CN107255793B - Array direction finding method and device for broadband OFDM communication signals - Google Patents

Array direction finding method and device for broadband OFDM communication signals Download PDF

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CN107255793B
CN107255793B CN201710456606.XA CN201710456606A CN107255793B CN 107255793 B CN107255793 B CN 107255793B CN 201710456606 A CN201710456606 A CN 201710456606A CN 107255793 B CN107255793 B CN 107255793B
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武震
臧维明
蒋景飞
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CETC 29 Research Institute
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
    • G01S3/14—Systems for determining direction or deviation from predetermined direction
    • G01S3/28—Systems for determining direction or deviation from predetermined direction using amplitude comparison of signals derived simultaneously from receiving antennas or antenna systems having differently-oriented directivity characteristics
    • G01S3/30—Systems for determining direction or deviation from predetermined direction using amplitude comparison of signals derived simultaneously from receiving antennas or antenna systems having differently-oriented directivity characteristics derived directly from separate directional systems
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
    • G01S3/74—Multi-channel systems specially adapted for direction-finding, i.e. having a single antenna system capable of giving simultaneous indications of the directions of different signals
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2647—Arrangements specific to the receiver only
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Abstract

The invention relates to a direction finding technology in the field of broadband array signal processing, which selects a focusing reference frequency point, decomposes OFDM signals received by an array and carries out DFT processing to obtain broadband array signals; calculating a focusing matrix of each corresponding frequency point by using the constraint condition of the minimum error between the focused array flow pattern and the reference frequency point array flow pattern and the array flow pattern matrix; according to the focusing matrix, carrying out focusing transformation on the array received data in each sub-period to obtain a single frequency point data covariance matrix, and further obtaining a reference frequency point covariance matrix; calculating an arithmetic mean value R of the covariance matrix of each reference frequency point; decomposing the characteristic value of the R to obtain a signal subspace and a noise subspace, and further obtain a spatial spectrum expression of the broadband MUSIC algorithm; and searching according to the spatial spectrum expression to obtain the angle positions corresponding to the P maximum values, namely the estimated value of the incoming wave direction of the broadband OFDM signal.

Description

Array direction finding method and device for broadband OFDM communication signals
Technical Field
The invention relates to a direction finding technology in the field of broadband array signal processing, in particular to an array direction finding method and device for broadband OFDM communication signals.
Background
The music (multiple SIgnal classification) algorithm was proposed by Schmidt et al in 1979, and its basic idea is to perform characteristic decomposition on a covariance matrix of arbitrary array output data to obtain a SIgnal subspace corresponding to a SIgnal component and a noise subspace orthogonal to the SIgnal component, and then perform a spectral peak search using the orthogonality of the two subspaces to estimate the incident direction of the SIgnal.
For broadband OFDM communication signals, the conventional array direction-finding music (multiple SIgnal classification) algorithm cannot perform multi-SIgnal resolution and direction-of-arrival estimation on such signals, and only can process narrow-band and incoherent spatial signals, while the direction-finding algorithm adopting a phase-to-amplitude ratio system cannot simultaneously resolve a plurality of signals, and even cannot perform effective direction-of-arrival estimation. Therefore, it is necessary to solve the problem of estimating the direction of arrival of a wideband OFDM communication signal.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the problems in the prior art, an array direction finding method and device for broadband OFDM communication signals are provided. The method solves the technical problem that under the condition that a plurality of coherent broadband OFDM communication signals exist in space, a frequency focusing method is adopted to distinguish a plurality of signals by utilizing a uniform linear array or a uniform circular array, and the one-dimensional or two-dimensional direction of arrival of each signal is measured at the same time.
