CN108037487A - A kind of distributed MIMO radar emission signal optimum design method stealthy based on radio frequency - Google Patents

A kind of distributed MIMO radar emission signal optimum design method stealthy based on radio frequency Download PDF

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CN108037487A
CN108037487A CN201711155625.5A CN201711155625A CN108037487A CN 108037487 A CN108037487 A CN 108037487A CN 201711155625 A CN201711155625 A CN 201711155625A CN 108037487 A CN108037487 A CN 108037487A
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msub
mtd
mtr
mimo radar
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CN108037487B (en
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时晨光
汪飞
李海林
周建江
夏伟杰
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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
    • 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
    • G01S7/28—Details of pulse systems
    • G01S7/282—Transmitters

Abstract

The invention discloses a kind of distributed MIMO radar emission signal optimum design method stealthy based on radio frequency, including obtaining reflection matrix H of the target relative to radar system, environment clutter is relative to the reflection matrix C of radar system, coloured noise matrix N at radar receiver；Establish based on the stealthy distributed MIMO radar signal mathematical optimization models of radio frequency；Determine optimal Lagrange multiplierWillSubstitute into the optimal transmitting signal that KKT necessary conditions obtain distributed MIMO radarObtain the distributed MIMO radar emission signal with radio frequency Stealth Fighter.A kind of distributed MIMO radar emission signal optimum design method stealthy based on radio frequency of the present invention, from practical application, reduces the total transmission power of distributed MIMO radar system, lifts its radio frequency Stealth Fighter.

Description

A kind of distributed MIMO radar emission signal optimum design method stealthy based on radio frequency
Technical field
It is how defeated more particularly to a kind of distribution stealthy based on radio frequency the present invention relates to radar signal design optimizing Enter multi output (Multiple-Input Multiple-Output, MIMO) radar emission signal optimum design method.
Background technology
Distributed MIMO radar system is a kind of emerging active detection technology, causes lot of domestic and foreign in recent years Person and the great interest of scientific research institution.Each array element spacing is larger in distributed MIMO radar system, can observe from different perspectives Target, obtains larger space diversity gain, can effectively reduce target radar scattering cross-section (Radar Cross Section, RCS the influence brought to system detectio performance, tracking performance etc.) is flickered, spatial resolution, the more preferable target with higher The advantage such as detection performance and more flexible resource management design.
In general, being influenced by radar operating environment, clutter, noise and other various interference letters are contained in radar echo signal Number, and corresponding clutter, noise and interference signal are random distributions.Therefore, distributed MIMO radar system transmitting signal is set The studied emphasis of meter is how to handle signal, clutter and noise (interference), so that radar system performance is optimal.
In fact, distributed MIMO radar emission Design of Signal is not only constrained by system condition, while need in signal Carried out under design criteria.The constraints of system is limited by modern signal processing technology and hardware condition, as energy limits System, bandwidth limitation, time width limitation and permanent mould limitation etc.；And it is all to launch the task of Design of Signal criterion and radar, working environment etc. It is multifactor closely related, for target detection, usually with Signal to Interference plus Noise Ratio (Signal to Interference plus Noise Ratio, SINR), detection probability, detection time, signal and the correlation of clutter etc. be design criteria；It is more for target following It is that the mutual information (Mutual Information, MI) received with tracking error, radar between echo and target is accurate for design Then；For target identification, the MI's between distance measure, target and echo, target impulse response usually between target classification estimates Meter error is design criteria.Therefore, distributed MIMO radar emission Design of Signal process is as follows：It is accurate to establish transmitting Design of Signal Then, and under the criterion optimum waveform is produced, while in the design process, also needs to consider calculation amount to ensure system real time It is required that.
However, with the continuous innovation of passive detection technology, the detection of Passive Detention System and stationkeeping ability constantly strengthen, Distributed MIMO radar in modern battlefield also needs to possess radio frequency stealth capabilities.Radio frequency stealth technology is by controlling active spoke The methods of penetrating emittance, the waveform parameter of system, can significantly reduce active radiating system and be cut by enemy's Passive Detention System Obtain, find, sort, identify, and the probability attacked by antiradiation missile, so as to improve the war of its own and its carrying platform Field viability and penetration ability.Although the above method proposes radar emission signal optimization under clutter, noise and disturbed condition and sets The thought of meter, but these methods do not consider to be distributed mainly to maximize Radar Targets'Detection performance and tracking performance as target Based on the transmitting signal optimization design that radio frequency is stealthy under formula MIMO radar system.Therefore, it is necessary to study based on stealthy point of radio frequency Cloth MIMO radar launches signal optimization design problem.
