CN111859272A - Rapid MUSIC spectrum decomposition method, device and equipment for large-scale antenna - Google Patents

Rapid MUSIC spectrum decomposition method, device and equipment for large-scale antenna Download PDF

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CN111859272A
CN111859272A CN202010086714.4A CN202010086714A CN111859272A CN 111859272 A CN111859272 A CN 111859272A CN 202010086714 A CN202010086714 A CN 202010086714A CN 111859272 A CN111859272 A CN 111859272A
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李斌
曹先彬
赵成林
许方敏
张军
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Beihang University
Beijing University of Posts and Telecommunications
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Abstract

The invention discloses a rapid MUSIC spectrum decomposition method, a rapid MUSIC spectrum decomposition device and a rapid MUSIC spectrum decomposition device for large-scale antennas, wherein the rapid MUSIC spectrum decomposition device comprises the following steps: receiving a signal X, and estimating a high-dimensional autocorrelation matrix R according to the signal X; performing skeleton extraction on the high-dimensional autocorrelation matrix R to obtain a low-dimensional characterization matrix C; calculating to obtain a low-rank matrix Y, obtaining a low-dimensional approximate decomposition CY of a high-dimensional autocorrelation matrix R, and performing SVD on the low-dimensional approximate decomposition CY to obtain SVD of the high-dimensional autocorrelation matrix R
Figure DDA0002382315910000011
SVD approximate decomposition using high-dimensional autocorrelation matrix R
Figure DDA0002382315910000012
Constructing a signal space K, estimating a space spectrum P (theta) by using the signal space K, and detecting and estimating a target signal according to the space spectrum P (theta). The method reduces the computation complexity of the SVD from cubic increase to square or even linear increase rate while accurately estimating the MUSIC spatial spectrum, realizes the MUSIC spatial spectrum estimation with high precision and low complexity, and ensures the error precision of high-dimensional autocorrelation matrix approximation by using the minimization of matrix norm as an optimization criterion.

Description

Rapid MUSIC spectrum decomposition method, device and equipment for large-scale antenna
Technical Field
The invention relates to the field of information, in particular to a rapid MUSIC spectrum decomposition method, a rapid MUSIC spectrum decomposition device and rapid MUSIC spectrum decomposition equipment for large-scale antennas.
Background
The large-scale antenna array can increase the estimated signal-to-noise ratio and the spatial resolution, meanwhile, the required computational complexity and processing time delay can not be borne, and the large-scale antenna array is difficult to apply in typical application scenes such as millimeter wave radar target detection and phased array radar beam forming. The MUSIC method has the core idea that a signal or noise subspace is obtained by dividing based on characteristic value decomposition or singular value decomposition, the target space position is estimated through the signal or noise subspace, and when the number of antennas is large, the calculation complexity is extremely high; even if a high-performance CPU is adopted in the processing process, the processing time delay is long, and the application requirement for quickly implementing target estimation and data analysis is difficult to meet. Although the prior art provides a low-rank decomposition method, the computation complexity and the processing delay are reduced to a certain extent, the precision cannot be guaranteed, and the computation complexity and the processing delay cannot be borne as the number of antennas is further increased.
Disclosure of Invention
In view of this, the present invention provides a fast MUSIC spectrum decomposition method and apparatus for a large-scale antenna, so as to solve the defects of high processing delay, low precision and high computation complexity in the prior art.
Based on the above purpose, the present invention provides a fast MUSIC spectrum decomposition method for large-scale antennas, which includes:
receiving a signal X, and estimating a high-dimensional autocorrelation matrix R according to the signal X;
performing skeleton extraction on the high-dimensional autocorrelation matrix R to obtain a low-dimensional characterization matrix C;
determining a low-rank matrix Y, obtaining a low-dimensional approximate decomposition CY of the high-dimensional autocorrelation matrix R according to the C and the Y, and obtaining an SVD approximate decomposition of the high-dimensional autocorrelation matrix R by carrying out SVD on the low-dimensional approximate decomposition CY
Figure BDA0002382315890000021
SVD approximate decomposition using the high-dimensional autocorrelation matrix R
Figure BDA0002382315890000022
And constructing a signal space K, estimating a space spectrum P (theta) by using the signal space K, and detecting and estimating a target signal according to the space spectrum P (theta).
