CN108896963B - Airborne radar space-time self-adaptive dimension reduction processing method - Google Patents

Airborne radar space-time self-adaptive dimension reduction processing method Download PDF

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CN108896963B
CN108896963B CN201810456799.3A CN201810456799A CN108896963B CN 108896963 B CN108896963 B CN 108896963B CN 201810456799 A CN201810456799 A CN 201810456799A CN 108896963 B CN108896963 B CN 108896963B
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CN108896963A (en
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史江义
许志鹏
胡雪云
马佩军
员维维
陈琦璇
白永晨
汪滔
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Xidian University
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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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/023—Interference mitigation, e.g. reducing or avoiding non-intentional interference with other HF-transmitters, base station transmitters for mobile communication or other radar systems, e.g. using electro-magnetic interference [EMI] reduction techniques
    • 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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
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Abstract

The invention discloses a space-time adaptive dimension reduction processing method for airborne radar, which mainly solves the problems that the traditional space-time adaptive processing method needs more training samples and has high operation complexity. The method comprises the following implementation steps: 1) pre-filtering the space-time snapshot data received by the airborne radar system and the space-time guide vector of the unit to be detected by using a Doppler three-channel joint adaptive processing method to obtain space-time snapshot data after dimension reduction and space-time guide vector of the unit to be detected after dimension reduction; 2) solving the optimal weight vector of the space-time snapshot data after dimension reduction and the space-time guide vector of the unit to be detected after dimension reduction by using a multilevel wiener filter with an iterative correlation subtraction structure; 3) and performing weighted filtering processing on the space-time snapshot data after dimension reduction by using the optimal weight vector as a filtering coefficient to obtain target information data. The method has the advantages of small operand and good numerical stability, can enhance the real-time performance of the radar system, and can be used for detecting the moving target of the airborne radar.

Description

Airborne radar space-time self-adaptive dimension reduction processing method
Technical Field
The invention belongs to the technical field of radars, and further relates to a space-time adaptive dimension reduction processing method for an airborne radar, which can be used for detecting a moving target of the airborne radar.
Background
The airborne phased array radar is used for detecting and monitoring an invading target by the advantages of long acting distance, high flexibility and reliability and capability of scanning/tracking a plurality of targets/areas simultaneously, and plays a significant role in national defense and civil construction. Since airborne radars often work in a downward looking environment, not only are strong ground-sea clutter encountered, but also the clutter spectrum is broadened due to the motion of the vehicle. In addition, the emergence of stealth aircraft, electromagnetic interference, low-altitude penetration and other technologies and increasingly severe electromagnetic environments seriously affect the target searching capability of the radar. Therefore, clutter suppression and target enhancement of the received electromagnetic energy is necessary to effectively identify the target.
The space-time adaptive processing STAP is a technology for realizing adaptive clutter cancellation by simultaneously utilizing information acquired by a plurality of antenna elements and coherent pulse trains for multidimensional adaptive filtering, and comprises an all-STAP and a dimensionality-reduction STAP. Although the full STAP has excellent performance, it requires many training samples, consumes enormous computational resources, and is difficult to implement. The dimension reduction STAP technology aims to reduce the operation complexity while keeping clutter suppression performance close to that of the full STAP technology, and is a leading-edge and hot spot technology of radar signal processing in the engineering field.
The patent document filed by the university of western' an electronics science and technology and filed as an EFA and MWF-based airborne radar space-time adaptive processing method (application number 201610503844.7, publication number 105911527B) discloses an EFA and MWF-based airborne radar space-time adaptive processing method. The method has the defects that the traditional MWF method is poor in numerical stability, high in operation complexity and poor in real-time performance, and a blocking matrix needs to be calculated.
And a published paper "dimension reduction adaptive array signal processing and application thereof in MIMO radar" (doctor academic paper 2011.9 of Western Ann electronic science and technology university) provides a space-time two-dimensional adaptive cascade dimension reduction quasi-optimal method, wherein the algorithm firstly performs dimension reduction processing on space-time signals by using a space-time adjacent multi-beam STMB method to reduce clutter freedom degree, and then adopts a multi-stage wiener filter to process output signals and solve weight vectors. The method has the disadvantages that although the STMB operation amount is small, when the space domain has large array element errors, the clutter suppression performance is poor, and the multi-stage wiener filter needs to solve a blocking matrix, so that the real-time requirement is difficult to meet.
