CN100523865C - Range multi-aperture wide-swath synthetic aperture radar design method - Google Patents

Abstract

The design for distance to multi aperture receiving width measuring band synthetic aperture radar provides its optimal signal to noise ratio design principle, with theta0 being the center angle of the measuring band inner wave beam, r0 the corresponding slant distance of the wave beam center line, C being the optical speed, RE being the radius of the local earth, H synthetic aperture radar platform height, Fr pulse repeated frequency, D sub antenna distance oriented space, lambada wavelength, N measuring band number. It solves the conflict of the directional resolution and measuring bandwidth.

Description

Determine the method for range multi-aperture wide-swath synthetic aperture radar sub antenna spacing

Technical field

The present invention relates to the aerial survey technical field, particularly a kind of method for designing of range multi-aperture wide-swath synthetic aperture radar signal to noise ratio (S/N ratio).

Background technology

The wide swath synthetic aperture radar (SAR) is the hot issue of current synthetic-aperture radar research field, in needing many application such as global observation and the observation of high repetition period urgent demand is arranged.But the ultimate principle of conventional synthetic-aperture radar has determined that mapping bandwidth and orientation are a pair of conflicting restriction variablees between resolution, improve the orientation and will reduce the mapping bandwidth to resolution, improve the mapping bandwidth and will reduce the orientation to resolution, both can't improve simultaneously.

In order to solve the contradiction of orientation to resolution and mapping bandwidth, Chinese scholars has proposed the synthetic-aperture radar system of some wide swaths successively.The mapping method of range multi-aperture wide-swath synthetic aperture radar is the method that wherein a kind of complexity is low, signal to noise ratio (S/N ratio) is high, has very strong application prospect.Because the Analysis signal-to-noise ratio (SNR) of this method is very complicated, involves many non-linear variablees, just qualitatively the signal to noise ratio (S/N ratio) of system is analyzed in the research in the past, can't provide the optiaml ciriterion of signal to noise ratio (S/N ratio) design, has so just hindered the further application of this method.

Summary of the invention

The purpose of this invention is to provide a kind of method for designing that reaches range multi-aperture wide-swath synthetic aperture radar signal to noise ratio (S/N ratio), this method utilizes signal to noise ratio (S/N ratio) devise optimum criterion formulas to calculate distance to the sub antenna spacing, solved the contradiction of orientation, and this method is simply clear and definite to resolution and mapping bandwidth.

For achieving the above object, technical solution of the present invention is a kind of method of definite range multi-aperture wide-swath synthetic aperture radar sub antenna spacing, it provides the optimum signal to noise ratio (S/N ratio) design criteria of range multi-aperture wide-swath synthetic aperture radar method, that is:

$\cos ({\mathrm{\θ}}_0-\mathrm{\β})\frac{\cos {\mathrm{\θ}}_0(H+R_E)-r_0}{r_0(H+R_E)\sin {\mathrm{\θ}}_0}\frac{c}{{2F}_r}\frac{D}{\mathrm{\λ}}=\frac{1}{N}$

Wherein, θ ₀Be beam center visual angle in the mapping band, r ₀Be the oblique distance of beam central line correspondence, c is the light velocity, R _EBe local earth radius, H is the synthetic-aperture radar podium level, F _rBe pulse repetition rate, D be sub antenna distance to spacing, λ is a wavelength, N is the sub-swaths number.

Described method for designing, it at first determines mapping band scope, sub-swaths number and index of correlation according to application requirements, determines the sub antenna spacing according to optimum signal to noise ratio (S/N ratio) design criteria formula again.

Described method for designing comprises the following steps:

A) determine pulse repetition rate F according to the orientation to resolution requirement _r

B) determine sub-swaths width and sub-swaths number N according to pulse repetition rate;

C) divide sub-swaths according to sub-swaths width, mapping band position and width requirement;

D) determine the beam center view angle theta according to mapping band position and width ₀And corresponding oblique distance r ₀

E) according to optimum signal to noise ratio (S/N ratio) design criteria formula computed range to the sub antenna space D.