Alternatively, the signal X can be represented as
X＝AB+E
Wherein E ═ E1(t)e2(t)…eK(t)]TIs an independent and identically distributed noise matrix of dimension M x N, e1(t)e2(t)…eK(t) is a superimposed noise signal in the echo signals of the K targets, a ═ a (θ)1)a(θ2)…a(θk)]TIs a direction vector matrix of M × K dimension, a (theta)1)a(θ2)…a(θk) Direction vectors of K targets, B is a target signal matrix;
said estimating a high-dimensional autocorrelation matrix R from said signal X comprises:
calculating the high-dimensional autocorrelation matrix R-XX from the signal X estimate HWherein X and XHAre conjugated to each other.
Optionally, the low-dimensional characterization matrix
Figure BDA0002382315890000023
Wherein
Figure BDA0002382315890000024
Is a complex space, S is an equivalent extraction matrix, and the characteristics of the equivalent extraction matrix S comprise:
each row of elements has 1 and only 1 non-zero value, and the non-zero value positions are randomly distributed in the s length;
the non-zero value takes the value { +1, -1} with equal probability.
Optionally, the calculating to obtain the low rank matrix Y includes:
the low-rank matrix Y is obtained by constructing a first auxiliary low-dimensional framework matrix W and a second auxiliary low-dimensional framework matrix Z, the first auxiliary low-dimensional framework matrix W and the second auxiliary low-dimensional framework matrix Z are obtained by constructing a framework extraction matrix P, and the framework extraction matrix P is obtained by matrix PSAnd matrix PGAnd (4) forming.
Optionally, the first auxiliary low-dimensional skeleton matrix W selects P rows of the low-dimensional representation matrix C to construct according to the skeleton extraction matrix P.
Optionally, the second auxiliary low-dimensional skeleton matrix Z selects P rows of the high-dimensional autocorrelation matrix R to construct according to the skeleton decimation matrix P; the matrix PGEach element is subjected to independent Gaussian distribution with the same distribution, and normalization processing is carried out.
Optionally, the low-dimensional approximate decomposition CY of the high-dimensional autocorrelation matrix R is obtained, and the SVD approximate decomposition of the high-dimensional autocorrelation matrix R is obtained by performing SVD decomposition on the low-dimensional approximate decomposition CY
Figure BDA0002382315890000031
The method comprises the following steps:
obtaining the low-dimensional approximate decomposition CY according to the low-dimensional characterization matrix C and the low-rank matrix Y, and defining a matrix QWZ, matrix
Figure BDA0002382315890000032
Sum matrix
Figure BDA0002382315890000033
According to the matrix QWZ, matrix
Figure BDA0002382315890000034
Sum matrix
Figure BDA0002382315890000035
Obtaining an SVD approximate decomposition of the high-dimensional autocorrelation matrix R
Figure BDA0002382315890000036
Wherein U is the matrix QWA first K-order SVD decomposition matrix of Z, Σ being said matrix QWA second K-th order SVD decomposition matrix of Z, V being said matrix QWA third K-th order SVD decomposition matrix of Z, V' being said matrix
Figure BDA0002382315890000037
The SVD of (a) is decomposed,
Figure BDA0002382315890000038
is the matrix
Figure BDA0002382315890000039
The transposed matrix of (2).
Optionally, the signal space K is divided into a signal subspace and a noise subspace, and the spatial spectrum P (θ) is estimated through any one of the signal subspace and the noise subspace.
Based on the above object, an embodiment of the present invention further provides a fast MUSIC spectrum decomposition apparatus for a large-scale antenna, including:
an estimation module configured to receive a signal X from which a high-dimensional autocorrelation matrix R is estimated;
the extraction module is configured to perform skeleton extraction on the high-dimensional autocorrelation matrix R to obtain a low-dimensional characterization matrix C;
a decomposition module configured to calculate a low rank matrix Y, obtain a low-dimensional approximate decomposition CY of the high-dimensional autocorrelation matrix R, and obtain a SVD approximate decomposition of the high-dimensional autocorrelation matrix R by performing SVD on the low-dimensional approximate decomposition CY
Figure BDA00023823158900000310
An execution module configured toSVD approximate decomposition using the high-dimensional autocorrelation matrix R
Figure BDA00023823158900000311
A signal space K is constructed, with which the spatial spectrum P (θ) is estimated.