Disclosure of Invention
The invention aims to provide a space-time adaptive dimension reduction processing method for airborne radar, which aims to solve the problems that the traditional space-time adaptive processing method needs more training samples, has high operation complexity and poor real-time performance.
The basic idea for realizing the invention is as follows: firstly, carrying out transform domain processing on space-time snapshot data through Fast Fourier Transform (FFT), selecting 3 adjacent Doppler channels each time to carry out local filtering so as to reduce the degree of freedom of a signal subspace, and then solving an optimal weight vector by utilizing a multi-level wiener filter (CSA-MWF) with an iterative correlation subtraction structure to obtain target information data, wherein the implementation steps comprise the following steps:
(1) pre-filtering the space-time snapshot data x received by the airborne radar system and the space-time guide vector s of the unit to be detected by using a Doppler three-channel combined adaptive processing 3DT method to obtain space-time snapshot data x after dimension reductionrAnd the space-time guiding vector s of the unit to be detected after dimension reductionr；
(2) For space-time snapshot data x after dimension reductionrAnd the space-time guiding vector s of the unit to be detected after dimension reductionrSolving for the optimal weight vector w using an iterative correlation subtraction architecture multi-level wiener filterr：
(2a) Initializing an iterative correlation subtraction structure multistage wiener filter:
(2a1) setting p as the total number of stages of the filter; i is the stage index of the forward recursive decomposition of the filter, i is 1, 2. i 'is the stage index of the backward recursion synthesis of the filter, i' ═ p, p-1,...,2, i' has an initial value of p; reducing the space-time snapshot data x after dimension reductionrAs an initial observed signal y0I.e. y0＝xr(ii) a Reducing the space-time guide vector s of the unit to be detected after dimension reductionrNormalized and taken as the normalized cross-correlation vector h of filter level 11I.e. h1＝sr/||srIn the formula, | | | · | |, represents a2 norm of the vector;
(2a2) normalized cross-correlation vector h according to filter level 11And the initial observed signal y0To obtain the desired signal of the 1 st stage of the filter: d1＝h1 Hy0，(·)HRepresenting a transposed conjugate matrix;
(2b) normalized cross-correlation vector h according to filter level i-1i-1And observation signal yi-1Obtaining the normalized cross-correlation vector h of the ith level through normalization processingi：
Figure BDA0001659876470000031
In the formula, E [. cndot]Expressing the mathematical expectation, di-1The desired signal of the i-1 stage of the filter;
(2c) the observed signal y of the i-1 stage of the filteri-1Normalized cross-correlation vector h projected to filter ith stageiAnd h isiIn the orthogonal direction, the desired signal of the ith stage of the filter is obtained: di＝hi Hyi-1diAnd the observed signal of the i stage of the filter: y isi＝yi-1-hidi；
(2d) Adding 1 to i, and repeating the steps (2b) and (2c) until i is equal to p to obtain the desired signal d of the p-th stage of the filterpAnd the observed signal y of the p-th stage of the filterp(ii) a Desired signal d of p-th stage of filterpAs the output error signal of the p-th stage of the filter: epsilonp＝dp；
(2e) Desired signal d using filter stage i' -1i'-1And the output error signal epsilon of the ith' stage of the filteri', calculating scalar weight w of i' -1 stage of filteri'-1And output error signal epsilon of i' -1 stagei'-1：
wi'-1＝E[di'-1εi' *]/E[|εi'|2]，εi'-1＝di'-1-wi'-1 *εi'，
Wherein | represents a complex number of modes, (.)*Representing the conjugation;
(2f) and (3) enabling i 'to be reduced by 1, and repeating the step (2e) until i' is equal to 2 to obtain the scalar weight w of the 1 st stage of the filter1And the output error signal epsilon of the 1 st stage of the filter1；
(2g) Scalar weight w using filter stages1,w2,...,wp-1To obtain the backward integrated weight vector w of the filterr'：
Figure BDA0001659876470000032
Wherein Π represents multiplicative multiplication;
(2h) normalized cross-correlation vector h using filter stages1,h1,...,hpSum filter backward integrated weight vector wr'wr'And obtaining an optimal weight vector: w is ar＝[h1 h2 … hp]Twr'Wherein (·)TRepresenting a transpose;
(3) using the best weight vector wrAs a filter coefficient, the space-time snapshot data x after dimension reductionrCarrying out weighted filtering processing to obtain target information data: z is a radical ofr＝wr Hxr。
Compared with the prior art, the invention has the following advantages:
firstly, the time domain dimension reduction processing is carried out on the radar echo data before the optimal weight vector is solved, so that the problem that the traditional space-time adaptive processing method has high requirement on the sample size is solved, the performance loss is reduced, and the capability of a radar system for processing data in real time is improved.
