CN105068061A - Analog information conversion method based on chirp frequency mixing and system thereof - Google Patents

Abstract

The invention provides an analog information conversion method based on chirp frequency mixing and a system thereof, and belongs to the technical field of sampling. The conversion method comprises the steps that step one, a chirp signal is regulated, and modulation frequency of the chirp signal is enabled to be B/T; step two, the frequency mixing process of an analog signal and the chirp signal is expressed by a mathematical expression; step three, 1/M undersampling is performed on the analog signal, a single low-pass filter is constructed by the whole undersampling result by utilizing a mode of superposition of M adjacent elements, and an M-fold undersampling signal through the low-pass filter is obtained; step four, the analog signal is reconstructed by utilizing the M-fold undersampling signal according to a compression perception orthogonal matching algorithm so that a first reconstruction signal x1 is obtained; step five, modulation frequency of the chirp signal is set as 2B/T; step six, the process from the step one to the step four is repeated so that a second reconstruction signal x2 is obtained; and step seven, the signals x1 and x2 are averaged and added, and multiple maximum peak positions and energy values of the reconstruction signals are obtained by utilizing a maximum peak search method.

Description

Based on analog information conversion method and the system of chirp mixing

Technical field

The present invention relates to a kind of analog information conversion method based on chirp mixing and system, belong to Sampling techniques field.

Background technology

Super-broadband tech has the advantages such as higher data transmission rate, low cost, low-power consumption and antijamming capability are strong, becomes a kind of cutting edge technology in the field such as radio communication and radar detection.But according to Nyquist sampling theorem, the high bandwidth of ultra-broadband signal causes receiver to need high sampling rate when carrying out digital processing.Commercial company is devoted to the analog/digital converter (analogtodigitalconvertor, ADC) of release higher rate to seize high-end market.But data acquisition rate at a high speed brings series of problems: the problem being first hardware circuit design, being secondly that data store and transmission problem, is finally the problem of real time data processing.Therefore, the sampling of ultra-broadband signal becomes the technical bottleneck that restriction radio ultra wide band system develops to practical technique.

In a lot of practical application, as ultra broadband short-distance wireless communication, radar, sonar, medical detection system etc., target can be considered sparse relative to application background, and the information rate that namely signal carries is limited.Compressed sensing (compressivesensing, the CS) theory grown up nearly ten years most possibly utilizes this imbalance to reduce the technology of sampling rate by being.Simulating signal is converted to digital signal with sub-nyquist sampling rate by this compressed sensing principle that utilizes, and the method therefrom extracting sparse information is referred to as analog information converter (analogtoinformationconvertor, AIC).Its signals collecting end is general comparatively simple, and sampling rate is lower, and the general redundancy of signal of collection is very little, but from the signal gathered, reduce the process of original information general comparatively complicated, and this signal processing and current hardware advances level match.

In all multi-schemes of analog information converter (AIC), the AIC scheme based on random demodulation serves very large impetus to its development.The program is made up of high speed pseudorandom detuner, low-pass filter and low speed ADC.Wherein, pseudo-random sequence P _ct () value is { 1 ,-1}, and require that the rate of change of sequence is greater than the Nyquist rate of sampled signal.First high-frequency signal through a detuner (multiplier), is mixed to whole frequency band by frequency-domain sparse signal x (t), after low-pass filter filtering high frequency interference, then is sampled by a low speed ADC.

But to be operated on the nyquist sampling rate of actual signal due to high speed PRBS, therefore, when carrying out ultra broadband sampling, the clock jitter of random sequence generator and aperture effect result in it and create error in restructuring procedures, and this error can expand gradually, seriously limit the practical application of this system.

Summary of the invention

In order to overcome clock jitter and the aperture effect of pseudo-random sequence, the present invention proposes a kind of analog information conversion method based on chirp mixing and system, the present invention uses the chirp signal determined as mixed frequency signal, replaces PN, the random signals such as Gauss.Be difficult to except overcoming the latter's high frequency on hardware, except the defect of realization, better performance index can also be obtained.Especially test while needed for compressed sensing, minimal reconstruction is counted in discontented foot channel, PN, the random signals such as Gauss, can not reconstruct raw information, and this structure based on chirp mixing still can reconstruct raw information.

