CN108809873B - Signal synthesis method and system - Google Patents

Signal synthesis method and system Download PDF

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CN108809873B
CN108809873B CN201810611506.4A CN201810611506A CN108809873B CN 108809873 B CN108809873 B CN 108809873B CN 201810611506 A CN201810611506 A CN 201810611506A CN 108809873 B CN108809873 B CN 108809873B
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王雷欧
王东辉
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Institute of Acoustics CAS
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Abstract

The invention discloses a signal synthesis method and a signal synthesis system. Firstly, establishing an objective function related to a synthetic signal, and determining a characteristic matrix to be solved corresponding to a synthetic weight vector according to the objective function; then, calculating the characteristic matrix to be solved by adopting a matrix blocking recursive algorithm, and obtaining the solved characteristic matrix; then, calculating an optimal synthesis weight vector corresponding to the solved feature matrix; and finally, carrying out weighted coherent addition operation on the multipath signals according to the optimal synthesis weight vector to determine a synthesis signal. The method and the system provided by the invention can be used under the condition that the noise variances of all paths of signals are equal or unequal, and the performance of the synthesized signal is kept while the calculated amount is greatly simplified.

Description

Signal synthesis method and system
Technical Field
The invention relates to the technical field of sensor networks, in particular to a signal synthesis method and a signal synthesis system.
Background
The reliable reception of weak signals is always a hotspot in the field of signal processing. In particular, in recent years, as the detection distance and range of the sensor increase, the challenge of receiving a weak target signal is increasingly serious, and the noise of the receiver limits the receiving performance of a single sensor. An effective solution is to jointly receive the same signal by using a plurality of randomly arranged sensors, and to improve the signal-to-noise ratio of the received signal by a signal synthesis technique. The goal of signal synthesis is to maximize the signal-to-noise ratio of the synthesized signal, and besides to compensate the difference parameters such as time delay of the multipath received signals, the signal synthesis needs to perform weighted summation according to the optimal weight, and because the signals are partially coherently accumulated and the noise is partially randomly offset, the signal-to-noise ratio of the synthesized signal can be improved.
An eigenvalue decomposition algorithm (Signal-to-Noise Ratio Eigen, SNR Eigen) with the Signal-to-Noise Ratio of the synthesized Signal as an objective function is proposed in an article, "Eigen Theory for Optical Signal Combining: aided", published by k.m. cheung et al, wherein the common way to estimate the Noise correlation matrix is to assume that the Noise is white gaussian Noise and to obtain it by recording a segment of pure Noise and then performing a correlation calculation. The algorithm may provide optimal synthesis weights, but requires estimation of the noise correlation matrix. The maximum output power criterion and the maximum Signal-to-noise ratio criterion of the combined Signal are equivalent as specified in the Large-Array Signal processing for Deep Space Application, published by c.h. lee et al. The maximum Output signal Power criterion is to calculate the optimal synthesis weight value by taking the Power of the synthesized signal as an objective function, so that the Output Power of the synthesized signal is maximum (COP EIGEN). The eigenvalue decomposition algorithm using the synthesized signal power as the objective function assumes that the noise variances of the signals are equal, so the influence of noise can be ignored, and a noise correlation matrix does not need to be estimated. The article "On Eigen-Based Signal combining using the Autocorrelation compensation algorithm" published by Luo et al indicates that the criterion of the Autocorrelation Coefficient of the synthesized Signal and the maximum Signal-to-noise ratio of the synthesized Signal are equivalent (AC EIGEN), and the algorithm can obtain better synthesis performance than COP EIGEN when the noise variance of each path of Signal is inconsistent.
The calculation processes of the optimal synthesis weights of the SNR EIGEN, the COP EIGEN and the AC EIGEN of the three algorithms are similar, and the optimal value of the synthesis weight is the eigenvector corresponding to the maximum eigenvalue of a certain matrix. When the noise variances of the received signals of all paths are not equal, the synthesized weight vector calculated by adopting the COPEIGEN algorithm is biased. The SNR EIGEN and AC EIGEN algorithms can effectively overcome the problem that the synthesized weight vector is biased due to unequal noise variance of each path of received signals, but the SNR EIGEN and AC EIGEN algorithms need to be solved respectively
Figure BDA0001695655400000021
And
Figure BDA0001695655400000022
is performed. As the number N of paths of the received signal increases, the calculation amount of the matrix multiplication part increases sharply, and therefore, the calculation amount needs to be reduced greatly by improving the algorithm.