Secondly, the invention avoids the problem that the traditional multistage wiener filter needs to calculate a blocking matrix because of using the multistage wiener filter with the iterative correlation subtraction structure, effectively reduces the calculation amount of forward recursion of the multistage wiener filter, and enhances the real-time performance of the radar system.
Thirdly, the invention enhances the stability of radar system target identification by using the iterative correlation subtraction structure multi-stage wiener filter.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a sub-flowchart of the pre-filtering process using the 3DT method of the present invention;
FIG. 3 is a sub-flowchart of the present invention for solving the optimal weight vector using an iterative correlation subtraction architecture multi-level wiener filter;
FIG. 4 is a block diagram of an iterative correlation subtraction architecture multistage wiener filter used in the present invention;
FIG. 5 is a graph of the improvement factor as a function of normalized Doppler frequency for the present invention and prior methods;
FIG. 6 is a graph of filtered output power as a function of range gate count for the present invention and prior methods;
FIG. 7 is a graph of the amount of computation as a function of the number of array elements for the present invention and the prior art method.
The specific implementation mode is as follows:
the following detailed description is made with reference to the accompanying drawings and examples:
referring to fig. 1, the implementation steps of the invention are as follows:
step 1, pre-filtering space-time snapshot data x received by an airborne radar system and a space-time guide vector s of a unit to be detected by using a Doppler three-channel combined adaptive processing 3DT method to obtain space-time snapshot data x after dimensionality reductionrAnd the space-time guiding vector s of the unit to be detected after dimension reductionr。
Referring to fig. 2, the specific implementation of this step is as follows:
(1a) acquiring space-time snapshot data x received by an airborne radar system and a space-time guide vector s of a unit to be detected, wherein x is an NM multiplied by 6N dimensional matrix, s is an NM multiplied by 1 dimensional matrix, N is the number of array units distributed at equal intervals by the airborne radar system, and M is the number of pulses transmitted in a coherent pulse interval;
(1b) selecting a Doppler channel l where a unit to be detected is located and Doppler channels l +1, l-1 adjacent to the Doppler channel l on two sides of the Doppler channel l, and constructing a 3DT dimension reduction transformation matrix Tr：
Figure BDA0001659876470000051
Wherein, TtShowing the MN multiplied by 3N dimensional transformation matrix used for time domain dimension reduction by the Doppler three-channel combined adaptive processing 3DT method, TsThe N multiplied by N dimensional transformation matrix, namely the N multiplied by N dimensional identity matrix I, which represents the space-domain dimensionality reduction of the Doppler three-channel combined adaptive processing 3DT methodN；fd,l-1、fd,l、fd,l+1Normalized Doppler frequencies of the l-1 st, l +1 st and l-1 st Doppler channels respectively; j is the imaginary unit;
Figure BDA0001659876470000052
representing a kronecker product operator; e represents a natural constant;
(1c) dimension reduction transformation matrix T by using 3DTrFast Fourier transform is carried out on the Doppler channel l and two adjacent Doppler channels l +1 and l-1 on two sides of the Doppler channel l, x is converted into an array element-Doppler domain from an array element-pulse domain, and space-time snapshot data after dimension reduction is obtained: x is the number ofr＝Tr Hx；
(1d) Dimension reduction transformation matrix T by using 3DTrAnd performing fast Fourier transform on the space-time guide vector s of the unit to be detected to obtain the space-time guide vector of the unit to be detected after dimensionality reduction: sr＝Tr Hs。
Step 2, space-time snapshot data x after dimension reductionrAnd the space-time guiding vector s of the unit to be detected after dimension reductionrSolving for the optimal weight vector w using an iterative correlation subtraction architecture multi-level wiener filterr。
As shown in FIG. 4, the iterative correlation subtraction structure multi-level wiener filter CSA-MWF has a total number of p and is truncated at the p-th level, i.e. ε is takenp＝dpThe iterative correlation subtraction structure multi-level wiener filter CSA-MWF can perform rapid dimensionality reduction because the iterative correlation subtraction structure multi-level wiener filter CSA-MWF performs truncation operation on the decomposed series between forward recursion and backward recursion; y is0Is the initial observed signal of the filter; d1The desired signal for stage 1 of the filter; h is1Normalized cross-correlation vector for filter level 1; w is a1Scalar weight of the 1 st level of the filter; epsilon1Is the output error signal of stage 1 of the filter,. epsiloni'The output error signal of the p-th stage of the filter.
