WO2022016888A1 - 利用多极化宽带扩展阵列响应的密集多径参数估计方法 - Google Patents

利用多极化宽带扩展阵列响应的密集多径参数估计方法 Download PDF

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WO2022016888A1
WO2022016888A1 PCT/CN2021/081350 CN2021081350W WO2022016888A1 WO 2022016888 A1 WO2022016888 A1 WO 2022016888A1 CN 2021081350 W CN2021081350 W CN 2021081350W WO 2022016888 A1 WO2022016888 A1 WO 2022016888A1
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matrix
polarization
channel
dimensional
parameters
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王海明
杨本圣
张沛泽
余晨
洪伟
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Southeast University
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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
    • 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
    • H04L25/022—Channel estimation of frequency response
    • 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
    • H04L25/024—Channel estimation channel estimation algorithms
    • H04L25/0242—Channel estimation channel estimation algorithms using matrix methods

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  • the invention relates to a method for estimating dense multi-path parameters by utilizing multi-polarization broadband extended array response, which can be used in the fields of radio wave propagation characteristic measurement, indoor positioning and the like.
  • multipath parameter estimation methods have been widely studied, among which there are many well-known classical algorithms, such as Estimation of Signal Parameter via Rotational Invariance Techniques (ESPRIT), Multiple Signal Classification (Multiple Signal Classification) Signal Classification, MUSIC) and Alternating Generalized Expectation-Maximization (Space-Alternating Generalized Expectation-Maximization, SAGE) and so on.
  • ESPRIT Estimation of Signal Parameter via Rotational Invariance Techniques
  • MUSIC Multiple Signal Classification
  • Alternating Generalized Expectation-Maximization Space-Alternating Generalized Expectation-Maximization, SAGE
  • the traditional processing method is to smooth these sub-paths in the airspace, and finally use ESPRIT or MUSIC to obtain their airspace angle information.
  • the number of sub-paths resolved by this method is usually limited by the number of antenna array elements. Usually, the number of resolved sub-paths is less than the number of array elements.
  • the increase in the number of antennas will increase the complexity of the system, which makes a large number of space exist in the space. It is difficult to distinguish the sub-diameter effectively.
  • the known traditional multipath parameter estimation methods cannot effectively complete the estimation of a large number of subpath parameters.
  • the polarization characteristics in the radio wave propagation environment become more abundant, and the cross-polarization ratio of each sub-path can well reflect the polarization changes of these sub-paths.
  • the polarization ratio is usually obtained by turning the antenna 90 degrees. This method is relatively extensive and time-consuming to measure, and the accuracy of the obtained results is also relatively lacking.
  • the purpose of the present invention is to use a method for estimating dense multipath parameters using a multi-polarized broadband extended array response to estimate the number of neutrons in a time-resolvable path in a dense multipath environment that is greater than the number of array elements.
  • the time delay, the two-dimensional departure angle, and the two-dimensional arrival angle of the sub-path can be further estimated, and parameters such as initial phase, amplitude, and cross-polarization ratio can be further estimated.
  • a method for estimating dense multipath parameters using multipolarized broadband spread array responses comprising the following steps:
  • the number of groups is equal to the number of transmit antennas.
  • Each group of transmit signal sequences is divided into different segments, and the number of segments in each group is not less than the number of transmit antennas.
  • the length of a signal sequence is not less than the number of discrete Fourier transform points, and the received data of multiple snapshots are processed according to the known transmitted signal to obtain the channel response of the multi-polarization component at all frequency points in the frequency band;
  • step (2) From the two-dimensional matrix described in step (2), select the rows related to the reference array element at the receiving end to form a matrix, and the rows related to the reference array element at the transmitting end to form a matrix, and use frequency domain smoothing to reduce the channel matrix dimension, using the reduced-dimensional channel matrix to estimate the two-dimensional departure angle and arrival angle.
  • each group of transmission signal sequences is divided into multiple subsequences, the sequences do not require orthogonality, and the full rank of each subsequence matrix of the signal in the frequency domain is sufficient.
  • each column of the reconstructed channel response matrix contains the response of each polarized transceiver array element at all frequency points, and the number of columns of the channel matrix is equal to the number of snapshots.
  • the frequency domain smoothing refers to dividing all frequency points at equal intervals into multiple groups of frequency points with the same length, and adding and averaging their corresponding array channel responses to obtain a channel response matrix with a smaller number of rows, reducing Each row of the dimensioned channel matrix represents the sum of the channel responses at the corresponding added frequency points, and the number of columns of the channel response matrix does not change.
  • the parameter estimation method also includes estimation of initial phase, amplitude, and cross-polarization ratio parameters.
