CN108366025B - Signal synthesis method and system - Google Patents

Signal synthesis method and system Download PDF

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CN108366025B
CN108366025B CN201810060997.8A CN201810060997A CN108366025B CN 108366025 B CN108366025 B CN 108366025B CN 201810060997 A CN201810060997 A CN 201810060997A CN 108366025 B CN108366025 B CN 108366025B
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CN108366025A (en
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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. 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 symbol polarization method and a coordinate rotation digital calculation method to obtain 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 a synthesis signal. The device includes: the device comprises a determining unit, a first calculating unit, a second calculating unit and a processing unit. 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 synthesized signals have good performance 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
In recent years, sensor networks have been widely used for environmental monitoring, health care, smart homes, urban traffic and military safety, but because the sensor network nodes have limited signal sensing capability and insufficient receiving and processing capability for some weak signals, signals received by a plurality of nodes need to be synthesized, and then the signal-to-noise ratio of the received signals is improved. The goal of signal synthesis is to maximize the signal-to-noise ratio of the synthesized signal, and besides compensating the parameter differences such as time delay and frequency among multiple received signals to align the signals, the signal synthesis needs to perform weighted coherent addition according to the optimal weight. Since the signals are partially coherently added after alignment and the noise is randomly added, the power of the useful part of the composite signal is increased more than the noise power, and thus the signal-to-noise ratio of the composite signal is increased.
Article "origin Theory for Optical Signal Combining" published by K.M. Cheung et al: in the autonomous Approach, a Signal-to-Noise Ratio EIGEN (SNR EIGEN) is proposed, in which a Noise correlation matrix is estimated by assuming that Noise is white gaussian Noise and performing correlation calculation after recording a segment of pure Noise. However, on one hand, the complexity of the system is increased, and on the other hand, there is a risk that the noise characteristics in the signal bandwidth cannot be accurately reflected, so in practical application, the synthesized signal power is more adopted as the objective function to perform weight estimation. Lee et al, Large-Array Signal processing for Deep Space Application, states that the criterion for maximum output power and the criterion for maximum signal-to-noise ratio of the synthesized signal are equivalent. 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 correlation can be ignored, and a noise correlation matrix does not need to be estimated. The article On Eigen-based Combining Using the Autocorrelation compensation algorithm by Luo et al indicates that the Autocorrelation Coefficient of the synthesized signal is equivalent to the maximum criterion of the signal-to-noise ratio of the synthesized signal (Autocorrelation compensation, ACEIGEN).
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. But the main problem with these algorithms is that they are computationally expensive. In particular, as the number N of received signal paths and the length L of correlation calculation increase, the calculation amount for calculating the signal correlation matrix and solving the eigenvector corresponding to the maximum eigenvalue will be huge, and therefore, the calculation amount needs to be greatly reduced by improving the algorithm.
Disclosure of Invention
The invention aims to solve the problems of large calculation amount and large synthesis loss in the existing signal synthesis technology and provide a signal synthesis method and a signal synthesis system. 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 synthesized signals have good performance 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 symbol polarization method and a coordinate rotation digital calculation method to obtain a 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 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, includes:
establishing an objective function of the power of the synthesized signal, and determining the characteristic matrix to be solved as a received signal correlation matrix according to the objective function; or
And establishing an objective function of the autocorrelation coefficient of the synthesized signal, and determining the characteristic matrix to be solved as the product of two correlation matrixes of the received signal according to the objective function.
Preferably, the characteristic matrix to be solved includes a cross-correlation function of the received signals, and in calculating the characteristic matrix to be solved by using the symbol polarization method, the cross-correlation function of the received signals is calculated by using the following formula:
Figure GDA0002393068700000031
Figure GDA0002393068700000032
Figure GDA0002393068700000033
wherein i and j represent the number of the paths, N represents the total number of the paths, k represents the number of the sampling points, L represents the total number of the sampling points, and xi(k) Representing the signal received from the kth sample point in the ith path,
Figure GDA0002393068700000034
representing an estimate of the polarization signal, tau representing the amount of displacement of the signal,
Figure GDA0002393068700000035
represents an estimate of the cross-correlation function of the polarization signal,
Figure GDA0002393068700000036
representing an estimate of the cross-correlation function of the received signal.
