CN106680780A - Radar optimal waveform design method based on radio frequency stealth in frequency spectrum shared environment - Google Patents

Abstract

The present invention discloses a radar optimal waveform design method based on radio frequency stealth in a frequency spectrum shared environment, belonging to the radar design and manufacturing field. The method comprises: obtaining priori knowledge of detection area target frequency response of a radar and communication system and signals of a communication system, and assuming that the echo of the communication signals reflected through the target to the radar can be received and processed by the radar; and establishing an optimal waveform design mathematic model; and employing the Lagrange multiplier method to solve the optimal waveform design mathematic model and performing iterative computation to determine the optimal emission waveform of the radar system. The minimization of the total emission power of the radar is taken as a target, the emission waveform of the radar system is subjected to adaptive optimization design in the conditions of satisfying a certain target parameter estimation performance and the communication system channel capacity so as to ensure the channel capacity and the communication quality of the communication system and allow the radar system to ensure the optimal radio frequency stealth performance in the condition of satisfying a certain target parameter estimation performance.

Description

Based on the radar optimum waveform method for designing that radio frequency is stealthy under frequency spectrum share environment

Technical field

The present invention relates to a kind of radar waveform method for designing, is especially stealthy based on radio frequency under a kind of frequency spectrum share environment Radar optimum waveform method for designing, belong to Radar Design and manufacture field.

Background technology

Radar waveform optimization design is the important means for lifting radar system performance.In the actual frequency response of extension target It is determined that under the conditions of known, current radar waveform optimization design mainly has two methods：One is the optimal detection for target, should Method is by maximizing output Signal to Interference plus Noise Ratio (Signal-to-Interference-plus-Noise Ratio, SINR) by energy Amount is assigned in the most significant pattern of target response, to obtain for the optimum transmitted waveform of preferably detection extension target；Two It is the optimal estimation for target component, the method is by maximizing the mutual trust between radar reception echo and target impulse response Breath (Mutual Information, MI) as much as possible distributes energy between the different mode of target response, to obtain For preferably estimating to extend the optimum transmitted waveform of target.

In recent years, with the fast development of computer technology, communication technology and microwave integrated circuit, increasing sensing Device is incorporated integrated network and is participated in cooperation, and the radar waveform design under spectrum congestion environment has become a rich challenge The study hotspot of property.Traditional solution is to separate to avoid to each other on frequency spectrum by radar and other wireless systems Interfere.However, with radar and sharply increasing for wireless communication system quantity and further expanding for bandwidth of operation, radar Frequency spectrum share state is usually in communication system, therefore, the radar waveform method for designing under frequency spectrum share environment is urgently to be resolved hurrily.

In addition, modern radar battlefield surroundings are increasingly sophisticated, antiradiation missile causes the living environment of radar to have received seriously Threat and challenge.Radio frequency stealth technology can significantly reduce thunder by methods such as control radar emittance, optimization radar waveforms Up to by the detection of passive electronic reconnaissance equipment, the probability for finding, recognizing and attacked by antiradiation missile, so as to improve radar itself And its battlefield viability and fighting efficiency of carrying platform.

Although proposing the thought of radar waveform optimization design in prior art, the target detection of radar system is improve Can be with parameter estimation performance, but these methods are not considered based on the radar waveform optimization design of radio frequency Stealth Fighter.In addition, passing The radar waveform method for designing of system assumes that radar system is separated from each other on frequency spectrum, is independent of each other with communication system, however, In practical application, with the extension sharply increased with bandwidth of operation of radar and wireless communication system quantity, radar and communications system System is usually in frequency spectrum share state, and both sides can produce impact to mutual performance.

The content of the invention

The technical problem to be solved is to overcome prior art defect, there is provided a kind of in actual battlefield is considered In the case that radar and communications system spectrum is shared, radar system waveform total emission power is reduced, lift the radio frequency of radar system The radar optimum waveform method for designing of Stealth Fighter.

It is optimum based on the stealthy radar of radio frequency under the frequency spectrum share environment that the present invention is provided in order to solve above-mentioned technical problem Waveform design method, comprises the steps：

1) radar and communications system search coverage target frequency response H, is obtained_r[k]、H_s[k]、H_e[k] and communication system are believed Number X_sThe priori of [k], and assume that signal of communication Jing target reflections reach the echo of radar and can be received by radar, be processed；

2), according to the calculated thresholding MI of specified MI_min, set up optimum waveform X_rThe mathematical model of [k] design：

In formula,Represent K t easet ofasubcarriers；L_r[k], L_s[k], L_d[k], L_c[k], L_e[k] is respectively Constant, represents the propagation loss of power on k-th carrier wave；t_kRepresent the channel capacity of communication system on k-th carrier wave；P_max,kGeneration The maximum transmission power of radar system on k-th carrier wave of table；Represent the corresponding noise powers of carrier wave k.