The technical scheme adopted by the invention is as follows:
an array direction finding method for wideband OFDM communication signals includes:
selecting a focus reference frequency point f0Decomposing OFDM signal received by array and DFT processing to obtain wideband array signal Xk(fj)，j＝1,2,…,J；
Then, the constraint condition that the error between the focused array manifold and the reference frequency point array manifold is minimum and the array manifold matrix are utilized
Figure GDA0002948644240000021
Calculating a focusing matrix T (f) of each corresponding frequency pointj)；
According to the focusing matrix T (f)j) Focusing conversion is carried out on the array received data in each sub-period to obtain a single frequency point data covariance matrix Hk(fj) Further, a covariance matrix R of the reference frequency point is obtainedk；
Calculating covariance matrix R of each reference frequency point in K time periodskThe arithmetic mean value of R;
performing characteristic value decomposition on the R to obtain a signal subspace EsAnd noise subspace EnFurther obtaining a spatial spectrum expression of the broadband MUSIC algorithm;
and searching according to the spatial spectrum expression to obtain the angle positions corresponding to the P maximum values, namely the estimated value of the incoming wave direction of the broadband OFDM signal.
Further, according to the antenna array form, constructing an array manifold matrix of each frequency point in the signal bandwidth range
Figure GDA0002948644240000022
Figure GDA0002948644240000023
The dimension of M multiplied by P is an array manifold matrix, and the column-number steering vector of the matrix is as follows:
Figure GDA0002948644240000024
m is the number of array elements; tau isliRepresenting the time delay of the ith signal reaching the ith array element relative to the reference array element; i is 1,2, …, P.
Further, in the above-mentioned case,
Figure GDA0002948644240000025
with a broadband array signal Xk(fj) The relationship is:
Figure GDA0002948644240000026
j＝1,2,…,J；k＝1,2,…,K；Xk(fj),Nk(fj) Are all M × 1 dimensional vectors whose elements are respectively received by the array in the k-th time intervalk(t) and noise nk(t) at frequency fjDiscrete fourier coefficients of (ii); sk(fj) Is a P x 1 dimensional vector which is derived from the incident signal s in the k-th time intervalk(t) discrete fourier coefficients;
furthermore, an array form of a uniform circular array is formed by the omnidirectional antenna array elements according to the radius
Figure GDA0002948644240000027
The antenna arrays are arranged at intervals, and c is the light speed;
the uniform circular array is a three-dimensional array, and simultaneously reflects the signal azimuth and the pitching characteristic, and each column of guide vectors can be expressed as: i represents the number of coherent signals; i is more than or equal to 1 and less than M;
Figure GDA0002948644240000031
further, the calculation process of the focusing matrix of the uniform circular array antenna array is as follows:
selecting a focusing frequency as a center frequency f of the broadband OFDM signal0Total observation time is T0. Dividing the OFDM signal time domain snapshot received by the array into K time subsections, each section
Figure GDA0002948644240000032
Performing J-point FFT to obtain X for each time subsectionk(fj) The array signal output of the signal-superimposed noise is divided into J narrowband frequency components, where fjIs the jth narrowband frequency component;
adopting RSS method to construct array manifold matrix of each frequency point, and calculating focusing matrix T (f) of each corresponding frequency pointj) Completing the frequency component fjTo f0Focusing of (3).
Further, the antenna array of the uniform circular array refers to the frequency point covariance matrix RkThe arithmetic mean R of (a) is calculated as:
according to the focusing matrix T (f)j) Receiving data X for the array in the k time sub-segmentk(fj) Performing focus transformation to obtain Yk(fj) Further, a data covariance matrix H at a single frequency point in the kth time subsection is obtainedk(fj)；
After calculating all the frequency points of the division, all H are takenk(fj) The arithmetic mean value of the k time subsegment is obtained based on the reference frequency point f0Of the covariance matrix Rk；
Calculating the arithmetic mean value R of the covariance matrix based on the reference frequency point in all K time segmentskThen calculate RkObtaining a covariance matrix R of all data by the arithmetic mean value;
further, the calculation process of the estimated value of the incoming wave direction of the broadband OFDM communication signal is as follows: performing characteristic value decomposition on the R to obtain a signal subspace EsAnd noise subspace En；
And performing one-dimensional or two-dimensional spatial spectrum calculation and spectrum peak search according to a spatial spectrum expression of the broadband MUSIC algorithm, wherein the corresponding angles of the P maximum values are estimated values of the incoming wave directions of the P broadband OFDM communication signals.