Description of drawings

Fig. 1 distance is to multiple aperture theory of SAR synoptic diagram;

The geometric relationship figure of Fig. 2 target, synthetic aperture radar antenna;

Fig. 3 the present invention distance receives the process flow diagram of wideband synthetic aperture radar method for designing to multiple aperture.

Embodiment

The antenna of general synthetic-aperture radar is that transmitting-receiving is multiplexing, can not receive data during transponder pulse.For conventional synthetic-aperture radar, require echo between the twice emitting pulse, to get back to antenna, so the oblique distance scope in the mapping band is:

$(\frac{n}{F_r}+\mathrm{\&tau;})\frac{c}{2}<R<(\frac{n+1}{F_r}-\mathrm{\&tau;})\frac{c}{2}---\left(1\right)$

Wherein τ is the duration of pulse, F _rBe pulse repetition rate, c is the light velocity, and n is a certain integer.So maximum in theory mapping bandwidth is

$R_M=(\frac{1}{F_r}-2\mathrm{\&tau;})\frac{c}{2}---\left(2\right)$

F _rBe exactly the orientation to sampling rate, it must be greater than the orientation to bandwidth, and the orientation has determined the orientation to resolution to bandwidth, the pass between them is:

$\frac{v}{F_r}<\mathrm{\&sigma;}---\left(3\right)$

Wherein σ be the orientation to the resolution element size, so

$R_M<\frac{\mathrm{c\&sigma;}}{2v}-\mathrm{\&tau;c}---\left(4\right)$

Survey and draw bandwidth as can be seen and the orientation is a pair of contradiction to resolution from (4) formula.Improve mapping bandwidth R _MJust must increase the orientation to resolution element size σ, just reduce the orientation to resolution.

There are some scholars to propose some wide swath synthetic aperture radar (SAR) methods after the nineties in last century successively and solve mapping bandwidth and orientation contradiction to resolution, the wide swath method that multiple aperture receives is compared system with additive method relative simple, can in expansion mapping band, keep high resolving power, it is little to crosstalk between the sub-swaths, signal to noise ratio (S/N ratio) is higher, is a kind of application prospect wide swath synthetic aperture radar (SAR) method preferably.The ultimate principle of this method is as shown in Figure 1:

Antenna upwards is divided into N sub antenna, each sub antenna space D in distance.During emission with a beam transmission, the oblique distance scope of irradiation:

$(\frac{n}{F_r}+\mathrm{\&tau;})\frac{c}{2}<R<(\frac{n+N}{F_r}-\mathrm{\&tau;})\frac{c}{2},$ N is a certain integer (5)

Comprising N sub-swaths, their scope is:

$(\frac{n+i}{F_r}+\mathrm{\&tau;})\frac{c}{2}<R_i<(\frac{n+1+i}{F_r}-\mathrm{\&tau;})\frac{c}{2},0\&le;i\&le;N-1---\left(6\right)$

Receive respectively with N sub antenna during reception.Remember that this N sub antenna is A ₀, A ₁..., A _N-1

Obviously, the echo of this N sub-swaths can arrive antenna simultaneously, pulse before n the cycle of the 1st sub-swaths reflection just, the pulse before n+1 the cycle of the 2nd sub-swaths reflection ... the pulse echo before n+N-1 the cycle of N sub-swaths reflection arrives antenna simultaneously.The distance of conventional synthetic-aperture radar that Here it is is to fuzzy problem, if can extract the restriction that each sub-swaths signal just can be broken through (4) formula from aliasing signal.

