CN112363107A - Mixed signal direction-of-arrival estimation method based on co-prime array - Google Patents
Mixed signal direction-of-arrival estimation method based on co-prime array Download PDFInfo
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Abstract
The invention discloses a mixed signal direction-of-arrival estimation method based on a co-prime array, which utilizes the cyclicity and the non-cyclicity of mixed signals and the respective non-conjugate autocorrelation matrixes of received signals and conjugate signals thereof to calculate and combine to reconstruct a new signal model and can be applied to a mixed signal environment with non-cyclic signals and cyclic signals. Compared with the traditional co-prime array processing method, the method can expand the available virtual dimension to twice as much as the original virtual dimension at most. The invention can distinguish non-cyclic signals from cyclic signals, firstly estimate the direction of arrival of the non-cyclic signals, then estimate the power of the non-cyclic signals by utilizing a signal power estimation technology, delete the components corresponding to the non-cyclic signals from the autocorrelation matrix of the received signals, and estimate the direction of arrival of the cyclic signals according to the remaining signal components. Compared with the traditional co-prime array method, the method improves the degree of freedom, increases the number of the identification information sources, and improves the accuracy of the estimation of the direction of arrival.
Description
Technical Field
The invention relates to the field of signal processing, in particular to a mixed signal direction of arrival estimation method based on a co-prime array.
Background
The array signal processing technology is widely applied to aspects of national defense and life of people. Direction of arrival (DOA) estimation is an important issue in the field of array signal processing, and has many applications in radar, sonar, wireless communication, smart antennas, passive positioning, and the like. However, the conventional direction of arrival estimation method can only solve the situation that the number of targets is less than the number of array elements, so how to detect more targets with a small number of array elements becomes a new challenge. In recent years, the proposed linear array of a new geometry, the co-prime array, can reach the estimated DOA number far exceeding the array element number. Because the position distribution of the co-prime array elements is special, after mathematical operation processing, a virtual array with larger aperture can be formed, and the estimated target number is far larger than a uniform linear array with the same number of physical array elements.
Disclosure of Invention
The main purpose of the present invention is to overcome the disadvantages and shortcomings of the prior art, and to provide a mixed signal direction of arrival estimation method based on a co-prime array, which can separate the detection regions of non-cyclic signals and cyclic signals, further enhance the performance of the array, and resolve more signal sources with a smaller number of array elements.
The purpose of the invention is realized by the following technical scheme:
the mixed signal direction-of-arrival estimation method based on the co-prime array comprises the following steps:
array element distribution information of a receiving end antenna co-prime array is collected, and the number of signal sources is estimated approximately;
calculating a non-conjugate autocorrelation matrix of a received signal by using the cyclic and non-cyclic characteristics of a transmitted signal, multiplying the left of the obtained matrix by the conjugate transpose of the matrix to obtain a high-order correlation matrix, adjusting the order of the obtained high-order matrix, calculating the non-conjugate autocorrelation matrix of the conjugated signal of the received signal, combining the three matrices into a matrix and reconstructing a virtual received vector signal;
processing the virtual received vector signal, estimating the direction of arrival of the non-cyclic signal, and estimating the corresponding signal power; and deleting components corresponding to the non-cyclic signals from the autocorrelation matrix of the received signals, reconstructing a virtual received vector signal from the obtained autocorrelation matrix, and processing the virtual received vector signal to estimate the direction of arrival of the cyclic signals.
The array element distribution information of the co-prime array refers to the spatial distribution information of the receiving end antenna array.
The number of the signal sources refers to the number of the cyclic signals and the non-cyclic signals in the received signals.
The adjusting of the order of magnitude of the obtained high-order matrix means that the high-order matrix is divided by a certain coefficient, so that the obtained matrix and the original non-conjugate autocorrelation matrix keep the same order of magnitude.
The certain coefficient includes taking an absolute value of a trace of a non-conjugate autocorrelation matrix of the received signal as a coefficient, or taking a mean value of the matrix as a coefficient.