  • the specific method is to use the estimated delay and angle parameters to construct an array response, and then use the least squares method to obtain each Take a picture of the matrix containing the cross-polarization ratio, amplitude and initial phase of each polarization combination, calculate the argument of this matrix to obtain the initial phase of all sub-path horizontal and vertical polarization combinations, and then use each column of the obtained matrix to correlate with the cross-polarization.
  • the cross-polarization ratio is obtained from the relationship of the ratio, and finally the amplitude information of each sub-path in different snapshots is obtained by using the least squares estimation.
  • the present invention has the following advantages: (1) The present invention can estimate the spatial domain (two-dimensional departure angle and two-dimensional arrival angle) of indistinguishable sub-paths in the delay domain by using the wide-band extended array response. angle), initial phase, amplitude, and polarization domain (cross-polarization ratio) parameters. (2) Within the same time resolution path, the number of sub-paths that can be resolved can be greater than the number of array elements, breaking the limitation of the number of array elements on the estimated number of sub-paths. (3) Using this method can reduce the design complexity of the channel measurement system. The method requires relatively loose spacing between array elements, and the spacing between array elements can be greater than the half-carrier wavelength.
  • FIG. 1 is a flow chart of an estimation method implemented in the present invention.
  • FIG. 2 is a schematic structural diagram of a transmission signal in an embodiment of the present invention.
  • FIG. 3 is a schematic diagram of a background of channel transmission to which an embodiment of the present invention is applied.
  • FIG. 4 is a schematic diagram of the principle of a frequency domain smoothing technology in an embodiment of the present invention.
  • FIG. 6 is a graph showing the estimation result of the two-dimensional angle of arrival of the sub-radius within a single time-resolvable radius estimated by an embodiment of the present invention.
  • FIG. 7 is a graph showing the estimation result of the two-dimensional departure angle of the sub-radius within a single time-resolvable radius estimated by an embodiment of the present invention.
  • FIG. 8 is a diagram of an estimation result of an initial phase estimated by an embodiment of the present invention.
  • FIG. 9 is a graph of estimation results of the cross-polarization ratio under different signal-to-noise ratios according to an embodiment of the present invention.
  • FIG. 10 is a graph of an estimation result of an amplitude parameter according to an embodiment of the present invention.
  • the multi-polarized antenna in this specific embodiment adopts the most comprehensive distributed electromagnetic vector antenna (Electromagnetic Vector Antenna, EMVA) in polarization mode.
  • EMVA Electromagnetic Vector Antenna
  • the present invention discloses a method for estimating dense multipath parameters by utilizing multi-polarization broadband extended array responses.
  • the method can effectively estimate multipath parameters in a dense multipath environment, including but not limited to time-resolvable paths (hereinafter referred to as “resolvable paths”). is the parameter estimation of sub-paths that are more than the number of array elements in the path.
  • the method first transmits multiple groups of different transmit signal sequences through a multi-polarization antenna array, processes the received data of multiple snapshots according to the known transmit signals, and obtains the channel responses of the multi-polar components in all frequency points in the frequency band.
  • the multi-frequency channel response of each snapshot is vectorized into a column vector, and the channel responses of multiple snapshots are arranged in a two-dimensional matrix; then the frequency domain channel response of the reference lattice element pair is obtained.
  • Estimation, the acquisition of delay parameters can use subspace methods such as MUSIC or ESPRIT method, and then use the delay parameters and frequency domain smoothing to obtain the estimation of the two-dimensional angle information of the transceiver.
  • the estimated delay and angle parameters construct the array response, and then use the least squares method to obtain the matrix containing the cross-polarization ratio, amplitude and initial phase of each polarization combination under each snapshot, and calculate the argument of this matrix to obtain all the sub-arrays.
  • Fig. 1 shows the flow chart of the estimation method implemented in the present invention, wherein H represents the channel response matrix of all frequency points, H sm represents the channel response matrix after smoothing and dimension reduction, P represents the smoothing times, and L represents the distinguishable path in the time domain. Number of.
  • H represents the channel response matrix of all frequency points
  • H sm represents the channel response matrix after smoothing and dimension reduction
  • P represents the smoothing times
  • L represents the distinguishable path in the time domain. Number of.
  • FIG. 2 is a schematic diagram of the structure of the required transmission signal of the present invention.
  • M t represents the number of transmitting electromagnetic vector antennas
  • (m t , x) represents the x th component of the m t th distributed EMVA.
  • the meaning expressed is the 1 seq th subsequence signal sent by the (m t ,x) th polarized antenna component.
  • the structure of the transmitted signal sequence consists of a total of 6M t groups of different transmitted signals, each group of transmitted signals is composed of L seq sub-sequences, L seq ⁇ 6M t , and the length of each sub-sequence is N s symbols.