In view of the above object, an embodiment of the present invention further provides an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, where the processor implements any one of the above methods when executing the program.
From the above, it can be seen that the fast MUSIC spectrum decomposition method and apparatus for large-scale antennas provided by the present invention are different from the low rank SVD decomposition Block Lanczos algorithm in the prior art, the low-dimensional matrix skeleton extraction is directly carried out on the high-dimensional autocorrelation matrix, the approximate representation C of the low-dimensional skeleton space is constructed by a random sampling method to obtain the low-dimensional space approximate matrix decomposition, the CY is utilized to approximate the high-dimensional autocorrelation matrix R, SVD decomposition transformation is carried out on the low-rank decomposition matrixes C and Y, finally approximate SVD decomposition of the high-dimensional autocorrelation matrix R and quick MUSIC spectrum estimation are realized, the method can reduce the computation complexity and the processing time delay of the large-scale matrix decomposition to the maximum extent, can ensure that the precision of the MUSIC spectrum estimation is not influenced, has wide application scenes, the method has important theoretical value and application potential in future millimeter wave radar and air-space network signal processing.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flowchart of a fast MUSIC spectrum decomposition method for large-scale antennas according to an embodiment of the present invention;
FIG. 2 is a diagram illustrating a low-dimensional skeleton extraction principle of a high-dimensional autocorrelation matrix according to an embodiment of the present invention;
FIG. 3 is a block diagram of a fast MUSIC spectrum decomposition apparatus for large-scale antenna according to an embodiment of the present invention;
FIG. 4 is a block diagram of an electronic device according to an embodiment of the invention;
FIG. 5 is a comparison graph of CPU computation delays for the method of the present invention and the prior art spectral estimation method in an embodiment of the present invention;
FIG. 6 is a graph comparing processing time gain for the method of the present invention and the prior art in an embodiment of the present invention;
fig. 7 is a comparison graph of the spatial spectrum obtained by the method of the present invention and full rank MUSIC spectrum estimation in the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to specific embodiments and the accompanying drawings.
It should be noted that all expressions using "first" and "second" in the embodiments of the present invention are used for distinguishing two entities with the same name but different names or different parameters, and it should be noted that "first" and "second" are merely for convenience of description and should not be construed as limitations of the embodiments of the present invention, and they are not described in any more detail in the following embodiments.
The embodiment of the invention provides a rapid MUSIC spectrum decomposition method, a rapid MUSIC spectrum decomposition device and rapid MUSIC spectrum decomposition equipment for a large-scale antenna.
Referring to fig. 1, a method of an embodiment of the invention includes the steps of:
s101, receiving a signal X, and estimating a high-dimensional autocorrelation matrix R according to the signal X.
In this step, K target signal sources are considered, wherein the K-th target emission signal is denoted as Sk(T) (T is 0,1, …, T), and the azimuth of arrival of the signal is θk(ii) a Suppose that the radar receiving system adopts M uniform linear arrays and meets M>K, then the kth target wave path difference relative to the 1 st reference receiving antenna or sensor is
Figure BDA0002382315890000051
Wherein d is the array element arrangement distance, lambda is the signal wavelength, and the signal wavelength is related to the working frequency band of the target detection signal; defining an orientation vector as a (theta) k) The K target signal matrixes are B ═ B1(t)b2(t)…bK(t)]Then the overall received signal can be expressed as:
X＝AB+E
wherein the content of the first and second substances,
Figure BDA0002382315890000052
is a, b1(t)b2(t)…bK(t) K target echo signals, E ═ E1(t)e2(t)…eK(t)]TIs an independent and identically distributed noise matrix of dimension M x N, e1(t)e2(t)…eK(t) is a superimposed noise signal in the echo signals of the K targets, a ═ a (θ)1)a(θ2)…a(θk)]TIs an M multiplied by K dimension direction vector matrix. By means of array signal processing, noise can be effectively suppressed, and then a plurality of target azimuth angles can be estimated, and the process is realized by utilizing a MUSIC algorithm.
S102, performing skeleton extraction on the high-dimensional autocorrelation matrix R to obtain a low-dimensional characterization matrix C.
