CN117763832A - Digital array pattern null optimization control method based on channel amplitude and phase error dynamic compensation - Google Patents
Digital array pattern null optimization control method based on channel amplitude and phase error dynamic compensation Download PDFInfo
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Abstract
The invention discloses a digital array pattern null optimization control method based on channel amplitude-phase error dynamic compensation, which is used for determining an amplitude-phase self-calibration interference-noise ratio INR threshold psi according to expected null depth, and carrying out amplitude-phase compensation on an interference subspace on the basis of interference detection and angle estimation based on two-dimensional Fourier transform FFT acceleration and an orthogonal projection algorithm based on Schmitt orthogonalization, so as to dynamically carry out optimal control on the anti-interference null depth and width of a pattern. The invention can dynamically calibrate the amplitude-phase error and realize the optimal control of the depth and the width of the interference null; matrix inversion in the interference subspace projection matrix is avoided through Schmitt orthogonalization, and the operation complexity is reduced; the amplitude-phase self-calibration threshold is determined through the expected null depth, a two-dimensional FFT interference detection and Schmidt orthogonalization orthogonal projection algorithm is adopted, and the amplitude-phase error self-calibration is calculated in parallel by utilizing a strong interference source meeting the threshold, so that the aim of updating the amplitude-phase error in real time while working is achieved.
Description
Technical Field
The invention belongs to the technical field of digital array antenna airspace anti-interference, and particularly relates to a digital array directional diagram null optimization control method based on channel amplitude-phase error dynamic compensation.
Background
The digital array antenna can realize airspace anti-interference by controlling the directional diagram to form nulls in the interference direction, and has the advantages of rapid beam switching, flexible beam directional diagram control, strong airspace interference suppression capability and the like. Since each radio frequency channel of the digital array antenna is composed of linear or nonlinear active devices such as mixers, amplifiers and filters. There is an inevitable amplitude-phase error between the radio frequency channels and it will change slowly with changes in ambient temperature and differences in temperature between the channels. The channel amplitude and phase errors can influence the signal source angle estimation precision and the array gain, and seriously influence the interference null depth, the sidelobe level and the like of the array directional diagram. Therefore, for digital array antennas with low sidelobes and deep nulls anti-interference requirements, dynamic channel amplitude and phase error calibration must be performed.
The existing calibration algorithm is mainly divided into an active calibration method and a self-calibration method. The active calibration method needs to enter a special calibration mode before the system normally works, and uses an auxiliary signal source with accurately known spatial position for calibration, so that the calibration can not be performed while working. The self-calibration algorithm may simultaneously perform joint estimation of channel amplitude and phase error parameters and source direction of arrival (Direction ofArrival, DOA). The self-calibration method is to obtain more accurate DOA estimation through amplitude and phase calibration, and can not dynamically realize the optimal control of the anti-interference pattern null depth and width of amplitude and phase compensation under the condition of rapid change of interference angle.
Disclosure of Invention
The invention aims to solve the problems in the background art and provides a digital array pattern nulling optimization control method based on channel amplitude and phase error dynamic compensation.
In order to achieve the purpose of the invention, the invention discloses a digital array pattern null optimization control method based on channel amplitude and phase error dynamic compensation, which comprises the following steps:
step 1, performing two-dimensional FFT processing on an array received data vector x (k), performing fast interference detection according to the relation between two-dimensional FFT output and beam forming output and an interference detection threshold T obtained by calculation, and estimating the number of interference P and the interference angleINR and INR p ,(p＝1,…,P)；
Step 2 (a), when p=1 and INR P When ≡is not less than, calculating covariance matrix of x (k) by exponentiation methodIs>By->Interference vector->Is a difference estimation amplitude phase error->
Step 2 (b), when P>0, i.e. in the presence of effective interference, according to P,And the nulling broadening widths Deltau, deltav in the u, v direction construct an interference subspace C with nulling broadening characteristics, and the amplitude-phase error +.>Correction C is performed to obtain->
Step 3, pairingAnd performing Schmidt orthogonalization processing, and calculating an empty domain null anti-interference weight w optimally controlled by the null depth and the null width by adopting an orthographic projection algorithm.