Further, the data covariance matrix R calculation process:
carrying out weighted average on the divided K time subsections to obtain a data covariance matrix in the whole observation time section
Figure GDA0002948644240000041
Further, the array direction finding device of the array direction finding method comprises:
wideband array signal Xk(fj) A calculation module for selecting a focus reference frequency point f0Decomposing OFDM signal received by array and DFT processing to obtain wideband array signal Xk(fj)，j＝1,2,…,J；
A focusing matrix calculation module for utilizing the constraint condition of minimum error between the focused array manifold and the reference frequency point array manifold and the array manifold matrix
Figure GDA0002948644240000042
Calculating a focusing matrix T (f) of each corresponding frequency pointj)；
A reference frequency point covariance matrix calculation module for calculating a covariance matrix according to the focusing matrix T (f)j) Focusing conversion is carried out on the array received data in each sub-period to obtain a single frequency point data covariance matrix Hk(fj) Further, a covariance matrix R of the reference frequency point is obtainedk；
A covariance matrix mean calculation module for calculating covariance matrix R of each reference frequency point in K time periodskThe arithmetic mean value of R;
a calculation module for the estimated value of the incoming wave direction of the broadband OFDM signal, which is used for decomposing the characteristic value of R to obtain a signal subspace EsAnd noise subspace EnFurther obtaining a spatial spectrum expression of the broadband MUSIC algorithm; searching according to spatial spectrum expressionsAnd obtaining the angle positions corresponding to the P maximum value points, namely the estimated value of the incoming wave direction of the broadband OFDM signal.
In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:
the invention adopts a broadband focusing method, designs and uses uniformly distributed array antennas to distinguish coherent broadband OFDM communication signals, and provides one-dimensional (azimuth angle) and two-dimensional (azimuth angle and pitch angle) direction-of-arrival estimation results of a plurality of targets, compared with the traditional array processing method, the two methods are as follows:
1) when the array covariance matrix R is calculated, the traditional MUSIC method directly performs coherent accumulation by using time domain snapshots collected by an array, and the method is effective for narrow-band signals but has no effect on broadband OFDM signals. By adopting a frequency focusing matrix, the estimation of the direction of arrival of the broadband communication signal can be effectively realized by a method of calculating the frequency domain snapshot of the observation data by time-frequency domain conversion and segmentation;
2) the traditional MUSIC spectrum estimation method cannot distinguish a plurality of coherent signals, and can distinguish a plurality of coherent broadband OFDM signals existing in the space at the same time after adopting a broadband focusing method;
3) in the process of estimating the direction of arrival of a broadband OFDM communication signal, the traditional MUSIC method adopts a one-dimensional uniform linear array, so that only the arrival angle of the signal in the azimuth can be acquired;
4) compared with the resolving power and direction-finding performance of the traditional MUSIC method and the RSS method aiming at the same broadband OFDM signal, the method proves that the traditional MUSIC method and the RSS method have more excellent broadband signal super-resolution direction-finding performance and are more effective in practical application.
In conclusion, by adopting the broadband focusing method in the invention and combining with the corresponding array form, the performance requirements which cannot be met by the conventional MUSIC algorithm can be met, the direction finding and resolving power of the broadband OFDM communication signal can be obviously enhanced, and a scientific technical solution is provided for performing one-dimensional and two-dimensional direction of arrival estimation on the broadband signal by using the array processing method.
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The invention will now be described, by way of example, with reference to the accompanying drawings, in which:
FIG. 1 is a time domain waveform of a broadband OFDM communication signal received by an array element in an embodiment
FIG. 2 is a frequency domain waveform of a wideband OFDM communication signal received by an array element in an embodiment
FIG. 3 is a comparison of the present method and the conventional spectrum estimation method for the direction-finding capability of the same broadband OFDM signal (linear array)
FIG. 4 is a comparison of the present method and the conventional spectrum estimation method for the same broadband OFDM signal direction finding capability (circular array)
FIG. 5 is the Monte-Carlo simulation result (200 points) of the uniform linear array direction finding precision along with the signal-to-noise ratio variation curve
Detailed Description
All of the features disclosed in this specification, or all of the steps in any method or process so disclosed, may be combined in any combination, except combinations of features and/or steps that are mutually exclusive.
Any feature disclosed in this specification may be replaced by alternative features serving equivalent or similar purposes, unless expressly stated otherwise. That is, unless expressly stated otherwise, each feature is only an example of a generic series of equivalent or similar features.