Preferably, in the calculation of the feature matrix to be solved by using the coordinate rotation numerical calculation method, the following formula pairs are adopted
Figure GDA0002393068700000037
And (3) calculating:
zl+1＝zl-δlarctan(2-l)l＝0,1,2,…,n-1
Figure GDA0002393068700000038
Figure GDA0002393068700000039
wherein the content of the first and second substances,
Figure GDA0002393068700000041
l denotes the number of iterations and n denotes the total number of iterations.
Preferably, the calculating the optimal synthesis weight vector corresponding to the solved feature matrix includes:
and calculating the optimal synthetic weight vector corresponding to the solved feature matrix by adopting a power method algorithm or a CW iteration method.
In another aspect, the present invention provides a signal synthesis system. The system comprises
The determining unit is used for establishing an objective function related to the synthesized signal and determining a characteristic 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 symbol polarization method and a coordinate rotation digital calculation method so as to obtain 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 processing 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 signals.
Preferably, the determining unit is specifically configured to:
establishing an objective function of the power of the synthesized signal, and determining the characteristic matrix to be solved as a received signal correlation matrix according to the objective function; or
And establishing an objective function of the autocorrelation coefficient of the synthesized signal, and determining the characteristic matrix to be solved as the product of two correlation matrixes of the received signal according to the objective function.
Preferably, the feature matrix to be solved determined by the determining unit includes a cross-correlation function of the received signals, and the first calculating unit calculates the cross-correlation function of the received signals by using the following formula:
Figure GDA0002393068700000042
Figure GDA0002393068700000043
Figure GDA0002393068700000044
wherein i and j represent the number of the paths, N represents the total number of the paths, k represents the number of the sampling points, L represents the total number of the sampling points, and xi(k) Representing the signal received from the kth sample point in the ith path,
Figure GDA0002393068700000051
representing an estimate of the polarization signal, tau representing the amount of displacement of the signal,
Figure GDA0002393068700000052
represents an estimate of the cross-correlation function of the polarization signal,
Figure GDA0002393068700000053
representing an estimate of the cross-correlation function of the received signal.
Preferably, in the first calculation unit, the following formula pair is adopted
Figure GDA0002393068700000054
And (3) calculating:
zl+1＝zl-δlarctan(2-l)l＝0,1,2,…,n-1
Figure GDA0002393068700000055
Figure GDA0002393068700000056
wherein the content of the first and second substances,
Figure GDA0002393068700000057
l denotes the number of iterations and n denotes the total number of iterations.
Preferably, the second computing unit is specifically configured to:
and calculating the optimal synthetic weight vector corresponding to the solved feature matrix by adopting a power method algorithm or a CW iteration method.
The invention provides a signal synthesis method and a system, which adopt a symbol polarization method and a coordinate rotation digital calculation method to calculate a correlation matrix of a received signal, and adopt a power method algorithm or a CW iteration method to calculate an optimal synthesis weight vector corresponding to the correlation matrix. 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 synthesized signals have good performance while the calculated amount is greatly simplified.
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Fig. 1 is a schematic flow chart of a signal synthesis method according to an embodiment of the present invention;
fig. 2 is a schematic flow chart of another signal synthesis method according to an embodiment of the present invention;
fig. 3 is a graph of the synthetic loss when the noise variance is equal to N-4 according to an embodiment of the present invention;
fig. 4 is a diagram of the synthetic loss when the noise variances N are not equal to 4 according to an embodiment of the present invention;
fig. 5 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, an objective function of the synthesized signal power is established, and a feature matrix to be solved is determined as a received signal correlation matrix according to the objective function.
Or establishing an objective function of the autocorrelation coefficient of the synthesized signal, and determining the characteristic matrix to be solved as the product of two correlation matrixes of the received signal according to the objective function.
In one possible embodiment, the COP EIGEN algorithm is used to establish the composite signal powerAccording to the objective function, determining the matrix to be solved as the correlation matrix of the received signal
Figure GDA0002393068700000061
And the specific process 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 synthesis weight vector for synthesizing the multipath signals is as follows:
Figure GDA0002393068700000062
in equation (2), the superscript T denotes transpose, and the resultant signal can be expressed as:
Figure GDA0002393068700000071
in equation (3), the superscript H denotes the conjugate transpose, and:
Figure GDA0002393068700000072
correlation matrix of received signal
Figure GDA0002393068700000073
Is defined as:
Figure GDA0002393068700000074
in equation (5), the received signal cross-correlation function Rxixj(τ)Is defined as:
Figure GDA0002393068700000075
in equation (6), L represents the total number of sample point numbers in each channel of signal (which may also be referred to as the length of correlation).