Disclosure of Invention
The invention aims to solve the problem of large calculation amount in the existing signal synthesis technology and provides a signal synthesis method and a signal synthesis system, which adopt a matrix blocking recursion algorithm to calculate a characteristic matrix to be solved. The method and the system can be used under the condition that the noise variances of all paths of signals are equal or unequal, and the performance of the synthesized signal is kept while the calculated amount is greatly simplified.
To achieve the above object, in one aspect, the present invention provides a signal synthesis method. The method comprises the following steps:
establishing an objective function related to the synthesized signal, and determining a feature matrix to be solved corresponding to the synthesized weight vector according to the objective function;
calculating the characteristic matrix to be solved by adopting a matrix blocking recursion algorithm, and obtaining the solved characteristic matrix;
calculating an optimal synthesis weight vector corresponding to the solved feature matrix;
and carrying out weighted coherent addition operation on the multipath signals according to the optimal synthesis weight vector to determine the synthesis signals.
Preferably, the objective function is an objective function of the autocorrelation coefficient of the synthesized signal, and the feature matrix to be solved is a product of an inverse matrix of the first received signal correlation matrix and the second received signal correlation matrix.
Preferably, the objective function is an objective function of the signal-to-noise ratio of the synthesized signal, and the feature matrix to be solved is a product of an inverse matrix of a noise correlation matrix and a received signal correlation matrix.
Preferably, the calculating the feature matrix to be solved by using a matrix blocking recursive algorithm includes:
determining a corresponding second-order block matrix according to the inverse matrix of the noise correlation matrix;
zero-assigning blocks to the blocks which do not contain main diagonal elements in the second-order block matrix, and obtaining a corresponding zero-assigning block matrix;
and calculating the product of the zero-assigning block matrix and the received signal correlation matrix by adopting a matrix blocking recursive algorithm.
Preferably, the obtaining the solved feature matrix includes obtaining the solved feature matrix by using the following formula:
Figure BDA0001695655400000031
wherein the content of the first and second substances,
Figure BDA0001695655400000032
representing the zero-assigned block matrix and,
Figure BDA0001695655400000033
a correlation matrix representing the received signal is generated,
Figure BDA0001695655400000034
the matrix is divided into intermediate matrices in a block recursive algorithm.
In another aspect, the present invention provides a signal synthesis system. The system comprises:
an establishing unit for establishing an objective function related to the synthesized signal;
the determining unit is used for determining a feature matrix to be solved corresponding to the synthesized weight vector according to the objective function;
the first calculation unit is used for calculating the characteristic matrix to be solved by adopting a matrix blocking recursive algorithm and obtaining the solved characteristic matrix;
the second calculation unit is used for calculating the optimal synthesis weight vector corresponding to the solved feature matrix;
and the synthesis unit is used for carrying out weighted coherent addition operation on the multipath signals according to the optimal synthesis weight vector so as to determine the synthesis signal.
Preferably, the objective function is an objective function of the autocorrelation coefficient of the synthesized signal, and the feature matrix to be solved is a product of an inverse matrix of the first received signal correlation matrix and the second received signal correlation matrix.
Preferably, the objective function is an objective function of the signal-to-noise ratio of the synthesized signal, and the feature matrix to be solved is a product of an inverse matrix of a noise correlation matrix and a received signal correlation matrix.
Preferably, the first computing unit is specifically configured to:
determining a corresponding second-order block matrix according to the inverse matrix of the noise correlation matrix;
zero-assigning blocks to the blocks which do not contain main diagonal elements in the second-order block matrix, and obtaining a corresponding zero-assigning block matrix;
and calculating the product of the zero-assigning block matrix and the received signal correlation matrix by adopting a matrix blocking recursive algorithm.
Preferably, the first calculating unit includes obtaining the solved feature matrix by using the following formula:
Figure BDA0001695655400000041
wherein the content of the first and second substances,
Figure BDA0001695655400000042
representing the zero-assigned block matrix and,
Figure BDA0001695655400000043
a correlation matrix representing the received signal is generated,
Figure BDA0001695655400000044
the matrix is divided into intermediate matrices in a block recursive algorithm.
In the signal synthesis method and system provided by the invention, a matrix blocking recursive algorithm is adopted to calculate the characteristic matrix to be solved. The method and the system can be used under the condition that the noise variances of all paths of signals are equal or unequal, and the performance of the synthesized signal is kept while the calculated amount is greatly simplified.