The method takes full advantage of chirp sequence and PN sequence has similar spread spectrum feature, fully can realize the mixing to original signal.Meanwhile, chirp signal is due to the feature of self, and the impact being subject to clock jitter and aperture effect reduces greatly, can be conducive to the reconstruct of AIC system.The technical scheme taked is as follows:

The object of the present invention is to provide a kind of analog information conversion method based on chirp mixing and system, described analog information conversion method process comprises:

Step one, regulate the chirp signal being used for mixing, make the duration of described chirp signal consistent with the duration of simulating signal x (t), the frequency modulation rate of described chirp signal is B/T; Wherein, B is priori bandwidth information, and T is the duration of simulating signal x (t);

Step 2, described simulating signal x (t) and chirp signal optical mixing process mathematic(al) representation are showed, described mathematic(al) representation is: y ₁=C ₁x, wherein, C ₁for constant matrices, its diagonal entry is be the chirp sequence of B/T for frequency modulation rate, and all the other elements are 0;

Step 3, carries out the lack sampling of 1/M to described simulating signal x (t), utilize the mode of an adjacent M element overlaid by the simply constructed low-pass filter of whole lack sampling result, and obtain the M after by low-pass filter times of undersampled signal y' ₁=Hy ₁=HC ₁x; Wherein, M be greater than zero positive integer, H is the equivalent convolution matrix of low-pass filter, and

Step 4, according to the orthogonal matching algorithm (orthogonalmatchingpursuit, OMP) of compressed sensing, utilizes described M times undersampled signal to be reconstructed described simulating signal x (t), draws the first reconstruction signal x ₁;

Step 5, is set to 2B/T by the frequency modulation rate of the signal of chirp described in step one;

Step 6, repeats step one to the process of step 4 based on the chirp signal after amendment frequency modulation rate, obtains the second reconstruction signal x ₂;

Step 7, by described first reconstruction signal x ₁with described second reconstruction signal x ₂average addition, i.e. x'=(x ₁+ x ₂)/2, utilize peak-peak way of search to obtain maximum multiple peak and the energy value of reconstruction signal, thus the reconstruct of realize target signal.

Preferably, described simulating signal to be converted is radar signal.

Preferably, the process of the orthogonal matching algorithm related in described step 4 is:

The first step, first time iteration, find the most matched atoms coordinate k of restructuring matrix, and solve the maximal value of x;

Second step, obtains corresponding element matrix, and utilizes least square method to solve described corresponding element matrix equation;

3rd step, upgrades surplus, enters second time iteration, repeats the process of the first step to the 3rd step;

4th step, obtains institute's maximizing, iteration ends after several iteration.

Preferably, when described simulating signal to be converted is radar signal, the concrete steps of signal conversion are as follows:

Step one, the radar signal of described reception is its duration of pulse T ₀=1us, pulse-recurrence time PRT=8T ₀, priori bandwidth information B=64MHz and target are counted S=8; Chirp Design of Signal for mixing is as follows: getting duration of chirp consistent with input signal is T ₀=1us, and get its frequency modulation rate and equal K ₀=B/T=6.4 × 10 ¹³, i.e. C ₀=exp (j2 π K ₀t ²);

Step 2, is expressed as the process mathematic(al) representation of original signal and the mixing of chirp signal: y ₁=C ₁x; Wherein C ₁diagonal entry be C ₀repeat displacement, be full of the whole burst length, namely all the other elements are 0;

Step 3, supposes lack sampling original signal being carried out to 1/4, then whole lack sampling result is by the simply constructed low-pass filter H of the mode of adjacent 4 element overlaid

By obtaining the undersampled signal of 1/4 after low-pass filter be:

y' ₁＝Hy ₁＝HC ₁x

Step 4, according to orthogonal matching pursuit (orthogonalmatchingpursuit, the OMP) algorithm of compressed sensing, by undersampled signal y' ₁reconstruct original radar signal and obtain x ₁;

Step 5, is set to 2K by the frequency modulation rate of the chirp signal being used for mixing in step one ₀=1.32 × 10 ¹⁴,

Step 6, repeats step one to the process of step 4 based on the chirp signal after amendment frequency modulation rate, obtains the second reconstruct radar signal x ₂;

Step 7, by described first reconstruct radar signal x ₁with described second reconstruct radar signal x ₂average addition, i.e. x'=(x ₁+ x ₂)/2, by adopting the mode of peak-peak search, obtain maximum multiple peak and the energy value of reconstruction signal, thus the reconstruct of realize target signal.