As can be seen from the above formulas (4) to (6):
Figure GDA0002393068700000076
as can be seen from equations (5) and (6), the correlation matrix of the received signal
Figure GDA0002393068700000077
For a Hemitian matrix, it can be decomposed into:
Figure GDA0002393068700000078
Figure GDA0002393068700000079
Figure GDA00023930687000000710
wherein the content of the first and second substances,
Figure GDA00023930687000000711
is a diagonal matrix composed of eigenvalues, and the eigenvalues lambda1≥λ2≥…≥λN，
Figure GDA00023930687000000712
Is a matrix composed of the feature vectors,
Figure GDA00023930687000000713
corresponding to λiAnd is and
Figure GDA00023930687000000714
synthesizing weight vector
Figure GDA00023930687000000715
Can be expressed as feature vectors
Figure GDA00023930687000000716
The linear combination of (a):
Figure GDA00023930687000000717
Figure GDA00023930687000000718
Figure GDA00023930687000000719
Figure GDA00023930687000000720
wherein the content of the first and second substances,
Figure GDA00023930687000000721
is a coefficient vector. Thus, the objective function for the output power of the resultant signal is established as:
Figure GDA0002393068700000081
as can be seen from equation (15), the maximum value of the output power of the synthesized signal is the characteristic value λ1The synthesized weight vector at this time
Figure GDA0002393068700000082
Is the maximum eigenvalue lambda1Corresponding feature vector
Figure GDA0002393068700000083
Therefore, the COP EIGEN algorithm is adopted to assume that the noise variances of all paths of signals are equal, so that only a correlation matrix of the received signals needs to be calculated
Figure GDA0002393068700000084
In another possible embodiment, the present step comprises: establishing an objective function of the autocorrelation coefficients of the synthesized signal by adopting an AC EIGEN algorithm, and determining a matrix to be solved as two correlation matrices of the received signal according to the objective function
Figure GDA0002393068700000085
And
Figure GDA0002393068700000086
product of (2)
Figure GDA0002393068700000087
And the specific process is as follows:
the autocorrelation coefficients of the synthesized signal can be expressed as:
Figure GDA0002393068700000088
Figure GDA0002393068700000089
Figure GDA00023930687000000810
where τ is a displacement amount of the signal, and is an integer, and τ may be 1, for example.
To equation (16)
Figure GDA00023930687000000811
The partial derivative of (c) can yield:
Figure GDA00023930687000000812
from the above formula, the matrix
Figure GDA00023930687000000813
The eigenvector corresponding to the largest eigenvalue of (a) is the synthesis weight vector that maximizes the autocorrelation coefficient of the synthesized signal. Accordingly, the AC EIGEN algorithm only needs to calculate two correlation matrixes of the received signal
Figure GDA00023930687000000814
And
Figure GDA00023930687000000815
and step S120, calculating the feature matrix to be solved by adopting a symbol polarization method and a coordinate rotation digital calculation method to obtain the solved feature matrix.
As can be seen from the equations (5) and (6), the floating-point multiplication calculation amount of the correlation matrix in the COP EIGEN algorithm is O (N)2L), and as can be seen from equations (17) and (18), the floating-point multiplication calculation amount of the correlation matrix in the AC EIGEN algorithm is also O (N)2L)。
Specifically, based on the feature matrix to be solved, a Sign Polarization (SP) algorithm is used to perform Polarization operation on the received signal, and a COordinate rotation digital Computer (CORDIC) algorithm is used to calculate a sine function, so as to obtain the solved feature matrix, thereby solving the problem of optimization of the calculated amount of the correlation matrix.
In one possible embodiment, the SP algorithm and the CORDIC algorithm are used to correlate the received signal in the COP EIGEN algorithm
Figure GDA0002393068700000091
Calculating to obtain a solved feature matrix
Figure GDA0002393068700000092
In another possible embodiment, the SP algorithm and the CORDIC algorithm are adopted to carry out correlation on two correlation matrixes in the AC EIGEN algorithm
Figure GDA0002393068700000093
And
Figure GDA0002393068700000094
respectively calculating, and taking the product to obtain the solved feature matrix
Figure GDA0002393068700000095
Next, the correlation matrix of the received signal is solved by using SP algorithm and CORDIC algorithm
Figure GDA0002393068700000096
Of the respective received signal cross-correlation function RxixjThe process of (τ) is described. In the same way, can be according to this pair
Figure GDA0002393068700000097
And (6) performing calculation.