The content of the invention
Goal of the invention：For environment clutter in practical application and the simultaneous situation of coloured noise, it is proposed that one kind drop The low total transmission power of distributed MIMO radar system, lifts the distribution stealthy based on radio frequency of its radio frequency Stealth Fighter MIMO radar launches signal optimum design method.
Technical solution：A kind of distributed MIMO radar emission signal optimum design method stealthy based on radio frequency, including with Lower step：
(1) obtain target relative to radar system reflection matrix H, environment clutter relative to radar system reflection square Battle array C, coloured noise matrix N at radar receiver；
(2) establish based on the stealthy distributed MIMO radar signal mathematical optimization models of radio frequency；
(3) optimal Lagrange multiplier is determinedWillSubstitute into KKT necessary conditions and obtain the optimal of distributed MIMO radar Launch signal
(4) the distributed MIMO radar emission signal with radio frequency Stealth Fighter is obtained.
Further, distributed MIMO radar is set in the step (1) has M transmitting antenna and N number of reception antenna, Distributed MIMO radar emission signal matrix isWherein, the transmitting signal s of i-th antennaiFor K × 1 n dimensional vector n, K is radar emission signal length, and meets K >=M, K >=N, target relative to radar system reflection matrixZero-mean complex Gaussian random distribution is obeyed, and is metWherein, RHCovariance square is reflected for target Battle array；Environment clutter relative to radar system reflection matrixThe distribution of zero-mean complex Gaussian random vector is obeyed, and it is full FootWherein, RCFor environment clutter covariance matrix；Coloured noise at radar receiverIt is equal to obey zero It is worth multiple Gauss random distribution, and meetsWherein, RNFor coloured noise covariance matrix；Due to distribution Spacing is larger between each radar receiving antenna in MIMO radar system, H, C and N matrix respectively between row independently of each other, and S, N with H, C is unrelated.
Further, the step (2) includes：
(21) radiation parameter and performance of target tracking MI thresholdings γ of distributed MIMO radar system are determinedMIParameter
Demand according to radio frequency Stealth Fighter, it is assumed that radar signal length is K, and meets K >=M, K >=N, and radar receives Coloured noise power is σ at machinen,i, performance of target tracking thresholding γ is calculated according to given MIMI；
(22) according to performance of target tracking MI thresholdings γMI, establish based on the stealthy optimal hair of distributed MIMO radar of radio frequency Signal mathematical model of optimizing design is penetrated, as shown in formula (1)：
In formula, ()HThe conjugate transposition of representing matrix；
According to determinant property, above formula can abbreviation be further：
In formula, IKFor unit diagonal matrix；
(23) mathematical model in step (22) is converted
Using Eigenvalues Decomposition, covariance matrix RH、RC、RNIt can decompose respectively as follows：
In formula, UH、UCAnd UNRespectively unitary matrice, diagonal matrix ΛH=diag [σh,1,…,σh,M], ΛC=diag [σc,1,…,σc,M], ΛN=diag [σn,1,…,σn,M], wherein, σh,i、σc,iAnd σn,iThe feature of respectively corresponding diagonal matrix Value；
Through matrix operation, the mathematical model in step (22) can be converted into：
In formula,For the characteristic value of radar emission signal matrix S.
Further, the step (3) includes：
(31) Lagrange multiplier formula is built
Introduce Lagrange multiplierStructure Lagrange multiplier formula as shown in formula (5)：
(32) design can solve the KKT conditions of Lagrange multiplier formula optimization
To determine the optimal transmitting signal of MIMO Signal with Distributed Transmit AntennasBy in formula (5)Respectively to σs,iWith First-order partial derivative is sought, and is made：
Meet σ at the same times,i>=0 KKT necessary conditions solved with nonlinear optimization, it is as follows：
Wherein, target variable represents the optimal solution of each parameter respectively on all bands " * "；
(33) optimal Lagrange multiplier is determined through iterating to calculateWith the optimal transmitting of distributed MIMO radar system Signal
Further, in the step (33) optimal Lagrange multiplier is obtained by solving formula (7)And willSubstitute into the optimal transmitting signal that KKT necessary conditions obtain distributed MIMO radar systemFor：
In formula,
P*It is a constant, its size depends on MI thresholdings γMI：
Through iterative calculation, it will meet the P of formula (10)*It is worth in substitution formula (8), trying to achieve makes distributed MIMO radar system total One group of transmitting signal of transmission power minimumAs optimal solution, and finally determine that the transmitting signal of MIMO radar system is total Power.
