CN113671487A - Target search resource optimization method based on hybrid phased array-MIMO radar - Google Patents

Target search resource optimization method based on hybrid phased array-MIMO radar Download PDF

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CN113671487A
CN113671487A CN202110812556.0A CN202110812556A CN113671487A CN 113671487 A CN113671487 A CN 113671487A CN 202110812556 A CN202110812556 A CN 202110812556A CN 113671487 A CN113671487 A CN 113671487A
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array
search
radar
probability
airborne
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汪飞
黄晓彦
李海林
时晨光
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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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
    • G01S13/00—Systems 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
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • 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
    • 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
    • G01S7/36—Means for anti-jamming, e.g. ECCM, i.e. electronic counter-counter measures

Abstract

The invention discloses a target search resource optimization method based on a hybrid phased array-MIMO radar, which comprises the steps of firstly, forming the hybrid phased array-MIMO radar according to an airborne opportunistic array projection array surface, determining a search partition selection mode, and solving the area of the array surface of a search partition; secondly, establishing a relation between radar search parameters in a search array; determining peak power, subarray number, pulse width, pulse accumulation number and array surface selection form of the hybrid phased array-MIMO radar in the search array surface as optimization parameters; then, constructing constraint conditions, determining an objective function, and establishing a radio frequency stealth constraint optimization model under the condition of considering the projection array plane of the overlapped airborne opportunistic array; finally, the model is solved by a genetic algorithm. The invention designs an optimized radar target search algorithm, which meets good detection performance and improves the radio frequency stealth performance of the airborne opportunistic array radar.

Description

Target search resource optimization method based on hybrid phased array-MIMO radar
Technical Field
The invention relates to an airborne opportunistic array radar resource optimization technology, in particular to a target search resource optimization method based on a hybrid phased array-MIMO radar.
Background
With the emergence of a novel combat concept, the combat space of modern wars extends to the land, sea, air and day, the environment of the combat is changed into a plurality of types and is full of unknown challenges, and the information perception capability in the combat plays an important role in the victory or defeat of the wars. The radar system can detect and identify various targets by radio positioning, and is an important information perception system in battle. However, with the continuous upgrading and development of various combat system technologies, such as unmanned combat aircrafts, warship combat systems, anti-radiation missiles and the like, great threats are caused to the viability of the current radar systems. The phased array radar has the characteristics of rapid scanning of antenna beams, high search/tracking data rate, space-time adaptive processing, high radiation power, strong anti-interference capability and the like as the most widely used radar system at present. However, the phased array radar is difficult to meet the requirements of modern wars due to the fact that the detection distance is constrained by the power aperture area, the array arrangement unit is constrained by the half wavelength spacing and other physical constraints. The American Naval Postgradate School (NPS) proposes a novel radar system of opportunistic array radar aiming at ballistic defense of a hidden destroyer of the next generation Naval. The opportunistic array radar is different from the traditional mode that the radar is used as the design core of a combat system in the past, and the platform stealth design is used as the core; the digital array is used as a technical foundation, and functions of searching, tracking, communication and the like can be integrated; through the 'opportunistic' working mode, the opportunistic array radar has a more flexible working mode and effectively improves the stealth performance of the battle platform.
The opportunistic array radar has rich and flexible working modes, can be a mixture of multiple modes such as a phased array-MIMO mode, and simultaneously realizes multiple tasks such as searching, tracking, cooperative detection and the like. The method is applied to the optimization of target search resources based on the opportunistic array radar in the hybrid phased array-MIMO radar working mode, and in order to resist passive detectors with different sensitivities, two radiation power control strategies, namely a minimum power strategy and a minimum dwell time strategy, can be mainly adopted to improve the low interception performance of the hybrid phased array-MIMO radar. The minimum power strategy is to reduce the probability of passive interception in the energy domain by maximizing the dwell time and keeping the peak power at a relatively low level. The minimum radiated power strategy is difficult to handle when the passive sensitivity of the confronted adversary is large. In case of high sensitivity, the antenna gain is large, which results in small instantaneous coverage airspace area and long time spent in scanning the whole airspace under the same condition. Therefore, the radar radiates higher power, the residence time of the radar is controlled, the residence time of the radar is smaller than the passive interception time, and the probability of passive interception of the radar in a time-space domain is further reduced.