Firstly, a received signal is polarized by using an SP algorithm, and the specific process is as follows:
1) establishing a polarization signal model:
Figure GDA0002393068700000098
Figure GDA0002393068700000099
wherein the content of the first and second substances,
Figure GDA00023930687000000910
representing the estimation of the polarization signal, i represents the road number, k represents the number of sampling points, L represents the total number of sampling points, xi(k) Representing the signal received from the kth sample point in the ith path.
2) Calculating an estimate of the cross-correlation function of the polarization signal according to the polarization signal model:
Figure GDA0002393068700000101
wherein the content of the first and second substances,
Figure GDA0002393068700000102
represents the estimation of the cross-correlation function of the polarization signals, i and j represent the path numbers, N represents the total path number, and τ represents the displacement of the signals.
3) The estimate of the cross-correlation function of the received signals can be expressed as:
Figure GDA0002393068700000103
as can be seen from equations (20) to (23) and equation (23), by using the SP algorithm, the received signal cross-correlation function RxixjEstimation of cross-correlation function of polarized signals by floating-point multiplication in (tau)
Figure GDA0002393068700000104
The 1 adding and 1 subtracting operations (tau can be 1 or-1 in the formula (22)) and 1 time sine function operation (as shown in the formula (23)) are replaced, and the calculation amount is reduced.
Then, the CORDIC algorithm is used to calculate the sine function in the above equation (23), which includes the following steps:
Figure GDA0002393068700000105
Figure GDA0002393068700000106
Figure GDA0002393068700000107
wherein the content of the first and second substances,
Figure GDA0002393068700000108
l denotes the number of iterations, n denotes the total number of iterations, xlRepresenting the cosine function, x, after the first iterationl+1Is the cosine function after the (l + 1) th iteration, ylRepresenting the sine function after the l-th iteration, yl+1Is a sine function after the (l + 1) th iteration, zlDenotes the remaining non-rotation angle after the first iteration, zl+1Indicates the residue after the l +1 th iterationThe remaining rotation angle is the arc (2) in the formula (24)－l) And may be stored in a look-up table in advance.
As can be seen from equations (24) to (26) and equation (23), by using the CORDIC algorithm, the CORDIC algorithm can be applied
Figure GDA0002393068700000109
The sine operation in (1) is converted into a shift operation and an addition and subtraction operation, and each iteration only needs to carry out 3 times of addition and subtraction operations (respectively: one subtraction operation in equation (24), one subtraction operation and one addition operation in equation (26)) and 2 times of shift operation (in equation (26), 2 times of shift operation-lThe operation generated by adding 1 to l, the electric signal corresponding to 2-system is the shift operation) and one comparison operation (as shown in formula (25), thereby further simplifying the calculation amount.
It should be noted that the total number of iterations n may be determined according to the required calculation accuracy. The computational accuracy of the CORDIC algorithm is shown in table 1:
TABLE 1
Figure GDA0002393068700000111
As can be seen from table 1, when the iteration number n is equal to 4, the calculation accuracy is poor, when the iteration number n is equal to 12, the calculation accuracy is very good, and when the iteration number n is equal to 8, a better balance between the calculation accuracy and the calculation amount can be obtained, and n is preferably equal to 8 in the embodiment of the present invention.
Step S130, calculating the optimal synthesis weight vector corresponding to the solved feature matrix.
Specifically, an optimal synthetic weight vector corresponding to the solved feature matrix is calculated by adopting a power method algorithm or a CW iteration method.
In one possible embodiment, a Power Method (PM) algorithm is used to calculate the optimal composite weight vector corresponding to the solved feature matrix.
In the PM algorithm, the initial weight is assumed to be
Figure GDA0002393068700000121
And iterate through the following method:
Figure GDA0002393068700000122
wherein the content of the first and second substances,
Figure GDA0002393068700000123
representing the solved feature matrix, e.g.