Beneficial effect：The present invention proposes a kind of distributed MIMO radar emission signal optimization stealthy based on radio frequency and sets Meter method, the main task that this method is completed are to be directed to environment clutter and the simultaneous feelings of coloured noise in practical application Condition, on the basis of target, environment clutter reflection matrix and coloured noise matrix exgenvalue is obtained according to priori, with most The transmitting total power signal of smallization distributed MIMO radar system is target, under conditions of certain performance of target tracking is met, Transmitting signal to distributed MIMO radar system carries out adaptive optimal controls.
Compared with prior art, should present invention employs the optimal transmitting signal optimum design method of distributed MIMO radar Method is on the basis of target, environment clutter reflection matrix and coloured noise matrix exgenvalue is obtained, to minimize distribution The transmitting total power signal of MIMO radar system is target, under conditions of certain performance of target tracking is met, establishes and is based on penetrating Frequently stealthy distributed MIMO radar emission signal mathematical optimization models.It not only ensure that distributed MIMO radar system to mesh Target tracking performance, and effectively improve the radio frequency Stealth Fighter of radar system.Distributed MIMO radar system is set to have most Excellent radio frequency Stealth Fighter.
Brief description of the drawings
Fig. 1 is distributed MIMO radar signal optimum design method flow chart；
Fig. 2 is distributed MIMO radar system model；
Fig. 3 is distributed MIMO radar target, clutter and coloured noise characteristic value；
Fig. 4 is distributed MIMO radar emission signal power allocation result；
Fig. 5 is that radar emission general power contrasts under unlike signal optimum design method.
Embodiment
Technical scheme is described in detail with reference to the accompanying drawings and examples.
The present invention proposes a kind of distributed MIMO radar emission signal optimum design method stealthy based on radio frequency, should The main task that method is completed is to be directed to environment clutter and the simultaneous situation of coloured noise in practical application, in basis On the basis of priori obtains target, environment clutter reflection matrix and coloured noise matrix exgenvalue, to minimize distribution The transmitting total power signal of MIMO radar system is target, under conditions of certain performance of target tracking is met, to distribution The transmitting signal of MIMO radar system carries out adaptive optimal controls.
A kind of as shown in Figure 1, distributed MIMO radar emission signal optimization design side stealthy based on radio frequency of the present invention Method, comprises the following steps：
(1) determine target, environment clutter relative to coloured noise square at the reflection matrix and radar receiver of radar system Battle array
A kind of distributed MIMO radar emission signal optimum design method stealthy based on radio frequency proposed by the present invention.It The prioris such as target reflectance signature, environment clutter and receiver coloured noise are make use of, therefore, should first determine that target is opposite Reflection matrix H, environment clutter in distributed MIMO radar system relative to distributed MIMO radar system reflection matrix C And coloured noise matrix N at radar receiver.
It is assumed that distributed MIMO radar system model has M transmitting antenna as shown in Fig. 2, setting distributed MIMO radar With N number of reception antenna.It should be noted that distributed MIMO radar emission signal matrix isIts In, the transmitting signal s of i-th antennaiFor the n dimensional vector n of K × 1, K is radar emission signal length, and meets K >=M, K >=N.Mesh Mark the reflection matrix relative to radar systemZero-mean complex Gaussian random distribution is obeyed, and is met Wherein, RHCovariance matrix is reflected for target.Environment clutter reflection matrixObey zero-mean complex Gaussian random vector point Cloth, and meetWherein, RCFor environment clutter covariance matrix.Coloured noise at radar receiver Zero-mean complex Gaussian random distribution is obeyed, and is metWherein, RNFor coloured noise covariance matrix.Due to dividing Spacing is larger between each radar receiving antenna in cloth MIMO radar system, between H, C and each row of N matrix independently of each other, and S, N is unrelated with H, C.
