CN102375137A - Method for estimating parameters of imaging radar by adopting compressed sensing - Google Patents

Abstract

The invention discloses a method for estimating parameters of an imaging radar by adopting compressing and sensing, which relates to the imaging radar technology, and is characterized in that: a compressed-sensing-based imaging radar model is established by utilizing an information theory principle, the compressed-sensing-based imaging radar model is utilized to calculate the power of a transmitter of the compressed-sensing imaging radar, the signal-to-noise ratio of echo, the sparsity of a target scene and the image resolution capacity of the compressed-sensing imaging radar. Due to the adoption of the method, not only is an imaging process of the compressed-sensing imaging radar reflected, but also parameters of the compressed-sensing imaging radar system can be effectively and quantitatively estimated, the method is also suitable for the data after the transform processing and the variable and sparse target scene, and a promising popularization and application prospect can be realized.

Description

A kind of method of compressed sensing imaging radar parameter

Technical field

The present invention relates to the imaging radar technical field, is a kind of method of compressed sensing imaging radar parameter, is used for the sparse characteristic that imaging radar system utilizes object scene, estimates model and method based on the theoretical imaging radar system parameter of compressed sensing.

Background technology

Imaging radar is a kind of remote sensing equipment that can carry out high-resolution imaging on a surface target.It does not receive the restriction of weather and time, can round-the-clock, round-the-clock imaging, and the long microwave of wavelength has the ability that penetrates vegetation and surface layer, has a wide range of applications in field such as dual-use.Along with the demand of every field to radar image resolution improves constantly, with the Shannon's sampling theorem be based signal handle framework to sample rate and data processing speed require increasingly highly, thereby the difficulty that radar signal is obtained and handled increasingly sharpened.

In recent years, a kind of new sampling theory-compression sampling occurs, or claimed compressed sensing (CS; Compressive sampling or compressed sensing), this method is in sampling process, realizes signal compression; Promptly sample with the sampling rate that is lower than Nyquist rate; And can recover original signal with high accuracy rate and (, publish in IEEE Transactions on Information Theory, vol.52 referring to " Compressed sensing "; Apr.2006, pp.1289-1306).

Utilize the compressed sensing technology that data are handled and to possess an important hypothesis prerequisite, be i.e. the sparse property of data.For example, as matrix Ψ=[ψ of given N * N ₁| ψ ₂| ... | ψ _n] time, ψ wherein _iDuring the i row of representing matrix, the real signal X that length is N can be expressed as

S in above-mentioned formula (1) _iWhen coefficient had only K to be not equal to zero, signal X can be called as the K-sparse signal.In the compressed sensing technology, can owe sampling (promptly sampling) to signal X, and recover at receiving end to be lower than Nyquist rate.When realizing, (the matrix Φ of K＜M＜N), and calculate Y=Φ X obtains Y=Φ X=Φ Ψ S=Θ S (2) through introducing second M * N.

In the formula, S=[s ₁, s ₂..., s _N] ^T, the transposition of T representing matrix.Because M＜N, Y are the signal after sampling and the compression.At receiving end, recover S according to receiving signal Y earlier, and then recover X.But because the system of equations number in the above-mentioned formula (2) is less than the known variables number, so the much poorer group of the Xie Youyuan of S.Consider the sparse property of signal, to the recovery problem equivalent of signal in separates the most sparse seeking above-mentioned formula (2).

At present, existing a lot of documents have proposed method that signal is rebuild, like Basis Pursuit algorithm (referring to " Compressed Sensing "; Publish in IEEE Transactions on Information Theory; Vol.52, Apr.2006, pp.1289-1306), Orthogonal Matching Pursuit algorithm is (referring to " Signal Recovery from Random Measurements via Orthogonal Matching Pursuit "; Publish in IEEETransactions on Information Theory; Vol.53, Dec.2007, pp.4655-4666) or the like.

Can reduce the sampling rate of data based on the signal Processing of compressed sensing.Based on this theory, Baraniuk is applied to CS in the one-dimensional image and two-dimensional imaging of radar and (referring to " Compressive Radar Imaging ", publishes in IEEE Radar Conference; Boston, MA, USA; Apr.17-20,2007,128-133); Herman introduces the Alltop sequence and (referring to " High-Resolution Radar via Compressed Sensing ", publishes in IEEE Transactions on Signal Processing, vol.57 as the transponder pulse signal of two-dimentional CS imaging radar system; June 2009, pp.2275-2284).

At present, compressed sensing has received widely in Application in Radar and having paid close attention to, and wherein the research about compressed sensing imaging radar performance is important research aspect.More existing conclusions are merely able to explain that compressed sensing can be in application in radar, and do not provide quantitative results theoretically.

Summary of the invention

The objective of the invention is to disclose a kind of method of compressed sensing imaging radar parameter; Utilize information theory principle to set up compressed sensing imaging radar model; And utilize this model method to calculate the power of transmitter in the compressed sensing imaging radar; The signal to noise ratio (S/N ratio) of echo, the degree of rarefication of object scene and compressed sensing imaging radar result's resolution characteristic.This method has not only well reflected the process of compressed sensing radar imagery; And can effectively estimate the power of compressed sensing imaging radar system to transmitter; The signal to noise ratio (S/N ratio) of echo, the requirement of the degree of rarefication of object scene, and can calculate compressed sensing radar imagery result's resolution characteristic.

