estimation value with higher accuracy, it is necessary to obtain a channel coefficient with higher accuracy. The estimation performance of the whole estimation algorithm depends on the accuracy of channel coefficient estimation, and the estimation performance of the algorithm on XPD is analyzed by comparing the estimation error of the proposed algorithm and LS algorithm on the channel coefficient.
As can be seen from equation (6), the estimation error of the LS algorithm for the channel coefficient is:
Figure BDA0001406712260000062
as can be seen from equation (9), the estimation error of the proposed algorithm for the channel coefficient after the kth iteration is:
Figure BDA0001406712260000063
due to the fact that
Figure BDA0001406712260000064
And tr { RHAre all numbers greater than 0, so that
Figure BDA0001406712260000065
Namely, the estimation precision after each iteration is better than that of the last time. Due to the fact that
Figure BDA0001406712260000066
In combination with (17), the estimation error of the proposed algorithm for the channel coefficient is better than that of the LS, and will decrease with the increase of the iterationAnd little, eventually, will converge slowly.
And (3) simulation results:
the system adopts a dual-polarized antenna with 2 transmitting and 2 receiving, the channel uses a dual-polarized Rayleigh fading channel with the formula (2), and the setting of a polarization correlation matrix is as follows: theta-sigma-0 and delta1＝δ2I 1, μ 0.1, and χ 0.001. The shape of the transmitted pilot frequency adopts block pilot frequency, the pilot frequency power is | P | ═ 1, and the pilot frequency expression is as follows:
Figure BDA0001406712260000072
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, WN＝ej2π/N
In FIG. 1 and FIG. 2, LS and ISLS are shown respectively1(i.e., ISLS algorithm only performs one iteration and MMSE algorithm to obtain channel coefficient and XPD estimation error curve chart under different signal-to-noise ratios, it can be seen that, as the signal-to-noise ratio is continuously increased, because the influence of noise on signals is continuously reduced, the estimation errors of the three algorithms are also continuously reduced, under the condition of high signal-to-noise ratio, the estimation performances of the three algorithms tend to be the same, this is because, under high snr conditions, the gain due to the statistical properties of the channel is limited compared to the gain due to low snr conditions, under the condition of low signal-to-noise ratio, because the influence of noise is large, the LS algorithm does not consider the statistical property of the channel, therefore, the estimation performance is poor, and the MMSE utilizes two channel prior information, namely a channel autocorrelation matrix and noise power, and has better estimation performance ISLS.1A scattering factor is added on the basis of LS, and the statistical characteristics of a channel are considered while the complexity is kept low, so that the performance of the method is better than that of LS estimation. It can also be seen from fig. 1 and 2 that in estimating XPD, it tends to converge under higher snr conditions than the estimation of channel coefficients.
Fig. 3 and fig. 4 show channel coefficient and XPD estimation error graphs of an MMSE estimation algorithm under different snr conditions and an ISLS estimation algorithm under different iteration numbers, respectively. It can be seen that as the signal-to-noise ratio becomes larger, their estimation errors decrease and eventually approach the same as the noise has less influence on the signal. 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 is also correspondingly reduced and finally converges to MMSE. This is also the same as our analysis above, and the estimation accuracy of ISLS increases at each iteration. Meanwhile, as the number of iterations is continuously increased, the performance improvement of the ISLS estimation algorithm is correspondingly and slowly reduced, so that the improvement brought by the iterations is slowly reduced and finally tends to converge.
Therefore, the estimation algorithm has good estimation performance for estimating the channel coefficient and the XPD, and the estimation performance is better and better along with the increase of the iteration number and finally approaches to the estimation performance of MMSE. The algorithm has strong flexibility just because of the introduction of iteration. In practical cases, the number of iterations can be freely set according to the signal-to-noise ratio of the current channel and the requirement for estimation error.