The reconstructing of the obtained autocorrelation matrix into a virtual received vector signal means that all elements in the autocorrelation matrix are mapped to received signals of each array element in the virtual difference array and the virtual sum array according to spatial distribution information of the co-prime array, array elements and difference values of the virtual array are sorted, repeated items of the same value are combined into one item, and the autocorrelation matrix element corresponding to the virtual sum and difference value sequence with the largest continuous length is taken as the received signal of the virtual array.
The estimation of the corresponding signal power means that the non-conjugate autocorrelation matrix of the received signal and the direction of arrival of the estimated non-cyclic signal are used for operation to obtain the signal power corresponding to the estimated direction.
The deleting of the component corresponding to the non-cyclic signal from the autocorrelation matrix of the received signal means deleting the component corresponding to the non-cyclic signal, that is, the product of the steering vector, the signal power, the conjugate transpose of the steering vector, and the like, from the autocorrelation matrix of the received signal.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. the invention utilizes the cyclicity and the non-cyclicity of the mixed signal and utilizes the respective non-conjugate autocorrelation matrixes of the received signal and the conjugate signal thereof to calculate and combine so as to reconstruct a new signal model. Compared with the traditional co-prime array processing method, the method can expand the available virtual dimension to twice as much as the original virtual dimension at most. The invention can distinguish non-cyclic signals from cyclic signals, firstly estimate the direction of arrival of the non-cyclic signals, then estimate the power of the non-cyclic signals by utilizing a signal power estimation technology, delete the components corresponding to the non-cyclic signals from the autocorrelation matrix of the received signals, and estimate the direction of arrival of the cyclic signals according to the remaining signal components.
2. The DOA estimation method provided by the invention is based on the cyclicity and the non-cyclicity of the mixed signal, utilizes the information carried by the received signal and the conjugate thereof, can distinguish the non-cyclic signal from the cyclic signal, improves the degree of freedom, increases the number of identification information sources, and estimates that the number of targets is far larger than that of a uniform linear array with the same number of physical array elements. Compared with the traditional method for DOA estimation by adopting a co-prime array, the DOA estimation method improves the degree of freedom, increases the number of identification information sources and improves the accuracy of the estimation of the direction of arrival.
Drawings
Fig. 1 is a flowchart of a mixed signal direction of arrival estimation method based on a co-prime array according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.
The mixed signal direction of arrival estimation method based on the co-prime array comprises the following steps:
the system server needs to collect array element distribution information of the receiving end antenna co-prime array and roughly estimate the source number of signals in advance;
the system server needs to calculate a non-conjugate autocorrelation matrix of the received signal, multiply the left of the obtained matrix by the conjugate transpose of the system server to obtain a high-order correlation matrix, and adjust the order of magnitude of the obtained high-order matrix;
the system server needs to calculate a non-conjugate autocorrelation matrix of a conjugate signal of a received signal;
the system server needs to combine the three calculated matrixes into one matrix;
the system server needs to reconstruct the merged matrix into a virtual received vector signal;
the system server needs to process the virtual received vector signal and estimate the direction of arrival of the non-cyclic signal;
the system server needs to estimate the power value of the non-cyclic signal by using the non-conjugate autocorrelation matrix of the received signal;
the system server needs to delete the component corresponding to the non-cyclic signal from the received signal autocorrelation matrix and reconstruct another virtual received vector signal;
the system server needs to process another virtual received vector signal to estimate the direction of arrival of the cyclic signal.
According to the technical scheme, the DOA estimation of the mixed signal is divided into the differential step detection of two signals. In addition, simulation results show that the DOA estimation method can distinguish non-cyclic signals from cyclic signals, detect higher DOA number with the same array element number, reduce estimation errors and improve DOA angle estimation accuracy.