Description of the invention:
1. principle of OFDM modulation
OFDM is a highly efficient multi-carrier modulation scheme, and is known as Orthogonal Frequency Division Multiplexing (OFDM), which can effectively combat Frequency selective fading in wireless communication channels. The data symbols obtained by constellation mapping of the data bits are modulated to a plurality of mutually orthogonal subcarriers to realize the efficient utilization of the frequency spectrum. The frequency interval of the subcarrier and the duration of the data symbol on the subcarrier are reciprocal to each other, so that the obtained modulated subcarrier can be ensured to have the minimum frequency interval meeting the orthogonality condition. Before the data symbols are modulated by OFDM, the serial data symbols are firstly converted into parallel data, then the OFDM modulated multi-channel data are superposed and converted into serial data flow, a guard interval is inserted to form a transmitting signal, and finally the transmitting signal is transmitted out by a radio frequency unit through a forming filter. The OFDM demodulation is to acquire a data symbol carried on a subcarrier, perform parallel-to-serial conversion on the symbol, demodulate and output the symbol, and acquire transmitted bit information.
If N represents the number of sub-carriers, T represents the OFDM symbol width, dk(k is 0,1,2, …, N-1) is a data symbol allocated to each subcarrier, f is a symbol numbercIs the carrier frequency of the 0 th sub-carrier, rect (T) is 1, T | ≦ T/2, then from T ═ TsThe starting OFDM symbol may be represented as:
Figure GDA0002948644240000071
correspondingly, the OFDM equivalent baseband signal model is as follows:
Figure GDA0002948644240000072
neglecting the rectangular shaping pulse function, let t s0, for signal zB(t) is represented by
Figure GDA0002948644240000073
Is sampled at a rate of, i.e. order
Figure GDA0002948644240000074
It is possible to obtain:
Figure GDA0002948644240000075
as can be seen from the formula (3), snIs equivalent to pair dkAn IDFT (inverse Discrete Fourier transform) operation is performed. Also at the receiving end, to recover the original data symbols dkCan be paired with snAnd performing inverse transformation, namely DFT to obtain.
2. Wideband array signal model
Considering that the Array model is a Uniform Linear Array (ULA) with M Array elements arranged at equal intervals or a Uniform Circular Array (UCA) with Uniform angular intervals along the circumference, P broadband OFDM far-field communication signals are respectively radiated onto the Array from different angles, and the incident angles are respectively
Figure GDA0002948644240000076
Figure GDA0002948644240000077
Wherein θ and
Figure GDA0002948644240000078
respectively representing the azimuth and elevation angles of the incident signal. It is assumed that the wideband OFDM signal has the same bandwidth B and center frequency f0The noise is white Gaussian noise, the mean is 0, and the variance is sigma2And the signal is uncorrelated with noise, where the first array element is used as a reference array element, the received data (without considering the gain) on the ith array element can be expressed as:
Figure GDA0002948644240000079
wherein: si(t) is the ith incident signal, τliRepresenting the time delay of the ith signal arriving at the ith array element relative to the reference array element, c is the speed of light, nl(t) represents the noise of the l-th array element at time t.
