CN105182317A - Resource management method based on search pattern of centralized MIMO radar - Google Patents

Abstract

The invention belongs to the technical field of communication radar, and especially relates to a resource management method based on a search pattern of centralized MIMO radar. Through analyzing each parameter which influences search performance of MIMO radar, a resource management method based on a search pattern of centralized MIMO radar is provided. The method comprises: selecting the number of subarray division, searching frame period, using signal duty ratio and beam-dwell time as controllable parameters, and on the premise of satisfying searching performance requirement of the radar, minimizing radar resource consumption amount. The searching performance of the radar gives consideration to accumulation detection probability of the radial direction of a target, and gives consideration to accumulation detection probability of the tangent direction of the target for the first time. Finally, a genetic algorithm is used to solve the above optimization problem, to obtain search parameter configuration results in specific scenes.

Description

A kind of based on the method for managing resource under centralized MIMO radar search pattern

Technical field

The invention belongs to Radar-Communication technical field, particularly based on the method for managing resource under New System MIMO radar search pattern.

Background technology

In the modern war of comprehensive, multi-level, three-dimensional, in order to tackle increasingly sophisticated, fast changing electromagnetic environment, New System MIMO radar becomes current research emphasis (He Zishu, Han Chunlin, Liu Bo .MIMO Radar concepts and analysis of technical [J] thereof. electronic letters, vol, 2005,33 (12A): 2441-2445.).MIMO radar is by the different waveform of multiple emitting antenna independent transmission, adopts multiple antenna to receive the radar system realizing detection at receiving end.Compared to phased-array radar, the Subarray partition of MIMO radar is more flexible, angular resolution and Parameter Estimation Precision higher, effectively can also suppress multipath clutter simultaneously, to the detectability of Stealthy Target improve (Lv Hui. centralized MIMO radar signal processing method research [D]. Xi'an: Xian Electronics Science and Technology University, 2011).

Spacing according to antenna array is different, MIMO radar is divided into centralized (JianLiandP.Stoica.MIMOradarwithcolocatedantennas, IEEESignalProcessingMagazine, vol.24, no.5, pp.106-114, and distributed (A.M.Haimovich, R.S.Blum, andL.Cimini.MIMOradarwithwidelyseparatedantennas Sep2007.), IEEESignalProcessingMagazine, invitedpublication, vol.25, no.1, pp.116-129, Jan2008.).The running parameter of centralized MIMO radar adds Subarray partition number compared to phased-array radar, and make waveform selection more free, the degree of freedom of resource management is larger.Therefore need to implement effective resource management to it, thus make all kinds of resource by abundant efficiency utilization, better play the performance advantage of MIMO radar.

In resource management under search lighting pattern, Billiam (BillamER.ParameterOptimisationinPhasedArrayRadar [A] .IEEConferenceRadar-92,1992,34-37.) propose the parameter design rule for phased-array radar, namely make radar consumption of natural resource minimum meeting under given tracking initiation performance, and draw there is no the optimum search frame period under high priority loading condition on this basis.Lu Jianbin on the basis of Billiam with tracking initiation distance for objective function have studied the optimization problem of the limited lower search parameter of phased-array radar searching resource, give optimum criterion and the method (Lu Jianbin of search frame period and residence time calculating, Hu Weidong, Yu Wenxian. optimum search performance study [J] when phased-array radar is resource-constrained. systems engineering and electronic technology, 2004,26 (10): 1388-1390.).Zhang Litao etc. are then from concept and system perspective, describe each side problem that search performance optimization is involved in actual applications all sidedly, and propose selection principle and the defining method (Zhang Litao of search parameter, Lee's shield, kingdom is beautiful. phased-array radar search parameter research [J]. and modern radar, 2008,30 (10): 20:25.).Above-mentioned research all launches for phased-array radar, does not study for New System MIMO radar.