Therefore, the method has important significance for the research on the optimization of the search resources of the airborne opportunistic array radar. The optimization of radar search resources is mainly designed according to the parameters of search beam residence time, search distance, search time, search airspace range, search radiation energy, search signal waveform and the like. The existing research includes an optimized radar search time algorithm, an optimized search frame period and search distance algorithm, a radar self-adaptive search algorithm, a radar search algorithm based on wave position arrangement, and the like, and radar search resource optimization design methods such as guided search parameter optimization based on accumulated detection probability, search performance optimization with airspace coefficients as optimization functions, and the like.
Although the method described above satisfies a good detection probability and the search and detection capability of the radar is improved to some extent, the threat degree of the target is difficult to determine because the radar battle scene is complicated and changeable and a plurality of false targets and radiation sources with interference properties are not always present. Therefore, the application of the existing method in a complex battle scene has certain limitation, and the radio frequency stealth performance is not high.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a target search resource optimization method based on a hybrid phased array-MIMO radar.
The technical scheme is as follows: a target search resource optimization method based on a hybrid phased array-MIMO radar comprises the following steps:
s1, forming a hybrid phased array-MIMO radar according to the airborne opportunistic array projection array front, determining a search partition selection mode, and solving the area of the front of a search partition;
s2, establishing a relation between radar search parameters in the search partition projection array; determining peak power, subarray number, pulse width, pulse accumulation number and array surface selection form of the hybrid phased array-MIMO radar in the search array surface as radar search optimization parameters;
s3, constructing constraint conditions, determining an objective function, and establishing a radio frequency stealth constraint optimization model under the condition of considering the projection front of the overlapping airborne opportunistic array;
s4, solving the model by using a genetic algorithm; and (3) taking the peak power, the number of subarrays, the pulse width, the selection form of the array surface and the pulse accumulation number as optimization parameters, taking the minimum interception probability as a target function, and solving by adopting a genetic algorithm to obtain the optimal solution of the model meeting the constraint condition.
Further, step S1 includes the following steps:
s11, projecting the airborne opportunistic array to obtain an airborne opportunistic array projection array surface, cutting out a maximum inscribed rectangle array surface of the airborne opportunistic array projection array surface by taking a rectangular surface as a basic array surface, and uniformly dividing the maximum inscribed rectangle array surface of the airborne opportunistic array projection array surface to form a hybrid phased array-MIMO radar;
s12, dividing the space domain airborne opportunity array projection front into a plurality of search areas according to the azimuth angle, determining the airborne opportunity array projection front selection mode of the search subarea according to the principle that the search subarea overlapped projection front is not repeatedly used, sequentially determining the airborne opportunity array projection front selection modes of other search subareas according to the airborne opportunity array projection front selection mode of the first search subarea, thereby determining the priority of the search subareas, and solving the projection front area of each search subarea according to the selection mode that the search subarea airborne opportunity array overlapped projection front is not repeatedly used.
Further, step S2 includes the following steps:
s21, analyzing and influencing relevant parameters of interception factors according to the signal-to-noise ratio of the hybrid phased array-MIMO radar; specifically, the method comprises the following steps:
hybrid phased array-MIMO radar for NpAfter coherent accumulation of the pulses, the signal-to-noise ratio becomes N of the original signalpAnd the fourth power of the maximum detection distance of the radar becomes:
Figure BDA0003168760870000031
the square of the maximum intercept distance of the intercept receiver is:
Figure BDA0003168760870000032
wherein, PtFor the peak power of radar radiation, τ is the beam width, Gt,MIMOFor hybrid phased array-MIMO radar transmit gain, GrFor receive gain, λ is the wavelength, σ is the target radar scattering area, k is the Boltzmann constant, T0Effective noise temperature, F noise figure, Sr,minFor radar sensitivity, Si,minIn order to be the receiver sensitivity,
Figure BDA0003168760870000033
is the normalized propagation factor, with a maximum value of 1; l is the hybrid phased array-MIMO radar system loss,
Figure BDA0003168760870000034
theta is the azimuth angle and the pitch angle of the search area; giFor receiver reception gain, Ri,maxIs the detection range of the receiver; gIPTo handle the gain, it is expressed as
Figure BDA0003168760870000035
Where γ ∈ (0,1), denotes a non-coherent accumulation loss, and ∈ 3.14;
the interception factor is:
Figure BDA0003168760870000036
therefore, the fourth power of the interception factor is expressed as:
Figure BDA0003168760870000037
s22, estimating the accumulation detection probability;
assume that for the SwerlingI type target, the single detection probability is expressed as:
Figure BDA0003168760870000041
where SNR represents any signal-to-noise ratio;
for a target with a distance of R, the detection signal-to-noise ratio of the hybrid phased array-MIMO radar is as follows:
Figure BDA0003168760870000042
for a distance RdThe detection signal-to-noise ratio of the hybrid phased array-MIMO radar is as follows:
Figure BDA0003168760870000043
wherein the SNR0Representing the signal-to-noise ratio of the signal;
substituting the detection signal-to-noise ratio of the hybrid phased array-MIMO radar into a single detection probability expression, so that the target single detection probability is converted into:
Figure BDA0003168760870000044
and further obtaining an accumulated detection probability:
Figure BDA0003168760870000045
wherein R issFor radar detection of range, RcFor tracking the starting distance, V is the target radial velocity, j is the number of radar scan frames, SNRsIs a distance RsSignal to noise ratio, PfaAs false alarm probability, sub-array division number kr＝VTf/2RsK is Boltzmann constant, T0Effective noise temperature, F is the noise figure, coefficient kr＝VTf/2Rs，TfIs a search frame period.