(2) establish based on the stealthy distributed MIMO radar signal mathematical optimization models of radio frequency
(21) radiation parameter and performance of target tracking MI thresholdings γ of distributed MIMO radar system are determinedMIEtc. parameter
Demand according to radio frequency Stealth Fighter, it is assumed that radar signal length is K, and meets K >=M, K >=N, and radar receives Coloured noise power is σ at machinen,i, performance of target tracking thresholding γ is calculated according to given MIMI。
(22) according to requirement of the distributed MIMO radar system to performance of target tracking, establish based on stealthy point of radio frequency The optimal transmitting signal mathematical model of optimizing design of cloth MIMO radar, as shown in formula (1)：
In formula, ()HThe conjugate transposition of representing matrix；
According to determinant property, above formula can abbreviation be further：
In formula, IKFor unit diagonal matrix；
(23) mathematical model in step (22) is converted
Using Eigenvalues Decomposition, covariance matrix RH、RC、RNIt can decompose respectively as follows：
In formula, UH、UCAnd UNRespectively unitary matrice, diagonal matrix ΛH=diag [σh,1,…,σh,M], ΛC=diag [σc,1,…,σc,M], ΛN=diag [σn,1,…,σn,M], wherein, σh,i、σc,iAnd σn,iThe feature of respectively corresponding diagonal matrix Value；
Through matrix operation, the mathematical model in step (22) can be converted into：
In formula,For the characteristic value of radar emission signal matrix S.
(3) optimal Lagrange multiplier is determined
(31) Lagrange multiplier formula is built
Introduce Lagrange multiplierStructure Lagrange multiplier formula as shown in formula (5)：
(32) design can solve nonlinear equationThe KKT conditions of optimization
To determine the optimal transmitting signal of MIMO Signal with Distributed Transmit AntennasBy in formula (5)Respectively to σs,iWithFirst-order partial derivative is sought, and is made：
Meet σ at the same times,i>=0 Caro need-Kuhn-Tucker condition (Karush-Kuhn- solved with nonlinear optimization Tucker, KKT) necessary condition, it is as follows：
Wherein, target variable represents the optimal solution of each parameter respectively on all bands " * ".
(33) Lagrange multiplier is determined through iterating to calculateWith the optimal transmitting signal of distributed MIMO radar systemRealize nonlinear equationOptimization；
By solving formula (7), optimal Lagrange multiplier is obtainedAnd willSubstitute into KKT necessary conditions and obtain distribution The optimal transmitting signal of formula MIMO radar systemFor：
In formula,
P*It is a constant, its size depends on given MI thresholdings：
Through iterative calculation, it will meet the P of formula (10)*It is worth in substitution formula (8), trying to achieve makes distributed MIMO radar system total One group of transmitting signal of transmission power minimumAs optimal solution, by optimal transmitting signalIn substitution formula (1), i.e., It can obtain the minimum transmitting total power signal of MIMO radar system for meeting constraints.
(4) the distributed MIMO radar emission signal with radio frequency Stealth Fighter is obtained.
Operation principle：
The present invention knows first against environment clutter in practical application and the simultaneous situation of coloured noise according to priori Know, obtain target, the characteristic value of environment clutter reflection matrix and coloured noise matrix；Then, to minimize distributed MIMO Radar emission total power signal is target, under conditions of certain performance of target tracking is met, is established based on stealthy point of radio frequency Cloth MIMO radar launches signal mathematical optimization models, and model is solved by lagrange's method of multipliers.Through iteration meter Calculate, be chosen at and meet under conditions of certain performance of target tracking the signal so that distributed MIMO radar emission general power minimumAs optimal solution, by optimal transmitting signalIn substitution formula (1), you can obtain the minimum hair for meeting constraints Penetrate total power signal.
For environment clutter in practical application and the simultaneous situation of coloured noise, according to priori, obtain target, The characteristic value of environment clutter reflection matrix and coloured noise matrix, is calculated distributed MIMO radar by theory deduction and obtains The MI values obtained.
To minimize distributed MIMO radar emission total power signal as target, meeting certain performance of target tracking Under the conditions of, establish based on the stealthy distributed MIMO radar emission signal mathematical optimization models of radio frequency, and using formula (1) as mesh Scalar functions, solve this problem using lagrange's method of multipliers, through iterative calculation, determine that distributed MIMO radar is each The optimal transmitting signal of transmitting antenna
Simulation result：
Assuming that the parameter in (2) step is as shown in table 1.