The auxiliary amplitude-phase self-calibration threshold calculation module is used for determining an INR threshold psi of amplitude-phase error self-calibration by analyzing the relation between the expected null depth and the channel amplitude-phase error and the relation between the channel amplitude-phase error and the calibration source INR.
Further, the specific process of the step 1 is as follows:
step 1-1, two-dimensional FFT interference detection and angle estimation;
for a two-dimensional rectangular grid planar array, performing two-dimensional FFT processing on an array received data vector x (k) to obtain
Wherein,for the output signal of the nth array element, N x ,N y The number of array elements in the directions of the x axis and the y axis respectively;
two-dimensional FFT output channel (l) x ,l y ) And angle (u) p ,v p ) The corresponding relation is that
Wherein d x ,d y Array element spacing in the directions of an x axis and a y axis respectively, wherein lambda is wavelength;
step 1-2, calculating an interference detection threshold T;
first, the noise power P is calculated n
Wherein I is the number of two-dimensional FFT ranks, I P I for eliminating the number of larger peaks 0 To reject the point location set;
then, calculating the false alarm probability as P F Constant false alarm detection threshold factor alpha at time
Finally, according to P above n Calculating interference detection threshold T with alpha
T＝αP n
Step 1-3, estimating the interference number P and the interference angleINR and INR p ,(p＝1,…,P)；
When d x ,d y Greater than lambda/2, due to the periodic blurring, in the visible region (u 2 +v 2 In less than or equal to 1), the number of all possible positions corresponding to one interference after two-dimensional FFT processing is
Wherein,rounding down the symbol;
searching for a peak value exceeding an interference detection threshold T in the two-dimensional FFT processed data, and determining a channel position (l) according to the peak value x ,l y ) Estimating the interference angleGrouping the estimation results; phase difference between interference angle estimation values of the same groupThe integer multiple of the blur pitch requires only the selection of any one of the set of disturbance blur angles. Finally determining the number P of uncorrelated interference;
according to the peak position (l) corresponding to the interference x ,l y ) Calculating interference power
P p ＝|F(l x ,l y ,k)| 2
The corresponding dry-to-noise ratio is INR p ＝10log(P p /P n )。
Further, step 2 is two sub-steps of parallel computation, specifically:
step 2 (a), when p=1 and INR P When the amplitude and phase errors are not less than psi, calculating and updating the amplitude and phase errors
Calculating covariance matrix of x (k)Iterative estimation of ++by exponentiation>Is>The interference guidance vector is:Wherein x is n ,y n For the array element position, n=1, 2, …, N is the number of array elements, +.>
And->The relation of (2) is that
Wherein,calculating to obtain amplitude-phase error estimated values obtained by dividing other array elements by normalized reference array element (first array element)
Wherein,
step 2 (b), when P>At 0, an interference subspace compensating for amplitude and phase errors is calculated
According to P,And null spread width deltau in u, v direction, deltav constructing interference subspace c= [ C ] with null spread characteristics 1 ,C 2 ,…,C P ]Wherein
Using the amplitude and phase errors calculated in step 2 (a)Correction C is performed to obtain->
Further, the step 3 specifically comprises:
for a pair ofIs subjected to a schmitt orthogonalization process to obtain +.>
Interference orthogonal subspace projection matrix Z ⊥ Is that
Airspace null anti-interference weight optimally controlled by calculating null depth and width by adopting orthogonal projection algorithm
Wherein w is 0 Is a static weight without null.
Compared with the prior art, the invention has the remarkable progress that: 1) The channel amplitude and phase errors can be dynamically estimated and compensated according to the expected zero depth and width of the directional diagram, so that the optimal control of the anti-interference zero depth and width of the directional diagram is realized; 2) Matrix inversion operation in an interference subspace projection matrix is avoided through Schmidt orthogonalization calculation, and operation complexity is reduced; 3) The amplitude-phase self-calibration threshold is determined through the expected null depth, the two-dimensional FFT interference detection and angle estimation algorithm and the orthogonal projection algorithm based on Schmidt orthogonalization are adopted, the amplitude-phase error self-calibration is calculated in parallel by using a strong interference source meeting the self-calibration threshold, and the aim of updating the amplitude-phase error in real time while working is achieved.