In order to achieve the above object, technical solution of the present invention is:

A kind of method of compressed sensing imaging radar parameter, it comprises:

A) utilize information theory principle to set up based on compressed sensing imaging radar model;

According to the generative process of echoed signal, the echo of compressed sensing imaging radar is write as like drag:

Y＝Φ·X+N＝Θ·H·X+N＝S+N

Wherein, The echoed signal of

expression desired compression perception imaging radar;

is that the observing matrix of compressed sensing imaging radar system (is called for short: observing matrix);

is the sparseness measuring matrix; The observing matrix of

expression imaging radar system;

representes sparse echo signal, expression systematic observation noise;

B) transmitter power of calculating accurate reconstructed object signal desired compression perception imaging radar system from echo data;

C) calculate the accurate needed minimum sampling number of reconstructed object signal from echo data;

When d) calculating from echo data accurately the reconstructed object signal, the relation that the degree of rarefication of echo signal need satisfy;

E) the target resolution characteristic of calculating compressed sensing imaging radar system finishes.

The method of described compressed sensing imaging radar parameter, in its said a) step based on compressed sensing imaging radar model: Y=Φ X+N=Θ HX+N=S+N is a Channel Transmission model from the information source to the stay of two nights, it by two independently channel cascaded form:

Channel 1:S=Φ X is a projection channel from higher-dimension to low dimension;

Channel 2:Y=S+N is the Gaussian channel of a parallel connection.

The method of described compressed sensing imaging radar parameter, its said b) in the step, the transmitter power of desired compression perception imaging radar system is:

$P_t=\frac{n{\left(4\mathrm{\π}\right)}^3{R}^4\left(K_0{T}_0{F}_{n}L\right)}{k{N}_a{T}_p{G}_t{G}_r{\mathrm{\λ}}^2\mathrm{\σ}}({(N_{q}n/k)}^{c\·\frac{2k}{m}}-1)$

Wherein R is the target oblique distance, K ₀Be Boltzmann constant, T ₀Be receiver absolute temperature, F _nBe receiver noise factor, L is system loss, G _tBe transmitter antenna gain (dBi), G _rBe receiving antenna gain; λ is an electromagnetic wavelength, and σ is long-pending for the target area backscattering cross, and n is the length of sparse echo signal; K is the number of nonzero element in the sparse echo signal; M is the echoed signal sampling number based on the radar imagery of compressed sensing, and c is the constant of a value between 1～5, N _qThe resolution number of degrees of expression radar image, N _aBe the sampling number in the beam angle, T _pBe the duration of pulse.

The method of described compressed sensing imaging radar parameter, its said c) the minimum sampling number in the step is:

m＝2ck?log _1+SNR(N _qn/k)

Wherein m is a compressed sensing imaging radar echoed signal sampling number, and c is the constant of a value between 1～5, and n is the length of sparse echo signal, and k is the number of nonzero element in the sparse echo signal, and SNR is the signal to noise ratio (S/N ratio) of compressed sensing imaging radar echoed signal, N _qThe resolution number of degrees of expression radar image.

The method of described compressed sensing imaging radar parameter, its said d) in the step, the relation that the degree of rarefication of echo signal need satisfy is:

$\mathrm{\&eta;}{\log }_{1+\mathrm{SNR}}\left(\mathrm{\&eta;}{N}_q\right)=-\frac{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HSA00000234816500012.png"\; state="\{\{state\}\}">m</figure-callout>}}{2\mathrm{cn}}$

In the formula, degree of rarefication does

Be the ratio of length n of number k and the echo signal of nonzero element in the signal; M is a compressed sensing imaging radar echoed signal sampling number; C is the constant of a value between 1～5, and n is the length of sparse echo signal, and k is the number of nonzero element in the sparse echo signal; SNR is the signal to noise ratio (S/N ratio) of compressed sensing imaging radar echoed signal, N _qThe resolution number of degrees of expression radar image.

The method of described compressed sensing imaging radar parameter, its said e) in the step, the target resolution characteristic of calculating the compressed sensing imaging radar system is:

${\mathrm{\&rho;}}_{\mathrm{CS}}=\frac{L_t}{n}=\frac{N_q{L}_t}{k\&CenterDot;{(1+\mathrm{SNR})}^{\frac{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HSA00000234816500012.png"\; state="\{\{state\}\}">m</figure-callout>}}{2\mathrm{kc}}}}$

In the formula, ρ _CSBe the target resolution characteristic of compressed sensing radar, the minimum interval of two target resolution elements promptly can accurately distinguishing in the imaging results of compressed sensing imaging radar, L _tBe the size of object scene, n is the length of sparse echo signal, and k is the number of nonzero element in the sparse echo signal; SNR is the signal to noise ratio (S/N ratio) of compressed sensing imaging radar echoed signal; M is a compressed sensing imaging radar echoed signal sampling number, and c is the constant of a value between 1～5, N _qThe resolution number of degrees of expression radar image.