1 simulation parameter of table is set
Distributed MIMO radar target, clutter response are with coloured noise characteristic value as shown in figure 3, distributed MIMO radar It is as shown in Figure 4 to launch signal power allocation result.Based on the stealthy distributed MIMO radar emission signal optimization design side of radio frequency Method is to be responded relative to distributed MIMO radar signature according to target, had at environment clutter characteristic response and radar receiver The optimal transmitting signal that coloured noise power calculation obtains.As seen from Figure 4, each transmitting antenna of distributed MIMO radar system Power distribution result is mainly by target with respect to the reflection matrix characteristic value of MIMO radar, clutter reflection matrix characteristic value and coloured Noise matrix characteristic value determines, radar emission signal power mainly distribute to maximum target and clutter response characteristic value it Than the antenna with minimum coloured noise characteristic value.It is distributed in order to be minimized on the premise of certain performance of target tracking is ensured Mimo system launch total power signal, based on the stealthy distributed MIMO radar emission signal optimum design method of radio frequency according to Water-filling carries out power distribution, i.e., with the ratio between maximum target and clutter response characteristic value, minimum coloured noise characteristic value Antenna at distribute most power.
Fig. 5 gives radar emission general power under unlike signal optimum design method and contrasts.As shown in Figure 5, with to mesh The raising of tracking performance requirement is marked, the total emission power of distributed MIMO radar system constantly increases.In addition, optimal radar hair Penetrate the radar emission general power obtained by signal optimum design method and be significantly less than even power distribution Design of Signal method, so that The former radio frequency Stealth Fighter is better than the latter, this is because even power distribution transmitting signal is no any on target It is in the case of the prioris such as characteristic response, clutter characteristic response and radar receiver coloured noise power, radar signal is total Power is evenly distributed to each transmitting antenna, and therefore, it has worse radio frequency Stealth Fighter.
From above-mentioned simulation result, based on the stealthy distributed MIMO radar emission signal optimum design method of radio frequency, Connect obtaining target according to priori relative to the response of distributed MIMO radar signature, environment clutter characteristic response and radar It is right to minimize the transmitting total power signal of distributed MIMO radar system as target on the basis of receipts machine coloured noise power The transmitting signal of distributed MIMO radar system carries out adaptive optimal controls, so as to meet certain performance of target tracking Under the conditions of, effective radio frequency Stealth Fighter for lifting distributed MIMO radar system.

Claims (5)

  1. A kind of 1. distributed MIMO radar emission signal optimum design method stealthy based on radio frequency, it is characterised in that including with Lower step：
    (1) target is obtained relative to the reflection matrix H of radar system, and environment clutter is relative to the reflection matrix C of radar system, thunder Coloured noise matrix N at up to receiver；
    (2) establish based on the stealthy distributed MIMO radar signal mathematical optimization models of radio frequency；
    (3) optimal Lagrange multiplier is determinedWillSubstitute into the optimal transmitting that KKT necessary conditions obtain distributed MIMO radar Signal
    (4) the distributed MIMO radar emission signal with radio frequency Stealth Fighter is obtained.
  2. A kind of 2. distributed MIMO radar emission signal optimization design side stealthy based on radio frequency according to claim 1 Method, it is characterised in that：Distributed MIMO radar is set in the step (1) has M transmitting antenna and N number of reception antenna, distribution Formula MIMO radar launches signal matrixWherein, the transmitting signal s of i-th antennaiTieed up for K × 1 Vector, K is radar emission signal length, and meets K >=M, K >=N, target relative to radar system reflection matrix Zero-mean complex Gaussian random distribution is obeyed, and is metWherein, RHCovariance matrix is reflected for target；Environment is miscellaneous Ripple relative to radar system reflection matrixThe distribution of zero-mean complex Gaussian random vector is obeyed, and is metWherein, RCFor environment clutter covariance matrix；Coloured noise at radar receiverObey zero-mean Multiple Gauss random distribution, and meetWherein, RNFor coloured noise covariance matrix；Due to distributed MIMO thunder Spacing is larger between each radar receiving antenna up in system, and, and S, N are unrelated with H, C between H, C and each row of N matrix independently of each other.