  • DFT discrete Fourier transform
  • Transmission model employed in the present invention is shown in Figure 3, where each sub-paths by a pair of numbers in parentheses indicate, for example, (l, l K) represents the sub-paths l K l th path, the l th path
  • the number of sub-paths within is represented by K l , here it is assumed that there are a total of Sliver diameter.
  • M r in the figure is the number of receiving electromagnetic vector antennas.
  • the above formula represents the expression of the n s symbol of the l seq subsequence of the n th snapshot received, the operator represents the Kronecker product operation, the operator Represents a Kronecker product by columns.
  • the subscript f represents the frequency
  • the superscript T represents the transpose of the matrix.
  • z n represents the noise of the nth snapshot.
  • g t and g r represent the pattern gains of the electromagnetic vector antennas at the transmitter and receiver in the directions of ⁇ t,lk and ⁇ r,lk , respectively.
  • the variable T represents the symbol width of the transmitted sequence, and ⁇ l represents the delay parameter of the first path.
  • ⁇ n, lk represent the amplitude of the k lth sub-path in the n-th snapshot
  • the parameters involved are ⁇ , ⁇ r , ⁇ t , ⁇ respectively represent the time delay of the path, and the two-dimensional angle of arrival of all the sub-paths , the two-dimensional transmission angle and the set of polarization parameters, some of which are defined as follows:
  • ⁇ is the cross-polarization ratio
  • ⁇ hh , ⁇ hv , ⁇ vh , ⁇ vv are the initial phases of the four combinations of horizontal and vertical polarization.
  • u t, lk represent the coordinates of the m t EMVA and the direction cosine of the kl th sub-diameter departure angle, respectively.
  • the coordinates here are three-dimensional row vectors in the space Cartesian coordinate system.
  • the direction cosine represents the unit 3D column vector in that direction.
  • c represents the propagation speed of electromagnetic waves in free space.
  • d t,lk (f, ⁇ t,lk ) represents the spatial phase shift vector of the distributed EMVA at the transmitter
  • ⁇ t ( ⁇ t,lk ) represents the steering matrix of the antenna polarization domain of the transmitter electromagnetic vector
  • r ex , rey , r ez , r hx , r hy , and r hz respectively represent the position coordinates of multiple polarized component antennas relative to the EMVA.
  • the number of polarizations is 6, which can also be taken as partial polarization.
  • the steering matrix at the receiver replace the subscript 't' in the above expression with 'r'.
  • T( ⁇ lk ) is the polarization torsion matrix, which can be expressed as
  • each subsequence can obtain the channel response at each frequency point, and then extract the channel responses of the same frequency point and classify them together. All N snapshots perform the same operation.
  • the multi-polarization response of the i-th frequency point can be expressed as The specific expression is as follows
  • vec represents the operation of vectorizing the matrix in columns.
  • step (1) the obtained multi-frequency channel responses under each snapshot are vectorized into a column vector, and the channel responses under multiple snapshots are arranged in a two-dimensional matrix Its display form is as follows
  • the reference lattice element of the transceiver end can be arbitrarily selected, and set its coordinates as the reference origin), and use the channel response of the reference lattice element to obtain the delay of multipath propagation parameter.
  • a subspace method such as MUSIC or ESPRIT can be used to obtain the delay parameter.
  • the channel response of the reference lattice element is Decompose H ⁇ to obtain the noise subspace, and then use the traditional subspace algorithm to estimate the delay parameter (for details, please refer to R. Schmidt's "Multiple emitter location and signal parameter estimation" in IEEE Transactions on Antennas and Propagation).
  • the estimation result of the delay parameter of the path is given in Figure 5.
  • step (5) For the estimation of the two-dimensional departure angle, select the rows in H related to the reference array element at the receiving end to form a matrix H t , and perform the following step (5), for the two-dimensional angle of arrival, select the reference array in H related to the transmitting end.
  • the rows related to the array elements form a matrix H r , and then step (5) is performed, wherein the corresponding subscript 't' can be replaced with a subscript 'r'.
  • the channel response matrix H t is divided into P sub-sections by row.
  • P is the number of sub-arrays divided, and it is also the number of smoothing.
  • P can be divisible by N s .
  • Each sub-array contains the channel response of N s /P frequency points.
  • RD-MUSIC reduced rank subspace algorithm
  • ⁇ represents the Hadamard product operation. Represents an all-ones matrix of dimension 6M t N s /P ⁇ K.
  • ⁇ t,lk is as follows
  • ⁇ f is the interval between frequency bins.