In order to more clearly describe the functional characteristics and structural parameters of the present invention, the following description is made with reference to the accompanying drawings and detailed description.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiments of the invention and together with the description serve to explain the invention and do not constitute a limitation on the invention. In the drawings:
FIG. 1 is a flow chart of an algorithm implementation of the present invention;
FIG. 2 is a schematic diagram of the distribution of the array surface of a rectangular grid planar array with 64 array elements;
FIG. 3 is a schematic diagram showing the relationship between the null depth and the amplitude error, the amplitude error and the interference source INR through simulation analysis according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of two-dimensional FFT interference detection and angle estimation results when a sidelobe interference exists at different array element pitches in an embodiment of the present invention;
fig. 5 is a graph of the contrast of the amplitude-phase compensated interference pattern nulls and the output signal-to-interference-plus-noise ratio as a function of the number of snapshots in an embodiment of the invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are only some, but not all embodiments of the invention; all other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Referring to fig. 1, a digital array pattern null optimization control method based on channel amplitude and phase error dynamic compensation comprises the following main steps:
step 1, performing two-dimensional FFT processing on an array received data vector x (k), and according to the relation between two-dimensional FFT output and beam forming output and the interference detection threshold T obtained by calculation, performing constant false alarm detection, peak detection, angle ambiguity discrimination and the like on the data after the two-dimensional FFT processing, and estimating the interference number P and the interference angleINR and INR p ,(p＝1,…,P)；
Step 2 (a), when p=1 and INR P When ≡is not less than, iteratively estimating covariance matrix of x (k) by exponentiationIs>By->Interference vector->Is a difference estimation amplitude phase error-> Is a diagonal matrix.
Step 2 (b), when P>0, i.e. in the presence of effective interference, according to P,And the nulling broadening widths Deltau, deltav in the u, v direction construct an interference subspace C with nulling broadening characteristics, and the amplitude-phase error +.>And C, correcting to obtain:
Step 3, forAnd performing Schmidt orthogonalization processing, and calculating an empty domain null anti-interference weight w optimally controlled by the null depth and the null width by adopting an orthographic projection algorithm.
The specific refinement treatment process of the step 1 is as follows:
step 1-1, two-dimensional FFT interference detection and angle estimation;
for a two-dimensional rectangular grid planar array, (u) p ,v p ) The directional beam outputs are:
wherein,is the nth arrayOutput signal of element N x ,N y The number of array elements in the directions of the x axis and the y axis respectively, d x ,d y The array element spacing in the x-axis and y-axis directions, respectively, and λ is the wavelength.
And carrying out two-dimensional FFT processing on x (k) to obtain:
it can be seen that the beamformed output of x (k) y (u p ,v p K) and a two-dimensional FFT output F (l x ,l y There is a direct correspondence between k), namely:
and then obtain:
the two-dimensional FFT output channel (l) which makes detection decision on the two-dimensional FFT output and is given by the above x ,l y ) And angle (u) p ,v p ) And obtaining interference detection and angle estimation results according to the corresponding relation.
Step 1-2, calculating an interference detection threshold T;
first, the noise power P is calculated n ：
Wherein I is the number of two-dimensional FFT ranks, I P I for eliminating the number of larger peaks 0 To reject the point location set.
Then, calculating the false alarm probability as P F Constant false alarm detection threshold factor α:
finally, according to P above n And calculating an interference detection threshold T with alpha:
T＝αP n (7)
step 1-3, estimating the interference number P and the interference angleINR and INR p ,(p＝1,…,P)；
When d x ,d y Greater than λ/2, since the two-dimensional FFT has periodicity, there is:
F(l x ,l y ,k)＝F(l x ±r 1 N x ,l y ±r 2 N y ,k),(r 1 =0,1,2,…；r 2 ＝0,1,2,…) (8)
then, the two-dimensional FFT output channel (l x ,l y ) And angle (u) p ,v p ) The correspondence becomes:
there are cases where the same disturbance corresponds to a plurality of blurring angles, in which the line blurring angle interval u dim And column ambiguity angle spacing v dim The method comprises the following steps of:in the visible region (u) 2 +v 2 In less than or equal to 1), the number of all possible positions corresponding to one disturbance is:Wherein (1)>To round down the symbol.