Figure GDA0002393068700000124
Or
Figure GDA0002393068700000125
m represents the number of iterations and,
Figure GDA0002393068700000126
the composite weight vector representing the mth iteration is increased with the increase of the iteration number, and finally
Figure GDA0002393068700000127
Will converge to the eigenvector corresponding to the largest eigenvalue
Figure GDA0002393068700000128
And the convergence speed is defined by2/λ1Determine and due to
Figure GDA0002393068700000129
In conjunction with equations (11) and (27), the iterative process can be expressed as:
Figure GDA00023930687000001210
Figure GDA00023930687000001211
equation (29) represents normalization after each iteration. Known as λ1Is the largest eigenvalue, (lambda)i/λ1)<1, as m increases (λ)i/λ1)mConverging to 0.
In another possible embodiment, a CW (collitz-Wielandt, CW for short) iteration method is used to calculate the optimal composite weight vector corresponding to the solved feature matrix.
In the CW iteration method, let
Figure GDA00023930687000001212
For arbitrary irreducible non-negative matrix of NxN order, the definition is accompanied by
Figure GDA00023930687000001213
The Collatz-Wielandt function is:
Figure GDA00023930687000001214
wherein the content of the first and second substances,
Figure GDA00023930687000001215
or
Figure GDA00023930687000001216
Can be used as
Figure GDA00023930687000001217
Order to
Figure GDA00023930687000001218
Wherein the content of the first and second substances,
Figure GDA00023930687000001219
for the identity matrix, the CW algorithm assumes an initial weight of
Figure GDA00023930687000001220
And iterate through the following method:
Figure GDA00023930687000001221
Figure GDA0002393068700000131
Figure GDA0002393068700000132
equation (33) represents normalization after each iteration. Lambda [ alpha ]1Is the value of the largest characteristic that is,
Figure GDA0002393068700000133
is the corresponding feature vector, i.e. the composite weight vector.
Step S140, performing weighted coherent addition operation on the multipath signals according to the optimal synthesis weight vector to determine a synthesis signal.
As can be seen from the above, in the signal synthesis method provided by the present invention, the symbol polarization method and the coordinate rotation digital calculation method are used to calculate the correlation matrix of the received signal, and the power method algorithm or the CW iteration method is used to calculate the optimal synthesis weight vector corresponding to the correlation matrix. The method can be used under the condition that the noise variances of all paths of signals are equal or unequal, and ensures that the synthesized signals have good performance while greatly simplifying the calculated amount.
Fig. 2 is a schematic flow chart of another signal synthesis method according to an embodiment of the present invention. As shown in fig. 2, the method includes steps S210-S270:
in step S210, the signal synthesis algorithm starts.
In step S220, the input signal is polarized by using the polarization model in formula (20), which requires a comparison operation.
Step S230, according to the correlation matrix
Figure GDA0002393068700000134
Or
Figure GDA0002393068700000135
(for example, when the noise variance of each signal is equal, the correlation matrix in COP EIGEN algorithm is selected
Figure GDA0002393068700000136
Or, when the noise variance of each path of signal is not equal, selecting the correlation matrix in the AC EIGEN algorithm
Figure GDA0002393068700000137
The estimate of the cross-correlation function of each polarization signal is computed sequentially using equation (22)
Figure GDA0002393068700000138
This step only requires the addition of 1 and subtraction of 1.
Step S240, obtaining the estimation of the cross-correlation function of the received signal by using the CORDIC algorithm
Figure GDA0002393068700000139
This step requires shifting and addition and subtraction operations.
Step S250, checking whether the calculation of the correlation matrix part is completed, if not, returning to the step S230, calculating the estimation of the cross-correlation function of the next polarization signal
Figure GDA00023930687000001310
If so, step S260 is performed.
Step S260, solving the eigenvector of the correlation matrix by using a PM algorithm or a CW algorithm to obtain a synthetic weight vector.
In step S270, the signal synthesis algorithm is completed.
As can be seen from the above, in the signal synthesis method provided by the present invention, the symbol polarization method and the coordinate rotation digital calculation method are used to calculate the correlation matrix of the received signal, and the power method algorithm or the CW iteration method is used to calculate the optimal synthesis weight vector corresponding to the correlation matrix. The method can be used under the condition that the noise variances of all paths of signals are equal or unequal, and ensures that the synthesized signals have good performance while greatly simplifying the calculated amount.