The method of described compressed sensing imaging radar parameter, it is equally applicable to data and the sparse object scene of conversion after the conversion process; Comprise:

A) echo data of gathering

is carried out conversion process; Be to multiply each other with Y with a matrix

, the echo data after the conversion process

is expressed as

Y′＝T·Y＝T·Φ·X+T·N＝T·Θ·H·X+T·N＝S′+N′

Wherein, Compressed sensing imaging radar echoed signal after expression conversion process;

is the observing matrix of compressed sensing imaging radar system;

representes transformation matrix;

is the sparseness measuring matrix;

expression imaging radar system observing matrix;

representes sparse echo signal;

expression systematic observation noise, the systematic observation noise after

expression conversion;

B) if object scene is not sparse in time domain; And in certain transform domain Ψ, be sparse; Be echo signal

wherein

represent sparse transformation matrix,

representes sparse coefficient vector; As observing matrix, α is as echo signal this moment with Φ Ψ, and the generative process of compressed sensing imaging radar echoed signal can be write as like drag so:

Y＝Φ·X+N＝Θ·H·X+N＝Θ·H·Ψ·α+N＝S+N

Wherein, The desirable compressed sensing imaging radar echoed signal of

expression;

is the observing matrix of compressed sensing imaging radar system; is the sparseness measuring matrix;

expression imaging radar system observing matrix; representes sparse transformation matrix;

representes sparse echo signal,

expression systematic observation noise;

Wherein,

Y＝Φ·X+N＝Θ·H·X+N＝S+N，

Y '=TY=T Φ X+TN=T Θ HX+TN=S '+N ' with

Y＝Φ·X+N＝Θ·H·X+N＝Θ·H·Ψ·α+N＝S+N

Three formulas have identical expression, and the method for said model is equally applicable to data and the sparse object scene of conversion after the conversion process.

The present invention is a kind of method of compressed sensing imaging radar parameter; Utilize information theory principle to set up based on compressed sensing imaging radar model; And utilize this model to calculate the power of transmitter in the compressed sensing radar imagery, the signal to noise ratio (S/N ratio) of echo, the degree of rarefication of object scene and compressed sensing radar imagery result's resolution characteristic; The process that has not only reflected the compressed sensing radar imagery, and can effectively estimate the performance of compressed sensing imaging radar system.The inventive method has good popularization and application prospect.

Description of drawings

Fig. 1 is the method for a kind of compressed sensing imaging radar parameter of the present invention, the compressed sensing radar imagery illustraton of model that utilizes information theory principle to set up;

Fig. 2 is projection channel model figure of the present invention;

Fig. 3 is a parallelly connected Gaussian channel illustraton of model of the present invention;

Fig. 4 is the coding block diagram of sparse echo signal of the present invention;

Fig. 5 carries out compressed sensing radar imagery process flow diagram with echo data.

Embodiment

For making the object of the invention, technical scheme and advantage clearer, the present invention is made further detailed description below in conjunction with accompanying drawing and embodiment simulation scenarios.

The method of a kind of compressed sensing imaging radar parameter of the present invention; Utilize information theory principle to set up compressed sensing radar imagery model; And utilize this model method to calculate the power of transmitter in the compressed sensing radar imagery; The signal to noise ratio (S/N ratio) of echo, the degree of rarefication of object scene and compressed sensing radar imagery result's resolution characteristic is used for the performance of compressed sensing radar imagery system is analyzed.

As shown in Figure 1, be the compressed sensing radar imagery illustraton of model that method of the present invention utilizes information theory principle to set up, according to the generative process of the echoed signal of radar imagery, can the compressed sensing radar return be write as like drag:

Y＝Φ·X+N＝Θ·H·X+N＝S+N (1)

Wherein, The echoed signal of

expression desired compression perception radar imagery;

is that the observing matrix of compressed sensing radar imagery system (is called for short: observing matrix);

is the sparseness measuring matrix;

expression radar imagery systematic observation matrix;

representes sparse echo signal,

expression systematic observation noise.

Above-mentioned model can be regarded a Channel Transmission model from the information source to the stay of two nights as, it by two independently channel cascaded form:

Channel 1:S=Φ X can regard a projection channel from higher-dimension to low dimension as, and is as shown in Figure 2.

Channel 2:Y=S+N is the Gaussian channel of a parallel connection, and is as shown in Figure 3.

Because two channels in this cascaded channel are fully independently, so we can carry out independent analysis to them respectively.

Channel 1 is a projection channel from higher-dimension to low dimension, and Here it is, and initial compressed sensing does not have the model of making an uproar, and it is theoretical to have proposed compressed sensing based on this model by people such as Donoho.People such as Candes point out when observing matrix satisfies specific RIP; Sparse echo signal X can utilize the individual measured value S accurate reconstruction of m=O (klog (n/k)) (referring to " Decoding by linear programming "; Publish in IEEE Transactions on Information Theory; Vol.51, Dec.2005, pp.4203-4215).