Referring to fig. 3, the specific implementation of this step is as follows:
(2a) initializing an iterative correlation subtraction structure multistage wiener filter:
(2a1) setting p as the total stage number of the filter, i as the stage number index of the forward recursive decomposition of the filter, i being 1, 2. i 'is a backward recursion integrated series index of the filter, i' ═ p, p-1,. 2; reducing the space-time snapshot data x after dimension reductionrAs an initial observed signal y0I.e. y0＝xr(ii) a Reducing the space-time guide vector s of the unit to be detected after dimension reductionrNormalized and taken as the normalized cross-correlation vector h of filter level 11I.e. h1＝sr/||srIn the formula, | | | · | |, represents a2 norm of the vector;
(2a2) normalized cross-correlation vector h according to filter level 11And the initial observed signal y0To obtain the desired signal of the 1 st stage of the filter: d1＝h1 Hy0，(·)HRepresenting a transposed conjugate matrix;
(2b) normalized cross-correlation vector h according to filter level i-1i-1And observation signal yi-1Obtaining the normalized cross-correlation vector h of the ith level of the filter by normalization processingi：
Figure BDA0001659876470000061
In the formula, E [. cndot]Expressing the mathematical expectation, di-1The desired signal of the i-1 stage of the filter;
(2c) the observed signal y of the i-1 stage of the filteri-1Normalized cross-correlation vector h projected to filter ith stageiAnd h isiIn the orthogonal direction, the desired signal d of the i-th stage of the filter is obtainediAnd the observation signal y of the i-th stagei：
di＝hi Hyi-1，
yi＝yi-1-hidi；
(2d) Adding 1 to i, and repeating the steps (2b) and (2c) until i is equal to p to obtain the desired signal d of the p-th stage of the filterpAnd the observed signal y of the p-th stage of the filterpAnd the desired signal d of the p-th stage of the filterpAs the output error signal of the p-th stage of the filter: epsilonp＝dp；
(2e) Desired signal d using filter stage i' -1i'-1And the output error signal epsilon of the ith' stage of the filteri'Calculating scalar weight w of i' -1 stage of filteri'-1And output error signal epsilon of i' -1 stagei'-1：
wi'-1＝E[di'-1εi' *]/E[|εi'|2]，
εi'-1＝di'-1-wi'-1 *εi'，
Wherein | represents a complex number of modes, (.)*Representing the conjugation;
(2f) and (3) enabling i 'to be reduced by 1, and repeating the step (2e) until i' is equal to 2 to obtain the scalar weight w of the 1 st stage of the filter1And the output error signal epsilon of the 1 st stage of the filter1；
(2g) Scalar weight w using filter stages1,w2,...,wp-1To obtain the backward integrated weight vector w of the filterr'：
Figure BDA0001659876470000071
Wherein Π represents multiplicative multiplication;
(2h) normalized cross-correlation vector h using filter stages1,h1,...,hpSum filter backward integrated weight vector wr'And obtaining an optimal weight vector: w is ar＝[h1 h2 … hp]Twr'Wherein (·)TIndicating transposition.