Drawings
Fig. 1 is a schematic flow chart of a signal synthesis method according to an embodiment of the present invention;
fig. 2 is a flow chart of a signal synthesis method according to an embodiment of the present invention;
FIG. 3 is a graph of multiplication and addition ratios provided by an embodiment of the present invention;
FIG. 4 is a graph of the synthetic loss for equal noise variance provided by an embodiment of the present invention;
FIG. 5 is a graph of the synthetic loss when the noise variances provided by the embodiments of the present invention are not equal;
fig. 6 is a schematic structural diagram of a signal synthesizing system according to an embodiment of the present invention.
Detailed Description
The technical solution of the present invention is further described in detail by the accompanying drawings and examples.
Fig. 1 is a schematic flow chart of a signal synthesis method according to an embodiment of the present invention. As shown in fig. 1, the method includes steps S110-S140:
step S110, an objective function related to the synthesized signal is established, and a feature matrix to be solved corresponding to the synthesized weight vector is determined according to the objective function.
Specifically, the established objective function is an objective function of a signal-to-noise ratio of the synthesized signal, and the corresponding feature matrix to be solved is a product of an inverse matrix of the noise correlation matrix and a received signal correlation matrix.
Or, establishing an objective function of the autocorrelation coefficient of the synthesized signal, wherein the corresponding characteristic matrix to be solved is the product of the inverse matrix of the correlation matrix of the first received signal and the correlation matrix of the second received signal.
In one possible embodiment, an SNR EIGEN algorithm is adopted to establish an objective function of the signal-to-noise ratio of the synthesized signal, and a characteristic matrix to be solved is determined as a received signal correlation matrix according to the objective function
Figure BDA0001695655400000061
And a noise correlation matrix
Figure BDA0001695655400000062
Inverse matrix of
Figure BDA0001695655400000063
Product of (2)
Figure BDA0001695655400000064
The specific process of this embodiment is as follows:
first, the multipath signals received by the sensor are modeled as:
xi(k)＝si(k)+ni(k) i＝1,2,…,N (1)
in the formula (1), k is a sampling point number, the subscript i represents a road number, and xi(k) Indicating the signal received by the ith path, N is the total number of paths, si(k) Representing the source signal received in the i-th path, ni(k) Representing the noise component of the i-th signal, n being generallyi(k) Modeling was zero mean white gaussian noise.
The composite signal can thus be expressed as:
Figure BDA0001695655400000065
Figure BDA0001695655400000066
Figure BDA0001695655400000067
Figure BDA0001695655400000068
Figure BDA0001695655400000069
wherein x isc(k) Is a composite signal, sc(k) Is the signal portion of the synthesis, nc(k) Is the noise part of the synthesis and is,
Figure BDA00016956554000000610
the composite weight vector is represented by a vector of weights,
Figure BDA00016956554000000611
denotes the receive gain vector, superscript T denotes the transpose, and superscript H denotes the conjugate transpose. From the above, the composite signal-to-noise ratio can be expressed as:
Figure BDA00016956554000000612
Figure BDA00016956554000000613
Figure BDA00016956554000000614
wherein the content of the first and second substances,
Figure BDA00016956554000000615
a correlation matrix representing the received signal is generated,
Figure BDA00016956554000000616
a correlation matrix representing the source signal is generated,
Figure BDA0001695655400000071
representing a noise correlation matrix. Solving for the formula (9)
Figure BDA0001695655400000072
The partial derivative of (c) can yield:
Figure BDA0001695655400000073
wherein the content of the first and second substances,
Figure BDA0001695655400000074
is defined as:
Figure BDA0001695655400000075
wherein R isninj(τ) is defined as:
Figure BDA0001695655400000076
wherein
Figure BDA0001695655400000077
Is that
Figure BDA0001695655400000078
Inverse matrix of Rninj(τ) represents the cross-correlation function of each path of noise, τ represents the delay value, and L is the length of the correlation calculation. As can be seen from the formula (10), the synthesized weight vector with the maximum signal-to-noise ratio is obtained
Figure BDA0001695655400000079
I.e. a matrix
Figure BDA00016956554000000710
The feature vector corresponding to the maximum feature value. Therefore, the characteristic matrix to be solved corresponding to the SNR EIGEN algorithm is
Figure BDA00016956554000000711
In another possible embodiment, the present step comprises: establishing an objective function of the autocorrelation coefficient of the synthesized signal by adopting an AC EIGEN algorithm, and determining a matrix to be solved as an inverse matrix of a correlation matrix of the first received signal according to the objective function
Figure BDA00016956554000000712
And a second received signal correlation matrix
Figure BDA00016956554000000713
Product of (2)
Figure BDA00016956554000000714
The specific process of this embodiment is as follows:
the autocorrelation coefficients of the synthesized signal can be expressed as:
Figure BDA00016956554000000715
where τ is a displacement amount of the signal, and is an integer, and τ may be 1, for example.