Searching for a peak value exceeding an interference detection threshold T in the two-dimensional FFT processed data, and determining a channel position (l) according to the peak value x ,l y ) Estimating the interference angleAnd grouping the estimation results, wherein the phase difference between the estimation values of the same group of angles is an integer multiple of the fuzzy interval, and inhibiting one angle can inhibit other fuzzy angles, so that any interference estimation angle in each group is selected, and finally the uncorrelated interference number P is determined.
According to the peak position (l) corresponding to the interference x ,l y ) Calculating interference power:
P p ＝|F(l x ,l y ,k)| 2 (10)
the corresponding dry-to-noise ratio is: INR (INR) p ＝10log(P p /P n ). Wherein P is calculated n In the process, the number I of the eliminating points P Generally, the product of the maximum interference number and the fuzzy angle number is slightly larger than the product.
Step 2 is divided into two sub-steps of parallel computation, and the specific refinement processing process is as follows:
first, assume that the amplitude and phase errors of the nth channel of the digital array channel are α respectively n And beta n The array amplitude-phase error matrix is expressed as:n is the number of array elements.
Step 2 (a), when p=1 and INR P When the amplitude and phase errors are not less than psi, calculating and updating the amplitude and phase errors
Iterative estimation of covariance matrix of x (k) by exponentiationMaximum feature vector +.>The iteration formula of the first iteration of the exponentiation method is as follows:
wherein,refers to->The largest element in the middle mode.
First, randomly initializing an iteration vectorSetting an iteration count l=1; next, calculate +.>Order theIf V is (l) Less than a selected threshold->Ending iteration, otherwise, setting l=l+1, and continuing iteration; finally, obtaining a main characteristic value +.>The corresponding principal eigenvector is->
The interference guidance vector is:wherein x is n ,y n For the array element position, n=1, 2, …, N, +.>
And->The relation of (2) is:Namely:
wherein,calculating to obtain the amplitude-phase error estimated value obtained by dividing other array elements by the normalized reference array element (first array element):
step 2 (b), when P>At 0, an interference subspace compensating for amplitude and phase errors is calculated
According to P,And null spread width deltau in u, v direction, deltav constructing interference subspace c= [ C ] with null spread characteristics 1 ,C 2 ,…,C P ]Wherein:
using the amplitude and phase errors calculated in step 2 (a)And C, correcting to obtain:
Further, the step 3 specifically includes:
for a pair ofColumn vector ε i Performing Schmidt orthogonalization to obtain +.>Wherein (1)>Each column vector gamma i (i=1, 2, …, 5P) is calculated as follows:
at this time, the liquid crystal display device,interference orthogonal subspace projection matrix Z ⊥ The method comprises the following steps:
and calculating an airspace null anti-interference weight optimally controlled by the null depth and the width by adopting an orthogonal projection algorithm:
wherein w is 0 Is a static weight without nulling, such as beam pointing direction (u 0 ,v 0 ) Is a vector of the vector a (u) 0 ,v 0 ) Or low side lobe weights for amplitude weighting.