And people such as Martin Wainwright are from the error probability theory; The condition m=O (klog (n/k)) that utilizes the needed minimum sampling number of sparse reconstruction that information theory analyzes is (referring to " Information-Theoretic Limits on Sparsity Recovery in the High-Dimensional and Noisy Setting "; Publish in IEEE Transactions on Information Theory; Vol.55, Dec.2009, pp.5728-5741).

The condition that the reconstruction that comprehensive these two kinds of diverse ways obtain is counted, we can obtain making information source to satisfy m=O (klog (n/k)) with regard to requiring minimum sampling number from through accurate reconstruction the stay of two nights behind the projection channel 1.

Because channel 1 is two separate channels with channel 2, so when considering the transport property of channel 2, we might as well establish channel 1 and be lossless channel.

Channel 2 can be regarded the Gaussian channel of a parallel connection as.Information capacity C with parallelly connected Gaussian channel in information theory is defined as:

$C=\underset{f(s_1,{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HSA00000234816500012.png"\; state="\{\{state\}\}">s</figure-callout>}}_2,\&CenterDot;\&CenterDot;\&CenterDot;,s_m):\mathrm{\&Sigma;}{\mathrm{<figure-callout\; id="2"\; label="ES\; j"\; filenames="HSA00000234816500012.png"\; state="\{\{state\}\}">ES</figure-callout>}}_j^{}\&le;P}{\max }I(S_1,{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HSA00000234816500012.png"\; state="\{\{state\}\}">S</figure-callout>}}_2,\&CenterDot;\&CenterDot;\&CenterDot;S_m;Y_1,{\mathrm{<figure-callout\; id="2"\; label="Y"\; filenames="HSA00000234816500012.png"\; state="\{\{state\}\}">Y</figure-callout>}}_2,\&CenterDot;\&CenterDot;\&CenterDot;Y_m)$

$=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{1}{2}\log (1+\frac{P_i}{N_i})---\left(2\right)$

N wherein _iBe noise power,

∑ P _i=P.

Because f (x)=log (x) is following convex function, utilizes Characteristics of Convex Function to obtain:

$C\&le;\frac{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HSA00000234816500012.png"\; state="\{\{state\}\}">m</figure-callout>}}{2}\log (1+\frac{P}{m})=\frac{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HSA00000234816500012.png"\; state="\{\{state\}\}">m</figure-callout>}}{2}\log (1+\mathrm{SNR})---\left(3\right)$

Here the ratio of expectation and the expectation of noise energy that being defined as of signal to noise ratio (snr) is not had the energy of the observation vector of making an uproar:

$\mathrm{SNR}\stackrel{\mathrm{\&Delta;}}{=}\frac{E\left[{\left|\right|S\left|\right|}_2^2\right]}{E\left[{\left|\right|N\left|\right|}_2^2\right]}=\frac{P}{m}---\left(4\right)$

In the time of can knowing that by the message source and channel separation theorem of the steady ergodic signal of the continuous amplitude of discrete time information capacity C that and if only if can extract surpasses the information capacity R (D) that quantizes information source from channel; Information source X can be by this Channel Transmission, and can reach amount distortion D.

So information source X can then be had by this Channel Transmission

$R\left(D\right)\&le;C\&le;\frac{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HSA00000234816500012.png"\; state="\{\{state\}\}">m</figure-callout>}}{2}\log (1+\mathrm{SNR})---\left(5\right)$

Have so

$m\&GreaterEqual;\frac{2R\left(D\right)}{\log (1+\mathrm{SNR})}---\left(6\right)$

Length is that the quantity of information that the k sparse signal of n is comprised can be divided into positional information and amplitude information, so when it is encoded, can carry out according to mode shown in Figure 4, promptly its positional information and amplitude information is encoded respectively.So the quantity of information that information source comprised can be expressed as

H(X)＝H(T)+b (7)

Because length is the positional information T of the k sparse signal X of n is one the stochastic variable of

individual equiprobability value is arranged, so have

$H\left(T\right)=-\underset{T}{\mathrm{\&Sigma;}}p\left(T\right)\log p\left(T\right)=\log {(}_k^n)---\left(8\right)$

And represent that the required code check of this sparse signal amplitude information depends on the prior distribution f and the rate distortion amount D of its amplitude.