To equation (13)
Figure BDA00016956554000000716
The partial derivative of (c) can yield:
Figure BDA00016956554000000717
from the above formula, the matrix
Figure BDA0001695655400000081
The eigenvector corresponding to the largest eigenvalue of (a) is the synthesis weight vector that maximizes the autocorrelation coefficient of the synthesized signal. Therefore, the feature matrix to be solved corresponding to the aceegen algorithm is
Figure BDA0001695655400000082
As can be seen from the above analysis, the SNR EIGEN and AC EIGEN algorithms need to be solved separately
Figure BDA0001695655400000083
And
Figure BDA0001695655400000084
of a computational complexity of O (N)3). As the number N of paths of the received signal increases, the amount of calculation for solving the matrix multiplication portion increases sharply, and therefore a new method is required to reduce the amount of calculation.
And step S120, calculating the feature matrix to be solved by adopting a matrix blocking recursive algorithm, and obtaining the solved feature matrix.
The present steps are explained below in conjunction with the description of the inventive concept of the present invention:
in the first aspect, as can be seen from equations (10) and (14), the SNR EIGEN and AC EIGEN algorithms need to be solved separately
Figure BDA0001695655400000085
And
Figure BDA0001695655400000086
conventional matrix multiplication can be expressed as:
Figure BDA0001695655400000087
Figure BDA0001695655400000088
Figure BDA0001695655400000089
Figure BDA00016956554000000810
wherein
Figure BDA00016956554000000818
Is an input matrix that participates in the multiplication operation,
Figure BDA00016956554000000812
is the matrix obtained after the multiplication operation,
Figure BDA00016956554000000813
and
Figure BDA00016956554000000814
respectively representing the block matrices of the corresponding matrix. From the above formulas (15) to (18), it is possible to obtain:
Figure BDA00016956554000000815
Figure BDA00016956554000000816
Figure BDA00016956554000000817
Figure BDA0001695655400000091
when the number R of rows or columns of the matrix is 2, the equations (19) to (22) are completeThe matrix multiplication requires 8 multiplications and 4 additions. As R increases, conventional matrix multiplication requires N when R ═ N3The sub-multiplication sum N3-N2And (4) secondary addition.
The article "Gaussian interpolation is not Optimal" published by Strassen indicates that the matrix multiplication can be expressed as:
Figure BDA0001695655400000092
Figure BDA0001695655400000093
Figure BDA0001695655400000094
Figure BDA0001695655400000095
Figure BDA0001695655400000096
Figure BDA0001695655400000097
Figure BDA0001695655400000098
wherein
Figure BDA0001695655400000099
And
Figure BDA00016956554000000910
for the intermediate matrix, the matrix sought can be obtained by:
Figure BDA00016956554000000911
Figure BDA00016956554000000912
Figure BDA00016956554000000913
Figure BDA00016956554000000914
when the number R of rows or columns of the matrix is 2, 7 multiplications and 18 additions are required to complete the matrix multiplication by using the Strassen method, as shown in equations (23) to (33). With the increase of R, the number of multiplication operations required for completing matrix multiplication by using the Strassen method is less than that of the traditional method, and the number of addition operations gradually approaches that of the traditional method.
Based on the above analysis, the invention proposes to utilize Strassen method to complete SNR EIGEN
Figure BDA0001695655400000101
And in ACEIGEN
Figure BDA0001695655400000102
Is performed by the matrix multiplication operation of (1).
Accordingly, in one embodiment, the order may be according to equation (15)
Figure BDA0001695655400000103
Figure BDA0001695655400000104
Then
Figure BDA0001695655400000105
Then, the calculation is carried out according to the formulas (16), (23) to (33)
Figure BDA0001695655400000106
In another embodiment, it is possible to have the formula (15) as
Figure BDA0001695655400000107
Then
Figure BDA0001695655400000108
Then, the calculation is carried out according to the formulas (16), (23) to (33)
Figure BDA0001695655400000109
In the second aspect, the problem with directly using the Strassen method is that when R is small, the number of addition operations is larger than in the conventional method, which affects the reduction effect of the calculation amount. To further reduce the amount of computation, SNR EIGEN was analyzed
Figure BDA00016956554000001010
The matrix properties of (a).