In this step, a skeleton is extracted from the high-dimensional autocorrelation matrix R to obtain a low-dimensional characterization matrix C, i.e., the dimensionality of the high-dimensional autocorrelation matrix is reduced from mxm to mxs, see fig. 2, e.g., the high-dimensional autocorrelation matrix RM×MThe dimension of (A) is MxM, and a matrix C with the dimension of Mxs is obtained by utilizing skeleton extractionM×sRS and a matrix X of dimension sxms×MAnd dimension reduction is realized. To this end, an equivalent extraction matrix is defined as
Figure BDA0002382315890000053
In particular, the S matrix has the following two features: each row of elements has 1 non-zero value, and the positions of the non-zero values are randomly distributed in the s length; the non-zero value takes the value { +1, -1} with equal probability. The extracted low-dimensional skeleton matrix is marked as
Figure BDA0002382315890000054
In actual operation, s ≧ K needs to be ensured in order to ensure the calculation accuracy.
S103, calculating to obtain a low-rank matrix Y, obtaining a low-dimensional approximate decomposition CY of the high-dimensional autocorrelation matrix R, and performing SVD (singular value decomposition) on the low-dimensional approximate decomposition CY to obtain an SVD approximate decomposition of the high-dimensional autocorrelation matrix R
Figure BDA0002382315890000061
In this step, a low-dimensional matrix decomposition CY is further searched in the skeleton matrix space to approximate a high-dimensional autocorrelation matrix R, and since the low-dimensional skeleton matrix C is already obtained, only another low-dimensional projection matrix Y needs to be constructed. For this purpose, it is first necessary to construct a first auxiliary low-dimensional skeleton matrix
Figure BDA0002382315890000062
And a second auxiliary low-dimensional skeleton matrix
Figure BDA0002382315890000063
Wherein p > s > K. Directly adopting a construction method similar to the equivalent extraction matrix S, fusing Gaussian projection matrixes, and respectively constructing
Figure BDA0002382315890000064
And
Figure BDA0002382315890000065
as an alternative embodiment, a new skeleton extraction matrix is defined as
Figure BDA0002382315890000066
Wherein
Figure BDA0002382315890000067
Completely consistent with the construction process of the equivalent extraction matrix S, each row only has one nonzero element { +1, -1}, and the positions are randomly distributed and only change in dimension, p1Representing a dimension index; for the
Figure BDA0002382315890000068
A gaussian projection matrix is directly used in which each element is a random variable subject to an independent identically distributed gaussian distribution. At the same time, the matrix P needs to be aligned SAnd matrix PGRespectively carrying out normalization processing, thus obtaining a first auxiliary low-dimensional framework matrix W and a second auxiliary low-dimensional framework matrix Z:
Figure BDA0002382315890000069
wherein P isTIs a transposed matrix of the matrix P, PG TIs a matrix PGTransposed matrix of (1), PS TIs a matrix PSOn this basis, the low-dimensional projection matrix Y can be obtained by solving the following matrix norm optimization problem:
Figure BDA00023823158900000610
where rank (Y) is the rank of the low-dimensional projection matrix Y. The optimal projection matrix that satisfies the matrix norm optimization problem is finally obtained as follows:
Figure BDA00023823158900000611
wherein [ Q ]W,RW]QR (QR) (W) stands for QR decomposition for matrix W,
Figure BDA00023823158900000612
is a matrix RWThe transpose of (c) is conjugated. Based on the matrix approximate decomposition process, the product CY of two low-dimensional matrixes in the low-dimensional framework space can be adopted to approximate the high-dimensional autocorrelation matrix R.