Each sub antenna is also carried out distance with same distance after pulse compression to matched filter with same local oscillator demodulation, carry out synchronized sampling,, can be similar to and think that oblique distance is respectively τ sampled value constantly

,

The aliasing signal of terrain object signal.Because this N terrain object is different with the angle of antenna normal to the line of antenna, so this N terrain object signal can produce different phase shifts at each aerial panel.The angle (leave antenna normal up for be to bear just, down) of remembering this N point and the line of antenna and antenna normal is respectively α ₀(τ), α ₁(τ) ..., α _N-1(τ).Make the angle of α (r), then can draw according to target and antenna relative position (as shown in Figure 2) for the target visual angle of oblique distance r and antenna normal

$\mathrm{\&alpha;}\left(r\right)=\arccos \left[\frac{r^2+H^2+{2\mathrm{HR}}_E}{2r\&CenterDot;(H+R_E)}\right]-\mathrm{\&beta;}---\left(7\right)$

β be synthetic-aperture radar to the line in the earth's core and the normal angle of synthetic aperture radar antenna panel, H is the height of synthetic-aperture radar, R _EBe earth radius.

So ${\mathrm{\&alpha;}}_i\left(\mathrm{\&tau;}\right)=\mathrm{\&alpha;}\left[\frac{c}{2}(\mathrm{\&tau;}+\frac{n+i}{F_r})\right].$

Such the 1st point is at A ₀, A ₁..., A _N-1On phase shift be respectively

The 2nd point is at A ₀, A ₁..., A _N-1On phase shift be respectively

Other point is at A ₀, A ₁..., A _N-1On phase shift can similarly write out.As long as this N group phase shift linear independence just can utilize the different phase shift of this N group to extract the signal of this N point in the signal of aliasing.

Being write as matrix form is

F(τ)＝W(τ)σ(τ) (8)

F (τ)=[f wherein ₀(τ), f ₁(τ) ..., f _N-1(τ)] ^TBe the sampled value of each data channel, σ (τ)=[σ ₀(τ), σ ₁(τ) ..., σ _N-1(τ)] ^TFor oblique distance is respectively

...,

The complex reflection coefficient of terrain object.

As long as W (τ) is reversible, the echoed signal of each sub-swaths just can be separated by following formula from aliasing signal F (τ):

σ(τ)＝W ^-1(τ)F(τ) (10)

The anti-processing that solves behind each sub-swaths signal is just the same with conventional synthetic-aperture radar.Suppose that the counter noise average power of separating preceding each receiving cable of signal all is P _n, and it is uncorrelated mutually, be respectively and be δ ₀(τ), δ ₁(τ) ..., δ _N-1(τ), the noise after counter the separating is

Like this

δ′(τ)＝W ^-1(τ)δ(τ) (11)

Wherein $\mathrm{\&delta;}\&prime;\left(\mathrm{\&tau;}\right)={[{\mathrm{\&delta;}}_0^{\&prime;}\left(\mathrm{\&tau;}\right),{\mathrm{\&delta;}}_1^{\&prime;}\left(\mathrm{\&tau;}\right),\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&delta;}}_{N-1}^{\&prime;}\left(\mathrm{\&tau;}\right)]}^T,$ δ(τ)＝[δ ₀(τ)，δ ₁(τ)，…，δ _N-1(τ)] ^T

According to the method for inverting of Vandermonde, for matrix

Inverse matrix A ^-1Each element be

$A_{m,n}^{-1}=\frac{b_{m,n}}{\underset{k=0,k\&NotEqual;m}{\overset{N-1}{\mathrm{\&Pi;}}}(x_m-x_k)}---\left(13\right)$

B wherein _{M, n}Be following polynomial coefficient

$Y_m\left(x\right)=\underset{k=0,k\&NotEqual;m}{\overset{N-1}{\mathrm{\&Pi;}}}(x-x_k)=\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{b}_{m,n}{x}^n---\left(14\right)$

As long as order $x_k=\exp \left[j\frac{2\mathrm{\&pi;}D\sin {\mathrm{\&alpha;}}_k\left(\mathrm{\&tau;}\right)}{\mathrm{\&lambda;}}\right],$ Substitution (13) formula just can compute matrix W inverse matrix.