Claims (2)

1. A polarized channel XPD estimation method based on iterative scattering factors is characterized in that channel coefficient estimation precision is improved at a receiving end in an iterative mode;
firstly, LS estimation method is used to obtain channel matrix
Figure FDA0002463869450000011
Sum mean square error JLSThe specific expression is as follows:
Figure FDA0002463869450000012
Figure FDA0002463869450000013
wherein P represents a pilotSignal, P+＝PH(PPH)-1Is the generalized inverse of P, Y represents the received signal, (. DEG)-1Is the inversion operation of the matrix and is,
Figure FDA0002463869450000014
representing the noise power of the channel, r the number of rows of the channel, tr {. cndot } the trace of the matrix, E {. cndot } the mean calculation, H the channel matrix,
Figure FDA0002463869450000015
a two-norm representing a matrix;
followed by rewriting
Figure FDA0002463869450000016
And JLSAnd is recorded as:
Figure FDA0002463869450000017
as an initial value for the iteration;
is provided with
Figure FDA0002463869450000018
For the channel matrix estimate after the kth iteration,
Figure FDA0002463869450000019
is the mean square error, gamma, after the kth iterationkRepresenting the scattering factor after the k-th iteration, in order to obtain
Figure FDA00024638694500000110
By the following calculation procedure:
the estimation error of the channel coefficient is expressed as follows:
Figure FDA00024638694500000111
wherein R isH＝E{HHH is the autocorrelation matrix of the channel;
to obtain the minimum value of equation (3), by deriving both sides, we obtain:
Figure FDA00024638694500000112
will gammakCarry over equation (3), obtain the mean square error as:
Figure FDA00024638694500000113
the channel estimation matrix obtained at the same time is:
Figure FDA00024638694500000114
is provided with
Figure FDA00024638694500000115
And calculating by recursion to obtain the final output value of the algorithm:
Figure FDA00024638694500000116
by obtaining an initial estimate of the channel
Figure FDA00024638694500000117
And the scattering coefficient gamma of each iterationkTo obtain the final output value of the algorithm
Figure FDA00024638694500000118
The polarization channel is represented as:
Figure FDA00024638694500000119
wherein h isXYRepresenting the channel elements transmitted by the Y antenna and received by the X antenna;
XPD describes the power leakage between co-polarized and cross-polarized channels under dual-polarized channels, expressed as:
Figure FDA0002463869450000021
2. the method of claim 1, wherein the XPD value of the channel is obtained by estimating the channel autocorrelation matrix to overcome the poor XPD estimation performance in the XPD formula due to the estimation error of the numerator denominator;
as shown in equation (9), to obtain the XPD value of the channel, the coefficient of the channel must be first determined; but due to channel coefficients h derived from channel estimationvvAnd hhvThere are estimation errors, which divide up to make the estimation performance of the estimation algorithm worse; in order to improve the estimation accuracy of XPD, the polarization correlation matrix R is estimatedpObtaining XPD value as chi-1＝XPD；
Polarization correlation matrix RpThe acquisition process is as follows:
Figure FDA0002463869450000022
where vec (-) denotes matrix vectorization, g is a scalar satisfying a complex gaussian distribution, used to model channel fading,
Figure FDA0002463869450000023
representing the correlation and power imbalance under the influence of the channel depolarization effect, and mu and chi represent the main polarization ratio and the cross polarization ratio, respectively, i.e., mu { | hhh|2/|hvv|2}，χ＝E{|hhv|2/|hvv|2σ denotes the received polarization correlation coefficient for vertically or horizontally polarized antenna transmission, i.e. reception polarization correlation coefficient for vertically and horizontally polarized antenna reception
Figure FDA0002463869450000024
Theta denotes vertically and horizontally polarized antenna transmission, vertically or horizontally polarized antennaReceived transmit polarization correlation coefficient, i.e.
Figure FDA0002463869450000025
δ1Indicating the main polarization correlation coefficient between the vertically polarized antenna receiving channel and the horizontally polarized antenna receiving channel, i.e. transmitting
Figure FDA0002463869450000026
δ2Representing the inverse-polarization correlation coefficient between the vertically-polarized antenna transmitting horizontally-polarized antenna receiving channel and the horizontally-polarized antenna transmitting vertically-polarized antenna receiving channel, i.e.
Figure FDA0002463869450000027
Calculated according to the formulas (7) and (10),
Figure FDA0002463869450000028
thus, XPD ═ χ is calculated-1I.e. the XPD value of the channel.
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