Further, step S3 includes the following steps:
s31, constructing constraint conditions;
after the scanning mode is determined, the wave bit number of the search subarea is determined, and the relationship between the residence time and the search frame period is considered when the residence time of the wave beam on each wave bit is set; the detection probability in the subarea of the search array surface also needs to meet the preset detection probability; searching three regions divided by the array surface, and selecting and not overlapping; it should satisfy: n is a radical ofB,itB,i≤Tf,iWherein, Tf,i、NB,i、tB,iRespectively searching frame period, wave digit number and residence time of the searching partition i;
second, search for the detection probability p within partition id,iAnd searching for the cumulative detection probability p within partition iD,iIt is also desirable to satisfy the following equation:
pd,i≥pD,i；
at the same time A, B, C three search area fronts are selected to be constrained to:
Figure BDA0003168760870000051
wherein A isarray、Barray、CarrayA, B, C search area projection fronts respectively;
s32, estimating the joint interception probability and establishing an objective function;
considering the passive joint interception probability of the radar in the time domain-power domain:
Figure BDA0003168760870000052
wherein, PDwellFor probability of interception in the time domain, PDFor the probability of interception in the power domain, Q represents the Marcum Q function, tBRepresenting radar radiation time, TIIndicating the search time of the acquisition receiver, AFDenotes the antenna beam coverage area, DIRepresenting the intercepted receiver density;
for multi-beam scanning, the joint intercept probability is expressed as:
Figure BDA0003168760870000053
the established interception probability objective function is as follows:
Figure BDA0003168760870000054
wherein N isB,nRepresenting the wave bit number of the nth wave beam;
s33, finally obtaining a radio frequency stealth constraint planning model as follows:
min PI(Pt,i,τi,Ki,Si,Np)
Figure BDA0003168760870000055
wherein, Pt,i、τi、Ki、Si、NpThe radar radiation peak power, the pulse width, the sub-array number, the array surface selection form and the pulse accumulation number in the search subarea i are respectively.
Further, step S4 is specifically:
shape selection of peak power, number of subarrays, pulse width, number of pulse accumulations, and wavefrontThe formula is used as an optimization parameter, real number coding is adopted, and a real number group { P) consisting of five parameters is adoptedt,i,τi,Ki,Si,NpForming a candidate solution with a certain population size; according to the target function, the inverse of the pulse accumulation power of the product of the interception probability and the detection probability is used as an adaptive value; according to the size of the fitness value, selecting operation is carried out by a roulette method; in the cross operation, a greedy arithmetic cross operator is adopted, namely two parent candidate solutions F1And F2Generating 4 sub-generation candidate solutions S after cross operation1，S2，S3，S4(ii) a In the mutation operation, determining the mutation scale according to the mutation rate, and randomly mutating each gene value of the solution with the minimum adaptive value in the feasible solutions; and finally, when the fitness value of the optimal individual reaches a given threshold value, or the fitness value of the optimal individual and the population fitness value do not rise any more, or the iteration number reaches a preset algebra, terminating the algorithm.