In addition, the calculation amount of the present invention and its related algorithm is analyzed, and the calculation amount required by different signal synthesis algorithms is shown in table 2.
TABLE 2
Figure GDA0002393068700000141
As can be seen from the above table, N is required for SNR EIGEN, COP EIGEN and AC EIGEN to calculate each correlation matrix2For L floating-point multiplication operations, N is needed for the calculation and solution of the eigenvector part3And (5) performing secondary operation. As the number of signal paths N and the correlation computation length L increase, the amount of computation increases dramatically.
The PM algorithm and the CW algorithm only calculate the eigenvector corresponding to the maximum eigenvalue, so the operation of the eigenvector solving part is reduced, but the method does not solve the problem of the calculation quantity optimization of the correlation matrix part.
The MF (Matrix-free) algorithm is the same as the COP EIGEN algorithm, and when the noise variance of each path of signal is not equal, the resultant weight vector calculated by the algorithm will be biased.
If the sine function is calculated by fitting Chebyshev Polynomials (CP for short):
Figure GDA0002393068700000151
Figure GDA0002393068700000152
wherein p is the Chebyshev polynomial order, θpAre the corresponding polynomial coefficients. Taking the chebyshev third order polynomial as an example, the estimate of the cross-correlation function of the received signals is approximately equal to:
Figure GDA0002393068700000153
the calculation accuracy of the CP algorithm is shown in table 3:
TABLE 3
Figure GDA0002393068700000154
As can be seen from table 3, when the polynomial order p is equal to 1, the calculation accuracy is poor, when the polynomial order p is equal to 5, the calculation accuracy is very good, and when the polynomial order p is equal to 3, a better balance between the calculation accuracy and the calculation amount can be obtained, where p is equal to 3 in the embodiment of the present invention.
For the SP + CP algorithm, as shown in equation (37), when solving the estimate of the cross-correlation function of each received signal, 4 floating-point multiplications are included for CP with p equal to 3, each floating-point multiplication includes 32 additions, subtractions, and 32 shift operations, taking a 32-bit hardware system as an example, and 4 ＊ 32-128 additions, subtractions, and 4 ＊ 32-128 shift operations are required for the 4 floating-point multiplications.
When the algorithm SP + CORDIC provided by the invention is used for solving the estimation of each received signal cross-correlation function, the CORDIC with n equal to 8 only comprises 24 times of addition and subtraction, 16 times of shift operation and 8 times of comparison operation, so that the calculation amount of a correlation matrix part can be further simplified.
Compared with the MF algorithm, the SP + CORDIC + PM algorithm or the SP + CORDIC + CW algorithm can be flexibly applied to COP EIGEN or AC EIGEN according to different conditions of noise variance, and the problem that the synthesized weight vector is biased is avoided.
The fast signal synthesis method proposed by the present invention is further described below by an embodiment.
To evaluate the algorithm performance, a synthetic loss ζ is defined:
Figure GDA0002393068700000161
wherein the theoretical maximum composite signal to noise ratio gammaxcmaxEqual to:
Figure GDA0002393068700000162
in the examples
Figure GDA0002393068700000163
And P issWhich represents the signal power, 1 in the example.
Actual composite signal to noise ratio in equation (38)
Figure GDA0002393068700000165
Figure GDA0002393068700000164
Wherein the signal power PsReception gain αiNoise variance σi 2All are known simulation parameters, and the synthesis weight w is calculated by different algorithmsiAnd then obtain
Figure GDA0002393068700000171
The invention is compared with algorithms such as COP EIGEN, AC EIGEN, MF, SP + CP, etc. s (k) adopts 80KHz sine signal, and the sampling rate is 1.4MHz, ni(k) For white gaussian noise, 500 independent tests were performed.
In embodiment 1, the number of signal paths N is 4, and the combining loss when the noise variance is equal is shown in fig. 3, where the length L of the correlation calculation in fig. 3 (a) is 1024 and the length L of the correlation calculation in fig. 3 (b) is 2048. It can be seen that the synthetic loss of the algorithm SP + CORDIC + PM provided by the invention is basically the same as that of COP EIGEN, MF and SP + CP + PM, while that of AC EIGEN is the largest. Meanwhile, as L increases, the synthesis loss of each algorithm is reduced.