In example 1, N is 4, L is 1024, the signal-to-noise ratio is 0dB, the noise variance is equal, and 500 independent tests are performed, SNR egen
Figure BDA00016956554000001011
Equal to:
Figure BDA00016956554000001012
from the above formula
Figure BDA00016956554000001013
Is a strict diagonal dominance matrix, i.e. the main diagonal element is much larger than the sum of other elements in the same row.
Therefore, the temperature of the molten metal is controlled,
Figure BDA00016956554000001014
can be approximated by
Figure BDA00016956554000001015
Main diagonal element of and
Figure BDA00016956554000001016
is obtained by matrix multiplication.
Bonding ofThe invention is based on the analysis of the above two aspects
Figure BDA00016956554000001017
The diagonal dominant matrix characteristic and Strassen matrix blocking recursion algorithm put forward a Zero Block Strassen (Zero Block Strassen, ZBS) method to complete SNR EIGEN
Figure BDA00016956554000001018
Is performed by the matrix multiplication operation of (1). The matrix multiplication of ZBS can be expressed as:
Figure BDA00016956554000001019
Figure BDA0001695655400000111
Figure BDA0001695655400000112
wherein
Figure BDA0001695655400000113
For input matrices not containing zero-blocks of main diagonal elements, i.e. in equation (17)
Figure BDA0001695655400000114
And
Figure BDA0001695655400000115
a matrix of zero-assigned blocks is formed,
Figure BDA0001695655400000116
the ZBS method is utilized to complete the matrix obtained by the multiplication operation,
Figure BDA0001695655400000117
represents
Figure BDA0001695655400000118
Of the block matrix. Combined with Strassen method, supraThe matrix multiplication can be expressed as:
Figure BDA0001695655400000119
Figure BDA00016956554000001110
Figure BDA00016956554000001111
Figure BDA00016956554000001112
Figure BDA00016956554000001113
Figure BDA00016956554000001114
Figure BDA00016956554000001115
wherein the content of the first and second substances,
Figure BDA00016956554000001116
and
Figure BDA00016956554000001117
for the intermediate matrix of the ZBS method, the matrix can be obtained by the following formula:
Figure BDA00016956554000001118
Figure BDA00016956554000001119
Figure BDA00016956554000001120
Figure BDA00016956554000001121
when the number R of rows or columns of the matrix is 2, it can be seen from equations (38) to (48) that 4 multiplications and 4 additions are required to complete the matrix multiplication using the ZBS method, which is superior to the conventional method and the Strassen method. With the increase of R, the times of multiplication and addition required by the ZBS method for completing matrix multiplication are obviously superior to those of the traditional method and the Strassen method.
Therefore, in the SNR EIGEN algorithm
Figure BDA0001695655400000121
The calculation method of matrix multiplication can be summarized as follows:
step one, initial setting:
Figure BDA0001695655400000122
Figure BDA0001695655400000123
second step, to
Figure BDA0001695655400000124
In the block matrix zero-assigning block not containing main diagonal elements, obtaining a zero-assigning block matrix:
Figure BDA0001695655400000125
will be provided with
Figure BDA0001695655400000126
And
Figure BDA0001695655400000127
as an input matrix participating in matrix multiplication, a matrix blocking recursive calculation process is started by using a ZBS method:
Figure BDA0001695655400000128
Figure BDA0001695655400000129
Figure BDA00016956554000001210
Figure BDA00016956554000001211
Figure BDA00016956554000001212
Figure BDA00016956554000001213
Figure BDA00016956554000001214
Figure BDA00016956554000001215
fourthly, when the matrix can not be partitioned again, the recursive computation is finished to obtain
Figure BDA0001695655400000131
Figure BDA0001695655400000132
Further, the following formula can be obtained from formulas (49) - (51), (56) - (60):
Figure BDA0001695655400000133
in the above manner, the solved feature matrix can be obtained.
Step S130, calculating the optimal synthesis weight vector corresponding to the solved feature matrix.
Step S140, performing weighted coherent addition operation on the multipath signals according to the optimal synthesis weight vector to determine the synthesis signal.
