CN110850383B - MIMO radar signal processing method based on conformal array - Google Patents

MIMO radar signal processing method based on conformal array Download PDF

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CN110850383B
CN110850383B CN201910942685.4A CN201910942685A CN110850383B CN 110850383 B CN110850383 B CN 110850383B CN 201910942685 A CN201910942685 A CN 201910942685A CN 110850383 B CN110850383 B CN 110850383B
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赵永波
胡毅立
何学辉
刘宏伟
苏洪涛
水鹏朗
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Xidian University
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S7/00Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/418Theoretical aspects
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S13/00Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/006Theoretical aspects
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S13/00Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S7/00Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/023Interference 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
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S13/00Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S2013/0236Special technical features
    • G01S2013/0245Radar with phased array antenna

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Abstract

The invention belongs to the technical field of radars, and particularly relates to a MIMO radar signal processing method based on a conformal array, which comprises the following steps: setting a conformal array arrangement form, and transmitting an MIMO signal through a transmitting end of the conformal array arrangement form; obtaining a plurality of transmitting guide vectors and a plurality of receiving guide vectors according to the conformal array arrangement form; acquiring an echo signal, a plurality of emission radiation intensities and a plurality of reception radiation intensities; obtaining a receiving digital beam forming weight corresponding to the receiving guide vectors according to the receiving radiation intensities and the corresponding receiving guide vectors; obtaining a transmitting digital beam forming weight corresponding to the plurality of transmitting guide vectors according to the plurality of corresponding transmitting guide vectors; obtaining a matched filter weight according to the MIMO transmitting signal and the plurality of transmitting radiation intensities; obtaining a pulse comprehensive coefficient according to the transmitting digital beam forming weight and the matched filter weight; and obtaining an MIMO signal processing result according to the receiving digital beam forming weight and the pulse comprehensive coefficient. The invention improves the signal-to-noise ratio of the output signal.

Description

MIMO radar signal processing method based on conformal array
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a MIMO radar signal processing method based on a conformal array.
Background
In some special industries such as airplanes, missiles, satellites and the like, in order to expand the beam scanning range of an antenna array, save the limited space of a carrier, and also require a low profile characteristic, not affect the aerodynamic performance of the carrier, have higher installation freedom degree and reduce the radar scattering cross section (RCS), an antenna unit is required to be attached to the surface of the carrier, and a conformal array is the antenna array with the antenna unit attached to a non-planar surface.
The prior typical conformal array antenna forms are of two types, one type is a conformal array formed by a cylindrical array, a conical array and the like, the conformal array can realize omnibearing scanning by switching working modes of different array elements, and the problems of main lobe broadening and auxiliary lobe lifting of a planar phased array during large-range scanning are solved, but the antenna array cannot completely conform to a machine body, so that the pneumatic performance of a carrier can be influenced; the other type is that the antennas are distributed on two wings of the aircraft, the antennas are attached to the surfaces of the two wings to achieve perfect conformality, electromagnetic waves are radiated in an end-fire mode, horizontal wide-angle beam scanning can be achieved, but the size of the aircraft wing in the vertical direction is limited, and the angle resolution in the vertical direction is low.
A Multiple Input Multiple Output (MIMO) radar is a new system radar developed in recent years, which can ensure the effective coverage of the transmitted energy in the space by transmitting a plurality of signals which are orthogonal or partially related, carry out matched filtering on the signals of each transmitting antenna at a receiving end, synthesize the signals after phase compensation to complete the formation of transmitting beams, and carry out the formation of receiving digital beams among a plurality of receiving antennas, thereby simultaneously obtaining the gains of the transmitting and receiving antennas. Because digital beam forming is adopted in both transmitting and receiving, the MIMO radar has good performance in the aspects of interference resistance, clutter resistance, low interception, angle resolution and the like. Based on the characteristics, the conformal array and the MIMO radar can be combined, and the inherent problem of the conformal array is solved.
The conformal array generally has a side lobe level higher than a main lobe level relative to the linear array, and the zero point depth of a directional diagram is relatively shallow, so that appropriate directional array elements are introduced in signal processing of the conformal array. The geometric position structure of the conformal array makes the directions of different array elements relative to the target different, and the directional array elements make the radiation intensities of the array elements in different directions different, so that the directional array elements are in the structural model of the conformal array, and the amplitude of the signal is influenced by the radiation directional diagram of the directional array elements no matter the emission signal or the received echo signal of the target is reached. There are two traditional signal processing methods for MIMO radar, matching filtering before beam forming and receiving beam forming before pulse synthesis, however, the receiving beam forming before pulse synthesis method does not require that the transmitted signal is orthogonal and is widely used. In the traditional processing method of the MIMO, the influence of directional array elements on signal amplitude modulation under the conformal array environment is not considered, so that the traditional processing method of the MIMO can not be successfully matched with the amplitude during digital beam forming and pulse synthesis, and the output signal-to-noise ratio is further reduced.