According to the above description, and in combination with the algorithm implementation flowchart of the present invention shown in fig. 1, the implementation method of the present invention mainly comprises the following two parts:
1. interference detection and estimation:
performing two-dimensional FFT processing on the array received data vector x (k), performing rapid interference detection according to the relation between two-dimensional FFT output and beam forming output and the interference detection threshold obtained by calculation, and estimating the interference number P and the interference angleINR and INR p ,(p＝1,…,P)；
2. And (5) anti-interference weight calculation:
when p=1 and INR P When ≡is not less than, calculating covariance matrix of x (k) by exponentiation methodIs>By means ofInterference vector->Is a difference estimation amplitude phase error->
When P>0, i.e. in the presence of effective interference, according to P,And the nulling broadening widths Deltau, deltav in the u, v direction construct an interference subspace C with nulling broadening characteristics, and the amplitude-phase error +.>Correction C is performed to obtain->
For a pair ofAnd performing Schmidt orthogonalization processing, and calculating an empty domain null anti-interference weight w optimally controlled by the null depth and the null width by adopting an orthographic projection algorithm.
The auxiliary steps are an amplitude-phase self-calibration threshold calculation module: and determining an INR threshold psi for self calibration of the amplitude-phase error by analyzing the relation between the expected null depth and the amplitude-phase error of the channel and the relation between the amplitude-phase error of the channel and the calibration source INR.
The present invention will be described in detail with reference to specific examples.
Examples
The invention provides a method for dynamically calibrating channel amplitude and phase errors by using a strong interference source meeting a self-calibration threshold according to the expected pattern null depth and width, and further effectively controlling the pattern null depth and width. The method flow chart is seen in fig. 1.
In this example, an n=64 array element matrix grid planar array is adopted, the unit antennas are isotropic omni-directional antennas, and the rectangular grid array model used is shown in fig. 2 without considering mutual coupling among the array elements. Beam pointingInterference fromThe INR is 10dB, the noise is an additive Gaussian white noise vector, and the noise and the signal are mutually incoherent. Amplitude-phase error exists between channels, and the amplitude error alpha is n And phase error beta n All obey uniform distribution, alpha n ＝1+r n ,β n ＝s n WhereinI.e. alpha n And beta n Root mean square of>And selecting-35 dB Chebyshev amplitude weighting to carry out low sidelobe processing. The present example desirably achieves a null depth of-45 dB, and a null spread requirement au, av of 0.0348, i.e., a null spread of about ±2°. And respectively carrying out analysis and verification of the two-dimensional FFT angle ambiguity problem when different array element distances are carried out, comprising the following steps: (1) The array element spacing is equal to the wavelength, i.e. the array element spacing in the x-axis and y-axis directions is d x ＝λ,d y =λ; (2) The array element spacing is equal to half wavelength, i.e. the array element spacing in the x-axis and y-axis directions is d x ＝0.5λ,d y ＝0.5λ。
Aiming at the matrix grid plane array of 64 array elements with two array element pitches, the implementation of the digital array pattern null optimization control method based on channel amplitude and phase error dynamic compensation comprises the following processing steps:
firstly, through an auxiliary step, simulating the relation between the amplitude-phase error and INR of a channel and the relation between the zero-notch depth and the amplitude-phase error, and determining that the amplitude-phase self-calibration INR threshold when the expected zero-notch depth is-45 dB is satisfied is as follows: ψ=5 dB. The simulation result of determining the threshold is shown in fig. 3.
Graph (a) in fig. 3 simulates the root mean square (σ) of the four channel amplitude phase errors α ,σ β ) The residual amplitude-phase error value versus INR for (0.25 db,2.5 °), (0.5 db,5 °), (0.75 db,7.5 °), (1.0 db,10 °) respectively. Graph (b) in fig. 3 shows the null depth versus residual amplitude-phase error. Graph (b) marks the range of the amplitude phase calibration residual with a null depth better than-45 dB, and the root mean square of the residual amplitude error cannot exceed 0.18dB for the array used for simulation, and the root mean square of the residual phase error cannot exceed 8 °. Meanwhile, under the condition that the channel residual amplitude-phase error meets the requirement by combining the simulation result of the graph (a), the self-calibration INR threshold psi=5dB is obtained.
Step 1: setting false alarm probability of interference detection as P F ＝10 -4 The number of two-dimensional FFT rank points I is 128, and the threshold factor α=9.21 is calculated using equation (6). And respectively calculating the number of interference angle estimation fuzzy angles under the condition of two array element spacing according to a two-dimensional FFT interference detection and angle estimation algorithm.