And (4) performing indirect SVD on R by using low-dimensional approximate decomposition CY. Specifically, Q is first definedWZ＝UΣVTWherein
Figure BDA0002382315890000071
Is a matrix QWThe first K-th order SVD decomposition matrix of Z,
Figure BDA0002382315890000072
is a matrix QWThe second K-th order SVD decomposition matrix of Z,
Figure BDA0002382315890000073
is a matrix QWA third K order SVD decomposition matrix of Z, wherein
Figure BDA0002382315890000074
For real space, the corresponding computational complexity is
Figure BDA0002382315890000075
At the same time, define
Figure BDA0002382315890000076
Wherein
Figure BDA0002382315890000077
Is a matrix
Figure BDA0002382315890000078
Is performed in a first SVD decomposition of (a),
Figure BDA0002382315890000079
is a matrix
Figure BDA00023823158900000710
Is generated by the second SVD decomposition of (1),
Figure BDA00023823158900000711
Is a matrix
Figure BDA00023823158900000712
Of a corresponding computational complexity of
Figure BDA00023823158900000713
Further define the
Figure BDA00023823158900000714
And obtaining SVD approximate decomposition of a high-dimensional autocorrelation matrix R:
Figure BDA00023823158900000715
s104 SVD approximate decomposition using the high-dimensional autocorrelation matrix R
Figure BDA00023823158900000716
And constructing a signal space K, estimating a space spectrum P (theta) by using the signal space K, and detecting and estimating a target signal according to the space spectrum P (theta).
In this step, the matrix is decomposed according to the low-dimensional approximated SVD
Figure BDA00023823158900000717
And calculating to obtain a final MUSIC spectrum estimation result. Note that since the above approximate decomposition only yields a signal subspace, the noise space is not included in the calculation and estimation process; the signal subspace is further relied upon to perform the MUSIC spectrum estimation procedure. Specifically, there are
Figure BDA00023823158900000718
Wherein the content of the first and second substances,
Figure BDA00023823158900000719
σ2is the noise variance, I is the identity matrix; finally, the MUSIC spatial spectrum is calculated by using the following relation:
Figure BDA00023823158900000720
wherein a isH(theta) and a (theta) are conjugate to each other,
Figure BDA00023823158900000721
and
Figure BDA00023823158900000722
are conjugated to each other.As an optional embodiment, the obtained MUSIC spatial spectrum is used for environment sensing, target signal detection, estimation and tracking of a vehicle-mounted radar, accurate radar signal detection and accurate target signal estimation are realized in a radar satellite system and a wireless communication system, and the method has no special requirements on signal transmission characteristics, so that the method can be directly expanded to a more complex multipath scattering environment.
A high-dimensional autocorrelation matrix R can be approximated by performing low-dimensional matrix decomposition using a low-dimensional skeleton space; then, the SVD problem aiming at the high-dimensional autocorrelation matrix R is converted into the SVD process of the small matrixes C and Y in the low-dimensional skeleton space, so that the complexity of the decomposition calculation of the high-dimensional autocorrelation matrix R can be reduced on the whole. In summary, the computational complexity involved in the proposed method of the present invention mainly includes three parts. The first part is a matrix dimension reduction and skeleton extraction process, and the first part mainly relates to the linear combination of column vectors of a high-dimensional autocorrelation matrix R, and the required computational complexity is { +1, -1} due to the weighting coefficients
Figure BDA0002382315890000081
The second part further obtains a matrix approximation decomposition in the low-dimensional space, similar to the first part, in which a new skeleton extraction matrix is calculated
Figure BDA0002382315890000082
The required computational complexity is
Figure BDA0002382315890000083
Then, in order to calculate the W and Z matrices, the required computational complexity is
Figure BDA0002382315890000084
Especially when the high-dimensional autocorrelation matrix R has sparse characteristics, the complexity is about
Figure BDA0002382315890000085
Where nnz (R) is the number of non-zero elements in the high-dimensional autocorrelation matrix R, and the complexity required to finally calculate the matrix Y is about
Figure BDA0002382315890000086
Third, for small low-dimensional matrices
Figure BDA0002382315890000087
And QWThe SVD decomposition of Z requires a computational complexity of
Figure BDA0002382315890000088
The overall computational complexity of the method of the invention is
Figure BDA0002382315890000089
When the high-dimensional autocorrelation matrix R has sparse characteristics, the complexity is linear with the number M of antennas, and when R does not have sparse characteristics, the required calculation complexity is
Figure BDA00023823158900000810
Complexity approaching 1 st order SVD decomposition
Figure BDA00023823158900000811
Complexity compared to full rank SVD decomposition
Figure BDA00023823158900000812
And K order SVD decomposition complexity
Figure BDA00023823158900000813
In other words, the method can effectively reduce the computational complexity, the processing time delay and the power consumption overhead of the MUSIC spectrum estimation method.