From the above, in the signal synthesis method provided by the present invention, the feature matrix to be solved is calculated by using a matrix blocking recursive algorithm. The method can be used under the condition that the noise variances of all paths of signals are equal or unequal, and the performance of the synthesized signal is kept while the calculated amount is greatly simplified.
The signal synthesis method based on the SNR EIGEN algorithm and the ZBS method is further explained below according to the flow chart provided in fig. 2. As shown in fig. 2, the method includes steps S210-S280:
s210, the signal synthesis algorithm starts.
S220, obtaining a noise correlation matrix by using the formulas (11) and (12)
Figure BDA0001695655400000134
And a received signal correlation matrix
Figure BDA0001695655400000135
S230, initial setup, according to the formulas (49) and (50), will
Figure BDA0001695655400000136
And
Figure BDA0001695655400000137
as input matrices participating in matrix multiplication operations
Figure BDA0001695655400000138
And
Figure BDA0001695655400000139
s240, to
Figure BDA00016956554000001310
The zero-assigning block of the block matrix without the main diagonal element is obtained according to the formula (51)
Figure BDA00016956554000001311
S250, the matrix blocking recursive computation process is started according to equations (52), (53), (54), (55), (56), (57), (58), and (59).
S260, when the matrix can not be partitioned again, the recursive computation is finished, and the result is obtained according to the formula (60)
Figure BDA0001695655400000141
Namely, it is
Figure BDA0001695655400000142
And S270, solving the synthesized weight vector according to the SNR EIGEN.
And S280, finishing a signal synthesis algorithm.
From the above, in the signal synthesis method provided by the present invention, the feature matrix to be solved is calculated by using a matrix blocking recursive algorithm. The method can be used under the condition that the noise variances of all paths of signals are equal or unequal, and the performance of the synthesized signal is kept while the calculated amount is greatly simplified.
Further, comparing the computation amounts of the ZBS method of the present invention, the conventional matrix multiplication, the Strassen method multiplication and addition, as shown in table 1:
TABLE 1
Figure BDA0001695655400000143
As can be seen from the above table, as N increases, the number of multiplication operations required to complete matrix multiplication by using the Strassen method is less than that of the conventional method, and the number of addition operations gradually approaches that of the conventional method. The number of multiplication operations and the number of addition operations required for completing matrix multiplication by using the ZBS method provided by the invention are both obviously superior to those of the traditional method and the Strassen method.
The multiplication and addition ratios required for the ZBS method, the Strassen method of the present invention to multiply with a conventional matrix are shown in fig. 3. As shown in the above figure, the number of multiplications required by the Strassen method to complete matrix multiplication is less than that of the conventional method, and when N is smaller, the number of additions required by the Strassen method is much greater than that of the conventional method, and as N increases, the number of additions required by the Strassen method gradually approaches that of the conventional method. The number of multiplication operations and the number of addition operations required by the ZBS method to complete matrix multiplication are both significantly superior to those of the traditional method and the Strassen method.
The fast signal synthesis method proposed by the present invention is further described below by way of examples. To evaluate the algorithm performance, a synthetic loss ζ is defined:
Figure BDA0001695655400000151
in which the theoretical maximum composite signal-to-noise ratio
Figure BDA0001695655400000152
Equal to:
Figure BDA0001695655400000153
in the examples
Figure BDA0001695655400000154
And P issWhich represents the signal power, 1 in the example.
Actual composite signal to noise ratio in equation (7)
Figure BDA0001695655400000155
Figure BDA0001695655400000156
Wherein the signal power PsReception gain αiVariance of noise
Figure BDA0001695655400000157
All are known simulation parameters, and the synthesis weight w is calculated by different algorithmsiAnd then obtain
Figure BDA0001695655400000158
The invention firstly proposes to use the Strassen method to finish SNR EIGEN (SNR + Strassen method) and ACEIGEN (AC + Strassen method)
Figure BDA0001695655400000159
And
Figure BDA00016956554000001510
the number of addition operations required by the Strassen method is much larger than that of the conventional method because N is small. To further reduce the amount of computation, by analyzing SNR EIGEN
Figure BDA00016956554000001511
The invention proposes that the ZBS method completes SNR EIGEN (SNR + ZBS method)
Figure BDA0001695655400000161
Is performed by the matrix multiplication operation of (1).