(1) Under the condition of large array element spacing, calculating a visible region (u 2 +v 2 The number of angles of internal mold pasting is less than or equal to 1)Thus an interference will be detected at two angles in the visible area, at the intervals: u (u) dim ＝λ/d x ＝1,v dim ＝λ/d y After the angle blur discrimination, it can be determined that only one disturbance exists, p=1.
(2) Under the condition of small array element spacing, the number of fuzzy angles in the visible area is calculated to be 0, so that the problem of angle fuzzy does not exist, and p=1.
The graphs (a) and (b) in fig. 4 simulate the two-dimensional FFT interference detection and angle estimation results under the conditions of large array element spacing and normal array element spacing respectively, and are redThe area surrounded by the color broken line is a visible area. Simulation results show that the array element spacing in the first case is larger than lambda/2, angle blurring occurs in a visible area, and any one angle in the group of blurring angles is selected, for exampleI.e. < ->Calculating interference power using (10) and obtaining interference-to-noise ratio INR P Approximately 10dB; in the second case, the array element spacing is equal to lambda/2, no angle ambiguity exists in the visible area, and the estimation result is interferedI.e. < ->INR P ≈10dB。
Step 2 (a): p=1, inr P Not less than 5dB, calculating amplitude and phase error
The number of snapshots is set to 256, and the covariance matrix of x (k) is calculatedThreshold for terminating the iteration by the selected exponentiation method +.>Estimated->Is> And interference guidance vector->The relation of (2) is:
Simulation setting initial amplitude and phase error sigma alpha=1 dB, sigma beta=10°, inr=10 dB, and estimating according to formula (13) to obtain an amplitude and phase error matrixTable 1 shows the comparison of the actual amplitude and phase errors of the set channels with the amplitude and phase errors estimated by the algorithm.
TABLE 1 comparison of channel real amplitude phase error and estimated amplitude phase error
From the data analysis in table 1, the amplitude phase error is estimated to be substantially close to the true amplitude phase error using an amplitude phase calibration algorithm.
Step 2 (b), P>At 0, an interference subspace compensating for amplitude and phase errors is calculated
Setting the array element spacing as lambda/2, constructing an interference subspace C with null widening characteristics by using a formula (14), and obtaining a two-dimensional FFT angle estimation result by the step oneP=1. The null widening widths Deltau, deltav are 0.0348, C in formula (14) 1 Expressed as:
C 1 ＝[a(0.5625,0),a(0.5625,0-0.0348),a(0.5625,0+0.0348),a(0.5625+0.0348,0),a(0.5625-0.0348,0)]
by means ofMake correction C 1 The method comprises the following steps of:
Step 3: using the pair of (15)Performing Schmidt orthogonalization to obtain +.>The interference orthogonal subspace projection matrix is:And calculating an airspace null anti-interference weight optimally controlled by the null depth and the width by adopting an orthogonal projection algorithm:
wherein w is 0 Low side lobe weights weighted for chebyshev amplitude of-35 dB. Specific values of w are given in table 2.
TABLE 2 airspace null anti-interference weight w coefficient
In fig. 5, graphs (a) and (b) simulate the contrast of the interference null pattern of the amplitude phase compensation and the contrast of the change condition of the output signal-to-interference-noise ratio along with the number of snapshots. It can be seen that the pattern null depth after compensating the amplitude-phase error is better than-45 dB, the widening null of about + -2 degrees is formed near the interference, and the output signal-to-interference-and-noise ratio is larger than that without amplitude-phase compensation.