In embodiment 2, the number N of signal paths is 4, and the combining loss when the noise variances are not equal is shown in fig. 4, where the length L of the correlation calculation in (a) in fig. 4 is 1024, and the length L of the correlation calculation in (c) in fig. 4 is 2048. It can be seen that ACEIGEN has the smallest synthetic loss, while the synthetic losses of the algorithms SP + CORDIC + PM and SP + CP + PM proposed by the present invention are much smaller than those of COP EIGEN and MF.
By combining the results of the above embodiments, the fast signal synthesis method of the present invention can be flexibly applied to signal synthesis algorithms such as COP EIGEN and AC EIGEN under the condition of equal noise variance or unequal noise variance, and obtain good signal synthesis performance. Meanwhile, the method can greatly simplify the calculated amount and is easy to realize hardware.
Corresponding to the above signal synthesis method, an embodiment of the present invention further provides a signal synthesis system, as shown in fig. 5, the system 500 includes:
a determining unit 510, configured to establish an objective function related to the synthesized signal, and determine, according to the objective function, a feature matrix to be solved corresponding to the synthesized weight vector;
the first calculating unit 520 is configured to calculate a feature matrix to be solved by using a symbol polarization method and a coordinate rotation digital calculation method to obtain a solved feature matrix;
a second calculating unit 530, configured to calculate an optimal composite weight vector corresponding to the solved feature matrix;
the processing unit 540 performs a weighted coherent addition operation on the multipath signals according to the optimal synthesis weight vector to determine a synthesized signal.
Preferably, the determining unit 510 is specifically configured to:
establishing an objective function of the synthesized signal power, and determining a characteristic matrix to be solved as a received signal correlation matrix according to the objective function; or
And establishing an objective function of the autocorrelation coefficient of the synthesized signal, and determining a characteristic matrix to be solved as a product of two correlation matrixes of the received signal according to the objective function.
Preferably, the feature matrix to be solved determined by the determining unit 510 includes a cross-correlation function of the received signals, and in the first calculating unit 520, the following formula is adopted to calculate the cross-correlation function of the received signals:
Figure GDA0002393068700000181
Figure GDA0002393068700000182
Figure GDA0002393068700000183
wherein i and j represent the number of the paths, N represents the total number of the paths, k represents the number of the sampling points, L represents the total number of the sampling points, and xi(k) Representing the signal received from the kth sample point in the ith path,
Figure GDA0002393068700000184
representing an estimate of the polarization signal, tau representing the amount of displacement of the signal,
Figure GDA0002393068700000185
represents an estimate of the cross-correlation function of the polarization signal,
Figure GDA0002393068700000186
representing an estimate of the cross-correlation function of the received signal.
Preferably, in the first calculation unit 520, the following formula pairs are adopted
Figure GDA0002393068700000187
And (3) calculating:
zl+1＝zl-δlarctan(2-l) l＝0,1,2,…,n-1
Figure GDA0002393068700000188
Figure GDA0002393068700000189
wherein the content of the first and second substances,
Figure GDA00023930687000001810
l denotes the number of iterations and n denotes the total number of iterations.
Preferably, the second calculating unit 530 is specifically configured to:
and calculating the optimal synthetic weight vector corresponding to the solved feature matrix by adopting a power method algorithm or a CW iteration method.
As can be seen from the above, in the signal synthesis system provided in the present invention, the first calculating unit 520 calculates the correlation matrix of the received signal by using the symbol polarization method and the coordinate rotation digital calculation method, and the second calculating unit 530 calculates the optimal synthesis weight vector corresponding to the correlation matrix by using the power method algorithm or the CW iteration method. The method can be used under the condition that the noise variances of all paths of signals are equal or unequal, and ensures that the synthesized signals have good performance while greatly simplifying the calculated amount.