In the embodiment, the comparison is made with algorithms such as SNR EIGEN, COP EIGEN, and AC EIGEN, respectively. s (k) adopts 80KHz sine signal, and the sampling rate is 1.4MHz, ni(k) Is gaussian white noise. In AC EIGEN algorithm
Figure BDA0001695655400000162
Figure BDA0001695655400000162
1. When the noise variances are not equal, taking N-4 as an example, the ratio of the noise variances of each path is equal to 1:1:1.5:1.5, and so on. The examples were tested a total of 500 independent tests.
In example 2, N is 4, L is 1024, the SNR is 0dB, the noise variance is equal, and the SNR EIGEN is obtained by a conventional method
Figure BDA0001695655400000163
Equal to:
Figure BDA0001695655400000164
SNR EIGEN is obtained by Strassen method
Figure BDA0001695655400000165
Equal to:
Figure BDA0001695655400000166
SNR EIGEN is obtained by ZBS method
Figure BDA0001695655400000167
Equal to:
Figure BDA0001695655400000168
comparing the three formulas, it can be seen that the Strassen method is used to complete SNR EIGEN
Figure BDA0001695655400000169
Does not affect the matrix multiplication operation
Figure BDA00016956554000001610
The calculation accuracy of (2). Implementation of SNR EIGEN in ZBS method
Figure BDA00016956554000001611
Is paired with matrix multiplication operation
Figure BDA00016956554000001612
The error of the calculation precision of (2) is very small, and the maximum error is less than 0.37%.
In example 3, N is 4 and L is 1024. When the noise variances are equal, as shown in fig. 4, the composite loss of the SNR EIGEN algorithm and the SNR + Strassen algorithm is the smallest, and the composite loss of the SNR + ZBS is better than the COP EIGEN, the AC EIGEN, and the AC + Strassen algorithm. When the noise variances are not equal, as shown in fig. 5, the SNR EIGEN algorithm and the SNR + Strassen algorithm still have the minimum composite loss, and the composite loss of the SNR + ZBS is slightly more than that of the SNREIGEN algorithm and the SNR + Strassen algorithm, better than that of the AC EIGEN algorithm and the AC + Strassen algorithm, and obviously better than that of the COP EIGEN.
Combining the results of the above embodiments, the fast signal synthesis methods SNR + Strassen, AC + Strassen and SNR + ZBS proposed by the present invention can be flexibly applied to the case where the noise variance is equal or unequal. Compared with SNR EIGEN and AC EIGEN, SNR + Strassen and AC + Strassen do not affect the signal synthesis performance while reducing the calculation amount, and SNR + ZBS has little synthesis loss compared with SNR EIGEN, but can obviously reduce the calculation amount of the matrix multiplication part, and is easy to realize by hardware.
Corresponding to the above signal synthesis method, an embodiment of the present invention further provides a signal synthesis system, as shown in fig. 6, where the system 600 includes:
an establishing unit 610 for establishing an objective function related to the synthesized signal;
a determining unit 620, configured to determine, according to the objective function, a feature matrix to be solved corresponding to the synthesized weight vector;
the first calculating unit 630 is configured to calculate the feature matrix to be solved by using a matrix blocking recursive algorithm, and obtain a solved feature matrix;
a second calculating unit 640, configured to calculate an optimal composite weight vector corresponding to the solved feature matrix;
and a synthesizing unit 650, configured to perform a weighted coherent addition operation on the multipath signals according to the optimal synthesis weight vector, so as to determine the synthesized signal.
In a possible embodiment, the objective function is an objective function of the autocorrelation coefficients of the synthesized signal, and the feature matrix to be solved is a product of an inverse matrix of the first received signal correlation matrix and the second received signal correlation matrix.
In a possible embodiment, the objective function is an objective function of the signal-to-noise ratio of the synthesized signal, and the feature matrix to be solved is a product of an inverse matrix of a noise correlation matrix and a received signal correlation matrix.
In a possible embodiment, the first computing unit 630 is specifically configured to:
determining a corresponding second-order block matrix according to the inverse matrix of the noise correlation matrix;
zero-assigning blocks to the blocks which do not contain main diagonal elements in the second-order block matrix, and obtaining a corresponding zero-assigning block matrix;
and calculating the product of the zero-assigning block matrix and the received signal correlation matrix by adopting a matrix blocking recursive algorithm.
In a possible embodiment, the first calculating unit 630 includes the following formula to obtain the solved feature matrix:
Figure BDA0001695655400000181
wherein the content of the first and second substances,
Figure BDA0001695655400000182
representing the zero-assigned block matrix and,
Figure BDA0001695655400000183
a correlation matrix representing the received signal is generated,
Figure BDA0001695655400000184
the matrix is divided into intermediate matrices in a block recursive algorithm.