In radar imagery, suppose that generally radar reflectivity factor X obeys evenly distribution, that is:

f _X(x)＝1/(β ₂-β ₁) (β ₂＞x＞β ₁＞0) (9)

We are defined as maximum reconstruction errors error with distortion metrics D, that is:

$D=\underset{i\&Element;T}{\max }|x_i-{\hat{x}}_i|$

Note

$R^{\&prime;}\left(D\right)=\underset{i\&Element;T,f\left(x_i\right|{\hat{x}}_i):|x_i-{\hat{x}}_i|\&le;D}{\min }I(X_i;{\hat{X}}_i)---\left(10\right)$

$I(X_i;{\hat{X}}_i)=h\left(X_i\right)-h\left(X_i\right|{\hat{X}}_i)$

$=\log ({\mathrm{\&beta;}}_2-{\mathrm{\&beta;}}_1)-h(X_i-{\hat{X}}_i|{\hat{X}}_i)$

$\&GreaterEqual;\log ({\mathrm{\&beta;}}_2-{\mathrm{\&beta;}}_1)-h(X_i-{\hat{X}}_i)$

$\&GreaterEqual;\log ({\mathrm{\&beta;}}_2-{\mathrm{\&beta;}}_1)-h\left(U(0,D)\right)---\left(11\right)$

$=\log ({\mathrm{\&beta;}}_2-{\mathrm{\&beta;}}_1)-\log \left(D\right)$

$=\log (({\mathrm{\&beta;}}_2-{\mathrm{\&beta;}}_1)/D)$

The top sign of inequality can be got when X and

are separate, so have

$R^{\&prime;}\left(D\right)=\left\{\begin{array}{cc}\log (({\mathrm{\&beta;}}_2-{\mathrm{\&beta;}}_1)/D)& 0\&le;D\&le;({\mathrm{\&beta;}}_2-{\mathrm{\&beta;}}_1)\\ 0& D>({\mathrm{\&beta;}}_2-{\mathrm{\&beta;}}_1)\end{array}\right.---\left(12\right)$

Satisfy 0≤D≤(β at amount distortion D ₂-β ₁) time, but length is the rate distortion function approximate representation of the k sparse signal of n do

$R\left(D\right)\&ap;\log {(}_k^n)+k\log (({\mathrm{\&beta;}}_2-{\mathrm{\&beta;}}_1)/D)---\left(13\right)$

Because the sparse characteristic of echo signal, thus have k＜＜n, utilize classical Stirling estimation formulas to obtain

$\log {(}_k^n)\&ap;k\log (n/k)---\left(14\right)$

With (13), (14) formula substitution (6) formula can obtain

$m\&GreaterEqual;\frac{2k\log (n/k)+2k\log (({\mathrm{\&beta;}}_2-{\mathrm{\&beta;}}_1)/D)}{\log (1+\mathrm{SNR})}---\left(15\right)$

$=2k{\log }_{1+\mathrm{SNR}}(({\mathrm{\&beta;}}_2-{\mathrm{\&beta;}}_1)n/\mathrm{Dk})$

The result of surface analysis will make original sparse signal from observation signal, rebuild before comprehensive, just requires the line number of observing matrix to satisfy:

m＝max{O(klog(n/k))，O(2klog _1+SNR((β ₂-β ₁)n/Dk))} (16)

Note N _q=(β ₂-β ₁)/D, N _qThe resolution number of degrees of radar image just.

Because in the imaging radar system of reality; The signal to noise ratio (S/N ratio) of echo is generally all smaller; So can obtain in the compressed sensing imaging radar system according to (16) formula, the relation between the signal to noise ratio snr of the sampling number m of echo, the degree of rarefication η=n/k of object scene and echoed signal does

$\frac{m}{2k{\log }_{1+\mathrm{SNR}}(N_{q}n/k)}=c---\left(17\right)$

Wherein c is that a value is 1～5 constant, N _qThe resolution number of degrees of expression radar image.

1. the power of transmitter computes

With last and (17) formula distortion can obtain from echoed signal accurately that the signal to noise ratio (S/N ratio) of reconstructed object signal desired compression perception imaging radar system is:

$\mathrm{SNR}={(N_{q}n/k)}^{c\&CenterDot;\frac{2k}{m}}-1---\left(18\right)$

Wherein n is the length of sparse echo signal, and k is the number of nonzero element in the sparse echo signal, and m is a compressed sensing radar imagery echoed signal sampling number, and c is the constant of a value between 1～5, N _qThe resolution number of degrees of expression radar image.

Radar equation is:

${\mathrm{SNR}}_{\mathrm{\&sigma;}}=\frac{P_t{G}_t{G}_r{\mathrm{\&lambda;}}^2\mathrm{\&sigma;}}{{\left(4\mathrm{\&pi;}\right)}^3{R}^4\left(k_0{T}_0{\mathrm{BF}}_{n}L\right)}---\left(19\right)$

P wherein _tBe antenna peak power, G _tBe transmitter antenna gain (dBi), G _rFor receiving antenna gain, λ are that wavelength, σ are for the target area backscattering cross is long-pending, R is target oblique distance, k ₀Be Boltzmann constant, T ₀For receiver absolute temperature, B are that receiver bandwidth, L are system loss, F _nBe receiver noise factor.

Radar equation has provided the signal to noise ratio (S/N ratio) of single-point in the original echo, and ignores the energy of clutter, and is the signal to noise ratio (S/N ratio) of whole scene according to the signal to noise ratio (S/N ratio) of (4) definition, so between it and the single-point signal to noise ratio (S/N ratio) that obtains through radar equation following relation is arranged

$\mathrm{SNR}=\frac{k}{n}\&CenterDot;N_a\&CenterDot;N_r\&CenterDot;{\mathrm{SNR}}_{\mathrm{\&sigma;}}---\left(20\right)$

N wherein _aBe the sampling number in the beam angle, N _rIt is the sampling number in the duration of pulse.