Disclosure of Invention
In order to solve the above problems in the prior art, the present invention provides a method for processing MIMO radar signals based on conformal arrays. The technical problem to be solved by the invention is realized by the following technical scheme:
a MIMO radar signal processing method based on conformal array includes:
setting a conformal array arrangement form, and transmitting an MIMO signal through a transmitting end of the conformal array arrangement form;
obtaining a plurality of transmitting guide vectors and a plurality of receiving guide vectors according to the conformal array arrangement form;
acquiring an echo signal, a plurality of emission radiation intensities and a plurality of reception radiation intensities;
obtaining a receiving digital beam forming weight corresponding to the receiving guide vectors according to the receiving radiation intensities and the receiving guide vectors;
obtaining a plurality of transmitting digital beam forming weights corresponding to the transmitting guide vectors according to the plurality of corresponding transmitting guide vectors;
obtaining a matched filter weight according to the MIMO transmitting signal and the plurality of transmitting radiation intensities;
obtaining a pulse synthesis coefficient according to the transmitting digital beam forming weight and the matched filter weight;
and carrying out MIMO signal processing on the echo signals according to the receiving digital beam forming weight and the pulse comprehensive coefficient to obtain an MIMO signal processing result.
In an embodiment of the present invention, the expression of the echo signal is:
Figure GDA0002364734050000022
the specific expression form is as follows:
Figure GDA0002364734050000021
wherein alpha is a signal attenuation coefficient and theta 00 ) Is a target direction, a r00 ) Is N r X 1 receive steering vector, a t00 ) Is N t X 1 of the transmitted steering vector, V Nr00 ) For the receiving end N r X 1 directed array element radiation gain vector, V Nt00 ) Is a transmitting terminal N t A directional array element radiation gain vector of x 1, S (k) is N t The k-th sampled signal vector of each transmitting array element, N (k) is mutually independent white Gaussian noise sampled at the k-th time of the receiving end [ ·] T Indicating a transpose operation, an, indicates a Hadamard product.
In one embodiment of the invention, the conformal array arrangement has N t A transmitting antenna and N r A receiving antenna.
In one embodiment of the invention, the received radiation intensity is expressed as:
Figure GDA0002364734050000031
wherein (theta) 00 ) In the direction of the space,
Figure GDA0002364734050000032
is at (theta) 00 ) The amplitude gain of the nr array element at the receiving end in the direction, nr =1,2, \ 8230;, N r
In an embodiment of the present invention, the receive digital beamforming weights are:
Figure GDA0002364734050000035
in one embodiment of the invention, the expression of the emitted radiation loudness is:
Figure GDA0002364734050000034
wherein (theta) 00 ) Is a spatial direction, v nt00 ) Is at (theta) 00 ) The amplitude gain of the nt array element at the receiving end in the direction, nt =1,2, \8230;, N t
In one embodiment of the invention, the pulse synthesis coefficients are:
Figure GDA0002364734050000033
wherein S (k) is a MIMO signal.
The invention has the beneficial effects that:
in the invention, when the MIMO signal of the conformal array is processed, directional array elements are introduced at the output end and the input end in order to reduce the sidelobe level, so that when the MIMO signal processing is carried out on a receiving beam forming part and a pulse synthesis part, the amplitude factor is considered in a digital beam forming weight and a pulse synthesis coefficient, the digital beam forming part and the pulse synthesis part are ensured to be respectively matched with the amplitude and the phase of the corresponding weight, and finally the output signal-to-noise ratio of the digital beam forming part and the pulse synthesis part is improved.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Drawings
Fig. 1 is a flow chart of a method for processing MIMO radar signals based on a conformal array according to an embodiment of the present invention;
fig. 2 shows 16 directional pattern gains of an array element in a method for processing MIMO radar signals based on conformal arrays according to an embodiment of the present invention;
fig. 3 is an output gain diagram for improving pulse synthesis in a MIMO radar signal processing method based on a conformal array according to an embodiment of the present invention;
fig. 4 is an output gain diagram for improving digital beam forming in a MIMO radar signal processing method based on a conformal array according to an embodiment of the present invention;
fig. 5 is an output gain diagram of the joint action of improving digital beam forming and improving impulse synthesis in the MIMO radar signal processing method based on the conformal array according to the embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to specific examples, but the embodiments of the present invention are not limited thereto.