The rapid MUSIC spectrum decomposition method and device for the large-scale antenna are different from the low-rank SVD decomposition Block Lanczos algorithm in the prior art, the low-dimensional matrix skeleton extraction is directly carried out on the high-dimensional autocorrelation matrix, the approximate representation C of the low-dimensional skeleton space is constructed by a random sampling method to obtain the low-dimensional space approximate matrix decomposition, the CY is utilized to approximate the high-dimensional autocorrelation matrix R, SVD decomposition transformation is carried out on the low-rank decomposition matrixes C and Y, finally approximate SVD decomposition of the high-dimensional autocorrelation matrix R and quick MUSIC spectrum estimation are realized, the method can reduce the computation complexity and the processing time delay of the large-scale matrix decomposition to the maximum extent, can ensure that the precision of the MUSIC spectrum estimation is not influenced, has wide application scenes, the method has important theoretical value and application potential in future millimeter wave radar and air-space network signal processing.
Based on the same inventive concept, the embodiment of the invention also provides a rapid MUSIC spectrum decomposition device facing the large-scale antenna, which comprises an estimation module, an extraction module, a decomposition module and an execution module.
Referring to fig. 3, the apparatus includes:
an estimation module configured to receive a signal X from which a high-dimensional autocorrelation matrix R is estimated;
the extraction module is configured to perform skeleton extraction on the high-dimensional autocorrelation matrix R to obtain a low-dimensional characterization matrix C;
a decomposition module configured to calculate a low rank matrix Y, obtain a low-dimensional approximate decomposition CY of the high-dimensional autocorrelation matrix R, and obtain a SVD approximate decomposition of the high-dimensional autocorrelation matrix R by performing SVD on the low-dimensional approximate decomposition CY
Figure BDA0002382315890000091
An execution module configured to utilize SVD approximate decomposition of the high-dimensional autocorrelation matrix R
Figure BDA0002382315890000092
And constructing a signal space K, estimating a space spectrum P (theta) by using the signal space K, and detecting and estimating a target signal according to the space spectrum P (theta).
The apparatus of the foregoing embodiment is used to implement the corresponding method in the foregoing embodiment, and has the beneficial effects of the corresponding method embodiment, which are not described herein again.
Based on the same inventive concept, an embodiment of the present invention further provides an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the method when executing the computer program.
Fig. 4 is a schematic diagram illustrating a more specific hardware structure of an electronic device according to this embodiment, where the electronic device may include: a processor 401, a memory 402, an input/output interface 403, a communication interface 404, and a bus 405. Wherein the processor 401, the memory 402, the input/output interface 403 and the communication interface 404 are communicatively connected to each other within the device by a bus 405.
The processor 401 may be implemented by a general-purpose CPU (Central Processing Unit), a microprocessor, an Application Specific Integrated Circuit (ASIC), or one or more Integrated circuits, and is configured to execute related programs to implement the technical solutions provided in the embodiments of the present specification.
The Memory 402 may be implemented in the form of a ROM (Read Only Memory), a RAM (Random access Memory), a static storage device, a dynamic storage device, or the like. The memory 402 may store an operating system and other application programs, and when the technical solution provided by the embodiments of the present specification is implemented by software or firmware, the relevant program codes are stored in the memory 402 and called to be executed by the processor 401.
The input/output interface 403 is used for connecting an input/output module to realize information input and output. The input/output/modules may be configured in the device as components or may be external to the device to provide corresponding functionality. The input devices may include a keyboard, a mouse, a touch screen, a microphone, various sensors, etc., and the output devices may include a display, a speaker, a vibrator, an indicator light, etc.
The communication interface 404 is used for connecting a communication module to realize communication interaction between the device and other devices. The communication module can realize communication in a wired mode (such as USB, network cable and the like) and also can realize communication in a wireless mode (such as mobile network, WIFI, Bluetooth and the like).
The bus 405 includes a path that transfers information between the various components of the device, such as the processor 401, memory 402, input/output interface 403, and communication interface 404.