Has the advantages that: compared with the prior art, the target search resource optimization method based on the hybrid phased array-MIMO radar has stronger adaptability to complex and variable combat environments by taking the interception probability as a target function under the condition of meeting certain detection probability and time constraint conditions; in addition, compared with the existing search performance optimization method based on the guide search parameter optimization of the accumulated detection probability and taking the space domain coefficient as the optimization function, the target search resource optimization algorithm based on the hybrid phased array-MIMO radar provided by the invention has the advantages that the interception probability is smaller than that of the guide search parameter optimization based on the accumulated detection probability and the search performance optimization method based on the space domain coefficient as the optimization function under the condition of meeting a certain detection probability, so that the airborne opportunistic array radar has better radio frequency stealth performance.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic diagram of an airspace airborne opportunistic array projection array overlap;
FIG. 3 is a schematic diagram showing the selection of the search area wavefront A;
FIG. 4 is a simulation diagram of the sub-region detection probability and interception probability of the method of the present invention varying with the iteration times of the genetic algorithm; the simulation graph comprises a sub-region detection probability simulation graph and a sub-region interception probability simulation graph, wherein (a) the sub-region detection probability simulation graph changes along with the iteration times of a genetic algorithm, and (b) the sub-region interception probability simulation graph changes along with the iteration times of the genetic algorithm;
FIG. 5 shows an interception probability simulation chart of the method of the present invention and three methods of guiding search parameter optimization based on accumulated detection probability and search performance optimization using space domain coefficients as optimization functions.
Detailed Description
The invention is further described with reference to the following figures and specific examples.
As shown in fig. 1, a target search resource optimization method based on a hybrid phased array-MIMO radar of the present invention includes the following steps:
and S1, forming a hybrid phased array-MIMO radar according to the airborne opportunistic array projection front, determining a search partition selection mode, and solving the front area of the search partition.
S11, projecting the airborne opportunistic array to obtain an airborne opportunistic array projection array surface, cutting out a maximum inscribed rectangle array surface of the airborne opportunistic array projection array surface by taking a rectangular surface as a basic array surface, and uniformly dividing the maximum inscribed rectangle array surface of the airborne opportunistic array projection array surface to form a hybrid phased array-MIMO radar; specifically, the method comprises the following steps:
the method takes the rectangular array surface as a basic array surface, cuts out the maximum inscribed rectangular array surface of the airborne opportunity array projection array surface in the search partition, uniformly divides the maximum inscribed rectangular array surface of the airborne opportunity array projection array surface to form the hybrid phased array-MIMO radar, and researches the radio frequency stealth performance of the hybrid phased array-MIMO radar. The hybrid phased array-MIMO radar works in a phased array mode inside each sub-array which is uniformly divided by the maximum inscribed rectangle array surface of the airborne opportunity array projection array surface, and works in the MIMO mode among the sub-arrays, so that the whole system not only obtains coherent processing gain of the phased array radar, but also has the advantages of high target resolution, interference resistance, radio frequency stealth and the like of the MIMO radar. By adopting the rectangular array surface, a directional diagram can be quickly formed, the time cost is saved, and the directional diagram can be reconfigured into sub-arrays divided by the rectangular array surface in various different modes.
S12, dividing the space domain airborne opportunity array projection front into a plurality of search areas according to the azimuth angle, determining the airborne opportunity array projection front selection mode of the search subarea according to the principle that the search subarea overlapped projection front is not reused, sequentially determining the airborne opportunity array projection front selection modes of other search subareas according to the airborne opportunity array projection front selection mode of the first search subarea, thereby determining the search subarea priority, and solving the projection front area of the search subarea according to the search subarea selection mode;
in this embodiment, a radio frequency stealth target search resource optimization algorithm of a hybrid phased array-MIMO radar under an overlapping array surface is considered. The projection array plane of the space domain airborne opportunistic array is divided into [0 degrees and 60 degrees ] according to the azimuth angle]，[60°,120°]，[120°,180°]Three sub-regions with pitch angles of 0,30 °]The three subregions correspond to search regions A, B and C, and projection array surface overlapping regions exist among the search subregions. Therefore, the radar according to the figure 2 shows the superposition of the airborne opportunity array projection fronts of three search airspaces during target detection. The areas of the non-overlapping array element searching areas A, B and C are respectively as follows: sA＝0.32m2，SB＝2.14m2，SC＝0.25m2。
According to the schematic diagram of the projection wavefront selection form of the search area a in fig. 3, there are 8 wavefront selection ways for the search area a, and the values of the wavefront areas are calculated as SA ═ 0.32,1.39,0.92,0.94,0.47,0.77,1.54,1.09]m2. After the searching area A is subjected to parameter optimization, the searching area A determines the form of the array surface, and the array surface searching area B and the searching area C which are used in the searching area A cannot be used, so that the priority of the searching area is determined, and then the searching area B and the searching area C are subjected to array surface selection and parameter optimization flexibly through an algorithm.