Referring to fig. 1, fig. 1 is a flowchart of a method for processing MIMO radar signals based on a conformal array according to an embodiment of the present invention, including:
setting a conformal array arrangement form, and transmitting an MIMO signal through a transmitting end of the conformal array arrangement form;
obtaining a plurality of transmitting guide vectors and a plurality of receiving guide vectors according to the conformal array arrangement form;
acquiring an echo signal, a plurality of emission radiation intensities and a plurality of reception radiation intensities;
obtaining a receiving digital beam forming weight corresponding to the receiving guide vectors according to the receiving radiation intensities and the receiving guide vectors;
obtaining a plurality of transmitting digital beam forming weights corresponding to the transmitting guide vectors according to the plurality of corresponding transmitting guide vectors;
obtaining a matched filter weight according to the MIMO transmitting signal and the plurality of transmitting radiation intensities;
obtaining a pulse synthesis coefficient according to the transmitting digital beam forming weight and the matched filter weight;
and performing MIMO signal processing on the echo signals according to the received digital beam forming weight and the pulse comprehensive coefficient to obtain an MIMO signal processing result.
When the MIMO signal of the conformal array is processed, the receiving beam forming part and the pulse synthesis part consider the amplitude factor into the digital beam forming weight and the pulse synthesis coefficient, and ensure that the digital beam forming part and the pulse synthesis part can be respectively matched with the amplitude and the phase of the corresponding weight so as to improve the output signal-to-noise ratio of the digital beam forming part and the pulse synthesis part.
In an embodiment of the present invention, the expression of the echo signal is:
Figure GDA0002364734050000042
the specific expression form is as follows:
Figure GDA0002364734050000041
wherein alpha is a signal attenuation coefficient and theta 00 ) Is a target direction, a r00 ) Is N r A received steering vector of x 1 and,
Figure GDA0002364734050000051
a t00 ) Is N t A transmit steering vector of x 1,
Figure GDA0002364734050000052
Figure GDA0002364734050000053
for the receiving end N r A x 1 directional array element radiates the gain vector,
Figure GDA0002364734050000054
is a transmitting terminal N t A directional array element radiation gain vector of x 1, S (k) being N t The k-th sampled signal vector of each transmitting array element, N (k) beingMutual independent white Gaussian noise of kth sampling of receiving end [ ·] T Indicating a transpose operation, an indicates a Hadamard product.
The invention takes into consideration
Figure GDA0002364734050000055
And
Figure GDA0002364734050000056
the influence on the conventional digital beam forming and pulse synthesis is realized, and the influence is modulated into the weight value and pulse synthesis of the digital beam forming.
In one embodiment of the invention, the conformal array arrangement has N t A transmitting antenna and N r A receiving antenna.
Further, the MIMO signal transmitted by the transmitting end in the conformal array arrangement form is S (k), which is specifically expressed as follows:
Figure GDA0002364734050000057
wherein the antenna in conformal array arrangement form has N t A transmitting antenna and N r A receiving antenna, wherein the antenna is a directional array element,
Figure GDA0002364734050000058
in order to transmit the radiation pattern gain,
Figure GDA0002364734050000059
for receiving radiation pattern gain, phase of receiving antenna
Figure GDA00023647340500000510
In relation to the array of the antenna arrays, in the embodiment, the receiving antenna arrays are arranged on a circle with radius r at equal intervals, and then the phase of each receiving antenna can be expressed as
Figure GDA00023647340500000511
Wherein
Figure GDA00023647340500000512
λ is the signal wavelength, phi nr The included angle between the connecting line from the array element of the receiving antenna to the circle center and the horizontal axis of the coordinate system is nr =1,2, \ 8230;, N r -1;
Figure GDA00023647340500000513
In this embodiment, if the arrangement of the transmitting antenna and the receiving antenna is the same, the phase of the transmitting antenna is
Figure GDA00023647340500000514
N (k) is N r White gaussian noise independent of each other in x 1 dimension.