Step 3, utilizing the optimal weight vector wrAs a filter coefficient, the space-time snapshot data x after dimension reductionrCarrying out weighted filtering processing to obtain target information data: z is a radical ofr＝wr Hxr。
The effects of the present invention can be further demonstrated by the following experiments.
Simulation conditions:
the working wavelength of the radar is lambda is 0.67m, the number of the antenna array elements distributed at equal intervals is N is 18, and the interval of the array units is half of the working wavelength, namely d is 0.33 m; the number of consecutively received pulses in a CPI is M-36, the pulse repetition frequency is fr1500Hz and the speed of the carrier is va＝250m·s-1The height of the carrier is 9000m, the noise-to-noise ratio CNR is 60dB, and the linear array axis is vertical to the motion direction of the loader.
(II) simulation content and result:
simulation I, filtering radar echo data by using the existing full space-time adaptive processing, Doppler three-channel joint adaptive processing 3DT and the method of the invention under the same background, and comparing clutter suppression performance, the result is shown in FIG. 5.
As can be seen from fig. 5, the clutter suppression performance of the present invention is equivalent to that of the 3DT method, and the difference between the clutter suppression performance of the present invention and that of the full space-time adaptive processing method is within 5dB, so that the present invention has good clutter suppression performance.
And in the second simulation, 216 range gates with the numbers of 1-216 are selected, radar echo data are subjected to filtering processing by using the existing full space-time adaptive processing method, the existing Doppler three-channel combined adaptive processing method 3DT and the three methods of the invention under the same background, and the filtering output power is compared, so that the result is shown in fig. 6.
As can be seen from fig. 6, the present invention, the full space-time adaptive processing method and the 3DT method can correctly detect the target at the same range gate, and the present invention can effectively separate the moving target from the clutter, interference and noise background.
And thirdly, under the same background, performing space-time adaptive dimension reduction processing on radar echo data by using a Doppler three-channel combined adaptive processing 3DT and the two methods of the invention, and comparing the operation complexity, wherein the result is shown in FIG. 7. In fig. 7, the amount of computation required to solve the inverse of the covariance matrix is estimated using a QR decomposition-based method.
As can be seen from fig. 7, the computation workload of the present invention is significantly smaller than that of the 3DT method, and as the number of array cells increases, the computation workload of the present invention increases relatively less, and has fast convergence.
While the foregoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.

Claims (2)

1. A space-time adaptive dimension reduction processing method for airborne radar is characterized by comprising the following steps:
(1) pre-filtering the space-time snapshot data x received by the airborne radar system and the space-time guide vector s of the unit to be detected by using a Doppler three-channel combined adaptive processing 3DT method to obtain space-time snapshot data x after dimension reductionrAnd the space-time guiding vector s of the unit to be detected after dimension reductionr；
(2) For space-time snapshot data x after dimension reductionrAnd the space-time guiding vector s of the unit to be detected after dimension reductionrSolving for the optimal weight vector w using an iterative correlation subtraction architecture multi-level wiener filterr：
(2a) Initializing an iterative correlation subtraction structure multistage wiener filter:
(2a1) setting p as the total number of stages of the filter; i is the stage index of the filter forward recursion decomposition, i is 1, 2. i ' is a series index of backward recursion synthesis of the filter, and the initial value of i ' ═ p, p-1,. and 2, i ' is p; reducing the space-time snapshot data x after dimension reductionrAs an initial observed signal y0I.e. y0＝xr(ii) a Reducing the space-time guide vector s of the unit to be detected after dimension reductionrNormalized and taken as the normalized cross-correlation vector h of filter level 11I.e. h1＝sr/||srIn the formula, | | | · | |, represents a2 norm of the vector;
(2a2) normalized cross-correlation vector h according to filter level 11And the initial observed signal y0To obtain the desired signal of the 1 st stage of the filter: d1＝h1 Hy0，(·)HRepresenting a transposed conjugate matrix;