From the above, in the signal synthesis system provided by the present invention, the feature matrix to be solved is calculated by using a matrix blocking recursive algorithm. The method can be used under the condition that the noise variances of all paths of signals are equal or unequal, and the performance of the synthesized signal is kept while the calculated amount is greatly simplified.
The above embodiments are provided to further explain the objects, technical solutions and advantages of the present invention in detail, it should be understood that the above embodiments are merely exemplary embodiments of the present invention and are not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (10)

1. A signal synthesis method, comprising:
establishing an objective function related to the synthesized signal, and determining a feature matrix to be solved corresponding to the synthesized weight vector according to the objective function;
calculating the characteristic matrix to be solved by adopting a Strassen matrix block recursive algorithm, and obtaining the solved characteristic matrix;
calculating an optimal synthesis weight vector corresponding to the solved feature matrix;
and carrying out weighted coherent addition operation on the multipath signals according to the optimal synthesis weight vector to determine the synthesis signals.
2. The method of claim 1, wherein the objective function is an objective function of autocorrelation coefficients of the synthesized signal, and wherein the eigen matrix to be solved is a product of an inverse of a first received signal correlation matrix and a second received signal correlation matrix.
3. The method of claim 1, wherein the objective function is an objective function of a signal-to-noise ratio of the synthesized signal, and the feature matrix to be solved is a product of an inverse matrix of a noise correlation matrix and a received signal correlation matrix.
4. The method according to claim 3, wherein the computing the feature matrix to be solved by using Strassen matrix block recursive algorithm comprises:
determining a corresponding second-order block matrix according to the inverse matrix of the noise correlation matrix;
zero-assigning blocks to the blocks which do not contain main diagonal elements in the second-order block matrix, and obtaining a corresponding zero-assigning block matrix;
and calculating the product of the zero-assigning block matrix and the received signal correlation matrix by adopting a Strassen matrix block recursive algorithm.
5. The method of claim 4, wherein said obtaining a solved feature matrix comprises obtaining the solved feature matrix using the following equation:
Figure FDA0002358369120000011
wherein the content of the first and second substances,
Figure FDA0002358369120000012
representing the zero-assigned block matrix and,
Figure FDA0002358369120000013
a correlation matrix representing the received signal is generated,
Figure FDA0002358369120000021
represents an intermediate matrix in the Strassen matrix block recursive algorithm.
6. A signal synthesis system, comprising:
an establishing unit for establishing an objective function related to the synthesized signal;
the determining unit is used for determining a feature matrix to be solved corresponding to the synthesized weight vector according to the objective function;
the first calculation unit is used for calculating the characteristic matrix to be solved by adopting a Strassen matrix blocking recursive algorithm and obtaining the solved characteristic matrix;
the second calculation unit is used for calculating the optimal synthesis weight vector corresponding to the solved feature matrix;
and the synthesis unit is used for carrying out weighted coherent addition operation on the multipath signals according to the optimal synthesis weight vector so as to determine the synthesis signal.
7. The system of claim 6, wherein the objective function is an objective function of autocorrelation coefficients of the synthesized signal, and wherein the eigen matrix to be solved is a product of an inverse of a first received signal correlation matrix and a second received signal correlation matrix.
8. The system of claim 6, wherein the objective function is an objective function of a signal-to-noise ratio of the synthesized signal, and the feature matrix to be solved is a product of an inverse matrix of the noise correlation matrix and the received signal correlation matrix.
9. The system of claim 8, wherein the first computing unit is specifically configured to:
determining a corresponding second-order block matrix according to the inverse matrix of the noise correlation matrix;
zero-assigning blocks to the blocks which do not contain main diagonal elements in the second-order block matrix, and obtaining a corresponding zero-assigning block matrix;
and calculating the product of the zero-assigning block matrix and the received signal correlation matrix by adopting a Strassen matrix block recursive algorithm.
10. The system according to claim 9, wherein the first computing unit includes a matrix of solved features obtained by using the following formula:
Figure FDA0002358369120000031
wherein the content of the first and second substances,
Figure FDA0002358369120000032
representing the zero-assigned block matrix and,
Figure FDA0002358369120000033
a correlation matrix representing the received signal is generated,
Figure FDA0002358369120000034
represents an intermediate matrix in the Strassen matrix block recursive algorithm.
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