Preferably, a kind of system for realizing said method, described analog information converting system is made up of two groups of AIC random demodulation systems based on chirp mixing and totalizer; The signal input port of described two groups of AIC random demodulation systems is the input end of analog signal mouth of described analog information converting system, for receiving same simulating signal; The signal output port of described two groups of AIC random demodulation systems is connected with two signal input ports of totalizer respectively; The signal output port of described totalizer is the signal output port of described analog information converting system, for exporting reconfiguration information signal;

Described two groups of AIC random demodulation systems based on chirp mixing are used for the conversion of described simulating signal and reconstruct; Described totalizer is used for described first reconstruction signal x ₁with described second reconstruction signal x ₂superposition.

Preferably, the described AIC random demodulation system based on chirp mixing comprises: chirp detuner 1, low-pass filter 2, low speed ADC3, compression reconfiguration module 4; The signal input port a of described chirp detuner 1 is the signal input port of described AIC random demodulation system, the chirp signal input port b of described chirp detuner 1 receives chirp sequence, and the mixed frequency signal output port c of described chirp detuner 1 is connected with the signal input port of low-pass filter 2; The signal output port of described low-pass filter 2 is connected with the signal input port of described low speed ADC3; The signal output port of described low speed ADC3 is connected with the signal input port of described compression reconfiguration module 4; The described signal output port of compression reconfiguration module 4 is connected with one of signal input port of totalizer;

Described chirp regulator 1, for the mixing of chirp signal and simulating signal x (t), obtains mixed frequency signal; Described low-pass filter 2 is for the high-frequency interferencing signal in mixed frequency signal described in filtering; Described low speed ADC3 is used for the lack sampling of simulating signal, obtains undersampled signal; Described compression reconfiguration module 4, for implementing the orthogonal matching algorithm of compressed sensing to described undersampled signal, obtains reconstruction signal.

Preferably, simulating signal to be converted described in said system is radar signal.

Preferably, the process of orthogonal matching algorithm described in said system is:

The first step, first time iteration, find the most matched atoms coordinate k of restructuring matrix, and solve the maximal value of x;

Second step, obtains corresponding element matrix, and utilizes least square method to solve described corresponding element matrix equation;

3rd step, upgrades surplus, enters second time iteration, repeats the process of the first step to the 3rd step;

4th step, obtains institute's maximizing, iteration ends after several iteration.

Preferably, above-mentioned radar simulation signal translating system is made up of two groups of AIC random demodulation systems based on chirp mixing and totalizer; The signal input port of described two groups of AIC random demodulation systems is the input end of analog signal mouth of described analog information converting system, for receiving same radar signal; The signal output port of described two groups of AIC random demodulation systems is connected with two signal input ports of totalizer respectively; The signal output port of described totalizer is the signal output port of described analog information converting system, for exporting reconfiguration information signal;

Described two groups of AIC random demodulation systems based on chirp mixing are used for the conversion of described radar signal and reconstruct; Described totalizer is used for described first reconstruct radar signal x ₁with described second reconstruct radar signal x ₂superposition;

Preferably, above-mentioned radar simulation signal translating system, the described AIC random demodulation system based on chirp mixing comprises: chirp detuner 1, low-pass filter 2, low speed ADC3, compression reconfiguration module 4; The signal input port a of described chirp detuner 1 is the signal input port of described AIC random demodulation system, the chirp signal input port b of described chirp detuner 1 receives chirp sequence, and the mixed frequency signal output port c of described chirp detuner 1 is connected with the signal input port of low-pass filter 2; The signal output port of described low-pass filter 2 is connected with the signal input port of described low speed ADC3; The signal output port of described low speed ADC3 is connected with the signal input port of described compression reconfiguration module 4; The described signal output port of compression reconfiguration module 4 is connected with one of signal input port of totalizer;