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 (2)

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; the method comprises the following steps: establishing an objective function of the power of the synthesized signal, and determining the characteristic matrix to be solved as a received signal correlation matrix according to the objective function; or, establishing an objective function of the autocorrelation coefficient of the synthesized signal, and determining the characteristic matrix to be solved as the product of two correlation matrixes of the received signal according to the objective function;
calculating the characteristic matrix to be solved by adopting a symbol polarization method and a coordinate rotation digital calculation method to obtain a solved characteristic matrix; wherein, the characteristic matrix to be solved comprises a cross-correlation function of the received signals, and the calculation of the characteristic matrix to be solved by adopting the symbol polarization method comprises the following steps:
Figure FDA0002393068690000011
Figure FDA0002393068690000012
Figure FDA0002393068690000013
wherein i and j represent the number of the paths, N represents the total number of the paths, k represents the number of the sampling points, L represents the total number of the sampling points, and xi(k) Representing the signal received from the kth sample point in the ith path,
Figure FDA0002393068690000014
representing an estimate of the polarization signal, tau representing the amount of displacement of the signal,
Figure FDA0002393068690000015
represents an estimate of the cross-correlation function of the polarization signal,
Figure FDA0002393068690000016
an estimate representing a cross-correlation function of the received signals;
the calculation of the characteristic matrix to be solved by adopting the coordinate rotation digital calculation method comprises the following formula pairs
Figure FDA0002393068690000017
And (3) calculating:
zl+1＝zl-δlarctan(2-l) l＝0,1,2,…,n-1
Figure FDA0002393068690000018
Figure FDA0002393068690000021
wherein the content of the first and second substances,
Figure FDA0002393068690000022
l denotes the number of iterations, n denotes the total number of iterations, xlRepresenting the cosine function, x, after the first iterationl+1Is the cosine function after the (l + 1) th iteration, ylRepresenting the sine function after the l-th iteration, yl+1Is a sine function after the (l + 1) th iteration, zlDenotes the remaining non-rotation angle after the first iteration, zl+1Representing the remaining non-rotation angle after the (l + 1) th iteration;
calculating an optimal synthesis weight vector corresponding to the solved feature matrix; the method comprises the following steps: calculating the optimal synthetic weight vector corresponding to the solved feature matrix by adopting a power method algorithm or a Colltz-Wielandt iteration method;
and carrying out weighted coherent addition operation on the multipath signals according to the optimal synthesis weight vector to determine the synthesis signals.
2. A signal synthesis system, comprising:
the determining unit is used for establishing an objective function related to the synthesized signal and determining a characteristic matrix to be solved corresponding to the synthesized weight vector according to the objective function; the method comprises the following steps: establishing an objective function of the power of the synthesized signal, and determining the characteristic matrix to be solved as a received signal correlation matrix according to the objective function; or, establishing an objective function of the autocorrelation coefficient of the synthesized signal, and determining the characteristic matrix to be solved as the product of two correlation matrixes of the received signal according to the objective function;
the first calculation unit is used for calculating the characteristic matrix to be solved by adopting a symbol polarization method and a coordinate rotation digital calculation method so as to obtain the solved characteristic matrix; wherein, the characteristic matrix to be solved comprises a cross-correlation function of the received signals, and the calculation of the characteristic matrix to be solved by adopting the symbol polarization method comprises the following steps:
Figure FDA0002393068690000023
Figure FDA0002393068690000031
Figure FDA0002393068690000032
wherein i and j represent the number of the paths, N represents the total number of the paths, k represents the number of the sampling points, L represents the total number of the sampling points, and xi(k) Representing the signal received from the kth sample point in the ith path,
Figure FDA0002393068690000033
representing an estimate of the polarization signal, tau representing the amount of displacement of the signal,
Figure FDA0002393068690000034
represents an estimate of the cross-correlation function of the polarization signal,
Figure FDA0002393068690000035
an estimate representing a cross-correlation function of the received signals;
the calculation of the characteristic matrix to be solved by adopting the coordinate rotation digital calculation method comprises the following formula pairs
Figure FDA0002393068690000036
And (3) calculating:
zl+1＝zl-δlarctan(2-l) l＝0,1,2,…,n-1
Figure FDA0002393068690000037
Figure FDA0002393068690000038
wherein the content of the first and second substances,
Figure FDA0002393068690000039
l denotes the number of iterations, n denotes the total number of iterations, xlRepresenting a cosine function after the l-th iteration, wherein xl +1 is the cosine function after the l + 1-th iteration, yl represents a sine function after the l-th iteration, yl +1 is the sine function after the l + 1-th iteration, zl represents a residual non-rotation angle after the l-th iteration, and zl +1 represents a residual non-rotation angle after the l + 1-th iteration;
the second calculation unit is used for calculating the optimal synthesis weight vector corresponding to the solved feature matrix; the method comprises the following steps: calculating the optimal synthetic weight vector corresponding to the solved feature matrix by adopting a power method algorithm or a Colltz-Wielandt iteration method;
and the processing 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 signals.
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