If the time T is to be observed0Is divided into K subsections, and each subsection has a time TkIf the time interval T is taken, in order to ensure that the output data of the array are uncorrelated in the frequency domainkIs long enough to satisfy tauli＜TkTime delay τliWhich can be translated into a phase shift in the frequency domain. Performing J-point Discrete Fourier Transform (DFT) on the observation data to obtain a wideband array signal model in a k time interval frequency domain:
Figure GDA0002948644240000081
wherein: xk(fj),Nk(fj) Are all M × 1 dimensional vectors whose elements are respectively received by the array in the k-th time intervalk(t) and nk(t) noise at frequency fjDiscrete fourier coefficients of (ii); sk(fj) Is a P x 1 dimensional vector which is derived from the incident signal s in the k-th time intervalk(t) discrete fourier coefficients;
Figure GDA0002948644240000082
the dimension of M × P is an array manifold matrix, and the i (i ═ 1,2, …, P) th column steering vector is:
Figure GDA0002948644240000083
3. the working process is as follows: as shown in figure 1
3.1 focusing matrix T (f)j) The construction process comprises the following steps:
the formula derivation of the present invention is for the two-dimensional case (where the one-dimensional case is understood to be
Figure GDA0002948644240000084
Special two-dimensional case of). The basic idea of the incoming wave direction estimation method based on the broadband focusing matrix is to change the data of each frequency point into the data of a reference frequency point through the focusing matrix, and the key point is the selection of the focusing matrix. From the broadband signal model (5), the key problem is to construct the focusing matrix T (f)j) So that it satisfies the formula (6):
Figure GDA0002948644240000085
the broadband focusing matrix is obtained by calculation through a rotating signal subspace transformation algorithm, and the working principle of the broadband focusing matrix is that the error between the focused array manifold and the reference frequency point array manifold is minimum, namely:
Figure GDA0002948644240000086
constraint T (f)j) As unitary matrices, i.e. TH(fj)T(fj) I (I denotes an identity matrix).
Wherein: i | · | purple windFIs Frobenius mode, theta is signal direction matrix [ theta ]1 θ2 … θP]T. The above process is actually by TjActing on array manifold
Figure GDA0002948644240000091
The subspace is formed by stretching to fit under the Frobenius norm least meaning
Figure GDA0002948644240000092
A sub-space is formed by stretching. (7) One solution of equation under the constraint is:
T(fj)＝V(fj)U(fj)H (8)
wherein: u (f)j) And V (f)j) Are respectively
Figure GDA0002948644240000093
The left singular value vector and the right singular value vector of (a) are a matrix with columns arranged.
3.2 Single frequency Point data covariance matrix Hk(fj) And (3) calculating:
mixing T (f)j) Substituting formula (5) with formula (9) to obtain formula (10):
Yk(fj)＝T(fj)Xk(fj)
＝T(fj)A(fj,θ)Sk(fj)+T(fj)Nk(fj)
＝A(f0,θ)Sk(fj)+T(fj)Nk(fj) (9)
Figure GDA0002948644240000094
wherein: rs(fj) And σ2(fj) Respectively representing a frequency of fjThe covariance matrix and the noise power of the observed data.
3.3 reference frequency Point covariance matrix RkAnd a data covariance matrix R calculation process:
firstly, for each frequency point Hk(fj) Weighted average to obtain the k sub-period about the reference frequency point f0Of the covariance matrix Rk：
Figure GDA0002948644240000095
Then, carrying out weighted average on the divided K time subsections to obtain a data covariance matrix R in the whole observation time section:
Figure GDA0002948644240000096
3.4 spatial spectrum expression calculation process of wideband MUSIC algorithm:
finally, eigenvalue decomposition is carried out on the covariance matrix R to obtain P large eigenvalues lambdai(i ═ 1,2, …, P), the eigenvectors corresponding to the P large eigenvalues span the signal subspace Es＝[e1 e2 … eP]And expanding the eigenvectors corresponding to the remaining M-P smaller eigenvalues into a noise subspace En＝[eP+1 eP+2 … eM]。
In summary, the spatial spectrum expression (13) of the wideband MUSIC algorithm can be obtained:
Figure GDA0002948644240000101
according to the idea based on the focusing matrix, the resolution and the direction of arrival of the broadband OFDM signal are estimated; and (4) searching a one-dimensional azimuth or a two-dimensional azimuth and a pitching spectral peak according to the spatial spectrum expression in the expression (13), wherein the angle positions corresponding to the P maximum values are estimated values of the incoming wave direction of the broadband OFDM signal.