It is noted that relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (4)
1. A digital array pattern null optimization control method based on channel amplitude and phase error dynamic compensation is characterized by comprising the following steps:
step 1, performing two-dimensional FFT processing on an array received data vector x (k), performing fast interference detection according to the relation between two-dimensional FFT output and beam forming output and an interference detection threshold T obtained by calculation, and estimating the number of interference P and the interference angleINR and INR p ,(p＝1,…,P)；
Step 2 (a), when p=1 and INR P When ≡is not less than, calculating covariance matrix of x (k) by exponentiation methodIs>By->Interference vector->Is a difference estimation amplitude phase error->
Step 2 (b), when P>0, i.e. in the presence of effective interference, according to P,And the nulling broadening widths Deltau, deltav in the u, v direction construct an interference subspace C with nulling broadening characteristics, and the amplitude-phase error +.>Correction C is performed to obtain->
Step 3, pairingAnd performing Schmidt orthogonalization processing, and calculating an empty domain null anti-interference weight w optimally controlled by the null depth and the null width by adopting an orthographic projection algorithm.
2. The digital array pattern null optimization control method based on channel amplitude and phase error dynamic compensation according to claim 1, wherein the specific process of step 1 is as follows:
step 1-1, two-dimensional FFT interference detection and angle estimation;
for a two-dimensional rectangular grid planar array, performing two-dimensional FFT processing on an array received data vector x (k) to obtain
Wherein,for the output signal of the nth array element, N x ,N y The number of array elements in the directions of the x axis and the y axis respectively;
two-dimensional FFT output channel (l) x ,l y ) And angle (u) p ,v p ) The corresponding relation is that
Wherein d x ,d y Array element spacing in the directions of an x axis and a y axis respectively, wherein lambda is wavelength;
step 1-2, calculating an interference detection threshold T;
first, the noise power P is calculated n
Wherein I is the number of two-dimensional FFT ranks, I P I for eliminating the number of larger peaks 0 To reject the point location set;
then, calculating the false alarm probability as P F Constant false alarm detection threshold factor alpha at time
Finally, according to P above n Calculating interference detection threshold T with alpha
T＝αP n
Step 1-3, estimating the interference number P and the interference angleINR and INR p ,(p＝1,…,P)；
When d x ,d y Greater than lambda/2, due to the periodic blurring, in the visible region (u 2 +v 2 In less than or equal to 1), the number of all possible positions corresponding to one interference after two-dimensional FFT processing is
Wherein,rounding down the symbol;
searching for a peak value exceeding an interference detection threshold T in the two-dimensional FFT processed data, and determining a channel position (l) according to the peak value x ,l y ) Estimating the interference angleGrouping the estimation results; the interference angle estimation values in the same group differ by integer times of fuzzy spacing, and only any one angle in the group of interference fuzzy angles is needed to be selected; finally determining the number P of uncorrelated interference;
according to the peak position (l) corresponding to the interference x ,l y ) Calculating interference power
P p ＝|F(l x ,l y ,k)| 2
The corresponding dry-to-noise ratio is INR p ＝10log(P p /P n )。
3. The digital array pattern null optimization control method based on channel amplitude and phase error dynamic compensation according to claim 1, wherein step 2 is two parallel computing sub-steps, specifically:
step 2 (a), when p=1 and INR P When the amplitude and phase errors are not less than psi, calculating and updating the amplitude and phase errors
Calculating covariance matrix of x (k)Iterative estimation of ++by exponentiation>Is>The interference guidance vector isWherein x is n ,y n For the array element position, n=1, 2, …, N is the number of array elements, +.> And->The relation of (2) is that
Wherein,calculating to obtain amplitude-phase error estimated values obtained by dividing other array elements by normalized reference array element (first array element)
Wherein,
step (a)2 (b), when P>At 0, an interference subspace compensating for amplitude and phase errors is calculated
According to P,And null spread width deltau in u, v direction, deltav constructing interference subspace c= [ C ] with null spread characteristics 1 ,C 2 ,…,C P ]Wherein
Using the amplitude and phase errors calculated in step 2 (a)Correction C is performed to obtain->
4. The digital array pattern null optimization control method based on channel amplitude and phase error dynamic compensation according to claim 1, wherein the step 3 is specifically:
for a pair ofIs subjected to a schmitt orthogonalization process to obtain +.>
Interference orthogonal subspace projection matrix Z ⊥ Is that
Airspace null anti-interference weight optimally controlled by calculating null depth and width by adopting orthogonal projection algorithm
Wherein w is 0 Is a static weight without null.
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