S2, establishing a relation between radar search parameters in the search partition projection array; determining peak power, subarray number, pulse width, pulse accumulation number and array surface selection form of the hybrid phased array-MIMO radar in the search array surface as radar search optimization parameters;
s21, analyzing influence according to signal-to-noise ratio of hybrid phased array-MIMO radarIntercepting related parameters of factors; according to the single pulse signal-to-noise ratio SNR and the maximum detection distance R of the hybrid phased array-MIMO radarr,maxMaximum acquisition distance R of the receiveri,maxAnd interception factor
Figure BDA0003168760870000081
Parameter radar radiation peak power P can be establishedtSubarray division number K, beam width tau, pulse accumulation number NpAnd the interception factor alpha is in a constraint relation of: α. varies to f (P)t,K,τ,Np) (ii) a Specifically, the method comprises the following steps:
for the hybrid phased array-MIMO radar, under the condition that an antenna array receives and transmits common addresses, if the total number of array elements of the array is M and the whole rectangular array surface is divided into K sub-arrays, the number of the array elements of each sub-array is L. Obviously, M ═ KL. The signals transmitted by the sub-arrays are orthogonal to each other, while the transmitted signals within each sub-array are correlated. When the signal returns from the target, the signal is received and processed through matched filtering, equivalent transmitting beams and receiving beams are formed in sequence, and the echo signal-to-noise ratio of each channel (subarray) of the hybrid phased array-MIMO radar is reduced to 1/K of that of the phased array radar.
Hybrid phased array-MIMO radar for NpAfter coherent accumulation of the pulses, the signal-to-noise ratio becomes N of the original signalpAnd the fourth power of the maximum detection distance of the radar becomes:
Figure BDA0003168760870000082
the square of the maximum intercept distance of the intercept receiver is:
Figure BDA0003168760870000083
wherein, PtFor the peak power of radar radiation, τ is the beam width, Gt,MIMOFor hybrid phased array-MIMO radar transmit gain, GrFor receive gain, λ is the wavelength, σ is the target radar scattering area, Sr,minIs radar asSensitivity, Si,minIn order to be the receiver sensitivity,
Figure BDA0003168760870000084
is a normalized propagation factor, the maximum value of which is 1, L is the loss of the hybrid phased array-MIMO radar system,
Figure BDA0003168760870000091
theta is the azimuth angle and the pitch angle of the search area respectively. GiGain is received for the receiver. GIPTo handle the gain, it is expressed as
Figure BDA0003168760870000092
Here, γ ∈ (0,1), indicates a non-coherent accumulation loss, and ∈ 3.14.
The interception factor is:
Figure BDA0003168760870000093
therefore, the fourth party of the interception factor can be expressed as:
Figure BDA0003168760870000094
s22, estimating the accumulation detection probability; according to the monopulse signal-to-noise ratio SNR of the hybrid phased array-MIMO radar, the distance R is the targetsAccumulated detection probability P ofcdCan be described as the target being at a distance RsSNR of (signal to noise ratio)sFalse alarm probability PfaThe number of divisions of the subarray krSearch frame period TfA relationship of pcd∝g(kr,Tf,SNRs,Pfa) (ii) a Specifically, the method comprises the following steps:
assume that for the SwerlingI type target, the single detection probability is expressed as:
Figure BDA0003168760870000095
where SNR represents any signal-to-noise ratio.
For a target with a distance of R, the detection signal-to-noise ratio of the hybrid phased array-MIMO radar is as follows:
Figure BDA0003168760870000096
for a distance RdThe detection signal-to-noise ratio of the hybrid phased array-MIMO radar is as follows:
Figure BDA0003168760870000097
substituting the detection signal-to-noise ratio of the hybrid phased array-MIMO radar into a single detection probability expression, so that the target single detection probability can be:
Figure BDA0003168760870000098
and further obtaining the cumulative detection probability:
Figure BDA0003168760870000099
wherein R issFor radar detection of range, RcFor tracking the starting distance, V is the target radial velocity, j is the number of radar scan frames, SNRsIs a distance RsSignal to noise ratio, PfaIs the false alarm probability, k is the Boltzmann constant, T0Effective noise temperature, F is the noise figure, coefficient kr＝VTf/2Rs，krDenotes the kthrElement matrix, k is more than or equal to 0r≤K，TfIs a search frame period.
S3, constructing constraint conditions, determining an objective function, and establishing a radio frequency stealth constraint optimization model under the condition of considering the projection front of the overlapped airborne opportunistic array.
And S31, constructing a constraint condition. After the scanning mode is determined, the wave bit number of the search partition is determined, and when the dwell time of the wave beam on each wave bit is set, the dwell time and the search frame period are consideredThe relationship of the period; the detection probability in the subarea of the search array surface also needs to meet the preset detection probability; the three areas divided by the search front are not selected to coincide. It should satisfy: n is a radical ofB,itB,i≤Tf,i. Wherein, Tf,i、NB,i、tB,iRespectively, the search frame period, the wave bit number and the residence time of the search partition i.