  3. A kind of 3. distributed MIMO radar emission signal optimization design side stealthy based on radio frequency according to claim 1 Method, it is characterised in that the step (2) includes：
    (21) radiation parameter and performance of target tracking MI thresholdings γ of distributed MIMO radar system are determinedMIParameter
    Demand according to radio frequency Stealth Fighter, it is assumed that radar signal length is K, and meets K >=M, K >=N, is had at radar receiver Coloured noise power is σn,i, performance of target tracking thresholding γ is calculated according to given MIMI；
    (22) according to performance of target tracking MI thresholdings γMI, establish based on the optimal transmitting letter of the stealthy distributed MIMO radar of radio frequency Number mathematical model of optimizing design, as shown in formula (1)：
    <mrow> <mfenced open = "" close = "}"> <mtable> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <munder> <mi>min</mi> <mi>S</mi> </munder> <mi>t</mi> <mi>r</mi> <mo>{</mo> <msup> <mi>SS</mi> <mi>H</mi> </msup> <mo>}</mo> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> <mo>:</mo> </mrow> </mtd> <mtd> <mrow> <mi>N</mi> <mo>&amp;CenterDot;</mo> <mo>{</mo> <mi>log</mi> <mo>&amp;lsqb;</mo> <mi>det</mi> <mrow> <mo>(</mo> <msub> <mi>SR</mi> <mi>H</mi> </msub> <msup> <mi>S</mi> <mi>H</mi> </msup> <mo>+</mo> <msub> <mi>SR</mi> <mi>C</mi> </msub> <msup> <mi>S</mi> <mi>H</mi> </msup> <mo>+</mo> <msub> <mi>R</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>-</mo> <mi>log</mi> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <msub> <mi>SR</mi> <mi>C</mi> </msub> <msup> <mi>S</mi> <mi>H</mi> </msup> <mo>+</mo> <msub> <mi>R</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>}</mo> <mo>&amp;GreaterEqual;</mo> <msub> <mi>&amp;gamma;</mi> <mrow> <mi>M</mi> <mi>I</mi> </mrow> </msub> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mi>t</mi> <mi>r</mi> <mo>{</mo> <msup> <mi>SS</mi> <mi>H</mi> </msup> <mo>}</mo> <mo>&amp;GreaterEqual;</mo> <mn>0.</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
    In formula, ()HThe conjugate transposition of representing matrix；
    According to determinant property, above formula can abbreviation be further：
    <mrow> <mfenced open = "" close = "}"> <mtable> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <munder> <mi>min</mi> <mi>S</mi> </munder> <mi>t</mi> <mi>r</mi> <mo>{</mo> <msup> <mi>SS</mi> <mi>H</mi> </msup> <mo>}</mo> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> <mo>:</mo> </mrow> </mtd> <mtd> <mrow> <mi>N</mi> <mo>&amp;CenterDot;</mo> <mo>{</mo> <mi>log</mi> <mo>&amp;lsqb;</mo> <mi>det</mi> <mrow> <mo>(</mo> <msub> <mi>SR</mi> <mi>H</mi> </msub> <msup> <mi>S</mi> <mi>H</mi> </msup> <mo>/</mo> <mo>(</mo> <mrow> <msub> <mi>SR</mi> <mi>C</mi> </msub> <msup> <mi>S</mi> <mi>H</mi> </msup> <mo>+</mo> <msub> <mi>R</mi> <mi>N</mi> </msub> </mrow> <mo>)</mo> <mo>+</mo> <msub> <mi>I</mi> <mi>K</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>}</mo> <mo>&amp;GreaterEqual;</mo> <msub> <mi>&amp;gamma;</mi> <mrow> <mi>M</mi> <mi>I</mi> </mrow> </msub> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mi>t</mi> <mi>r</mi> <mo>{</mo> <msup> <mi>SS</mi> <mi>H</mi> </msup> <mo>}</mo> <mo>&amp;GreaterEqual;</mo> <mn>0.</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
    In formula, IKFor unit diagonal matrix；
    (23) mathematical model in step (22) is converted
    Using Eigenvalues Decomposition, covariance matrix RH、RC、RNIt can decompose respectively as follows：
    <mrow> <mfenced open = "" close = "}"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>H</mi> </msub> <mo>=</mo> <msub> <mi>U</mi> <mi>H</mi> </msub> <msub> <mi>&amp;Lambda;</mi> <mi>H</mi> </msub> <msubsup> <mi>U</mi> <mi>H</mi> <mi>H</mi> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>C</mi> </msub> <mo>=</mo> <msub> <mi>U</mi> <mi>C</mi> </msub> <msub> <mi>&amp;Lambda;</mi> <mi>C</mi> </msub> <msubsup> <mi>U</mi> <mi>C</mi> <mi>H</mi> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mo>=</mo> <msub> <mi>U</mi> <mi>N</mi> </msub> <msub> <mi>&amp;Lambda;</mi> <mi>N</mi> </msub> <msubsup> <mi>U</mi> <mi>N</mi> <mi>H</mi> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