According to the Parseval theorem

$\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{\left|b_{m,n}\right|}^2=\frac{1}{N}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{\left|B_{m,n}\right|}^2=\frac{1}{N}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{\left|Y_m\left[\exp \left(j\frac{2\mathrm{\&pi;n}}{N}\right)\right]\right|}^2$

$=\frac{1}{N}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{\left|\underset{k=0,k\&NotEqual;m}{\overset{N-1}{\mathrm{\&Pi;}}}[\exp \left(j\frac{2\mathrm{\&pi;n}}{N}\right)-x_k]\right|}^2$

(17)

$=\frac{1}{N}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\underset{k=0,k\&NotEqual;m}{\overset{N-1}{\mathrm{\&Pi;}}}{\left|\{\exp \left(j\frac{2\mathrm{\&pi;n}}{N}\right)-\exp \left[j\frac{2\mathrm{\&pi;}D\sin {\mathrm{\&alpha;}}_k\left(\mathrm{\&tau;}\right)}{\mathrm{\&lambda;}}\right]\}\right|}^2$

$=\frac{4^{N-1}}{N}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\underset{k=0,k\&NotEqual;m}{\overset{N-1}{\mathrm{\&Pi;}}}{\sin }^2[\frac{\mathrm{\&pi;n}}{N}-\frac{\mathrm{\&pi;}D\sin {\mathrm{\&alpha;}}_k\left(\mathrm{\&tau;}\right)}{\mathrm{\&lambda;}}]$

Like this

$\mathrm{\&rho;}\left(m\right)=\frac{\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\underset{k=0,k\&NotEqual;m}{\overset{N-1}{\mathrm{\&Pi;}}}{\sin }^2[\frac{\mathrm{n\&pi;}}{N}-\frac{\mathrm{\&pi;}D\sin {\mathrm{\&alpha;}}_k\left(\mathrm{\&tau;}\right)}{\mathrm{\&lambda;}}]}{N\underset{k=0,k\&NotEqual;m}{\overset{N-1}{\mathrm{\&Pi;}}}{\sin }^2[\frac{\mathrm{\&pi;}D\sin {\mathrm{\&alpha;}}_m\left(\mathrm{\&tau;}\right)}{\mathrm{\&lambda;}}-\frac{\mathrm{\&pi;}D\sin {\mathrm{\&alpha;}}_k\left(\mathrm{\&tau;}\right)}{\mathrm{\&lambda;}}]}---\left(18\right)$

Can prove

Wherein

Be arbitrary sequence of values, ψ is arbitrary constant.

Order like this $\mathrm{\&psi;}=\frac{\mathrm{\&pi;}D\sin {\mathrm{\&alpha;}}_m\left(\mathrm{\&tau;}\right)}{\mathrm{\&lambda;}},$ Just can obtain

$\mathrm{\&rho;}\left(m\right)=\frac{\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\underset{k=0,k\&NotEqual;m}{\overset{N-1}{\mathrm{\&Pi;}}}{\sin }^2[\frac{\mathrm{n\&pi;}}{N}-\frac{\mathrm{\&pi;}D\sin {\mathrm{\&alpha;}}_k\left(\mathrm{\&tau;}\right)}{\mathrm{\&lambda;}}]}{N\underset{k=0,k\&NotEqual;m}{\overset{N-1}{\mathrm{\&Pi;}}}{\sin }^2[\frac{\mathrm{\&pi;}D\sin {\mathrm{\&alpha;}}_m\left(\mathrm{\&tau;}\right)}{\mathrm{\&lambda;}}-\frac{\mathrm{\&pi;}D\sin {\mathrm{\&alpha;}}_k\left(\mathrm{\&tau;}\right)}{\mathrm{\&lambda;}}]}$

$=\frac{\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\underset{k=0,k\&NotEqual;m}{\overset{N-1}{\mathrm{\&Pi;}}}{\sin }^2[\frac{\mathrm{n\&pi;}}{N}+\frac{\mathrm{\&pi;}D\sin {\mathrm{\&alpha;}}_m\left(\mathrm{\&tau;}\right)}{\mathrm{\&lambda;}}-\frac{\mathrm{\&pi;}D\sin {\mathrm{\&alpha;}}_k\left(\mathrm{\&tau;}\right)}{\mathrm{\&lambda;}}]}{N\underset{k=0,k\&NotEqual;m}{\overset{N-1}{\mathrm{\&Pi;}}}{\sin }^2[\frac{\mathrm{\&pi;}D\sin {\mathrm{\&alpha;}}_m\left(\mathrm{\&tau;}\right)}{\mathrm{\&lambda;}}-\frac{\mathrm{\&pi;}D\sin {\mathrm{\&alpha;}}_k\left(\mathrm{\&tau;}\right)}{\mathrm{\&lambda;}}]}---\left(20\right)$