  • the coordinates r t,m here represent the position coordinates of the mth antenna element.
  • For the angle of arrival refer to (4) to replace H t in (5) with H r , and then use the same method and steps as the departure angle to estimate.
  • the two-dimensional arrival angle and departure angle of the sub-radius are estimated by Figures 6 and 7 are given.
  • the initial value of the phase can be estimated as Here arg represents the operation of taking the argument.
  • the estimate of the cross-polarization ratio is expressed as
  • the numbers (1, 2, 3, 4) in parentheses represent the (1, 2, 3, 4)th element of the vector v l,k. From the estimated initial phase and the estimate of the cross-polarization ratio can be constructed Then the magnitude of all snapshots of all sub-diameters can be estimated as
  • Fig. 8 shows the estimation result of the initial phase of the algorithm of the present invention.
  • Fig. 9 shows the estimation result of the cross-polarization ratio of the algorithm of the present invention.
  • Fig. 10 shows the estimation result of the magnitude of the algorithm of the present invention. It is not difficult to see from the estimated result graph that the initial phase, cross-polarization ratio and amplitude of each sub-path are consistent with the set values, and these parameters can be perfectly estimated by this method.

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Abstract

本发明公开了一种利用多极化宽带扩展阵列响应的密集多径参数估计方法，该方法首先通过多极化天线阵列发送多组不同的发送信号序列，根据已知的发送信号处理多个快拍的接收数据，获得多极化天线分量在频带内所有频点的信道响应，并将获得的多个快拍下的多频点信道响应矩阵扩展成一个大的二维信道响应矩阵；然后利用参考点阵元获得多径传播的时延参数，并利用频域平滑降维后的信道矩阵估计二维离开角和到达角；后对估计的离开角与到达角进行配对，再利用已估计参数估计获得子径的交叉极化比、初始相位和幅度参数，最终实现多维参数估计。本发明可以实现密集多径环境中多维子径参数的估计，可用于电波传播测量、室内定位等领域。

Description

利用多极化宽带扩展阵列响应的密集多径参数估计方法 技术领域
本发明涉及一种利用多极化宽带扩展阵列响应的密集多径参数估计方法，可用于电波传播特性测量、室内定位等领域。
背景技术
在过去几十年中，多径参数估计方法被广泛研究，其中不乏被人熟知的经典算法，例如旋转不变子空间算法(Estimation of Signal Parameter via Rotational Invariance Techniques，ESPRIT)、多重信号分类(Multiple Signal Classification，MUSIC)和交替广义期望最大化(Space-Alternating Generalized Expectation-Maximization，SAGE)等。由于多径传输环境的复杂性，发送信号经过多径信道到达接收端时通常伴有复杂的传播特性，例如时域上的多子径重叠效应，导致多条子径到达接收端的时间间隔非常接近甚至相同，空间上这些子径的离开和到达角度也较为密集，这些子径不仅在时域上很难分辨，而且其特性也为其在空域上的分辨带来很大挑战。传统处理方式是将这些子径在空域上做平滑预处理，最终采用ESPRIT或者MUSIC获得其空域角度信息。然而这种做法分辨的子径数量通常受到天线阵元数量的限制，通常分辨子径的数量小于阵元的数量，而天线数量的增加会带来系统复杂度的上升，这使得空间中大量存在的子径很难被有效的分辨出来。已知的传统多径参数估计方法不能有效完成大量的子径参数估计。