N so _rCan be expressed as

N _r＝BT _p (21)

T wherein _pBe the duration of pulse, B is a receiver bandwidth;

In the time of can obtaining carrying out the compressed sensing radar imagery according to flow process shown in Figure 5 by (18)～(21), accurately the transmitter power of the compressed sensing imaging radar system of reconstructed object signal demand is:

$P_t=\frac{n{\left(4\mathrm{\&pi;}\right)}^3{R}^4\left(K_0{T}_0{F}_{n}L\right)}{k{N}_a{T}_p{G}_t{G}_r{\mathrm{\&lambda;}}^2\mathrm{\&sigma;}}({(N_{q}n/k)}^{c\&CenterDot;\frac{2k}{m}}-1)---\left(22\right)$

Wherein R is the target oblique distance, K ₀Be Boltzmann constant, T ₀Be receiver absolute temperature, F _nBe receiver noise factor, L is system loss, G _tBe transmitter antenna gain (dBi), G _rBe receiving antenna gain; λ is an electromagnetic wavelength, and σ is long-pending for the target area backscattering cross, and n is the length of sparse echo signal; K is the number of nonzero element in the sparse echo signal; M is the echoed signal sampling number based on the radar imagery of compressed sensing, and c is the constant of a value between 1～5, N _qThe resolution number of degrees of expression radar image, N _aBe the sampling number in the beam angle, T _pBe the duration of pulse.

Length n in sparse echo signal; The number k of nonzero element in the sparse echo signal; Under the known situation of compressed sensing radar imagery echoed signal sampling number m; Can use formula (18) to calculate the required signal to noise ratio (S/N ratio) of compressed sensing imaging radar, and then calculate radar emission acc power required when carrying out the compressed sensing radar imagery respectively according to radar parameter and formula (22).

2. calculate the compressed sensing radar and rebuild required minimum counting

Length n in sparse echo signal; The number k of nonzero element in the sparse echo signal; Under the known situation of the signal to noise ratio snr of compressed sensing radar imagery echoed signal, can be expressed as by the minimum echoed signal hits that the accurate reconstructed object signal of compressed sensing imaging radar is required according to formula (17):

m＝2ck?log _1+SNR(N _qn/k) (23)

Wherein m is the acquisition length of compressed sensing radar imagery echoed signal, and c is the constant of a value between 1～5, N _qThe resolution number of degrees of expression radar image.

At the length n of sparse echo signal, under the known situation of the number k of nonzero element and compressed sensing imaging radar parameter, can use formula (23) to calculate the echoed signal sampling number that the compressed sensing imaging radar is rebuild required collection in the sparse echo signal.

3. the requirement of the degree of rarefication of compute sparse re-construct

We do a distortion with formula (17), and the degree of rarefication of the echo signal that can obtain from echo, accurately rebuilding does

$\mathrm{\&eta;}{\log }_{1+\mathrm{SNR}}\left(\mathrm{\&eta;}{N}_q\right)=-\frac{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HSA00000234816500012.png"\; state="\{\{state\}\}">m</figure-callout>}}{2\mathrm{cn}}---\left(24\right)$

Wherein η=n/k representes the degree of rarefication of target; M is the echoed signal sampling number of compressed sensing radar imagery sampling; C is the constant of a value between 1～5, and n is the length of sparse echo signal, and k is the number of nonzero element in the sparse echo signal; SNR is the signal to noise ratio (S/N ratio) of compressed sensing radar imagery echoed signal, N _qThe resolution number of degrees of expression radar image.

Radar system for a reality; Under the certain situation of emissive power; The signal to noise ratio (S/N ratio) of echo changes little; And the picking rate of system etc. has all had restriction (being that rate distortion amount D confirms), also is that the upper limit of echoed signal sampling number m is fixed, and can calculate the degree of rarefication requirement based on the large scene radar imagery object scene of compressed sensing through formula (24).

4. calculate the resolution characteristic of compressed sensing imaging radar

Echoed signal sampling number m at the compressed sensing imaging radar; Under the situation that the signal to noise ratio snr of the number k of sparse target and echoed signal is known in the object scene, the length that can obtain the echo signal that the compressed sensing imaging radar can accurately rebuild according to formula (17) is:

$n=\frac{k}{N_q}\&CenterDot;{(1+\mathrm{SNR})}^{\frac{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HSA00000234816500012.png"\; state="\{\{state\}\}">m</figure-callout>}}{2\mathrm{kc}}}---\left(25\right)$

Wherein c is the constant of a value between 1～5, and n is the length of sparse echo signal, N _qThe resolution number of degrees of expression radar image.

Because we are defined as the minimum interval of two target resolution elements can accurately distinguishing in the imaging results of compressed sensing imaging radar with the target resolution characteristic of compressed sensing imaging radar, that is:

${\mathrm{\&rho;}}_{\mathrm{CS}}=\frac{L_t}{n}---\left(26\right)$

Here L _tBe the size of object scene, n is the length of sparse echo signal.