Described chirp regulator 1 is for chirp signal and radar signal mixing, obtain mixed frequency signal; Described low-pass filter 2 is for the high-frequency interferencing signal in mixed frequency signal described in filtering; Described low speed ADC3 is used for the lack sampling of simulating signal, obtains undersampled signal; Described compression reconfiguration module 4, for implementing the orthogonal matching algorithm of compressed sensing to described undersampled signal, obtains reconstruction signal.

Above-mentioned module is run, and concrete steps are as follows:

Step one, the radar signal of described reception is its duration of pulse T ₀=1us, pulse-recurrence time PRT=8T ₀, priori bandwidth information B=64MHz and target are counted S=8; Chirp Design of Signal for mixing is as follows: getting duration of chirp consistent with input signal is T ₀=1us, and get its frequency modulation rate and equal K ₀=B/T=6.4 × 10 ¹³, i.e. C ₀=exp (j2 π K ₀t ²);

Step 2, is expressed as the process mathematic(al) representation of original signal and the mixing of chirp signal: y ₁=C ₁x; Wherein C ₁diagonal entry be C ₀repeat displacement, be full of the whole burst length, namely all the other elements are 0;

Step 3, supposes lack sampling original signal being carried out to 1/4, then whole lack sampling result is by the simply constructed low-pass filter H of the mode of adjacent 4 element overlaid

By obtaining the undersampled signal of 1/4 after low-pass filter be:

y' ₁＝Hy ₁＝HC ₁x

Step 4, according to orthogonal matching pursuit (orthogonalmatchingpursuit, the OMP) algorithm of compressed sensing, by undersampled signal y ' ₁reconstruct original radar signal and obtain x ₁;

Step 5, is set to 2K by the frequency modulation rate of the chirp signal being used for mixing in step one ₀=1.32 × 10 ¹⁴,

Step 6, repeats step one to the process of step 4 based on the chirp signal after amendment frequency modulation rate, obtains the second reconstruct radar signal x ₂;

Step 7, by described first reconstruct radar signal x ₁with described second reconstruct radar signal x ₂average addition, i.e. x'=(x ₁+ x ₂)/2, by adopting the mode of peak-peak search, obtain maximum multiple peak and the energy value of reconstruction signal, thus the reconstruct of realize target signal.

Beneficial effect of the present invention:

Analog information conversion method based on chirp mixing provided by the present invention and system are for solving clock jitter and the aperture effect of conventional high rate simulation PN sequence mixing existence; And relative to the analog information converting system of PN mixing, have higher signal reconstruction probability.Under making the analog information converting system based on chirp mixing to be operated in ultra wideband environment, and pass through the detection method of twice chirp mixing reconstruction signal superposition, the detection probability of the effective target of undersampled signal can be improved.

Accompanying drawing explanation

Fig. 1 is the analog information conversion system structure schematic diagram based on chirp mixing of the present invention;

Fig. 2 is the AIC random demodulation system architecture schematic diagram based on chirp mixing of the present invention;

Fig. 3 is adjacent target reconstruction result schematic diagram;

Fig. 4 is analog information converting system based on chirp mixing and the AIC random demodulation system based on chirp mixing and conventional P N mixing system performance comparison figure;

Fig. 5 is the reconstruction result contrast of 1/2 lack sampling;

Fig. 6 is the reconstruction result contrast of 1/4 lack sampling;

Fig. 7 is the reconstruction result contrast of 1/8 lack sampling;

Fig. 8 is the contrast of signal of communication lack sampling reconstruction result;

Embodiment

Composition graphs 1 and Fig. 2 are simulating signal to be converted for radar signal, and the described analog information conversion method based on chirp mixing comprises:

Experiment 1, the lack sampling test of radar signal

Step one, the radar signal of described reception is its duration of pulse T ₀=1us, pulse-recurrence time PRT=8T ₀, priori bandwidth information B=64MHz and target are counted S=8.Chirp Design of Signal then for mixing is as follows: getting duration of chirp consistent with input signal is T ₀=1us, and get its frequency modulation rate and equal K ₀=B/T=6.4 × 10 ¹³, i.e. C ₀=exp (j2 π K ₀t ²);

Step 2, is expressed as the process mathematic(al) representation of original signal and the mixing of chirp signal: y ₁=C ₁x; Wherein C ₁diagonal entry be C ₀repeat displacement, be full of the whole burst length, namely all the other elements are 0;

Step 3, supposes lack sampling original signal being carried out to 1/4, then whole lack sampling result is by the simply constructed low-pass filter H of the mode of adjacent 4 element overlaid,

By the signal of the lack sampling obtaining 1/4 after low-pass filter be:

y' ₁＝Hy ₁＝HC ₁x

Step 4, according to orthogonal matching pursuit (orthogonalmatchingpursuit, the OMP) algorithm of compressed sensing, by undersampled signal y' ₁reconstruct original radar signal and obtain x ₁;

Step 5, is set to 2K by the frequency modulation rate of the chirp signal being used for mixing in step one ₀=1.32 × 10 ¹⁴,

Step 6, repeats step one to the process of step 4 based on the chirp signal after amendment frequency modulation rate, obtains the second reconstruct radar signal x ₂;

Step 7, by described first reconstruct radar signal x ₁with described second reconstruct radar signal x ₂average addition, i.e. x'=(x ₁+ x ₂)/2, by adopting the mode of peak-peak search, obtain maximum multiple peak and the energy value of reconstruction signal, thus the reconstruct of realize target signal.

Orthogonal matching pursuit (orthogonalmatchingpursuit, OMP) the algorithmic derivation process of described compressed sensing is as follows:

Will about l ₀the Solve problems of norm is summed up as l ₁norm optimization problem:

$P_1:\underset{x\∈R^N}{\min }\left|\right|x|{|}_1$

s.t.Φx＝y

Wherein Φ x=y (Φ=[φ ₁, φ ₂... φ _i..., φ _n] be restructuring matrix) can be write as following form:

$\left\{\begin{array}{c}{\mathrm{\θ}}_{11}{x}_1+{\mathrm{\θ}}_{12}{x}_2+......+{\mathrm{\θ}}_{1N}{x}_N=y_1\\ {\mathrm{\θ}}_{21}{x}_1+{\mathrm{\θ}}_{22}{x}_2+......+{\mathrm{\θ}}_{2N}{x}_N=y_2\\ ................................................\\ {\mathrm{\θ}}_{M1}{x}_1+{\mathrm{\θ}}_{M2}{x}_2+......+{\mathrm{\θ}}_{MN}{x}_N=y_M\end{array}\right.$

Its least square solution is:

$\mathrm{\Φ}x=y\⇒{\mathrm{\Φ}}^T\mathrm{\Φ}x={\mathrm{\Φ}}^{T}y\⇒x={\left({\mathrm{\Φ}}^T\mathrm{\Φ}\right)}^{-1}{\mathrm{\Φ}}^{T}y$

Concrete calculation process is as follows:

As Φ (Φ=[φ ₁, φ ₂... φ _i..., φ _n], wherein φ _icolumn vector) when not being square formation, first time iteration, find the atomic coordinates k mated most, concrete operations are the modes this system of equations of Φ x=y being adopted feature decomposition:

$\begin{array}{c}\[{\mathrm{\φ}}_1,{\mathrm{\φ}}_2,\mathrm{...}{\mathrm{\φ}}_i,\mathrm{...},{\mathrm{\φ}}_N\]\left[\begin{array}{c}{x}_1\\ x_2\\ .\\ .\\ .\\ x_i\\ .\\ .\\ .\\ x_N\end{array}\right]=\left[\begin{array}{c}{y}_1\\ .\\ .\\ .\\ y_j\\ .\\ .\\ .\\ y_M\end{array}\right]\\ \⇒{\mathrm{\φ}}_1{x}_1+{\mathrm{\φ}}_2{x}_2+\mathrm{...}+{\mathrm{\φ}}_i{x}_i+\mathrm{...}{\mathrm{\φ}}_N{x}_N=y\end{array}$