At MIMO radar searching resource management aspect, the people such as HanaGodrich take the lead in discussing the problem (AittomakiT of power division in MIMO radar target detection, GodrichH, PoorHV, etal.ResourceallocationfortargetdetectionindistributedMI MOradars [C] //Signals, SystemsandComputers (ASILOMAR), 2011ConferenceRecordoftheFortyFifthAsilomarConferenceon. IEEE, 2011:873-877.).By optimizing the factor such as emissive power, aerial position, make the detection probability of target maximum, but this research is only for distributed MIMO radar.Document (Yang Shaowei, Cheng Ting, He Zi states the stealthy algorithm of radio frequency [J] under .MIMO search lighting pattern. electronics and information journal, 2014,36 (5): 1017-1022.) the radio frequency Stealth Fighter model under MIMO radar search pattern is established, but its target is for optimizing radar radio frequency Stealth Fighter, and does not consider tangential accumulation detection probability.

But present stage is not also to the research of the resource management aspect of centralized MIMO radar.

Summary of the invention

For above-mentioned existing problems or deficiency, the present invention is by analyzing the parameters affecting MIMO radar search performance, propose a kind of based on the method for managing resource under centralized MIMO radar search pattern, namely Subarray partition number, search frame period, signal dutyfactor, wave beam residence time is chosen as controllable parameter, under the prerequisite meeting search lighting performance requirement, minimize radar resource consumption.Wherein search lighting performance not only considers the accumulation detection probability of target radial, and considers the tangential accumulation detection probability of target first.Finally adopt the above-mentioned optimization problem of genetic algorithm for solving, obtain search parameter configuration result in concrete scene.

Based on the method for managing resource under centralized MIMO radar search pattern, comprise the following steps:

Step 1, set up MIMO signal transaction module: for the MIMO radar of transmitting-receiving array location altogether, array is divided into K submatrix, comprise L array element in each submatrix, then array comprises element number of array M=KL altogether.The signal to noise ratio (S/N ratio) deriving radar return signal is

Wherein the peak power of radar individual antenna is P _t, transmitter antenna gain (dBi) is G _t, antenna receiving gain is G _r, the radar cross section (RCS) of target for σ, λ be signal wavelength, N ₀for noise power spectral density, R is the radial distance that target arrives radar, and η is dutycycle, the t of signal _bfor wave beam residence time.

Step 2, calculate tangential accumulation detection probability: make the hunting zone of MIMO radar for [θ ₁, θ ₂], according to the concept of tracking initiation distance, definition tracking initiation angle θ _max,

θ _max＝(θ ₂-θ ₁)Q,Q∈(0,1)(2)

Namely for setting the goal, the angle that target is flown over when the tangential accumulation detection probability of radar reaches accumulative detection probability thresholding.Angle flies over θ _maxthe corresponding time period is [t ₀, t _max].Wherein,

The calculation procedure of tangential integration detection probability is as follows:

A, calculating [t ₀, t _max] in the time period, radar emission search wave beam number: target tangentially flies into region of search and reaches the accumulation detection probability time used for [t ₀, t _max], radar transmitting search wave beam number I=I altogether during this ₁+ I ₂.Wherein,

T ₀moment wave beam Counter Value n _count, n _count∈ [0, I-1] starts counting, until n _count=I-1 circulation is following to be calculated.

B, calculate the residence time of each search wave beam in target and single detection probability.Target flies into region of search t ₀in the moment, angle position is θ ₁, now search for wave beam and be numbered n ₀.

In transmitting n-th _countduring individual search lighting wave beam, beam position scope is

[θ _s1(t ₀),θ _s2(t ₀)]＝[θ ₁+(n _search(t ₀)-1)B _w,θ ₁+n _search(t ₀)B _w](6)

The corresponding search wave beam execution time is

Wherein, search frame period counter for

Search ripple bit number n _searchfor (n _search>=1)

The functional relation of moving target place angle and time is:

Then, the residence time of this search wave beam in target is solved.

Order solve and can try to achieve respectively with judge n-th _countthe irradiation time of individual wave beam with whether existence is occured simultaneously, and occurs simultaneously, represent target and arrived by this beam, the length t of common factor if exist _b' then represent irradiated time span.If t _b' ≠ 0, P _d(t _b')=0.Wherein,

C, the target detection probability of I search wave beam is carried out no-coherence cumulating, obtain target tangentially accumulative detection probability, as shown in Equation 11.