Second, search for the detection probability p within partition id,iAnd searching for the cumulative detection probability p within partition iD,iIt is also desirable to satisfy:
pd,i≥pD,i；
a, B, C three search area fronts simultaneously select constraints:
Figure BDA0003168760870000101
wherein A isarray、Barray、CarrayA, B, C search area projection fronts respectively;
s32, estimating the joint interception probability and establishing an objective function; according to the passive combined interception probability P of the radar in the time domain-power domainIProbability of interception in time domain PDwellProbability of interception P in the Power DomainDTo obtain the combined interception probability min P of the target functionI(Pt,i,τi,Ki,Si,Np) (ii) a Specifically, the method comprises the following steps:
considering the passive joint interception probability of the radar in the time domain-power domain:
Figure BDA0003168760870000102
wherein, PDwellFor the probability of interception in the time domain, the probability of interception in the power domain is denoted as PDQ denotes the Marcum Q function, tBRepresenting radar radiation time, TIIndicating the search time of the acquisition receiver, AFDenotes the antenna beam coverage area, DIRepresenting the intercept receiver density.
For multi-beam scanning, the joint intercept probability is expressed as:
Figure BDA0003168760870000111
when the airborne opportunistic array radar completes a search task, the lower the intercepted probability is, the less easily the airborne opportunistic array radar is found by an enemy. The established interception probability objective function is as follows:
Figure BDA0003168760870000112
NB,nindicating the number of bits of the nth beam.
S33, finally obtaining a radio frequency stealth constraint planning model as follows:
min PI(Pt,i,τi,Ki,Si,Np)
Figure BDA0003168760870000113
wherein, Pt,i、τi、Ki、Si、NpAnd the radar radiation peak power, the pulse width, the sub-array number, the array surface selection form and the pulse accumulation number in the search subarea i are respectively.
S4, solving the model by using a genetic algorithm; and (3) taking the peak power, the number of subarrays, the pulse width, the selection form of the array surface and the pulse accumulation number as optimization parameters, taking the minimum interception probability as a target function, and solving by adopting a genetic algorithm to obtain the optimal solution of the model meeting the constraint condition.
The peak power, the number of subarrays, the pulse width, the pulse accumulation number and the selection form of the array surface are used as optimization parameters, real number coding is adopted, and a real number group { P) consisting of five parameters is adoptedt,i,τi,Ki,Si,NpForming a candidate solution with a certain population size; accumulating the pulses by multiplying the interception probability and the detection probability several times according to the objective functionThe inverse of the power is taken as an adaptive value; according to the size of the fitness value, selecting operation is carried out by a roulette method; in the cross operation, a greedy arithmetic cross operator is adopted, namely two parent candidate solutions F1And F2Generating 4 sub-generation candidate solutions S after cross operation1，S2，S3，S4(ii) a In the mutation operation, the mutation scale is determined according to the mutation rate, and each gene value of the solution with the minimum adaptation value in the feasible solutions is randomly mutated. And finally, when the fitness value of the optimal individual reaches a given threshold value, or the fitness value of the optimal individual and the population fitness value do not rise any more, or the iteration number reaches a preset algebra, terminating the algorithm.
Simulation analysis:
at the expected detection probability of 0.95, the model solution at the starting distance of 100km is tracked. In the genetic algorithm control parameters, the iteration number is 200, the population size is 500, the cross probability is 0.7, the variation probability is 0.01, and the average value is obtained by calculating 100 times. In the airborne opportunistic array radar, the wavelength of a radar emission signal is assumed to be 0.03m, the false alarm probability is 10-6, the radar detection distance is 200km, and the target radar scattering cross section (RCS) is 1m2The expected detection probability is 0.95, the false alarm probability is 10-6, the signal duty ratio is 0.5, and the directional pattern factor
Figure BDA0003168760870000121
The azimuth angle range of airspace is [0 DEG, 180 DEG ]]The pitch angle range is [0 DEG, 30 DEG ]]Density of intercepted receiver 0.001/km2And intercepting the search time of the receiver for 10s, and intercepting the bandwidth of the receiver for 20 MHZ.
For the optimized parameters, the value range of the peak emission power is [10,100] kW, the pulse width is [10,100] mus, the search frame period is [10,20] s, the number of subarrays is [1,1000], and the number of pulse accumulation is [1,1000 ].
Table 1 shows the simulation result of the radio frequency stealth algorithm when the opportunistic array radar performs target search based on the consideration of the projection array of the partitioned overlapping airborne opportunistic array.