由于复杂传播环境的影响，这使得电波传播环境中极化特征变得更为丰富，每条子径的交叉极化比能够很好的反应这些子径的极化变化，但是目前已知的对于交叉极化比通常采用天线转向90度的方法进行获取，这种方法较为粗放且测量耗时，所得结果的准确性也较为欠缺。
发明内容
发明目的：针对以上问题，本发明目的是一种利用多极化宽带扩展阵列响应的密集多径参数估计方法，估计出密集多径环境中在时间可分辨径中子径数大于阵元数的情况下，子径的时延、二维离开角、二维到达角，并能进一步估计初始相位、幅度和交叉极化比等参数。
技术方案：为实现上述发明目的，本发明采用的技术方案为：
一种利用多极化宽带扩展阵列响应的密集多径参数估计方法，包括以下步骤：
(1)通过多极化天线阵列发送多组不同的发送信号序列，组数等于发送天线的个 数，每组发送信号序列分为不同的段，每组段数不小于发送天线的个数，每一段信号序列的长度不小于离散傅里叶变换的点数，根据已知的发送信号处理多个快拍的接收数据，获得多极化分量在频带内所有频点的信道响应；
(2)将获得的每个快拍下的多频点信道响应向量化成一个列向量，多个快拍下的信道响应排成一个二维矩阵；此二维矩阵每一列对应于一个快拍下的响应，每一行表示某个收发阵元对在某一频点多个快拍的响应；
(3)利用参考点阵元估计获得多径传播的时延参数；
(4)从步骤(2)中所述的二维矩阵中选取与接收端参考阵元有关的行形成矩阵，以及与发送端参考阵元有关的行形成矩阵，并利用频域平滑降低信道矩阵维度，利用降维后的信道矩阵估计二维离开角和到达角。
作为优选，构造与发送天线数相同组数的不同发送信号序列，每组发送信号序列分为多段子序列，序列不要求正交，满足信号每段子序列矩阵频域满秩即可。
作为优选，重构的信道响应矩阵每一列包含每个极化的收发阵元在所有频点的响应，信道矩阵的列数等于快拍数。
作为优选，所述频域平滑指将所有频点等间隔的分割成长度相同的多组频点，并将它们对应的阵列信道响应相加取平均，得到行数更小的信道响应矩阵，降维后的信道矩阵每一行代表了对应的相加频点处的信道响应之和，信道响应矩阵的列数不发生变化。
进一步地，所述参数估计方法还包括对初始相位、幅度、交叉极化比参数的估计，具体方法是利用已估计的时延和角度参数构建出阵列响应，再利用最小二乘方法获得各个快拍下包含交叉极化比、幅度和各极化组合初始相位的矩阵，对这个矩阵求辐角获得所有子径水平垂直极化组合的初始相位，再利用所求得矩阵每一列与交叉极化比的关系求得交叉极化比，最终利用最小二乘估计求得各个子径在不同快拍的幅度信息。
有益效果：与现有技术相比，本发明具有如下优点：(1)本发明利用宽带扩展的阵列响应能够估计时延域上不可分辨的子径的空间域(二维离开角和二维到达角)、初始相位、幅度和极化域(交叉极化比)参数。(2)在同一时间分辨径内，能分辨的子径数量可以大于阵元数，突破了阵元数对于子径估计数量的限制。(3)采用本方法能够降低信道测量系统的设计复杂度，本方法对阵元之间间距要求较为宽松，阵元间距可以大于半载波波长。
附图说明
图1是本发明实施估计方法的流程图。
图2是本发明实施例中发送信号的结构示意图。
图3是本发明实施例应用的信道传输背景示意图。
图4是本发明实施例中频域平滑技术的原理示意图。
图5是本发明实施例估计的多径时延结果图，N s＝1024。
图6是本发明实施例估计的单一时间可分辨径内子径的二维到达角估计结果图。
图7是本发明实施例估计的单一时间可分辨径内子径的二维离开角估计结果图。
图8是本发明实施例估计的初始相位的估计结果图。
图9是本发明实施例的交叉极化比在不同信噪比下的估计结果图。
图10是本发明实施例的幅度参数的估计结果图。
具体实施方式
下面结合附图和具体实施例，进一步阐明本发明，在本具体实施例中的多极化天线采用极化方式最全面的分布式电磁矢量天线(Electromagnetic Vector Antenna,EMVA)，应理解实施例仅用于说明本发明而不用于限制本发明的范围，在阅读了本发明之后，本领域技术人员对本发明的各种等价形式的修改均落于本申请所附权利要求所限定的范围。术语“多个”指两个或多于两个。本发明实施例中未详细说明的均为现有技术。
本发明公开了一种利用多极化宽带扩展阵列响应的密集多径参数估计方法，利用该方法能够有效估计密集多径环境中的多径参数，包括但不限于时间可分辨径(以下称之为径)内多于阵元数目的子径的参数估计。该方法首先通过多极化天线阵列发送多组不同的发送信号序列，根据已知的发送信号处理多个快拍的接收数据，获得多极化分量在频带内所有频点的信道响应，将获得的每个快拍下的多频点信道响应向量化成一个列向量，多个快拍下的信道响应排成一个二维矩阵；然后通过参考点阵元对的频域信道响应获得时延参数的估计，时延参数的获取可以采用子空间方法如MUSIC或者ESPRIT方法，再利用时延参数和频域平滑获得收发端二维角度信息的估计，这里采用MUSIC方法搜索二维角度谱峰，利用已估计的时延和角度参数构建出阵列响应，再利用最小二乘方法获得各个快拍下包含交叉极化比、幅度和各极化组合初始相位的矩阵，对这个矩阵求辐角可以获得所有子径水平垂直极化组合的初始相位，再利用所求得矩阵每一列与交叉极化比的关系求得交叉极化比的估计，最终利用最小二乘估计求得各个子径在不同快拍的幅度信息。本发明中涉及的具体参数提取原理为现有的传统子空间算法范畴。