D, make t ₀at [0, T _f] in be uniformly distributed, so, with as tracking initiation moment (t _max>T _f), the average tangential accumulative detection probability of radar to target is:

Optimized model under step 3, structure MIMO radar search pattern:

In one frame, the ratio of search wave beam time used and search frame period describes the resource distribution of system in time domain, signal dutyfactor then describes and searches for energy ezpenditure at every turn, Subarray partition number then describes the consumption of radar hardware resource, and three is added according to respective weight and describes MIMO radar resource consumption as objective function.Meanwhile, MIMO radar will keep search performance, then with target radial accumulation detection probability, target tangential accumulation detection probability is greater than accumulative detection probability threshold value, and it is constraint condition that time resource consumes rationality.Optimized model is

Step 4, the above-mentioned optimization problem of employing genetic algorithm for solving.

By solving the optimizing process of this Optimized model, obtain one group of parameter [K _opt, η _opt, t _bopt, T _fopt], under the prerequisite meeting search performance requirement, consumption of natural resource is minimum.

Principle of work of the present invention is: suppose MIMO radar transmitting-receiving array location altogether, array is divided into K submatrix, comprise L array element in each submatrix, then array comprises element number of array M=KL altogether.Each submatrix launches mutually orthogonal waveform, and transmitting of a kth submatrix is designated as s _kt (), in submatrix, each array element transmitted waveform is identical.So, kth height battle array transmit spatial domain formed composite signal can be expressed as:

Phase differential between each submatrix is φ _l=L φ, then K the sub-battle array composite signal formed in spatial domain that transmits can be expressed as:

Composite signal receives echoed signal by receiving array after target scattering, the loss that transmitting procedure and target scattering cause if ignore, then the signal that m array element receives can be expressed as:

y _m(t)＝x(t)e ^-j(m-1)φ+v _m(t)(16)

Wherein, v _mt () represents the noise of m receiving cable.

The Received signal strength of each receiving cable and all transmitted waveforms are carried out matched filtering, the signal of m receiving cable and s _kt the result of () matched filtering is:

Wherein, v _mkv _m(t) and s _kthe matched filtering result of (t), E _sfor the energy of transmitted waveform.

By the results added of m array element matched filtering, namely carry out equivalent launching beam formation, have:

Finally carry out received beam formation, have:

According to above-mentioned signal processing, can output signal-to-noise ratio be obtained:

If radar emission general power is P _t, transmitter antenna gain (dBi) is G _t, the radar cross section (RCS) of target is σ, G _rincrease for antenna receives, λ is signal wavelength, B _rfor radar receiver equivalent noise bandwidth, N ₀for noise power spectral density.So the signal to noise ratio (S/N ratio) of radar return signal meets:

For MIMO radar, P _t=Mp _t, wherein p _tfor single array element transmitted waveform peak power.Matched filtering and equivalent launching beam form the processing gain τ B brought _r, wherein τ is signal pulsewidth.In addition, multi-pulse accumulation is the common method that system improves signal to noise ratio (S/N ratio), and supposing the system adopts correlative accumulation technology, then through N _pindividual pulse accumulation, signal to noise ratio (S/N ratio) will be promoted to original N _pdoubly.Therefore,

Suppose the controllable parameter of MIMO radar comprise Subarray partition number K, signal dutycycle η, wave beam residence time t _bwith search frame period T _f.First set up the relation between controllable parameter and search lighting performance, build search performance Optimized model.

The parameter of monitor area search mission is designated as (K, η, t _b, T _f).Search frame period describes the resource distribution of system in time domain, and signal dutyfactor then describes and searches for energy ezpenditure at every turn, and Subarray partition number then describes the consumption of radar hardware resource.There is the system of good search performance, under the condition ensureing Radar Task implementation effect, should be minimum in the consumption of its time, energy, hardware resource.Therefore, following formula is adopted to describe objective function, i.e. radar resource consumption:

Wherein, N _brepresent the resident number of wave beam, it is relevant with Subarray partition number.C ₁, c ₂, c ₃be the weighting coefficient of three settings, the degree of concern of value reflection to system time, energy, hardware resource consumption amount.