TABLE 1 subregion optimization parameter values and array form
Figure BDA0003168760870000122
In fig. 4, (a) and (b) show simulation graphs of the detection probability and the interception probability of the search algorithm of the invention along with the change of the iteration times of the genetic algorithm, respectively, in the three partitions, the detection probability of the radar is greater than the expected detection probability, which indicates that certain detection performance is satisfied in the target search process, and the interception probability in the partitions is reduced along with the increase of the iteration times and the convergence rate is higher, which indicates that the method of the invention has good radio-frequency stealth performance.
In order to compare the detection performance of the three methods intuitively, fig. 5 shows the probability of interception of the three methods under multi-region integration. From fig. 5, it can be seen that the three methods have better low interception performance, but the method of the present invention has better interception performance than other methods.
In summary, the target search resource optimization algorithm based on the hybrid phased array-MIMO radar has good radio frequency stealth performance under the condition of meeting the detection performance of the target.

Claims (5)

1. A target search resource optimization method based on a hybrid phased array-MIMO radar is characterized by comprising the following steps:
s1, forming a hybrid phased array-MIMO radar according to the airborne opportunistic array projection array front, determining a search partition selection mode, and solving the area of the front of a search partition;
s2, establishing a relation between radar search parameters in the search partition projection array; determining peak power, subarray number, pulse width, pulse accumulation number and array surface selection form of the hybrid phased array-MIMO radar in the search array surface as radar search optimization parameters;
s3, constructing constraint conditions, determining an objective function, and establishing a radio frequency stealth constraint optimization model under the condition of considering the projection front of the overlapping airborne opportunistic array;
s4, solving the model by using a genetic algorithm; and (3) taking the peak power, the number of subarrays, the pulse width, the selection form of the array surface and the pulse accumulation number as optimization parameters, taking the minimum interception probability as a target function, and solving by adopting a genetic algorithm to obtain the optimal solution of the model meeting the constraint condition.
2. The method for optimizing target search resources based on hybrid phased array-MIMO radar as claimed in claim 1, wherein the step S1 includes the following steps:
s11, projecting the airborne opportunistic array to obtain an airborne opportunistic array projection array surface, cutting out a maximum inscribed rectangle array surface of the airborne opportunistic array projection array surface by taking a rectangular surface as a basic array surface, and uniformly dividing the maximum inscribed rectangle array surface of the airborne opportunistic array projection array surface to form a hybrid phased array-MIMO radar;
s12, dividing the space domain airborne opportunity array projection front into a plurality of search areas according to the azimuth angle, determining the airborne opportunity array projection front selection mode of the search subarea according to the principle that the search subarea overlapped projection front is not repeatedly used, sequentially determining the airborne opportunity array projection front selection modes of other search subareas according to the airborne opportunity array projection front selection mode of the first search subarea, thereby determining the priority of the search subareas, and solving the projection front area of each search subarea according to the selection mode that the search subarea airborne opportunity array overlapped projection front is not repeatedly used.
3. The method for optimizing target search resources based on hybrid phased array-MIMO radar as claimed in claim 1, wherein the step S2 includes the following steps:
s21, analyzing and influencing relevant parameters of interception factors according to the signal-to-noise ratio of the hybrid phased array-MIMO radar; specifically, the method comprises the following steps:
hybrid phased array-MIMO radar for NpAfter coherent accumulation of the pulses, the signal-to-noise ratio becomes N of the original signalpAnd the fourth power of the maximum detection distance of the radar becomes:
Figure FDA0003168760860000021
the square of the maximum intercept distance of the intercept receiver is:
Figure FDA0003168760860000022
wherein, PtFor the peak power of radar radiation, τ is the beam width, Gt,MIMOFor hybrid phased array-MIMO radar transmit gain, GrFor receive gain, λ is the wavelength, σ is the target radar scattering area, k is the Boltzmann constant, T0Effective noise temperature, F noise figure, Sr,minFor radar sensitivity, Si,minIn order to be the receiver sensitivity,
Figure FDA0003168760860000023
is the normalized propagation factor, with a maximum value of 1; l is the hybrid phased array-MIMO radar system loss,
Figure FDA0003168760860000024
theta is the azimuth angle and the pitch angle of the search area; giFor receiver reception gain, Ri,maxIs the detection range of the receiver; gIPTo handle the gain, it is expressed as
Figure FDA0003168760860000025
Where γ ∈ (0,1), denotes a non-coherent accumulation loss, and ∈ 3.14;
the interception factor is:
Figure FDA0003168760860000026
therefore, the fourth power of the interception factor is expressed as:
Figure FDA0003168760860000027
s22, estimating the accumulation detection probability;
assume that for the SwerlingI type target, the single detection probability is expressed as:
Figure FDA0003168760860000028
where SNR represents any signal-to-noise ratio;
for a target with a distance of R, the detection signal-to-noise ratio of the hybrid phased array-MIMO radar is as follows:
Figure FDA0003168760860000029
for a distance RdThe detection signal-to-noise ratio of the hybrid phased array-MIMO radar is as follows:
Figure FDA00031687608600000210
wherein the SNR0Representing the signal-to-noise ratio of the signal;
substituting the detection signal-to-noise ratio of the hybrid phased array-MIMO radar into a single detection probability expression, so that the target single detection probability is converted into:
Figure FDA0003168760860000031
and further obtaining an accumulated detection probability:
Figure FDA0003168760860000032
wherein R issFor radar detection of range, RcFor tracking the starting distance, V is the target radial velocity, j is the number of radar scan frames, SNRsIs a distance RsSignal to noise ratio, PfaAs false alarm probability, sub-array division number kr＝VTf/2RsK is Boltzmann constant, T0As effective noiseTemperature, F is the noise coefficient, coefficient kr＝VTf/2Rs，TfIs a search frame period.