In one embodiment of the invention, the received radiation intensity is expressed as:
Figure GDA00023647340500000515
wherein (theta) 00 ) In the direction of the space,
Figure GDA00023647340500000516
is at (theta) 00 ) The amplitude gain of the nr array element at the receiving end in the direction, nr =1,2, \ 8230;, N r
In an embodiment of the present invention, the receive digital beamforming weights are:
Figure GDA0002364734050000061
in one embodiment of the invention, the expression of the emitted radiation loudness is:
Figure GDA0002364734050000062
wherein (theta) 00 ) Is a spatial direction, v nt00 ) Is at (theta) 00 ) Receiving the nt array element of the end in the directionAmplitude gain, nt =1,2, \ 8230;, N t
In one embodiment of the invention, the pulse synthesis coefficients are:
Figure GDA0002364734050000063
wherein S (k) is a MIMO signal.
Further, the echo signal X (k) is firstly subjected to receiving beam forming and then pulse synthesis processing, so as to obtain an output signal y (k):
Figure GDA0002364734050000064
further, the signal-to-noise ratio SNR of the output of the invention new Comprises the following steps:
SNR new =β H00 )P(k)h H (k)/β H00 )N(k)h H (k),
the signal-to-noise ratio and SNR are output by the traditional method without considering the amplitude modulation of the directional array element new By comparison, an improvement in signal-to-noise ratio can be obtained.
The effects of the present invention will be further described with reference to the accompanying drawings
1. Simulation conditions
1.1 antenna pointing at a pitch angle θ 0 =90 °, azimuth angle Φ e [ -90 °,270 °]. The directional array element directional diagram of each antenna is synthesized by directional diagrams of two sub-arrays, the distance between the sub-arrays is half wavelength, the beam direction is the normal direction of the sub-arrays, the azimuth radiation range of the array elements is +/-90 degrees along the normal direction of the array elements, and the transmitting antennas are uniformly arranged on a circle with the radius of r;
1.2MIMO Radar N t =16 directional array elements constituting transmitting antenna, N r =1 receiving antenna, the directional array element is the response generated in simulation condition 1.1; the transmission signals are mutually orthogonal linear frequency modulation signals, the time width T =40us, B =4MHZ of the transmission signals, and critical sampling is carried out; the transmitting antennas are uniformly arranged on a semicircle with radius rThe nth transmitting antenna position
Figure GDA0002364734050000065
And k is 0 r =5, signal attenuation coefficient α =1; the received noise of each array element is independent and equally distributed Gaussian white noise;
1.3MIMO Radar has N t Transmitting antenna composed of =16 omnidirectional array elements, N r A receiving antenna constituted by =16 directional array elements, which are responses generated in the simulation condition 1.1; other conditions were the same as in simulation condition 1.2;
1.4 the receiving end and the transmitting end of the MIMO radar are array antennas composed of directional array elements, and N is t =N r =16, directed array element is a response generated in simulation condition 1.1; other conditions are the same as in the simulation condition 1.2.
2. Emulation content
2.1 the directional diagram gain synthesized by the two sub-arrays is used as the directional diagram gain of the directional array element of the MIMO radar, and in the case of the simulation condition 1.1, the N is shown in the graph of FIG. 2 t Pattern gain of =16 transmit antennas; the pattern shape of each antenna is the same, but the patterns of different antennas have phase shifts due to the antenna positions;
2.2 under the simulation condition 1.2, please refer to fig. 2 and fig. 3, where fig. 2 is a directional diagram gain of 16 directional array elements in the MIMO radar signal processing method based on the conformal array according to the embodiment of the present invention, and fig. 3 is an output gain diagram for improving pulse synthesis in the MIMO radar signal processing method based on the conformal array according to the embodiment of the present invention, and since the transmitting antenna is a directional array element and only one receiving antenna, i.e., only one receiving antenna, is provided
Figure GDA0002364734050000071
Figure GDA0002364734050000072
Is shown in fig. 2 with each antenna at (θ) 00 ) The amplitude vectors corresponding to the directions are adopted, and the amplitude responses of the transmitting ends at different sampling points are the same; since the transmitting antenna is a directional antenna and onlyThere is a receiving antenna, so the improvement of the output gain by the verification improvement method is equivalent to the improvement of the output gain by the verification improvement method in the impulse synthesis of the MIMO signal processing; FIG. 3 is a graph comparing the gain of the output signal obtained when the signal is processed by the conventional pulse synthesis method and the improved pulse synthesis method; further calculation shows that the output signal-to-noise ratio of the improved method is improved by about 1.91dB, which indicates that the improved pulse synthesis can improve the output signal-to-noise ratio under the conformal array environment;
2.3 under the simulation condition 1.3, the transmitting antenna is set to be an omnidirectional array element, and the receiving antenna is made to be a directional array element, namely