As shown in fig. 1, the mixed signal direction-of-arrival estimation method based on the co-prime array specifically includes the following steps:
s101, collecting array element number m of a receiving end antenna co-prime array, array element distribution information and source number k of approximate estimation signals, wherein the number of non-cyclic signal sources is k1The number of the cyclic signal sources is k2；
Step S102, sampling the mixed signals received by the antennas in the co-prime array to obtain received signals. Wherein the non-cyclic signal in the transmitting signal is marked as s1The corresponding direction matrix is denoted as A1The cyclic signal in the transmitted signal is denoted as s2The corresponding direction matrix is denoted as A2N represents the noise of the signal transmission, and the received signal is x ═ A1s1+A2s2+n；
Step S103, calculating the non-conjugate autocorrelation matrix of the received signal x in S102, namely Rxx1＝E(xxT)；
Step S104, conjugate is taken for the received signal x in S102 to obtain xt＝x*(ii) a Calculating its non-conjugate autocorrelation matrix, i.e. Rxx2＝E(xtxt T)；
Step S105, calculating R for the matrix obtained in S103xx3＝E(Rxx1Rxx1 H) And the order of magnitude thereof is adjusted,
step S106, the autocorrelation matrix Rxx1、Rxx2、Rxx3Combining into a matrix, and reconstructing into a virtual receiving vector, that is, mapping all elements in the autocorrelation matrix to the receiving signals of each array element in the virtual difference array and the virtual sum array according to the spatial distribution information of the co-prime array, sorting the array elements and the difference values of the virtual array, combining the repeated items of the same value into one item (such as taking the average value, but not limited to the average value), and taking the autocorrelation matrix element corresponding to the virtual sum and difference value sequence with the largest continuous length as the receiving signal z of the virtual array1；
Step S107, for z1Performing spatial smoothing to obtain a covariance matrix R1；
Step S108, for R1The spatial spectrum calculation is carried out by using the MUSIC algorithm, and the DOA of the estimated acyclic signal is recorded as
Step S109, estimating the power of the non-cyclic signal, and estimating the power coefficient of the signal k as
Direction vector
The direction of arrival of the non-cyclic signal estimated by S108 and the spatial distribution of the antenna array are jointly determined;
step S110, calculating autocorrelation matrix R of received signal x in S102xx0＝E(xxH)；
Step S111, deleting the non-cyclic signal information,
step S112, the autocorrelation matrix Rxx0Reconstructing into a virtual receiving vector, and obtaining a receiving signal z of a virtual differential array in the same S1062；
Step S113, for z2Performing spatial smoothing to obtain a covariance matrix R2；
Step S114, for R2The spatial spectrum calculation is carried out by using the MUSIC algorithm, and DOA of the estimated cyclic signal is recorded as
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.
Claims (9)
1. The mixed signal direction-of-arrival estimation method based on the co-prime array is characterized by comprising the following steps in sequence:
array element distribution information of a receiving end antenna co-prime array is collected, and the number of signal sources is estimated approximately;
calculating a non-conjugate autocorrelation matrix of a received signal by using the cyclic and non-cyclic characteristics of a transmitted signal, multiplying the left of the obtained matrix by the conjugate transpose of the matrix to obtain a high-order correlation matrix, adjusting the order of the obtained high-order matrix, calculating the non-conjugate autocorrelation matrix of the conjugated signal of the received signal, combining the three matrices into a matrix and reconstructing a virtual received vector signal;
processing the virtual received vector signal, estimating the direction of arrival of the non-cyclic signal, and estimating the corresponding signal power; and deleting components corresponding to the non-cyclic signals from the autocorrelation matrix of the received signals, reconstructing a virtual received vector signal from the obtained autocorrelation matrix, and processing the virtual received vector signal to estimate the direction of arrival of the cyclic signals.
2. The method according to claim 1, wherein the array element distribution information of the co-prime array is spatial distribution information of a receiving-end antenna array.
3. The method of claim 1, wherein the number of signal sources is the number of cyclic signals and acyclic signals in the received signal.
4. The method of claim 1, wherein the adjusting the order of magnitude of the high-order matrix is dividing the high-order matrix by a certain coefficient, so that the order of magnitude of the high-order matrix is the same as that of the original non-conjugate autocorrelation matrix.