4. The method for optimizing target search resources based on hybrid phased array-MIMO radar as claimed in claim 1, wherein the step S3 includes the following steps:
s31, constructing constraint conditions;
after the scanning mode is determined, the wave bit number of the search subarea is determined, and the relationship between the residence time and the search frame period is considered when the residence time of the wave beam on each wave bit is set; the detection probability in the subarea of the search array surface also needs to meet the preset detection probability; searching three regions divided by the array surface, and selecting and not overlapping; it should satisfy: n is a radical ofB,itB,i≤Tf,iWherein, Tf,i、NB,i、tB,iRespectively searching frame period, wave digit number and residence time of the searching partition i;
second, search for the detection probability p within partition id,iAnd searching for the cumulative detection probability p within partition iD,iIt is also desirable to satisfy the following equation:
pd,i≥pD,i；
at the same time A, B, C three search area fronts are selected to be constrained to:
Figure FDA0003168760860000033
wherein A isarray、Barray、CarrayA, B, C search area projection fronts respectively;
s32, estimating the joint interception probability and establishing an objective function;
considering the passive joint interception probability of the radar in the time domain-power domain:
Figure FDA0003168760860000041
wherein，PDwellFor probability of interception in the time domain, PDFor the probability of interception in the power domain, Q represents the Marcum Q function, tBRepresenting radar radiation time, TIIndicating the search time of the acquisition receiver, AFDenotes the antenna beam coverage area, DIRepresenting the intercepted receiver density;
for multi-beam scanning, the joint intercept probability is expressed as:
Figure FDA0003168760860000042
the established interception probability objective function is as follows:
Figure FDA0003168760860000043
wherein N isB,nRepresenting the wave bit number of the nth wave beam;
s33, finally obtaining a radio frequency stealth constraint planning model as follows:
min PI(Pt,i,τi,Ki,Si,Np)
Figure FDA0003168760860000044
wherein, Pt,i、τi、Ki、Si、NpThe radar radiation peak power, the pulse width, the sub-array number, the array surface selection form and the pulse accumulation number in the search subarea i are respectively.
5. The method for optimizing target search resources based on hybrid phased array-MIMO radar according to claim 1, wherein the step S4 specifically comprises:
the peak power, the number of subarrays, the pulse width, the pulse accumulation number and the selection form of the array surface are used as optimization parameters, real number coding is adopted, and the optimization parameters are composed of five parametersReal set { P }t,i,τi,Ki,Si,NpForming a candidate solution with a certain population size; according to the target function, the inverse of the pulse accumulation power of the product of the interception probability and the detection probability is used as an adaptive value; according to the size of the fitness value, selecting operation is carried out by a roulette method; in the cross operation, a greedy arithmetic cross operator is adopted, namely two parent candidate solutions F1And F2Generating 4 sub-generation candidate solutions S after cross operation1，S2，S3，S4(ii) a In the mutation operation, determining the mutation scale according to the mutation rate, and randomly mutating each gene value of the solution with the minimum adaptive value in the feasible solutions; and finally, when the fitness value of the optimal individual reaches a given threshold value, or the fitness value of the optimal individual and the population fitness value do not rise any more, or the iteration number reaches a preset algebra, terminating the algorithm.
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