Under search lighting pattern, resource management is under the condition ensureing radar system normal searching, reduces its resource consumption.Document (A.M.Haimovich, R.S.Blum, andL.Cimini.MIMOradarwithwidelyseparatedantennas, IEEESignalProcessingMagazine, invitedpublication, vol.25, no.1, pp.116-129, Jan2008.) in definition tracking initiation distance (for the distance set the goal when the accumulative detection probability of radar reaches set-point) search lighting performance is described.Here suppose that radar horizon is R _s, target radial velocity of approch is v, and search frame period is T _f, with R _tfor tracking initiation distance, radar to the average radial detection probability of target (Yang Shaowei, Cheng Ting, He Zi state the stealthy algorithm of radio frequency [J] under .MIMO search lighting pattern. electronics and information journal, 2014,36 (5): 1017-1022.) be:

Wherein, represent downward round numbers, Δ r=vT _f, represent target at twice by radial flying distance in the process that shines.P _dcradar correctly can identify the probability of target, P _di(r-i Δ r) represents the detection probability that the single that r-i Δ r place target adjusted the distance by radar is observed, when given false-alarm probability, the relational expression (obeying the target of Swerling-I type fluctuation characteristic) of the detection probability that single is observed and signal to noise ratio (S/N ratio) is as follows:

Visible, after given tracking initiation required distance, radial accumulation detection probability is relevant with all configurable parameters.

But in a practical situation, also need the situation considering that target is tangentially flown.Therefore, the present invention uses for reference the concept of tracking initiation distance, and definition tracking initiation angle is for the angle that target is flown over when the tangential accumulation detection probability of radar reaches set-point that sets the goal.Jointly search performance is described by two parameters.

In the derivation of average tangential accumulation detection probability, suppose that the hunting zone of MIMO radar is for [θ ₁, θ ₂], target is from θ ₁fly to angle θ _s=θ ₁+ θ _maxprocess in expect to be detected.Therefore integration detection probability in the process must reach thresholding.Definition tracking initiation angle is θ _max, θ _max=(θ ₂-θ ₁) Q, Q ∈ (0,1).If it is t that target flies into region ₀in the moment, fly to θ _splace is t _max, existing needs calculates at [t ₀, t _max] integration detection probability in the time, judge whether detection probability is greater than threshold value.Wherein, r _xfor radial distance when target is tangentially flown, v _xfor the tangential flying speed of target.

Target tangentially adds up the principle schematic of detection probability calculating as shown in Figure 1.In Fig. 1, dotted line represents search ripple parallactic angle degree and time relationship in every frame, [(k-1) t _b, kt _b] interior straight-line segment characterizes t _bthe angular range of wave cover in residence time, it equals T for the cycle _fperiodic function.For radar, residence time and the angular range of i-th search wave beam (i>=1) in jth frame (j>=1) search are respectively: [T _f(j-1)+(i-1) t _b, T _f(j-1)+it _b], [B _w(i-1)+θ ₁, B _w(i)+θ ₁].Such as, at [0, t _b] in search beam angular range be [θ ₁, θ ₁+ B _w].Fig. 1 chain lines represents target travel time and angular relationship, and the functional relation of target place angle and time is:

In order to calculate [t ₀, t _max] interior accumulation detection probability, then need to judge whether wave beam is irradiated to target.If the target of being irradiated to, then calculate target how long to stop in this wave beam, obtain the single target detection probability of correlative accumulation, then add up and carry out non-inherent accumulation in this time period internal radiation to the search wave beam number of target and obtain the tangential accumulation detection probability of target.

Finally, the t of known quantity will be thought in above-mentioned analysis ₀at [0, T _f] in be uniformly distributed, t ₀difference, the wave beam numbering searching target is different, and residence time is different.So obtain with as tracking initiation moment (t _max>T _f) the average tangential detection probability of radar to target be

For above-mentioned search procedure, there is following time-constrain:

Its implication is that the time availability sum of all subregion in search procedure is no more than 1.