It should be noted that although the above-mentioned device only shows the processor 401, the memory 402, the input/output interface 403, the communication interface 404 and the bus 405, in a specific implementation, the device may also include other components necessary for normal operation. In addition, those skilled in the art will appreciate that the above-described apparatus may also include only those components necessary to implement the embodiments of the present description, and not necessarily all of the components shown in the figures.
In order to intuitively show the advantages of the rapid MUSIC spectrum decomposition method and device facing to the large-scale antenna, the problems of MUSIC target detection and space angle estimation under the large-scale antenna array element are considered, the number of the antennas of the radar receiver is increased from 200 to 1500, K independent targets are assumed to be uniformly distributed in a [0,90] degree space, and a transmission channel adopts a Gaussian channel. In order to verify the effectiveness of the method, the conventional classical MUSIC method is analyzed and compared, namely, a full-rank SVD decomposition method is directly adopted to obtain a signal space K and a noise space E, and a MUSIC method based on a low-rank SVD decomposition method is adopted, different methods run on a Matlab platform, the working dominant frequency of a CPU (Central processing Unit) is 3.3GHz, the internal memory is 4GB, 64 bits of an operating system are independently carried out for 30 times in a simulation experiment, and then the average is carried out after the operations.
Referring to FIG. 5, the CPU processing time required for the different MUSIC methods, and to FIG. 6, the time gain of the new method relative to the prior method, wherein the processing time gain is defined as Tmusic/TnewAnd Tk-svd/TnewWherein T ismusic、Tk-svdAnd TnewRespectively representing the CPU processing time required by the full-rank SVD-MUSIC method, the low-rank K-SVD MUSIC method and the new method. It can be found that with the increase of the number of the antenna array elements, the processing time gain of the method is linearly increased compared with the classical full-rank SVD-MUSIC method, when the number of the antennas is 1500, the required calculation time of the MUSIC method can be reduced by about 1/45, and compared with the most efficient low-rank K-SVD MUSIC method, the hot-cut method can obtain about 5 times of processing gain.
Referring to fig. 7, the method of the present invention significantly reduces the computation complexity and processing delay, but the estimation accuracy is such that the detection performance is not affected, and the obtained MUSIC spatial spectrum estimation result is almost completely consistent with the full rank MUSIC method. The method of the invention does not sacrifice the estimation precision and the detection performance while fully reducing the complexity of the large-scale antenna radar signal processing, thereby having very important theoretical significance and practical application value for future high-resolution millimeter wave radar, large-scale antenna radar signal processing and large-scale phased array satellite communication.
Those of ordinary skill in the art will understand that: the discussion of any embodiment above is meant to be exemplary only, and is not intended to intimate that the scope of the disclosure, including the claims, is limited to these examples; within the idea of the invention, also technical features in the above embodiments or in different embodiments may be combined and there are many other variations of the different aspects of the invention as described above, which are not provided in detail for the sake of brevity. Therefore, any omissions, modifications, substitutions, improvements and the like that may be made without departing from the spirit and principles of the invention are intended to be included within the scope of the invention.

Claims (10)

1. A rapid MUSIC spectrum decomposition method facing a large-scale antenna is characterized by comprising the following steps:
receiving a signal X, and estimating a high-dimensional autocorrelation matrix R according to the signal X;
performing skeleton extraction on the high-dimensional autocorrelation matrix R to obtain a low-dimensional characterization matrix C;
determining a low-rank matrix Y, obtaining a low-dimensional approximate decomposition CY of the high-dimensional autocorrelation matrix R according to the C and the Y, and obtaining an SVD approximate decomposition of the high-dimensional autocorrelation matrix R by carrying out SVD on the low-dimensional approximate decomposition CY
Figure FDA0002382315880000011
SVD approximate decomposition using the high-dimensional autocorrelation matrix R
Figure FDA0002382315880000012
And constructing a signal space K, estimating a space spectrum P (theta) by using the signal space K, and detecting and estimating a target signal according to the space spectrum P (theta).
2. Method according to claim 1, characterized in that said signal X is representable as
X＝AB+E
Wherein E ═ E1(t) e2(t) … eK(t)]TIs an independent and identically distributed noise matrix of dimension M x N, e1(t) e2(t) …eK(t) is a superimposed noise signal in the echo signals of the K targets, a ═ a (θ)1) a(θ2) … a(θk)]TIs a direction vector matrix of M × K dimension, a (theta)1) a(θ2) … a(θk) Direction vectors of K targets, B is a target signal matrix;
said estimating a high-dimensional autocorrelation matrix R from said signal X comprises:
calculating the high-dimensional autocorrelation matrix R-XX from the signal X estimate HWherein X and XHAre conjugated to each other.