图1给出了本发明实施估计方法的流程图，其中H表示全频点的信道响应矩阵，H sm 表示平滑降维后的信道响应矩阵，P表示平滑次数，L表示时域上可分辨径的数目。与之相对应的具体实施步骤如下：
(1)通过多极化天线阵列发送多组不同的发送信号序列；根据已知的发送信号序列对多个快拍的接收数据进行处理，获得多极化分量在频带内所有频点的信道响应。包括以下子步骤：
1)发送信号序列的结构设计
图2给出了本发明所需发送信号的结构示意图。其中M t表示发送电磁矢量天线的个数，(m t,x)表示第m t个分布式EMVA的第x个分量。图中
Figure PCTCN2021081350-appb-000001
表达的含义是第(m t,x)个极化天线分量发送的第l seq个子序列信号。本例中，发送信号序列的构造总共6M t组不同发送信号，每组发送信号有L seq段子序列构成，L seq≥6M t，每段子序列的长度为N s个码元符号长度，也即离散傅里叶变换(DFT)的点数。
2)选择信道传输模型
本发明采用的传输模型如图3所示，其中每一条子径可由括号内的一对数字表示，例如，(l,k l)表示第l个径的第k l条子径，第l个径内的子径数量用K l来表示，这里假设传播环境中总共存在
Figure PCTCN2021081350-appb-000002
条子径。图中M r是接收电磁矢量天线的数量。
3)建立接收信号的表达式
Figure PCTCN2021081350-appb-000003
上式表示接收到的第n个快拍的第l seq个子序列的第n s个符号的表达式，运算符
Figure PCTCN2021081350-appb-000004
表示克罗内克积运算，运算符
Figure PCTCN2021081350-appb-000005
表示按列做克罗内克积。下标f表示频率，上标T表示矩阵的转置。z n表示第n个快拍的噪声。g t和g r分别表示发射端和接收端的电磁矢量天线在Θ t,lk和Θ r,lk方向的方向图增益。变量T表示发送序列的码元宽度，τ l表示第l径的时延参数。其中α n,lk表示第k l条子径在第n个快拍中的幅度，涉及到的参数有τ,Θ r,Θ t,Ξ分别表示径的时延，所有子径的二维到达角，二维发送角以及极化参数集合，部分参数 的定义如下：
Figure PCTCN2021081350-appb-000006
Figure PCTCN2021081350-appb-000007
是到达方位角(azimuth angle of arrival，AAoA)，
Figure PCTCN2021081350-appb-000008
是离开方位角(azimuth angle of departure，AAoD)，θ r是到达俯仰角(elevation angle of arrival，EAoA)，θ t是离开俯仰角(elevation angle of departure，EAoD)。κ是交叉极化比，ω hh,ω hv,ω vh,ω vv是水平和垂直极化四种组合的初始相位。a t(f,Θ t,lk)和A pdt(f,Θ t,lk)(即式1的a t,f(Θ t,lk)和A pdt,f(Θ t,lk)，为了体现对频率的依赖，将f放入括号)分别代表了发送端EMVA阵列空频域的导向矢量和发送端分布式EMVA阵元空域-极化域的联合导向矩阵。对于发射端，a t(f,Θ t,lk)和A pdt(f,Θ t,lk)的表达式可以分别写作如下
Figure PCTCN2021081350-appb-000009
Figure PCTCN2021081350-appb-000010
和u t,lk分别表示第m t个EMVA的坐标和第kl条子径离开角的方向余弦。这里的坐标是空间笛卡尔坐标系下的三维行向量。方向余弦表示的是该方向的单位三维列向量。c表示电磁波在自由空间中的传播速度。其中D t(f,Θ t,lk)表示如下
D t(f,Θ t,lk)＝diag[d t,lk(f,Θ t,lk)]        (式4)
d t,lk(f,Θ t,lk)表示发送端分布式EMVA的空间相移矢量，Ω t(Θ t,lk)表示发送端电磁矢量天线极化域的导向矩阵
Figure PCTCN2021081350-appb-000011
r ex,r ey,r ez,r hx,r hy,r hz分别表示多个极化分量天线相对于EMVA的位置坐标，对于最全面的EMVA而言，极化数量是6，也可以取其中的部分极化。对于接收端的导向矩阵，将以上表达式中下标‘t’替换成‘r’。
T(Ξ lk)是极化扭转矩阵，可以表示为
Figure PCTCN2021081350-appb-000012
Figure PCTCN2021081350-appb-000013