So-called OMP algorithm is exactly the orthogonality algorithm between hypothesis substrate, i.e. φ _i ^tφ _i=1, φ _i ^tφ _j=0 (i ≠ j), so for φ ₁x ₁+ φ ₂x ₂+ ... + φ _ix _i+ ... φ _nx _n=y then has:

$\begin{array}{c}{\mathrm{\φ}}_i^T({\mathrm{\φ}}_1{x}_1+{\mathrm{\φ}}_2{x}_2+\mathrm{...}+{\mathrm{\φ}}_i{x}_i+\mathrm{...}{\mathrm{\φ}}_N{x}_N)={\mathrm{\φ}}_i^{T}y\\ \⇒x_i={\mathrm{\φ}}_i^{T}y\end{array}$

Thus try to achieve the maximal value of x, obtaining corresponding element is Ψ=[φ _k], thus solve due to φ _knot square formation, when therefore solving, by least square method, namely

$\begin{array}{c}{\mathrm{\φ}}_{k}x=y\⇒{{\mathrm{\φ}}_k}^T{\mathrm{\φ}}_{k}x={{\mathrm{\φ}}_k}^{T}y\\ \⇒x={\left({{\mathrm{\φ}}_k}^T{\mathrm{\φ}}_k\right)}^{-1}{{\mathrm{\φ}}_k}^{T}y\end{array}$

Then surplus r is upgraded ₀=y-φ _kx=y-φ _k(φ _k ^tφ _k) ^-1φ _k ^ty, enters second time iteration:

Find the atomic coordinates k mated most ₁, then obtaining corresponding element is thus solve due to φ _knot square formation, when therefore solving, by least square method, namely

$\begin{array}{c}\[{\mathrm{\φ}}_k,{\mathrm{\φ}}_{k_1}\]x=y\⇒{\mathrm{\Ψ}}^T\mathrm{\Ψ}x={\mathrm{\Ψ}}^{T}y\\ \⇒x={\left({\mathrm{\Ψ}}^T\mathrm{\Ψ}\right)}^{-1}{\mathrm{\Ψ}}^{T}y\end{array}$

Then surplus r is upgraded ₀=y-Ψ x=y-Ψ (Ψ ^tΨ) ^-1Ψ ^ty, enters third time iteration, and circulation is gone down successively, after obtaining required maximal value number, and iteration ends.

Described analog information converting system is made up of two groups of AIC random demodulation systems based on chirp mixing and totalizer; The signal input port of described two groups of AIC random demodulation systems is the input end of analog signal mouth of described analog information converter, for receiving same simulating signal; The signal output port of described two groups of AIC random demodulation systems is connected with two signal input ports of totalizer respectively; The signal output port of described totalizer is the signal output port of described analog information converter, for exporting reconfiguration information signal.Described two groups of AIC random demodulation systems based on chirp mixing are used for the conversion of described simulating signal and reconstruct; Preferably described, totalizer is used for described first reconstruction signal x ₁with described second reconstruction signal x ₂superposition.

The described AIC random demodulation system based on chirp mixing comprises: chirp detuner 1, low-pass filter 2, low speed ADC3, compression reconfiguration module 4; The signal input port a of described chirp detuner 1 is the signal input port of described AIC random demodulation system, the chirp signal input port b of described chirp detuner 1 receives chirp sequence, and the mixed frequency signal output port c of described chirp detuner 1 is connected with the signal input port of low-pass filter 2; The signal output port of described low-pass filter 2 is connected with the signal input port of described low speed ADC3; The signal output port of described low speed ADC3 is connected with the signal input port of described compression reconfiguration module 4; The described signal output port of compression reconfiguration module 4 is connected with one of signal input port of totalizer.Described chirp regulator 1, for the mixing of chirp signal and simulating signal x (t), obtains mixed frequency signal; Described low-pass filter 2 is for the high-frequency interferencing signal in mixed frequency signal described in filtering; Described low speed ADC3 is used for the lack sampling of simulating signal, obtains undersampled signal; Described compression reconfiguration module 4, for implementing the orthogonal matching algorithm of compressed sensing to described undersampled signal, obtains reconstruction signal.