So the target resolution characteristic of compressed sensing imaging radar can be expressed as:

${\mathrm{\&rho;}}_{\mathrm{CS}}=\frac{N_q{L}_t}{k\&CenterDot;{(1+\mathrm{SNR})}^{\frac{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HSA00000234816500012.png"\; state="\{\{state\}\}">m</figure-callout>}}{2\mathrm{kc}}}}---\left(27\right)$

Here ρ _CSBe the target resolution characteristic of compressed sensing radar, L _tBe the size of object scene, k is the number of nonzero element in the sparse echo signal, and SNR is the signal to noise ratio (S/N ratio) of compressed sensing imaging radar echoed signal, and m is a compressed sensing imaging radar echoed signal sampling number, and c is the constant of a value between 1～5, N _qThe resolution number of degrees of expression radar image.

The number k of nonzero element in sparse echo signal, the signal to noise ratio snr of the length m of compressed sensing radar imagery echoed signal and compressed sensing radar imagery echoed signal and the big or small L of object scene _tUnder the known situation, can be earlier calculate the length n of the echo signal that the compressed sensing imaging radar can accurately rebuild, utilizing formula (27) to calculate the target resolution characteristic of compressed sensing imaging radar then with formula (25);

5. the application of data after the conversion process and the sparse scene of conversion

Echo data

to gathering carries out conversion process; Can be regarded as with a matrix

and multiply each other with Y, the echo data after the conversion process

is expressed as

Y′＝T·Y＝T·Φ·X+T·N＝T·Θ·H·X+T·N＝S′+N′ (28)

Wherein, Compressed sensing imaging radar echoed signal after

expression conversion process; is the observing matrix of compressed sensing imaging radar system;

representes transformation matrix;

is the sparseness measuring matrix;

expression imaging radar system observing matrix;

representes sparse echo signal;

expression systematic observation noise, the systematic observation noise after

expression conversion.

To utilize information theory principle to set up compressed sensing radar imagery model tormulation identical with us for formula (28), thus for the analysis of the compressed sensing radar imagery model performance of the data after the conversion process with top 1.～4. identical.

If object scene is not sparse in time domain; And in certain transform domain Ψ, be sparse; Be echo signal

wherein

represent sparse transformation matrix,

representes sparse coefficient vector.We can be with Φ Ψ as new observing matrix, and α is as echo signal this moment, according to the generative process of the echoed signal of radar imagery, can the compressed sensing radar return of this moment be write as like drag so:

Y＝Φ·X+N＝Θ·H·X+N＝Θ·H·Ψ·α+N＝S+N (29)

Wherein, The desirable compressed sensing radar imagery echoed signal of expression;

is the radar imagery systematic observation matrix of compressed sensing;

is the sparseness measuring matrix;

expression radar imagery systematic observation matrix;

representes sparse transformation matrix;

representes sparse echo signal,

expression systematic observation noise.

To utilize information theory principle to set up compressed sensing radar imagery model tormulation identical with us for formula (29); So we can utilize the compressed sensing radar imaging method to reconstruct sparse echo signal α earlier; Utilize conversion X=Ψ α to rebuild the original object signal then, for the analysis of the compressed sensing radar imagery model performance of the sparse object scene of conversion with top 1.～4. identical.

Claims (7)

1. the method for a compressed sensing imaging radar parameter is characterized in that, comprises step:

A) utilize information theory principle to set up based on compressed sensing imaging radar model;

According to the generative process of echoed signal, the echo of compressed sensing imaging radar is write as like drag:

Y＝Φ·X+N＝Θ·H·X+N＝S+N

Wherein, The echoed signal of

expression desired compression perception imaging radar;

is that the observing matrix of compressed sensing imaging radar system (is called for short: observing matrix);

is the sparseness measuring matrix; The observing matrix of

expression imaging radar system;

representes sparse echo signal,

expression systematic observation noise;

B) transmitter power of calculating accurate reconstructed object signal desired compression perception imaging radar system from echo data;

C) calculate the accurate needed minimum echoed signal sampling number of reconstructed object signal from echo data;

When d) calculating from echo data accurately the reconstructed object signal, the relation that the degree of rarefication of echo signal need satisfy;

E) the target resolution characteristic of calculating compressed sensing imaging radar system finishes.

2. the method for compressed sensing imaging radar parameter according to claim 1; It is characterized in that; In the said a) step based on compressed sensing imaging radar model: Y=Φ X+N=Θ HX+N=S+N; Be a Channel Transmission model from the information source to the stay of two nights, it by two independently channel cascaded form:

Channel 1:S=Φ X is a projection channel from higher-dimension to low dimension;

Channel 2:Y=S+N is the Gaussian channel of a parallel connection.