4. The implementation steps comprise:
4.1 selected Focus reference frequency Point f0Dividing the OFDM signal received by the array into K non-overlapping subsegments, dividing each subsegment into J narrow frequency bands and performing DFT to obtain Xk(fj)，j＝1,2,…,J；
And 4.2, constructing a one-dimensional or two-dimensional array manifold matrix of each frequency point in the signal bandwidth range according to the antenna array form, and then calculating the focusing matrix of each corresponding frequency point by using a formula (8). The array manifold of the two-dimensional area array can reflect the three-dimensional characteristics of signals in a space domain, so that the method has obvious advantages compared with a one-dimensional linear array in the resolution of a plurality of signals;
4.3 carrying out focusing transformation on the array received data in each sub-period according to the formula (9) to obtain Yk(fj) Obtaining a single frequency point data covariance matrix H by the formula (10)k(fj) Then, the covariance matrix R of the reference frequency point is obtained by taking the arithmetic mean of all the frequency points according to the formula (11)k；
4.4 calculating the arithmetic mean value R of the covariance matrix at each reference frequency point in K time periods according to the expression (12)kThe arithmetic mean value of R;
4.5 decomposing the characteristic value of R to obtain a signal subspace EsAnd noise subspace En；
And 4.6, searching a one-dimensional azimuth or two-dimensional azimuth and pitch spectrum peak according to the spatial spectrum expression in the expression (13), wherein the angle positions corresponding to the P maximum values are estimated values of the incoming wave direction of the broadband OFDM signal.
5. The first embodiment is as follows:
5.1 simulation conditions:
having the same center frequency f0A 2GHz wideband OFDM communication signal with a bandwidth B of 200MHz using qpsk (quadrature Phase Shift keying)I.e., 256 symbols, 64 subcarriers. Array noise n (t) is a stationary zero-mean band-limited (same bandwidth as the OFDM signal) Gaussian process, noise n for M array elementsm(t) (M ═ 1,2, …, M) are independent of each other and have the same statistical properties, they are also statistically independent of the signal. The signal-to-noise ratio is set to 20 dB. The sampling frequency of each array element is 4 GHz. The performance simulation test is carried out aiming at the following two array distribution forms, wherein the first linear array is the currently and commonly adopted array distribution form, and the second circular array is the new array type adopted in the text.
Antenna array form 1: 8 omnidirectional antenna array elements form a uniform linear array, and the array element spacing
Figure GDA0002948644240000111
c is the speed of light (antenna arrangement according to the array element interval), and three coherent signals are respectively
Figure GDA0002948644240000112
Figure GDA0002948644240000113
And
Figure GDA0002948644240000114
angle incidence, time domain SNAP 1000. The steering vector of each column of the array manifold matrix of the matrix 1 can be expressed by derivation:
Figure GDA0002948644240000115
antenna array pattern 2: 8 omnidirectional antenna array elements form a uniform circular array with radius
Figure GDA0002948644240000116
c is the speed of light (antenna arrangement is carried out according to the array element interval), and three coherent signals are respectively in azimuth and elevation
Figure GDA0002948644240000117
And
Figure GDA0002948644240000118
angle incidence, time domain SNAP 1000. The array manifold matrix of the array type 2 is different from the array type 1, is a three-dimensional matrix, can reflect the signal direction and the pitching characteristic at the same time, has wide applicability, and each column of guide vectors can be expressed as:
Figure GDA0002948644240000121
the detailed implementation steps for carrying out resolution and direction of arrival estimation on three broadband OFDM signals by adopting the scheme are as follows:
step 5.1 select the focusing frequency as the center frequency f of the broadband OFDM signal0Total observation time is T01.28 us. Dividing 1000 time domain snapshots of OFDM signal received by array into K-10 time subsections, each section
Figure GDA0002948644240000122
Step 5.2, perform 100-point FFT on each time subsection to obtain Xk(fj) The array signal output of the signal superimposed noise is then divided into J100 narrowband frequency components, where J50 is the wideband signal center frequency f0The frequency point where the frequency is located;
step 5.3, an array manifold matrix of each frequency point is constructed by adopting an RSS method, and a focusing matrix T (f) of each corresponding frequency point is calculatedj) Completing the frequency component fjTo f0Focusing of (3);
step 5.4 based on the focusing matrix T (f)j) Receiving data X for the array in the k time sub-segmentk(fj) Performing focus transformation to obtain Yk(fj) Further, a data covariance matrix H at a single frequency point in the kth time subsection is obtainedk(fj)；
Step 5.5 after calculating all the frequency points of the division, all H are takenk(fj) The arithmetic mean value of the k time subsegment is obtained based on the reference frequency point f0Of the covariance matrix Rk；
Step 5.6 the calculation method of step 5.4 to 5.5 is repeated to calculate the basis of all K time periodsArithmetic mean R of covariance matrix at reference frequency pointkThen calculate RkObtaining a covariance matrix R of all data by the arithmetic mean value;
step 5.6, carrying out characteristic value decomposition on the R to obtain a signal subspace EsAnd noise subspace En；
And 5.7, performing one-dimensional or two-dimensional spatial spectrum calculation and spectral peak search according to the formula (13), wherein the corresponding angles of the P maximum values are the estimated values of the incoming wave directions of the P broadband OFDM communication signals.