(2b) normalized cross-correlation vector h according to filter level i-1i-1And observation signal yi-1Obtaining the normalized cross-correlation vector h of the ith level through normalization processingi：
Figure FDA0003399490370000011
In the formula, E [. cndot]Expressing the mathematical expectation, di-1The desired signal of the i-1 stage of the filter;
(2c) the observed signal y of the i-1 stage of the filteri-1Normalized cross-correlation vector h projected to filter ith stageiAnd h isiIn the orthogonal direction, the desired signal of the ith stage of the filter is obtained: di＝hi Hyi-1diAnd the observed signal of the i stage of the filter: y isi＝yi-1-hidi；
(2d) Adding 1 to i, and repeating the steps (2b) and (2c) until i is equal to p to obtain the desired signal d of the p-th stage of the filterpAnd the observed signal y of the p-th stage of the filterp(ii) a Desired signal d of p-th stage of filterpAs the output error signal of the p-th stage of the filter: epsilonp＝dp；
(2e) Desired signal d using filter stage i' -1i'-1And the output error signal epsilon of the ith' stage of the filteri'Calculating scalar weight w of ith' stage of filteri'And output error signal epsilon of i' -1 stagei'-1：
wi'＝E[di'-1εi' *]/E[|εi'|2]，εi'-1＝di'-1-wi' *εi'，
Wherein | represents a complex number of modes, (.)*Representing the conjugation;
(2f) and (3) enabling i 'to be reduced by 1, and repeating the step (2e) until i' is equal to 1 to obtain the scalar weight w of the 1 st stage of the filter1And the output error signal epsilon of the 1 st stage of the filter1；
(2g) Scalar weight w using filter stages1,w2,...,wp-1To obtain the backward integrated weight vector w of the filterr'：
Figure FDA0003399490370000021
Wherein Π represents multiplicative multiplication;
(2h) normalized cross-correlation vector h using filter stages1,h1,...,hpSum filter backward integrated weight vector wr'And obtaining an optimal weight vector: w is ar＝[h1 h2 … hp]Twr'Wherein (·)TRepresenting a transpose;
(3) using the best weight vector wrAs a filter coefficient, the space-time snapshot data x after dimension reductionrCarrying out weighted filtering processing to obtain target information data: z is a radical ofr＝wr Hxr。
2. The method according to claim 1, characterized in that in step (1), the space-time snapshot data x received by the airborne radar system and the space-time guide vector s of the unit to be detected are pre-filtered by using a doppler three-channel joint adaptive processing 3DT method, and the method comprises the following steps:
(2a) acquiring space-time snapshot data x received by an airborne radar system and a space-time guide vector s of a unit to be detected, wherein x is an NM multiplied by 6N dimensional matrix, s is an NM multiplied by 1 dimensional matrix, N is the number of array units distributed at equal intervals by the airborne radar system, and M is the number of pulses transmitted in a coherent pulse interval;
(2b) selecting a Doppler channel l where a unit to be detected is located and Doppler channels l +1, l-1 adjacent to the Doppler channel l on two sides of the Doppler channel l, and constructing a 3DT dimension reduction transformation matrix Tr：
Figure FDA0003399490370000031
Wherein, TtShowing the MN multiplied by 3N dimensional transformation matrix used for time domain dimension reduction by the Doppler three-channel combined adaptive processing 3DT method, TsThe N multiplied by N dimensional transformation matrix, namely the N multiplied by N dimensional identity matrix I, which represents the space-domain dimensionality reduction of the Doppler three-channel combined adaptive processing 3DT methodN；fd,l-1、fd,l、fd,l+1Normalized Doppler frequencies of the l-1 st, l +1 st and l-1 st Doppler channels respectively; j is the imaginary unit;
Figure FDA0003399490370000032
representing a kronecker product operator; e represents a natural constant;
(2c) dimension reduction transformation matrix T by using 3DTrFast Fourier transform is carried out on the Doppler channel l and two adjacent Doppler channels l +1 and l-1 on two sides of the Doppler channel l, x is converted into an array element-Doppler domain from an array element-pulse domain, and space-time snapshot data after dimension reduction is obtained: x is the number ofr＝Tr Hx；
(2d) Dimension reduction transformation matrix T by using 3DTrAnd performing fast Fourier transform on the space-time guide vector s of the unit to be detected to obtain the space-time guide vector of the unit to be detected after dimensionality reduction: sr＝Tr Hs。
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