In sum, the present invention propose MIMO radar search pattern under optimization problem specifically can

Be expressed as:

Accompanying drawing illustrates:

Fig. 1 is the principle schematic that target tangentially adds up detection probability calculating;

Fig. 2 is the configuration result of different tracking initiation apart from lower search frame period;

Fig. 3 is the configuration result of different tracking initiation apart from lower signal dutyfactor;

Fig. 4 is the configuration result of different tracking initiation apart from lower Subarray partition number;

Fig. 5 is the configuration result of different tracking initiation apart from lower wave beam residence time;

Fig. 6 is the resource consumption degree of improvement of different tracking initiation distance MIMO radar relative to phased-array radar;

Fig. 7 is the configuration result of search frame period under different Rx;

Fig. 8 is the configuration result of signal dutyfactor under different Rx;

Fig. 9 is the configuration result of Subarray partition number under different Rx;

Figure 10 is the configuration result of wave beam residence time under different Rx.

Embodiment:

Based on detailed technology scheme of the present invention, to the optimization of MIMO radar by the technical program, while guarantee radar data reduction, the resource consumption of radar can be reduced.

Radar is selected to be the even linear array of M=2048 array element, wavelength X=5.45cm, Boltzmann constant k=1.38 × 10 ^-23j/K, standard temperature T=230K, noise figure F=2, antenna effective area dutycycle η _e=0.5, the total peak power of signal is P _t=10 ⁵w, the operating distance R of radar _s=200km.For Swerling-I type target in emulation, the average RCS of target gets 1m ², false-alarm probability P _fa=10 ^-6, integration detection probability threshold P _d=0.95.The angular range in region is θ ∈ [-40 °, 40 °].Radial velocity v _r=1.5Ma, tangential velocity v _t=1.5Ma.In genetic algorithm, setting population number is 500, and maximum genetic algebra is 300, and crossover probability is 0.7, and mutation probability is 0.05, and generation gap is 0.9.

Objective function weight: c1=0.8, c2=0.1, c3=0.1.The optional parameter collection of Subarray partition number K is that { 1,2,4,8,16,32,64,128,256,512,1024,2048}, dutycycle is η ∈ [0,0.25], wave beam residence time t _b∈ [0,26] ms, search frame period T _f∈ [0,20] s.

Emulation 1, supposes now Rx=30km, Q=0.2, and under different tracking initiation distance, parameter configuration result as Figure 2-Figure 5.

When tracking initiation distance is less, MIMO radar has more cumulative frequency, reduces the requirement to single detection signal-to-noise ratio accordingly.Along with the increase of tracking initiation distance, the division submatrix number of permission diminishes, and signal dutyfactor increases, and residence time increases and search frame period reduces to meet the detection perform requirement improved.But signal dutyfactor, Subarray partition number, wave beam residence time, search frame period restricts mutually, finally makes resources optimization choose rationally.The minimizing of Subarray partition number is conducive to improving single detection probability, but wishes that resource consumption is minimum in objective function simultaneously simultaneously, and therefore fluctuation appears in Subarray partition number.And when Subarray partition number reduces, then allow less residence time can meet detection perform requirement, the two variation tendency is almost consistent, less residence time needs enough large signal dutyfactor that single detection probability is kept, search frame period changes less in whole process, it is subject to radial direction simultaneously, the impact of tangential accumulative detection probability.

In addition, under the parameter configuration of emulation one, contrast MIMO radar and phased-array radar are in system resources consumption amount.Definition energy ezpenditure improves than the difference for phased array resource consumption and MIMO radar resource consumption divided by phased-array radar resource consumption.Simulation result as shown in Figure 6, can find out that the consumed resource of MIMO radar is less than phased-array radar under search pattern.And along with the increase of tracking initiation distance, resource consumption improves than reducing.This is because along with the increase of tracking initiation distance, residence time increases, and Subarray partition number reduces, and the advantage that MIMO radar is brought because of Subarray partition number weakens.