3. the method for compressed sensing imaging radar parameter according to claim 1 is characterized in that, said b) in the step, the transmitter power of desired compression perception imaging radar system is:

$P_t=\frac{n{\left(4\mathrm{\&pi;}\right)}^3{R}^4\left(K_0{T}_0{F}_{n}L\right)}{k{N}_a{T}_p{G}_t{G}_r{\mathrm{\&lambda;}}^2\mathrm{\&sigma;}}({(N_{q}n/k)}^{c\&CenterDot;\frac{2k}{m}}-1)$

Wherein R is the target oblique distance, K ₀Be Boltzmann constant, T ₀Be receiver absolute temperature, F _nBe receiver noise factor, L is system loss, G _tBe transmitter antenna gain (dBi), G _rBe receiving antenna gain; λ is an electromagnetic wavelength, and σ is long-pending for the target area backscattering cross, and n is the length of sparse echo signal; K is the number of nonzero element in the sparse echo signal; M is the echoed signal sampling number based on the radar imagery of compressed sensing, and c is the constant of a value between 1～5, N _qThe resolution number of degrees of expression radar image, N _aBe the sampling number in the beam angle, T _pBe the duration of pulse.

4. the method for compressed sensing imaging radar parameter according to claim 1 is characterized in that, said c) step in minimum echoed signal sampling number be:

m＝2ck?log _1+SNR(N _qn/k)

Wherein m is a compressed sensing imaging radar echoed signal sampling number, and c is the constant of a value between 1～5, and n is the length of sparse echo signal, and k is the number of nonzero element in the sparse echo signal, and SNR is the signal to noise ratio (S/N ratio) of compressed sensing imaging radar echoed signal, N _qThe resolution number of degrees of expression radar image.

5. the method for compressed sensing imaging radar parameter according to claim 1 is characterized in that, said d) in the step, the relation that the degree of rarefication of echo signal need satisfy is:

$\mathrm{\&eta;}{\log }_{1+\mathrm{SNR}}\left(\mathrm{\&eta;}{N}_q\right)=-\frac{m}{2\mathrm{cn}}$

In the formula, degree of rarefication does

Be the ratio of length n of number k and the echo signal of nonzero element in the signal; M is a compressed sensing imaging radar echoed signal sampling number; C is the constant of a value between 1～5, and n is the length of sparse echo signal, and k is the number of nonzero element in the sparse echo signal; SNR is the signal to noise ratio (S/N ratio) of compressed sensing imaging radar echoed signal, N _qThe resolution number of degrees of expression radar image.

6. the method for compressed sensing imaging radar parameter according to claim 1 is characterized in that, said e) in the step, the target resolution characteristic of calculating the compressed sensing imaging radar system is:

${\mathrm{\&rho;}}_{\mathrm{CS}}=\frac{L_t}{n}=\frac{N_q{L}_t}{k\&CenterDot;{(1+\mathrm{SNR})}^{\frac{m}{2\mathrm{kc}}}}$

In the formula, ρ _CSBe the target resolution characteristic of compressed sensing radar, the minimum interval of two target resolution elements promptly can accurately distinguishing in the imaging results of compressed sensing imaging radar, L _tBe the size of object scene, n is the length of sparse echo signal, and k is the number of nonzero element in the sparse echo signal; SNR is the signal to noise ratio (S/N ratio) of compressed sensing imaging radar echoed signal; M is a compressed sensing imaging radar echoed signal sampling number, and c is the constant of a value between 1～5, N _qThe resolution number of degrees of expression radar image.

7. the method for compressed sensing imaging radar parameter according to claim 1 is characterized in that, is equally applicable to data and the sparse object scene of conversion after the conversion process; Comprise:

A) echo data of gathering

is carried out conversion process; Be to multiply each other with Y with a matrix

, the echo data after the conversion process

is expressed as:

Y′＝T·Y＝T·Φ·X+T·N＝T·Θ·H·X+T·N＝S′+N′

Wherein, Compressed sensing imaging radar echoed signal after

expression conversion process;

is the observing matrix of compressed sensing imaging radar system;

representes transformation matrix;

is the sparseness measuring matrix;

expression imaging radar system observing matrix;

representes sparse echo signal; expression systematic observation noise, the systematic observation noise after expression conversion;

B) if object scene is not sparse in time domain; And in certain transform domain Ψ, be sparse; Be echo signal wherein

represent sparse transformation matrix,

representes sparse coefficient vector; As observing matrix, α is as echo signal this moment with Φ Ψ, and the generative process of compressed sensing imaging radar echoed signal can be write as like drag so:

Y＝Φ·X+N＝Θ·H·X+N＝Θ·H·Ψ·α+N＝S+N

Wherein, The desirable compressed sensing imaging radar echoed signal of

expression;

is the observing matrix of compressed sensing imaging radar system;

is the sparseness measuring matrix;

expression imaging radar system observing matrix;

representes sparse transformation matrix;

representes sparse echo signal,

expression systematic observation noise;

Wherein,

Y＝Φ·X+N＝Θ·H·X+N＝S+N，

Y '=TY=T Φ X+TN=T Θ HX+TN=S '+N ' with

Y＝Φ·X+N＝Θ·H·X+N＝Θ·H·Ψ·α+N＝S+N

Three formulas have identical expression, and the method for said model is equally applicable to data and the sparse object scene of conversion after the conversion process.

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