After antenna array design and computer simulation verification, 8-element uniform linear arrays and uniform circular arrays are respectively adopted, under the simulation condition in the implementation example, the resolution and the one-dimensional and two-dimensional direction of arrival estimation of three coherent broadband OFDM signals are completed according to the RSS calculation method and the calculation steps from 1) to 8), the effect is good, the estimation precision is obviously improved along with the improvement of the signal to noise ratio, and the robustness is strong (figure 3); in comparison, the signal resolution and direction of arrival estimation results using the conventional MUSIC spectrum estimation method under the same conditions are given (fig. 3, fig. 5). Theoretical analysis and computer simulation show that the broadband OFDM communication signal resolution and one-dimensional and two-dimensional direction of arrival estimation methods based on the broadband focusing matrix have obvious advantages compared with the traditional spectrum estimation calculation method, the high resolution capability is still kept under the condition that the traditional method cannot distinguish a plurality of signals, the accurate direction of arrival can be given for coherent broadband signals, the algorithm performance is remarkably improved, the engineering application range of the spatial spectrum estimation direction finding technology is widened, and the practicability is high.
The invention is not limited to the foregoing embodiments. The invention extends to any novel feature or any novel combination of features disclosed in this specification and any novel method or process steps or any novel combination of features disclosed.

Claims (5)

1. A method of array direction finding for wideband OFDM communication signals, comprising:
selecting a focus reference frequency point f0Decomposing OFDM signal received by array and DFT processing to obtain wideband array signal Xk(fj)，j＝1,2,…,J；
Then utilizing the constraint condition of minimum error between the focused array flow pattern and the reference frequency point array flow pattern and the array flow pattern matrix
Figure FDA0002948644230000011
Calculating a focusing matrix T (f) of each corresponding frequency pointj) Wherein θ and
Figure FDA0002948644230000012
respectively representing the azimuth angle and the pitch angle of the incident signal;
according to the focusing matrix T (f)j) Focusing conversion is carried out on the array received data in each sub-period to obtain a single frequency point data covariance matrix Hk(fj) Further, a covariance matrix R of the reference frequency point is obtainedk；
Calculating covariance matrix R of each reference frequency point in K time periodskThe arithmetic mean value of R;
performing characteristic value decomposition on the R to obtain a signal subspace EsAnd noise subspace EnFurther obtaining a spatial spectrum expression of the broadband MUSIC algorithm;
searching according to the spatial spectrum expression to obtain angle positions corresponding to the P maximum values, namely an estimated value of the incoming wave direction of the broadband OFDM signal;
wherein the array flow pattern matrix
Figure FDA0002948644230000013
According to the antenna array form, constructing each frequency point in the signal bandwidth range; the antenna array form is an antenna array form which forms a uniform circular array by omnidirectional antenna array elements and is according to the radius
Figure FDA0002948644230000014
The uniform circular array is a three-dimensional array and reflects the direction of signalsAnd pitch characteristics, each column steering vector can be expressed as a derived vector
Figure FDA0002948644230000015
i represents the number of coherent signals; i is not less than 1<M; c represents the speed of light;
the above-mentioned
Figure FDA0002948644230000016
The dimension M multiplied by P is an array flow pattern matrix, and the first column of guide vectors are as follows:
Figure FDA0002948644230000017
m is the number of array elements; tau isliRepresenting the time delay of the ith signal reaching the ith array element relative to the reference array element; i is 1,2, …, P;
Figure FDA0002948644230000021
with a broadband array signal Xk(fj) The relationship is:
Figure FDA0002948644230000022
j＝1,2,…,J；k＝1,2,…,K；Xk(fj) Representing the array received signal x in the k-th time intervalk(t) at frequency fjM x 1-dimensional vector of discrete fourier coefficients, Nk(fj) Representing array noise n in the k-th time intervalk(t) at frequency fjAn M × 1-dimensional vector of discrete fourier coefficients; sk(fj) Is a P x 1 dimensional vector which is derived from the incident signal s in the k-th time intervalk(t) discrete fourier coefficients;
the calculation process of the antenna array focusing matrix of the uniform circular array comprises the following steps:
selecting a focusing frequency as a center frequency f of the broadband OFDM signal0Total observation time is T0(ii) a Dividing the OFDM signal time domain snapshot received by the array into K time subsections, each section
Figure FDA0002948644230000023
Performing J-point FFT to obtain X for each time subsectionk(fj) The array signal output of the signal-superimposed noise is divided into J narrowband frequency components, where fjIs the jth narrowband frequency component;
adopting RSS method to construct array flow pattern matrix of each frequency point, and calculating focusing matrix T (f) of each corresponding frequency pointj) Completing the frequency component fjTo f0Focusing of (3).