In concrete actual Radar Design parameter request, general given tracking initiation distance, tracking initiation angle requirement, and now unique parameter changed is that target tangentially flies into when monitoring spatial domain and the radial distance Rx of radar in direction.Emulation three is at R _twhen=130km, Q=0.3, solve different R _xlower parameter optimization result.Parameter configuration result is as shown in Fig. 7 to Figure 10.

As can be seen from Fig. 8-10, Subarray partition number is more than or equal to 2 in submatrix number in 90km, is all greater than 4 afterwards.Therefore, search lighting parameter is determined in Rx segmentation: when Rx is less than or equal to 90km, Subarray partition number gets 2, signal dutyfactor 19.5%, wave beam residence time 1ms; When Rx is more than or equal to 90km, Subarray partition number gets 8, and signal dutyfactor is 20.3%, wave beam residence time 2ms.Search frame period is then breakpoint with 50km.

As fully visible, the requirement that the basis of tracking initiation distance increases tracking initiation angle has impact to parametric distribution result, increases tangential accumulation detection probability and describes search lighting performance together and there is its practical significance; And by contrasting with phased-array radar, under same searching requirement, the resource consumption of MIMO radar is less, therefore, this method effectively can reduce the wasting of resources, makes radar system can process search efficiently, and other tasks such as tracking.

Claims (1)

1., based on the method for managing resource under centralized MIMO radar search pattern, comprise the following steps:

Step 1, set up MIMO signal transaction module:

Be total to the MIMO radar of location for transmitting-receiving array, array is divided into K submatrix, comprise L array element in each submatrix, then array comprises element number of array M=KL altogether, and the signal to noise ratio (S/N ratio) deriving radar return signal is

$SNR=\frac{G_t{G}_r{\mathrm{Mp}}_t{\mathrm{\ηt}}_B{\mathrm{\σ\λ}}^2}{{\left(4\mathrm{\π}\right)}^3{N}_0{R}^4}---\left(1\right)$

Wherein the peak power of radar individual antenna is p _t, transmitter antenna gain (dBi) is G _t, antenna receiving gain is G _r, the radar cross section (RCS) of target for σ, λ be signal wavelength, N ₀for noise power spectral density, R is the radial distance that target arrives radar, and η is dutycycle, the t of signal _bfor wave beam residence time;

Step 2, calculate tangential accumulation detection probability:

Make the hunting zone of MIMO radar for [θ ₁, θ ₂], according to the concept of tracking initiation distance, definition tracking initiation angle θ _max,

θ _max＝(θ ₂-θ ₁)Q,Q∈(0,1)(2)

Namely for setting the goal, the angle that target is flown over when the tangential accumulation detection probability of radar reaches accumulative detection probability thresholding; Angle flies over θ _maxthe corresponding time period is [t ₀, t _max], wherein,

$t_{max}=t_0+\frac{{\mathrm{\θ}}_{\max }{R}_x}{v_x};$

The calculation procedure of tangential integration detection probability is as follows:

A, calculating [t ₀, t _max] in the time period, radar emission search wave beam number: target tangentially flies into region of search and reaches the accumulation detection probability time used for [t ₀, t _max], radar transmitting search wave beam number I=I altogether during this ₁+ I ₂, wherein,

$I_2=min\[\frac{\mathrm{mod}\left(\frac{(t_{max}-t_0)}{T_f}\right)*T_f}{t_B},N_B\]---\left(4\right)$

T ₀moment wave beam Counter Value n _count, n _count∈ [0, I-1] starts counting, until n _count=I-1 circulation is following to be calculated;

B, calculate the residence time of each search wave beam in target and single detection probability, target flies into region of search t ₀in the moment, angle position is θ ₁, now search for wave beam and be numbered n ₀,

In transmitting n-th _countduring individual search lighting wave beam, beam position scope is

[θ _s1(t ₀),θ _s2(t ₀)]＝[θ ₁+(n _search(t ₀)-1)B _w,θ ₁+n _search(t ₀)B _w](6)