Radar simulation signal translating system is made up of two groups of AIC random demodulation systems based on chirp mixing and totalizer; The signal input port of described two groups of AIC random demodulation systems is the input end of analog signal mouth of described analog information converting system, for receiving same radar signal; The signal output port of described two groups of AIC random demodulation systems is connected with two signal input ports of totalizer respectively; The signal output port of described totalizer is the signal output port of described analog information converting system, for exporting reconfiguration information signal;

Described two groups of AIC random demodulation systems based on chirp mixing are used for the conversion of described radar signal and reconstruct; Described totalizer is used for described first reconstruct radar signal x ₁with described second reconstruct radar signal x ₂superposition;

In above-mentioned radar simulation signal translating system, the described AIC random demodulation system based on chirp mixing comprises: chirp detuner 1, low-pass filter 2, low speed ADC3, compression reconfiguration module 4; The signal input port a of described chirp detuner 1 is the signal input port of described AIC random demodulation system, the chirp signal input port b of described chirp detuner 1 receives chirp sequence, and the mixed frequency signal output port c of described chirp detuner 1 is connected with the signal input port of low-pass filter 2; The signal output port of described low-pass filter 2 is connected with the signal input port of described low speed ADC3; The signal output port of described low speed ADC3 is connected with the signal input port of described compression reconfiguration module 4; The described signal output port of compression reconfiguration module 4 is connected with one of signal input port of totalizer;

Described chirp regulator 1 is for chirp signal and radar signal mixing, obtain mixed frequency signal; Described low-pass filter 2 is for the high-frequency interferencing signal in mixed frequency signal described in filtering; Described low speed ADC3 is used for the lack sampling of simulating signal, obtains undersampled signal; Described compression reconfiguration module 4, for implementing the orthogonal matching algorithm of compressed sensing to described undersampled signal, obtains reconstruction signal;

Composition graphs 3 to Fig. 7 illustrate conversion method described in present embodiment and validity, concrete simulation example and being analyzed as follows:

Table 1 radar signal optimum configurations

Suppose sparse positional number be S, PRT count as N, then compressed sensing is counted with high probability reconstruct original signal required reconstruct:

$M=O(S\·log(\frac{N}{S}))$

Rule of thumb value, sparse position be S=8, PRT count needed for the reconstruct of N=512 minimum count into:

$M=1.78S\·log\left(\frac{N}{S}\right)=1.78\×8\×log\left(\frac{512}{8}\right)=85$

The parameter arranged by table 1 can be obtained: when adopting nyquist sampling, and counting of signal is that to count shared by 64, PRT be 512.The equivalent position point that the equivalent delay of target is corresponding is: N _{τ 1}=64, N _{τ 2}=127, N _{τ 3}=128, N _{τ 4}=210, N _{τ 5}=277, N _{τ 6}=310, N _{τ 7}=389, N _{τ 8}=413.When the lack sampling of employing 1/2,1/4,1/8, counting of signal is followed successively by: 256, and 128,64.We carry out the performance evaluation of being correlated with for these parameters.

As can be seen from Figure 3, the main application of ultra broadband in radar is the high-resolution of target, and therefore all Undersampling technique can not have lost this characteristic of ultra broadband.In order to verify based on chirp mixing analog information converter realize lack sampling reconstruct time, the target resolution of wideband radar can be ensured, get adjacent two position: the N in above-mentioned 8 sparse targets _{τ 2}=127 and N _{τ 3}=128.Analog information converter based on chirp mixing can reconstruct adjacent target information accurately, and therefore it does not reduce the resolving power of target when carrying out compressed sensing lack sampling.

As can be seen from Figure 4, under the prerequisite not considering clock jitter and aperture effect, performance based on the AIC random demodulation system of chirp mixing is better than the reconstruction property of the analog information converting system based on the mixing of PN sequence, and the gain of more than 3dB is had especially based on the analog information converting system of chirp mixing, its reconstruction property is better.