3), by formula 1) in mathematical model be converted into：

In formula,

4), formula (2) is solved using lagrange's method of multipliers, and Jing is iterated to calculate, and determines the optimum transmitted wave of radar system Shape | X_r[k]|²。

In the present invention, the step 4) be：

41), Lagrange multiplier λ is introduced₁, λ₂With λ₃, Lagrange multiplier formula is built, respectively to x_k, λ₁, λ₂With λ₃Ask inclined Lead：

42), by order WithMeet x simultaneously_k>=0 Caro need-Kuhn-Tucker condition solved with nonlinear optimization Essential condition, obtain radar system optimum transmitted waveform x_kExpression formula is：

It is a constant, its size depends on MI thresholdings：

Formula (6) will be metIn value substitution formula (5), optimum of make radar system total transmission power minimum one group is tried to achieve Ejected wave shapeAs optimal solution.

The beneficial effects of the present invention is：It is (1), of the invention on the basis of considering that radar and communications system spectrum is shared, Regard the echo that signal of communication Jing target reflections reach radar receiver as useful signal, be to minimize radar total transmission power Target, under conditions of certain target component estimation performance and communication system channel capacity is met, to radar system transmitted waveform Carry out adaptive optimal controls.It had both ensured the channel capacity and communication quality of communication system, also made radar system meet one Guarantee that there is optimum radio frequency Stealth Fighter in the case of the parameter estimation that sets the goal performance.The reason for producing the advantage is the present invention Optimum waveform method for designing is employed, the method regards as the echo that signal of communication Jing target reflections reach radar receiver useful Signal, to minimize radar system total transmission power as target, sets up under conditions of certain systematic function is met and is based on radio frequency Stealthy optimum waveform designs a model.(2), compared with prior art, the present invention not only allows for radar emission waveform to communication The impact of system channel capacity, and ensure that the radio frequency Stealth Fighter of radar system, improve radar system practicality and Safety.

Description of the drawings

Fig. 1 is radar and communications system model under frequency spectrum share；

Fig. 2 is radar optimum waveform design flow diagram；

Fig. 3 is frequency response of the target relative to radar；

Fig. 4 is communication system transmitting signal；

Fig. 5 is designed for the optimum waveform of radar；

Fig. 6 be distinct methods under MI performances with system emission power change curve.

Specific embodiment：

Technical scheme is described in further details below in conjunction with the accompanying drawings.

The present invention, according to priori, obtains target relative first in the case where radar and communications system spectrum is shared In radar and the frequency response and communication system transmitting signal of communication system；Then, signal of communication Jing target reflections are reached into thunder Echo up to receiver regards useful signal as, to minimize radar system total transmission power as target, sets the goal ginseng meeting one Number is estimated under conditions of performance and communication system channel capacity, is set up based on the stealthy radar optimum waveform optimization design mould of radio frequency Type, and model is solved by lagrange's method of multipliers.Jing is iterated to calculate, and is chosen at and is met target component estimation performance bar The minimum radar emission waveform of radar total transmission power is caused under part | X_r[k]|²As optimal solution, by the optimum transmitted wave of radar Shape | X_r[k]|²In substituting into radar optimum waveform mathematical optimization models, you can the radar system for obtaining meeting constraints is minimum total Transmission power.As shown in Fig. 2 it is concretely comprised the following steps：

1st, determine that target frequency is responded and communication system transmitting signal

The present invention is proposed based on the radar optimum waveform method for designing that radio frequency is stealthy under a kind of frequency spectrum share environment, main sharp The signal of communication of radar receiver is reached with Jing target reflections, therefore, should first determine frequency response of the target relative to radar H_r[k], the frequency response H of target relative communication system_s[k]、H_e[k] and communication system transmitting signal X_s[k], and false letter signal Jing target reflections reach the echo of radar and can be received and be processed, radar and communications system model such as Fig. 1 under frequency spectrum share by radar It is shown, in figure, H_tRepresent communications system transmission response, H_dRepresent that communication base station is responded to the propagated of radar.

2nd, the radiation parameter and MI threshold parameters of radar system are determined

According to the demand of radio frequency Stealth Fighter, it is assumed that radar missile waveform maximum sub-carrier number is K, the transmitting of radar Antenna gain and receiving antenna gain are respectively G_t、G_r, communication system antenna gain is G_s, t_kRepresent communication system on k-th carrier wave The channel capacity of system；P_max,kRepresent the maximum transmission power of radar system on k-th carrier wave；Represent that carrier wave k is corresponding to make an uproar Acoustical power.Estimate that performance arranges MI thresholding MI according to specified target component_min。

3rd, the requirement of performance is estimated target component according to radar system, is set up based on stealthy optimum waveform X of radio frequency_r The mathematical model of [k] optimization design, it is as follows：

In formula,Represent K t easet ofasubcarriers；L_r[k], L_s[k], L_d[k], L_c[k], L_e[k] is respectively Constant, represents the propagation loss of power on k-th carrier wave；t_kRepresent the channel capacity of communication system on k-th carrier wave；P_max,kGeneration The maximum transmission power of radar system on k-th carrier wave of table；Represent the corresponding noise powers of carrier wave k.