Figure GDA0002364734050000073
Figure GDA0002364734050000074
For each receive antenna in fig. 2 at (theta) 00 ) Direction corresponding amplitude gain. Because the transmission is an omnidirectional antenna and the reception is a directional antenna, the method of the invention is used for signal processing, and actually, the improved digital beam forming is verified for the improvement condition of output gain; please refer to fig. 4, fig. 4 is a graph of an output gain of an improved digital beamforming in a MIMO radar signal processing method based on a conformal array according to an embodiment of the present invention, and further calculation shows that an output signal-to-noise ratio of the improved method is improved by about 1.96dB, which indicates that the improved digital beamforming method can improve the output signal-to-noise ratio in the environment of the conformal array;
2.4 in case of simulation condition 1.4, both the transmitting and receiving antennas are directional array element antennas, that is
Figure GDA0002364734050000075
And
Figure GDA0002364734050000076
are each at (theta) in fig. 2 00 ) Direction corresponding amplitude gain. As the receiving and the transmitting are directional antennas, the method of the invention is verified to process signals, and actually, the signals are processedVerifying the improvement of the overall performance when the improved digital beam forming and the improved pulse synthesis method work together; referring to fig. 5, fig. 5 shows the improvement of the output gain after the joint action of the improved digital beam forming and the improved pulse synthesis in the MIMO radar signal processing method based on the conformal array according to the embodiment of the present invention, and further calculation shows that the output signal-to-noise ratio of the improved method is improved by about 3.86dB, which indicates that the signal-to-noise ratio is improved more greatly when the improved digital beam forming and the pulse synthesis method work together.
The foregoing is a further detailed description of the invention in connection with specific preferred embodiments and it is not intended to limit the invention to the specific embodiments described. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (7)

1. A MIMO radar signal processing method based on conformal array is characterized by comprising the following steps:
setting a conformal array arrangement form, and transmitting an MIMO signal through a transmitting terminal of the conformal array arrangement form;
obtaining a plurality of transmitting guide vectors and a plurality of receiving guide vectors according to the conformal array arrangement form;
acquiring an echo signal, a plurality of emission radiation intensities and a plurality of reception radiation intensities;
obtaining a plurality of receiving digital beam forming weights corresponding to the receiving guide vectors according to the plurality of receiving radiation intensities and the plurality of corresponding receiving guide vectors;
obtaining a plurality of transmitting digital beam forming weights corresponding to the transmitting guide vectors according to the plurality of corresponding transmitting guide vectors;
obtaining a matched filter weight according to the MIMO transmitting signal and the plurality of transmitting radiation intensities;
obtaining a pulse synthesis coefficient according to the transmitting digital beam forming weight and the matched filter weight;
and carrying out MIMO signal processing on the echo signals according to the receiving digital beam forming weight and the pulse comprehensive coefficient to obtain an MIMO signal processing result.
2. The method of claim 1, wherein the echo signal is expressed as:
Figure FDA0002223346860000011
the specific expression form is as follows:
Figure FDA0002223346860000012
wherein alpha is a signal attenuation coefficient and theta 00 ) Is a target direction, a r00 ) Is N r Receive steering vector of x 1, a t00 ) Is N t A transmit steering vector of x 1,
Figure FDA0002223346860000013
for the receiving end N r A x 1 directional array element radiates the gain vector,
Figure FDA0002223346860000014
is a transmitting terminal N t A directional array element radiation gain vector of x 1, S (k) being N t The k-th sampled signal vector of each transmitting array element, N (k) is mutually independent white Gaussian noise sampled at the k-th time of the receiving end [ ·] T Indicating a transpose operation, an, indicates a Hadamard product.
3. The method of claim 1, wherein the conformal array arrangement has N t A transmitting antenna and N r A receiving antenna.
4. The method of claim 3, wherein the receive radiation gain is expressed as:
Figure FDA0002223346860000021
wherein (theta) 00 ) In the direction of the space,
Figure FDA0002223346860000022
is at (theta) 00 ) The amplitude gain of the nr array element at the receiving end in the direction, nr =1,2, \ 8230;, N r
5. The method of claim 4, wherein the receive digital beamforming weights are:
Figure FDA0002223346860000025
6. the method of claim 1, wherein the transmit radiation loudness expression is:
Figure FDA0002223346860000023
wherein (theta) 00 ) Is a spatial direction, v nt00 ) Is at (theta) 00 ) The amplitude gain of the nth array element of the transmitting end in the direction is nt =1,2, \8230, N t
7. The method of claim 6, wherein the pulse synthesis coefficients are:
Figure FDA0002223346860000024
wherein S (k) is a MIMO signal.
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