2. An array direction finding method for wideband OFDM communication signals as claimed in claim 1 wherein the array of uniform circular arrays is referenced to a frequency point covariance matrix RkThe arithmetic mean R of (a) is calculated as:
according to the focusing matrix T (f)j) Receiving data X for the array in the k time sub-segmentk(fj) Performing focus transformation to obtain Yk(fj) Further, a data covariance matrix H at a single frequency point in the kth time subsection is obtainedk(fj)；
After calculating all the frequency points of the division, all H are takenk(fj) The arithmetic mean value of the k time subsegment is obtained based on the reference frequency point f0Of the covariance matrix Rk；
Calculating the arithmetic mean value R of the covariance matrix based on the reference frequency point in all K time segmentskThen calculate RkThe arithmetic mean of (d) yields the covariance matrix R of all data.
3. An array direction-finding method for a wideband OFDM communication signal as claimed in claim 1 wherein the calculation of the estimated value of the incoming wave direction of the wideband OFDM communication signal is:
performing characteristic value decomposition on the R to obtain a signal subspace EsAnd noise subspace En；
And performing one-dimensional or two-dimensional spatial spectrum calculation and spectrum peak search according to a spatial spectrum expression of the broadband MUSIC algorithm, wherein the corresponding angles of the P maximum values are estimated values of the incoming wave directions of the P broadband OFDM communication signals.
4. An array direction finding method for wideband OFDM communication signals as claimed in claim 1 wherein said data covariance matrix R calculation process:
carrying out weighted average on the divided K time subsections to obtain a data covariance matrix in the whole observation time section
Figure FDA0002948644230000031
5. Array direction-finding device based on the array direction-finding method of one of claims 1 to 4, characterized by comprising:
wideband array signal Xk(fj) A calculation module for selecting a focus reference frequency point f0Decomposing OFDM signal received by array and DFT processing to obtain wideband array signal Xk(fj)，j＝1,2,…,J；
A focusing matrix calculation module for utilizing the constraint condition of minimum error between the focused array flow pattern and the reference frequency point array flow pattern and the array flow pattern matrix
Figure FDA0002948644230000032
Calculating a focusing matrix T (f) of each corresponding frequency pointj)；
A reference frequency point covariance matrix calculation module for calculating a covariance matrix according to the focusing matrix T (f)j) Focusing conversion is carried out on the array received data in each sub-period to obtain a single frequency point data covariance matrix Hk(fj) Further, a covariance matrix R of the reference frequency point is obtainedk；
A covariance matrix mean calculation module for calculating covariance matrix R of each reference frequency point in K time periodskThe arithmetic mean value of R;
a calculation module for the estimated value of the incoming wave direction of the broadband OFDM signal, which is used for decomposing the characteristic value of R to obtain a signal subspace EsAnd noise subspace EnFurther obtaining a spatial spectrum expression of the broadband MUSIC algorithm; and searching according to the spatial spectrum expression to obtain the angle positions corresponding to the P maximum values, namely the estimated value of the incoming wave direction of the broadband OFDM signal.
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