是第k l条子径水平和垂直极化四种组合(hh,hv,vh,vv)的初始相位。
4)计算各个子序列对应的信道响应
对于第n个快拍，将各个子序列的接收信号进行DFT变换，每个子序列都可获得在各个频点的信道响应，再将相同频点的信道响应提取出来归类在一起，对所有的N个快拍都进行相同的操作。例如对于第n个快拍，可以将第i个频点的多极化响应表示为
Figure PCTCN2021081350-appb-000014
具体表达式如下
Figure PCTCN2021081350-appb-000015
其中，
Figure PCTCN2021081350-appb-000016
中包含多个极化的信道响应。本发明中下标f i，i＝1,...,N s表示第i个频点。其中vec表示将矩阵按列向量化操作。
(2)通过步骤(1)，将获得的每个快拍下的多频点信道响应向量化成一个列向量，多个快拍下的信道响应排成一个二维矩阵
Figure PCTCN2021081350-appb-000017
其展现形式如下
Figure PCTCN2021081350-appb-000018
(3)在收发端各选取一个阵元作为参考点(收发端的参考点阵元可以任意选取，并将其坐标设置为参考原点)，利用参考点阵元的信道响应获得多径传播的时延参数。时延参数的获取可以采用子空间方法如MUSIC或者ESPRIT方法。这里假设参考点阵元的信道响应为
Figure PCTCN2021081350-appb-000019
对H τ进行特征分解，获得噪声子空间，再利用传统的子空间算法估计时延参数(具体可参考R.Schmidt的"Multiple emitter location and signal parameter estimation"in IEEE Transactions on Antennas and Propagation)。径的时延参数的估计结果由图5给出。
(4)对于二维离开角的估计，选取出H中与接收端参考阵元有关的行形成矩阵H t，执行下述步骤(5)，对于二维到达角，选取H中与发送端参考阵元有关的行形成矩阵H r，再执行步骤(5)，其中对应的下标‘t’以下标‘r’替换即可。
(5)利用频域平滑降低信道矩阵维度与运算量；利用降维后的信道矩阵估计二维离开角和到达角。通常，所获得的H t维度较高，需要对其进行平滑降维处理，以降低运算成本和噪声的影响，平滑的基本思路由图4给出，将信道响应矩阵H t按行分成P个子阵，P是分割出来的子阵的个数，也是平滑的次数，一般取P可以被N s整除，每个子阵包含N s/P个频点的信道响应，由于ω hh,ω hv,ω vh,ω vv等参数未知，所以采用降秩子空间算法(RD-MUSIC)估计二维到达角(具体可参考E.Ferrara和T.Parks"Direction finding with an array of antennas having diverse polarizations"in IEEE Transactions on Antennas and Propagation)。
本步骤需要注意的是，在对P个分割出来的子阵信道响应进行求和时得到H sm所对应的阵列流形与各个子阵的阵列流形相差一个相移因子，以发射端为例，相移因子表示为
Σ t,P＝(Φ t,0+Φ t,1+...+Φ t,P-1)         (式9)
其中Φ t,p的表达式为
Figure PCTCN2021081350-appb-000020
运算符⊙表示阿达玛积运算。
Figure PCTCN2021081350-appb-000021
表示维度为6M tN s/P×K的全1矩阵。φ t,lk的表达式如下
Figure PCTCN2021081350-appb-000022
其中，Δf是频点之间的间隔。此处的坐标r t,m表示第m个天线单元的位置坐标。对于到达角，参照(4)将(5)中的H t用H r替代即可，再与离开角采用相同的方法步骤即可估计，子径的二维到达角和离开角的估计结果由图6和图7给出。
(6)对估计出来的AoA与AoD进行配对，选取任意频点的阵列响应，将其定义为H pair，对H pair进行特征分解，得到噪声子空间U pair,n，寻找使得下式值最小的角度对，
Figure PCTCN2021081350-appb-000023
其中
Figure PCTCN2021081350-appb-000024
可以表示为
Figure PCTCN2021081350-appb-000025
其中
Figure PCTCN2021081350-appb-000026
表示估计得到的二维到达角和二维离开角。本例中顶标^表示估计所得的参数。
(7)利用已配对的角度参数估计获得子径的交叉极化比、初始相位与幅度参数的估计，最终实现时延、二维离开角、二维到达角和交叉极化比、初始相位以及幅度的多维参数估计。由于矩阵H可以表示为H＝BΓ+Z，B是总的导向矩阵，Γ表示所有快拍的子径幅度矩阵，Z是高斯白噪声。B可以写成B＝AΨ，A和Ψ分别表示如下
Figure PCTCN2021081350-appb-000027
Figure PCTCN2021081350-appb-000028
其中