$=\frac{1}{N}+\frac{\underset{n=1}{\overset{N-1}{\mathrm{\&Sigma;}}}\underset{k=0,k\&NotEqual;m}{\overset{N-1}{\mathrm{\&Pi;}}}{\sin }^2[\frac{\mathrm{n\&pi;}}{N}+\frac{\mathrm{\&pi;}D\sin {\mathrm{\&alpha;}}_m\left(\mathrm{\&tau;}\right)}{\mathrm{\&lambda;}}-\frac{\mathrm{\&pi;}D\sin {\mathrm{\&alpha;}}_k\left(\mathrm{\&tau;}\right)}{\mathrm{\&lambda;}}]}{N\underset{k=0,k\&NotEqual;m}{\overset{N-1}{\mathrm{\&Pi;}}}{\sin }^2[\frac{\mathrm{\&pi;}D\sin {\mathrm{\&alpha;}}_m\left(\mathrm{\&tau;}\right)}{\mathrm{\&lambda;}}-\frac{\mathrm{\&pi;}D\sin {\mathrm{\&alpha;}}_k\left(\mathrm{\&tau;}\right)}{\mathrm{\&lambda;}}]}\&GreaterEqual;\frac{1}{N}$

From (20) formula is counter as can be seen separate computing after, counter separate calculating after, each sub-swaths signal can rise to signal to noise ratio (S/N ratio) original N at most doubly.

If the beam center visual angle is θ in the mapping band ₀, the oblique distance of beam central line correspondence is r ₀, to sin α (r) at r=r ₀Place's Taylor expansion is also ignored the above item of second order, can get

$\sin \mathrm{\&alpha;}\left(r\right)\&ap;\sin ({\mathrm{\&theta;}}_0-\mathrm{\&beta;})+\cos ({\mathrm{\&theta;}}_0-\mathrm{\&beta;})\frac{\cos {\mathrm{\&theta;}}_0(H+R_E)-r_0}{r_0(H+R_E)\sin {\mathrm{\&theta;}}_0}(r-r_0)---\left(21\right)$

With (21) formula substitution (20) Shi Kede

$\mathrm{\&rho;}\left(m\right)\&ap;\frac{1}{N}+\frac{\underset{n=1}{\overset{N-1}{\mathrm{\&Sigma;}}}\underset{k=0,k\&NotEqual;m}{\overset{N-1}{\mathrm{\&Pi;}}}{\sin }^2[\frac{\mathrm{n\&pi;}}{N}+(m-k)\mathrm{\&xi;\&pi;}]}{N\underset{k=0,k\&NotEqual;m}{\overset{N-1}{\mathrm{\&Pi;}}}{\sin }^2\left[(m-k)\mathrm{\&xi;\&pi;}\right]}---\left(22\right)$

Wherein $\mathrm{\&xi;}=\cos ({\mathrm{\&theta;}}_0-\mathrm{\&beta;})\frac{\cos {\mathrm{\&theta;}}_0(H+R_E)-r_0}{r_0(H+R_E)\sin {\mathrm{\&theta;}}_0}\frac{c}{{2F}_r}\frac{D}{\mathrm{\&lambda;}},$ Can prove and find out to have only and work as

$\mathrm{\&xi;}=\frac{i}{N},$ I=kN+j, k are arbitrary positive integer, 1≤j≤N-1, and j and N are relatively prime

ρ (m) just can reach minimum value

But (22) formula is a first approximation, can amplify being similar to error if ξ is big more, so we should select the minimal solution of ξ, just

$\mathrm{\&xi;}=\cos ({\mathrm{\&theta;}}_0-\mathrm{\&beta;})\frac{\cos {\mathrm{\&theta;}}_0(H+R_E)-r_0}{r_0(H+R_E)\sin {\mathrm{\&theta;}}_0}\frac{c}{{2F}_r}\frac{D}{\mathrm{\&lambda;}}=\frac{1}{N}---\left(23\right)$

Here it is realizes the constraint criterion between the systematic parameter in the range multi-aperture wide-swath synthetic aperture radar system signal to noise ratio (S/N ratio) optimal design.