4th, x is made_k=| | X_r[k]|², Mathematical model (1) is converted into：

In formula, x=[x₁,x₂,…,x_k], d=[d₁,d₂,…,d_k], s.t.：For restrictive condition.

5th, Lagrange multiplier λ is introduced₁, λ₂With λ₃, build Lagrange multiplier formula L (x, λ₁,λ₂,λ₃), and determine satisfaction Target component estimates thresholding MI_minMinimum waveform general powerExpression formula：

In formula, subscript T representing matrixs (vector) transposition.

5th, design can solve nonlinear equation L (x, λ₁,λ₂,λ₃) optimized KKT conditions

To determine radar system optimum transmitted waveform x_k, by L (x, λ in above formula₁,λ₂,λ₃) respectively to x_k, λ₁, λ₂With λ₃Ask inclined Lead, and makeWithMeet x simultaneously_k>=0 Caro need-Kuhn-Tucker condition solved with nonlinear optimization The essential condition of (Karush-Kuhn-Tucker, KKT), as shown in formula (4)：

Wherein, target variable represents respectively the optimal solution of each parameter on all bands " * " in the present embodiment.

6th, nonlinear equation L (x, λ are realized₁,λ₂,λ₃) optimization

By solving formula (4), the sane transmitted waveform x of each radar_kIt is represented by：

It is a constant, its size depends on MI thresholdings：

Jing is iterated to calculate, and will meet formula (6)In value substitution formula (5), trying to achieve makes radar system total transmission power minimum One group of optimum transmitted waveformAs optimal solution, and finally determine the total transmission power of radar system.

Simulation result：Assume that the parameter in the 2nd step is as shown in table 1.

Target relative to radar system frequency response as shown in figure 3, communication system transmitting signal is as shown in Figure 4.It is based on The stealthy radar optimum waveform design result of radio frequency is as shown in Figure 5.Based on the optimum waveform that radio frequency is stealthy under frequency spectrum share environment Method for designing is the optimum transmitted waveform according to obtained by target frequency responds and communicate transmission signal calculating.As shown in Figure 5, radar The waveform transmission power of system is configured and mainly determined relative to the frequency response of radar system and communication transmission signal by target, In assigning process, radar transmission power mainly distributes to the low subcarrier of target frequency response height, communication signal power level.For Ensureing that minimizing radar system on the premise of certain target component estimates performance and communication system channel capacity always launches work( Rate, power distribution is carried out based on the stealthy radar optimum waveform method for designing of radio frequency according to water-filling, i.e., ring in target frequency Most power should be distributed at the minimum corresponding subcarrier of maximum, communication signal power.

Fig. 6 gives the change curve of MI performances under different wave method for designing with radar transmission power.It will be appreciated from fig. 6 that On the premise of certain target component estimation performance and communication system channel capacity is met, signal of communication Jing target reflections are reached The echo of radar receiver regards the optimum waveform method for designing gained transmitted waveform of useful signal as need to be than the optimum ignored Waveform saves more power, this is because the communication transmission signal that Jing target reflections reach radar receiver can be received by radar Machine is received and processed, so as to the target component for lifting radar system estimates performance.And the radio frequency being based on obtained by optimum transmitted waveform Stealth Fighter is substantially better than based on the radio frequency Stealth Fighter obtained by even power distribution transmitted waveform, and this is due to even power point With transmitted waveform be it is any with regard to target frequency respond and communicate transmission signal priori in the case of, by waveform send out Penetrate power to evenly distribute in whole frequency range, therefore, it has worst radio frequency Stealth Fighter.

From above-mentioned simulation result, based on the radar optimum waveform method for designing that radio frequency is stealthy under frequency spectrum share environment, Regard the echo that signal of communication Jing target reflections reach radar receiver as useful signal, be to minimize radar total transmission power Target, to radar emission waveform adaptive optimal controls are carried out, so as to ensure certain target component estimation performance and communication system Under conditions of system channel capacity, the radio frequency Stealth Fighter of system is effectively improved.

Concrete application approach of the present invention is a lot, and the above is only the preferred embodiment of the present invention, it is noted that for For those skilled in the art, under the premise without departing from the principles of the invention, some improvement can also be made, this A little improvement also should be regarded as protection scope of the present invention.