Figure PCTCN2021081350-appb-000029
Figure PCTCN2021081350-appb-000030
Figure PCTCN2021081350-appb-000031
和
Figure PCTCN2021081350-appb-000032
分别是a t(f i,Θ t,lk),g t(Θ t,lk)和A pdt(f i,Θ t,lk)的简写。根据估计得到的角度和时延参数，可以构建矩阵
Figure PCTCN2021081350-appb-000033
令Π＝ΨΓ，则
Figure PCTCN2021081350-appb-000034
上标‘+’表示矩阵的伪逆，对
Figure PCTCN2021081350-appb-000035
按列求和得到列向量v，其表示如下
Figure PCTCN2021081350-appb-000036
相位的初始值可以估计为
Figure PCTCN2021081350-appb-000037
这里arg表示取辐角运算。交叉极化比的估计表示为
Figure PCTCN2021081350-appb-000038
其中，小括号中的数字(1，2，3，4)表示向量v l,k的第(1，2，3，4)个元素。根据估计的初始相位和交叉极化比的估计可以构建
Figure PCTCN2021081350-appb-000039
则所有子径的所有快拍下的幅度可以估计为
Figure PCTCN2021081350-appb-000040
图8给出了本发明算法初始相位的估计结果。图9给出了本发明算法交叉极化比的估计结果。图10给出了本发明算法幅度的估计结果。从估计的结果图中不难看出，各个子径的初始相位、交叉极化比和幅度都与设定值相吻合，这些参数通过本方法能够完美估计出来。

Claims (5)

  1. 一种利用多极化宽带扩展阵列响应的密集多径参数估计方法，其特征在于，包括以下步骤：
    (1)通过多极化天线阵列发送多组不同的发送信号序列，组数等于发送天线的个数，每组发送信号序列分为不同的段，每组段数不小于发送天线的个数，每一段信号序列的长度不小于离散傅里叶变换的点数，根据已知的发送信号处理多个快拍的接收数据，获得多极化分量在频带内所有频点的信道响应；
    (2)将获得的每个快拍下的多频点信道响应向量化成一个列向量，多个快拍下的信道响应排成一个二维矩阵；此二维矩阵每一列对应于一个快拍下的响应，每一行表示某个收发阵元对在某一频点多个快拍的响应；
    (3)利用参考点阵元估计获得多径传播的时延参数；
    (4)从步骤(2)中所述的二维矩阵中选取与接收端参考阵元有关的行形成矩阵，以及与发送端参考阵元有关的行形成矩阵，并利用频域平滑降低信道矩阵维度，利用降维后的信道矩阵估计二维离开角和到达角。
  2. 根据权利要求1所述的利用多极化宽带扩展阵列响应的密集多径参数估计方法，其特征在于，构造与发送天线数相同组数的不同发送信号序列，每组发送信号序列分为多段子序列，序列不要求正交，满足信号每段子序列矩阵频域满秩即可。
  3. 根据权利要求1所述的利用多极化宽带扩展阵列响应的密集多径参数估计方法，其特征在于，重构的信道响应矩阵每一列包含每个极化的收发阵元在所有频点的响应，信道矩阵的列数等于快拍数。
  4. 根据权利要求1所述的利用多极化宽带扩展阵列响应的密集多径参数估计方法，其特征在于，所述频域平滑指将所有频点等间隔的分割成长度相同的多组频点，并将它们对应的阵列信道响应相加取平均，得到行数更小的信道响应矩阵，降维后的信道矩阵每一行代表了对应的相加频点处的信道响应之和，信道响应矩阵的列数不发生变化。
  5. 根据权利要求1所述的利用多极化宽带扩展阵列响应的密集多径参数估计方法，其特征在于，还包括对初始相位、幅度、交叉极化比参数的估计，具体方法是利用已估计的时延和角度参数构建出阵列响应，再利用最小二乘方法获得各个快拍下包含交叉极化比、幅度和各极化组合初始相位的矩阵，对这个矩阵求辐角获得所有子径水平垂直极化组合的初始相位，再利用所求得矩阵每一列与交叉极化比的关系求得交叉极化比，最终利用最小二乘估计求得各个子径在不同快拍的幅度信息。
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YANG BENSHENG; ZHANG PEIZE; WANG HAIMING; HONG WEI: "Efficient Delay and AoA Estimation Using Vector Antenna for Radio Propagation Measurements", 2019 IEEE INTERNATIONAL SYMPOSIUM ON ANTENNAS AND PROPAGATION AND USNC-URSI RADIO SCIENCE MEETING, IEEE, 7 July 2019 (2019-07-07), pages 2125 - 2126, XP033654285, DOI: 10.1109/APUSNCURSINRSM.2019.8888694 *

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