Through above-mentioned known formula or the law of utilizing, after the rigorous derivation, drawn the signal to noise ratio (S/N ratio) quantitative analysis method of range multi-aperture wide-swath synthetic aperture radar mapping method, provided the signal to noise ratio (S/N ratio) optimal design formula of this method:

$\cos ({\mathrm{\&theta;}}_0-\mathrm{\&beta;})\frac{\cos {\mathrm{\&theta;}}_0(H+R_E)-r_0}{r_0(H+R_E)\sin {\mathrm{\&theta;}}_0}\frac{c}{{2F}_r}\frac{D}{\mathrm{\&lambda;}}=\frac{1}{N}---\left(24\right)$

θ wherein ₀Be beam center visual angle in the mapping band, r ₀Be the oblique distance of beam central line correspondence, c is the light velocity, R _EBe local earth radius, H is the synthetic-aperture radar podium level, F _rBe pulse repetition rate, D be sub antenna distance to spacing, λ is a wavelength, N is the sub-swaths number.

After this optimal design formula had been arranged, we just can provide signal to noise ratio (S/N ratio) optimal design step, as shown in Figure 3, comprising:

5) determine pulse repetition rate F according to the orientation to resolution requirement _r

6) determine sub-swaths width and sub-swaths number N according to pulse repetition rate.

7) divide sub-swaths according to sub-swaths width, mapping band position and width requirement.

8) determine the beam center view angle theta according to mapping band position and width ₀And corresponding oblique distance r ₀

5) according to optimum signal to noise ratio (S/N ratio) design criteria computed range to the sub antenna space D.

Claims (1)

1. the method for a definite range multi-aperture wide-swath synthetic aperture radar sub antenna spacing is characterized in that, provides the optimum signal to noise ratio (S/N ratio) design criteria of range multi-aperture wide-swath synthetic aperture radar method, that is:

$\cos ({\mathrm{\&theta;}}_0-\mathrm{\&beta;})\frac{\cos {\mathrm{\&theta;}}_0(H+R_E)-r_0}{r_0(H+R_E)\sin {\mathrm{\&theta;}}_0}\frac{c}{2F_r}\frac{D}{\mathrm{\&lambda;}}=\frac{1}{N}$

Wherein, θ ₀Be beam center visual angle in the mapping band, r ₀Be the oblique distance of beam central line correspondence, c is the light velocity, R _EBe local earth radius, H is the synthetic-aperture radar podium level, F _rBe pulse repetition rate, D be sub antenna distance to spacing, λ is a wavelength, N is the sub-swaths number, β is that synthetic-aperture radar is to the line in the earth's core and the normal angle of synthetic aperture radar antenna panel;

At first determine that according to application requirements mapping band scope, sub-swaths number and orientation are to resolution, pulse repetition rate, sub-swaths width, beam center view angle theta ₀And corresponding oblique distance r ₀, determine the sub antenna spacing according to optimum signal to noise ratio (S/N ratio) design criteria formula again;

Specifically comprise the following steps:

1) determines pulse repetition rate F according to the orientation to resolution requirement _r

2) determine sub-swaths width and sub-swaths number N according to pulse repetition rate;

3) divide sub-swaths according to sub-swaths width, mapping band position and width requirement;

4) determine the beam center view angle theta according to mapping band position and width ₀And corresponding oblique distance r ₀

5) according to optimum signal to noise ratio (S/N ratio) design criteria formula computed range to the sub antenna space D.

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