Claims (2)

1. based on the radar optimum waveform method for designing that radio frequency is stealthy under a kind of frequency spectrum share environment, it is characterised in that including as follows Step：

1) radar and communications system search coverage target frequency response H, is obtained_r[k]、H_s[k]、H_e[k] and communication system signal X_s The priori of [k], and assume that signal of communication Jing target reflections reach the echo of radar and can be received by radar, be processed；

2), according to the calculated thresholding MI of specified MI_min, set up optimum waveform X_rThe mathematical model of [k] design：

$\left.\begin{array}{c}\underset{|X_r\[k\]{|}^2,k\∈F_k}{\min }\underset{k=0}{\overset{K-1}{\mathrm{\Σ}}}|X_r\[k\]{|}^2,\\ s.t.:\underset{k=0}{\overset{K-1}{\mathrm{\Σ}}}\log (1+\frac{|X_r\[k\]{|}^2|H_r\[k\]{|}^2{L}_r\[k\]+|X_s\[k\]{|}^2|H_s\[k\]{|}^2{L}_s\[k\]}{|X_s\[k\]{|}^2{L}_d\[k\]+{\mathrm{\σ}}_n^2\[k\]})\≥{\mathrm{MI}}_{\min },\\ \log (1+\frac{|X_s\[k\]{|}^2{L}_c\[k\]}{|X_r\[k\]{|}^2|H_e\[k\]{|}^2{L}_e\[k\]+{\mathrm{\σ}}_n^2\[k\]})\≥t_k,\\ 0\≤|X_r\[k\]{|}^2\≤P_{\max ,k}.\end{array}\right\}---\left(1\right)$

In formula,Represent K t easet ofasubcarriers；L_r[k], L_s[k], L_d[k], L_c[k], L_e[k] is respectively normal Number, represents the propagation loss of power on k-th carrier wave；t_kRepresent the channel capacity of communication system on k-th carrier wave；P_max,kRepresent The maximum transmission power of radar system on k-th carrier wave；Represent the corresponding noise powers of carrier wave k；

3), the mathematical model in formula (1) is converted into：

$\left.\begin{array}{c}\underset{x_k,k\∈F_k}{\min }\underset{k=0}{\overset{K-1}{\mathrm{\Σ}}}{x}_k,\\ s.t.:\underset{k=0}{\overset{K-1}{\mathrm{\Σ}}}\log (1+\frac{x_k}{a_k}+b_k)\≥{\mathrm{MI}}_{\min },\\ 0\≤x\≤d.\end{array}\right\}---\left(2\right)$

In formula, x_k=| X_r[k]|², d_k=min { P_max,k,c_k}；

4), formula (2) is solved using lagrange's method of multipliers, and Jing is iterated to calculate, and determines the optimum transmitted waveform of radar system | X_r [k]|²。

2. based on the radar optimum waveform method for designing that radio frequency is stealthy under frequency spectrum share environment according to claim 1, its It is characterised by the step 4) be：

41), Lagrange multiplier λ is introduced₁, λ₂With λ₃, Lagrange multiplier formula is built, respectively to x_k, λ₁, λ₂With λ₃Seek local derviation：

$L(x,{\mathrm{\λ}}_1,{\mathrm{\λ}}_2,{\mathrm{\λ}}_3)=\underset{k=0}{\overset{K-1}{\Σ}}{x}_k+{\mathrm{\λ}}_1^T(-x)+{\mathrm{\λ}}_2^T(x-d)+{\mathrm{\λ}}_3\[{\mathrm{MI}}_{\min }-\underset{k=0}{\overset{K-1}{\Σ}}log(1+\frac{x_k}{a_k}+b_k)\]---\left(3\right)$

42), by order WithMeet x simultaneously_k>=0 Caro need-Kuhn-Tucker condition solved with nonlinear optimization Essential condition, obtain radar system optimum transmitted waveform x_kExpression formula is：

$x_k^{*}=\left\{\begin{array}{cc}0,& a_k(1+b_k)\&GreaterEqual;{\mathrm{\&lambda;}}_3^{*},\\ {\mathrm{\&lambda;}}_3^{*}-a_k(1+b_k),& {\mathrm{\&lambda;}}_3^{*}-d_k<a_k(1+b_k)<{\mathrm{\&lambda;}}_3^{*},\\ d_k,& a_k(1+b_k)\&le;{\mathrm{\&lambda;}}_3^{*}-d_k.\end{array}\right.---\left(5\right)$

It is a constant, its size depends on MI thresholdings：

$\underset{k=0}{\overset{K-1}{\&Sigma;}}log(1+\frac{x_k^{*}}{a_k}+b_k)\&GreaterEqual;{\mathrm{MI}}_{min}---\left(6\right)$

Formula (6) will be metIn value substitution formula (5), the optimum transmitted wave of make radar system total transmission power minimum one group is tried to achieve ShapeAs optimal solution.