The corresponding search wave beam execution time is

$\begin{array}{c}\[t_{s1}\left(t_0\right),t_{s2}\left(t_0\right)\]=\\ \[\left(n_{T_f}\left(t_0\right)-1\right)T_f+\left(n_{search}\left(t_0\right)-1\right)t_B,\left(n_{T_f}\left(t_0\right)-1\right)T_f+n_{search}\left(t_0\right)t_B\]\end{array}---\left(7\right)$

Wherein, search frame period counter for

Search ripple bit number n _searchfor (n _search>=1)

$n_{search}\left(t_0\right)=\left\{\begin{array}{c}\mathrm{mod}\left(\frac{n_0\left(t_0\right)+n_{count}}{N_B}\right),n_0+n_{count}\≠{\mathrm{kN}}_B,k=1,2,\mathrm{...}\\ N_B,n_0\left(t_0\right)+n_{count}={\mathrm{kN}}_B,k=1,2,\mathrm{..}\end{array}\right.---\left(9\right)$

The functional relation of moving target place angle and time is:

${\mathrm{\θ}}_t\left(t\right)=\frac{v_x(t-t_0)}{r_x}+{\mathrm{\θ}}_1---\left(10\right)$

Then, the residence time of this search wave beam in target is solved;

Order ${\mathrm{\θ}}_{s_1}\left(t_0\right)=\frac{v({\tilde{t}}_1-t_0)}{r}+{\mathrm{\θ}}_1,{\mathrm{\θ}}_{s_2}\left(t_0\right)=\frac{v({\tilde{t}}_2-t_0)}{r}+{\mathrm{\θ}}_1,$ Solve and can try to achieve respectively with judge n-th _countthe irradiation time of individual wave beam with whether existence is occured simultaneously, and occurs simultaneously, represent target and arrived by this beam, the length t of common factor if exist _b' then represent irradiated time span, if t _b' ≠ 0, P _d(t _b')=0.Wherein,

C, the target detection probability of I search wave beam is carried out no-coherence cumulating, obtains target tangentially accumulative detection probability,

$\underset{n_{count}=1}{\overset{I}{\Π}}\[1-P_{dc}\·P_d\left({t_B}^{\′}\left(t_0\right),n_{count}\right)\]---\left(11\right);$

D, make t ₀at [0, T _f] in be uniformly distributed, so, with as tracking initiation moment (t _max>T _f), the average tangential accumulative detection probability of radar to target is:

$P_d\left({\mathrm{\θ}}_{max}\right)=\frac{1}{T_f}{\∫}_0^{T_f}\left\{1-\underset{n_{count}=1}{\overset{I}{\Π}}\[1-P_{dc}\·P_d\left({t_B}^{\′}\left(t\right),n_{count}\right)\]\right\}dt---\left(12\right);$

Optimized model under step 3, structure MIMO radar search pattern:

In one frame, the ratio of search wave beam time used and search frame period describes the resource distribution of system in time domain, signal dutyfactor then describes and searches for energy ezpenditure at every turn, Subarray partition number then describes the consumption of radar hardware resource, three is added according to respective weight and describes MIMO radar resource consumption as objective function, simultaneously, MIMO radar will keep search performance, then with target radial accumulation detection probability, target tangential accumulation detection probability is greater than accumulative detection probability threshold value, it is constraint condition that time resource consumes rationality, and Optimized model is

$\underset{\left(K,\mathrm{\η},t_B,T_f\right)}{\min }{c}_1\frac{t_B{N}_B}{T_f}+c_2\mathrm{\η}+c_3\frac{K}{M}$

$s.t.\left\{\begin{array}{c}{P}_d\left(R_t\right)\≥P_D\\ P_d\left({\mathrm{\θ}}_{\max }\right)\≥P_D\\ \frac{N_B{t}_B}{T_f}\≤1\end{array}\right.---\left(13\right)$

Step 4, the above-mentioned optimization problem of employing genetic algorithm for solving:

By solving the optimizing process of this Optimized model, obtain one group of parameter [K _opt, η _opt, t _bopt, T _fopt], under the prerequisite meeting search performance requirement, consumption of natural resource is minimum.