3. The method of claim 2, wherein the low-dimensional characterization matrix
Figure FDA0002382315880000013
Wherein
Figure FDA0002382315880000014
Is a complex space, S is an equivalent extraction matrix, and the characteristics of the equivalent extraction matrix S comprise:
each row of elements has 1 and only 1 non-zero value, and the non-zero value positions are randomly distributed in the s length;
the non-zero value takes the value { +1, -1} with equal probability.
4. The method of claim 1, wherein the computing results in a low rank matrix Y comprising:
the low-rank matrix Y is obtained by constructing a first auxiliary low-dimensional framework matrix W and a second auxiliary low-dimensional framework matrix Z, the first auxiliary low-dimensional framework matrix W and the second auxiliary low-dimensional framework matrix Z are obtained by constructing a framework extraction matrix P, and the framework extraction matrix P is obtained by matrix PSAnd matrix PGAnd (4) forming.
5. The method according to claim 4, wherein the first auxiliary low-dimensional skeleton matrix W is constructed by selecting P rows of the low-dimensional characterization matrix C according to the skeleton extraction matrix P.
6. The method according to claim 4, wherein the second auxiliary low-dimensional skeleton matrix Z selects P rows of the high-dimensional autocorrelation matrix R for construction according to the skeleton extraction matrix P; the matrix P GEach element is subjected to independent Gaussian distribution with the same distribution, and normalization processing is carried out.
7. The method according to claim 1, wherein said obtaining a low-dimensional approximate decomposition CY of said high-dimensional autocorrelation matrix R obtains a SVD approximate decomposition CY of said high-dimensional autocorrelation matrix R by performing a SVD decomposition on said low-dimensional approximate decomposition CY
Figure FDA0002382315880000021
The method comprises the following steps:
obtaining the low-dimensional approximate decomposition CY according to the low-dimensional characterization matrix C and the low-rank matrix Y, and defining a matrix QWZ, matrix
Figure FDA0002382315880000022
Sum matrix
Figure FDA0002382315880000023
According to the matrix QWZ, matrix
Figure FDA0002382315880000024
Sum matrix
Figure FDA0002382315880000025
Obtaining an SVD approximate decomposition of the high-dimensional autocorrelation matrix R
Figure FDA0002382315880000026
Wherein U is the matrix QWA first K-order SVD decomposition matrix of Z, Σ being said matrix QWA second K-th order SVD decomposition matrix of Z, V being said matrix QWA third K-th order SVD decomposition matrix of Z, V' being said matrix
Figure FDA0002382315880000027
The SVD of (a) is decomposed,
Figure FDA0002382315880000028
is the matrix
Figure FDA0002382315880000029
The transposed matrix of (2).
8. The method according to claim 1, characterized in that the signal space K is divided into a signal subspace and a noise subspace, the spatial spectrum P (θ) being estimated by either of the signal subspace and the noise subspace.
9. A fast MUSIC spectrum decomposition device facing a large-scale antenna is characterized by comprising:
An estimation module configured to receive a signal X from which a high-dimensional autocorrelation matrix R is estimated;
the extraction module is configured to perform skeleton extraction on the high-dimensional autocorrelation matrix R to obtain a low-dimensional characterization matrix C;
a decomposition module configured to calculate a low rank matrix Y and obtain a low-dimensional approximate decomposition CY of the high-dimensional autocorrelation matrix R by applying a decomposition to the low-dimensional autocorrelation matrixSVD approximate decomposition of the high-dimensional autocorrelation matrix R by SVD decomposition of the approximate decomposition CY
Figure FDA0002382315880000031
An execution module configured to utilize SVD approximate decomposition of the high-dimensional autocorrelation matrix R
Figure FDA0002382315880000032
And constructing a signal space K, estimating a space spectrum P (theta) by using the signal space K, and detecting and estimating a target signal according to the space spectrum P (theta).
10. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the method according to any of claims 1 to 8 when executing the program.
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