    In formula, UH、UCAnd UNRespectively unitary matrice, diagonal matrix ΛH=diag [σh,1,…,σh,M], ΛC=diag [σc,1,…, σc,M], ΛN=diag [σn,1,…,σn,M], wherein, σh,i、σc,iAnd σn,iThe characteristic value of respectively corresponding diagonal matrix；
    Through matrix operation, the mathematical model in step (22) can be converted into：
    <mrow> <mfenced open = "" close = "}"> <mtable> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <munder> <mi>min</mi> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>s</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> </munder> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>s</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> <mo>:</mo> </mrow> </mtd> <mtd> <mrow> <mi>N</mi> <mo>&amp;CenterDot;</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <mi>log</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>s</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>h</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>s</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&amp;GreaterEqual;</mo> <msub> <mi>&amp;gamma;</mi> <mrow> <mi>M</mi> <mi>I</mi> </mrow> </msub> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>s</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>&amp;GreaterEqual;</mo> <mn>0.</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
    In formula,For the characteristic value of radar emission signal matrix S.
  4. A kind of 4. distributed MIMO radar emission signal optimization design side stealthy based on radio frequency according to claim 1 Method, it is characterised in that the step (3) includes：
    (31) Lagrange multiplier formula is built
    Introduce Lagrange multiplierStructure Lagrange multiplier formula as shown in formula (5)：
    (32) design can solve the KKT conditions of Lagrange multiplier formula optimization
    To determine the optimal transmitting signal of MIMO Signal with Distributed Transmit AntennasBy in formula (5)Respectively to σs,iWithAsk one Rank partial derivative, and make：
    Meet σ at the same times,i>=0 KKT necessary conditions solved with nonlinear optimization, it is as follows：
    Wherein, target variable represents the optimal solution of each parameter respectively on all bands " * "；
    (33) optimal Lagrange multiplier is determined through iterating to calculateWith the optimal transmitting signal of distributed MIMO radar system
  5. A kind of 5. distributed MIMO radar emission signal optimization design side stealthy based on radio frequency according to claim 4 Method, it is characterised in that by solving formula (7) in the step (33), obtain optimal Lagrange multiplierAnd willSubstitute into KKT necessary conditions obtain the optimal transmitting signal of distributed MIMO radar systemFor：
    <mrow> <msubsup> <mi>&amp;sigma;</mi> <mrow> <mi>s</mi> <mo>,</mo> <mi>i</mi> </mrow> <mo>*</mo> </msubsup> <mo>=</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> <mo>&amp;lsqb;</mo> <mn>0</mn> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mi>B</mi> <mo>+</mo> <msqrt> <mrow> <msup> <mi>B</mi> <mn>2</mn> </msup> <mo>-</mo> <mn>4</mn> <mi>A</mi> <mi>C</mi> </mrow> </msqrt> </mrow> <mrow> <mn>2</mn> <mi>A</mi> </mrow> </mfrac> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
    In formula,
    P*It is a constant, its size depends on MI thresholdings γMI：
    <mrow> <mi>N</mi> <mo>&amp;CenterDot;</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msubsup> <mi>&amp;sigma;</mi> <mrow> <mi>s</mi> <mo>,</mo> <mi>i</mi> </mrow> <mo>*</mo> </msubsup> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>h</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <msubsup> <mi>&amp;sigma;</mi> <mrow> <mi>s</mi> <mo>,</mo> <mi>i</mi> </mrow> <mo>*</mo> </msubsup> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&amp;GreaterEqual;</mo> <msub> <mi>&amp;gamma;</mi> <mrow> <mi>M</mi> <mi>I</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
    Through iterative calculation, it will meet the P of formula (10)*It is worth in substitution formula (8), trying to achieve makes distributed MIMO radar system always launch work( One group of transmitting signal of rate minimumAs optimal solution, and finally determine the transmitting total power signal of MIMO radar system.
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