5. The method of claim 4, wherein the certain coefficients comprise absolute values of traces of a non-conjugate autocorrelation matrix of the received signal or a mean value of the matrix.
6. The method according to claim 1, wherein reconstructing a virtual received vector signal from the obtained autocorrelation matrix is performed by mapping all elements in the autocorrelation matrix to the received signals of each array element in the virtual difference array and the virtual sum array according to spatial distribution information of the co-prime array, sorting the array elements and difference values of the virtual array, combining the repeated entries of the same value into one entry, and taking the autocorrelation matrix element corresponding to the sequence of the virtual sum difference values with the largest continuous length as the received signal of the virtual array.
7. The method of claim 1, wherein the estimating the corresponding signal power is performed by using a non-conjugate autocorrelation matrix of the received signal and the estimated direction of arrival of the non-cyclic signal to obtain the signal power corresponding to the estimated direction.
8. The method according to claim 1, wherein the removing of the component corresponding to the non-cyclic signal from the autocorrelation matrix of the received signal is removing a component corresponding to the non-cyclic signal, i.e. a product of a steering vector, a signal power, a conjugate transpose of the steering vector, and the like, from the autocorrelation matrix of the received signal.
9. The method for estimating direction of arrival of mixed signal based on co-prime array as claimed in claim 1, comprising the steps of:
s101, collecting array element number m of a receiving end antenna co-prime array, array element distribution information and source number k of approximate estimation signals, wherein the number of non-cyclic signal sources is k1The number of the cyclic signal sources is k2；
Step S102, sampling a mixed signal received by an antenna in a co-prime array to obtain a received signal; wherein the non-cyclic signal in the transmitting signal is marked as s1The corresponding direction matrix is denoted as A1The cyclic signal in the transmitted signal is denoted as s2The corresponding direction matrix is denoted as A2N represents the noise of the signal transmission, and the received signal is x ═ A1s1+A2s2+n；
Step S103, calculating the non-conjugate autocorrelation matrix of the received signal x in step S102, namely Rxx1＝E(xxT)；
Step S104, conjugate is taken for the received signal x in step S102 to obtain xt＝x*(ii) a Calculating its non-conjugate autocorrelation matrix, i.e. Rxx2＝E(xtxt T)；
Step S105, calculating R for the matrix obtained in step S103xx3＝E(Rxx1Rxx1 H) And the order of magnitude thereof is adjusted,
step S106, the autocorrelation matrix Rxx1、Rxx2、Rxx3Combining into a matrix, and reconstructing into a virtual receiving vector, i.e. mapping all elements in the autocorrelation matrix to the receiving signals of each array element in the virtual difference array and the virtual summation array according to the spatial distribution information of the co-prime array, sequencing the array elements and the difference values of the virtual array, combining the repeated items of the same value into one item, and taking the autocorrelation matrix element corresponding to the virtual sum and difference value sequence with the maximum continuous length as the receiving signal z of the virtual array1；
Step S107, receiving signal z for virtual array1Performing spatial smoothing to obtain a covariance matrix R1；
Step S108, covariance matrix R1The spatial spectrum calculation is carried out by using the MUSIC algorithm, and the DOA of the estimated acyclic signal is recorded as
Step S109, estimating the power of the non-cyclic signal, and estimating the power coefficient of the signal k as
Direction vector
The direction of arrival of the non-cyclic signal estimated in step S108 and the spatial distribution of the antenna array are determined together;
step S110, calculating autocorrelation matrix R of received signal x in step S102xx0＝E(xxH)；
Step S111, deleting non-cyclic signal informationIn the form of a capsule, the particles,
step S112, the autocorrelation matrix Rxx0Reconstructing into a virtual received vector, and synchronizing S106 to obtain a received signal z of a virtual differential array2；
Step S113 of receiving a signal z for the virtual differential array2Performing spatial smoothing to obtain a covariance matrix R2；
Step S114, to covariance matrix R2The spatial spectrum calculation is carried out by using the MUSIC algorithm, and DOA of the estimated cyclic signal is recorded as
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