In as can be seen from Fig. 5 to Fig. 7, with 1/2 under compressed sensing is with the condition of the empirical parameter M=85 of high probability reconstruct original signal, 1/4, with under the environment of 1/8 lack sampling, contrast based on the analog information converter of chirp mixing and the impact of performance of traditional analog information converter based on PN sequence.Can find out that the advantage based on chirp mixing is more and more obvious along with the minimizing that lack sampling is counted.When 1/8 lack sampling, counting as 512/8=64 point after lack sampling, has been less than experience point 85 point of compressed sensing reconstruct.Based on PN sequence analog information converter can not high probability reconstruct original signal.Now, revise 8 times that the chirp signal frequency modulation rate being used for mixing is original signal frequency modulation rate, then when high s/n ratio, original signal can be reconstructed, thus achieve the reconstruct to the experience point being less than compressed sensing reconstruct.

Experiment 2, the experiment of communication real signal

Signal of communication is x (t)=cos (2 π f ₀t)+cos (2 π f ₁t), wherein f ₀=32Hz, f ₁=128Hz, then according to Shannon's theorems, Minimum sample rate is 256Hz, and detailed signal parameter is as table 2.Experimental procedure is similar with experiment 1, seldom describes here.

Table 2 communication signal parameters is arranged

Parameter	Value
		Signal sampling frequency	256Hz
Signal duration T	1s
		Lack sampling multiple	0.25
Cos signal number	2
		The frequency of cos signal	32Hz and 128Hz
Signal to noise ratio (S/N ratio)	15dB

As can be seen from Figure 8, the analog information conversion method based on chirp mixing effectively can reconstruct original signal information, and waits observing matrix to have identical normalized mean squared error with use Gauss.But chirp mixing uses determines signal mixing, there is relative to Gauss's observing matrix etc. the advantage being easy to produce and store.

Although the present invention with preferred embodiment openly as above; but it is also not used to limit the present invention, any person skilled in the art, without departing from the spirit and scope of the present invention; can do various change and modification, what therefore protection scope of the present invention should define with claims is as the criterion.

Claims (10)

1. based on analog information conversion method and the system of chirp mixing, it is characterized in that, described analog information conversion method process is:

Step one, regulate the chirp signal being used for mixing, make the duration of described chirp signal consistent with the duration of simulating signal x (t), the frequency modulation rate of described chirp signal is B/T; Wherein, B is priori bandwidth information, and T is the duration of simulating signal x (t);

Step 2, described simulating signal x (t) and chirp signal optical mixing process mathematic(al) representation are showed, described mathematic(al) representation is: y ₁=C ₁x, wherein, C ₁for constant matrices, its diagonal entry is be the chirp sequence of B/T for frequency modulation rate, and all the other elements are 0;

Step 3, carries out the lack sampling of 1/M to described simulating signal x (t), utilize the mode of an adjacent M element overlaid by the simply constructed low-pass filter of whole lack sampling result, and obtain the M after by low-pass filter times of undersampled signal y ' ₁=Hy ₁=HC ₁x; Wherein, M be greater than zero positive integer, H is the equivalent convolution matrix of low-pass filter, and

Step 4, according to the orthogonal matching algorithm of compressed sensing, utilizes described M times undersampled signal to be reconstructed described simulating signal x (t), draws the first reconstruction signal x ₁;

Step 5, is set to 2B/T by the frequency modulation rate of the signal of chirp described in step one;

Step 6, repeats step one to the process of step 4 based on the chirp signal after amendment frequency modulation rate, obtains the second reconstruction signal x ₂;

Step 7, by described first reconstruction signal x ₁with described second reconstruction signal x ₂average addition, utilizes peak-peak way of search to obtain maximum multiple peak and the energy value of reconstruction signal.

2. method according to claim 1, it is characterized in that, described simulating signal x (t) to be converted is radar signal.

3. method according to claim 1, it is characterized in that, the process of the orthogonal matching algorithm related in described step 4 is:

The first step, first time iteration, find the most matched atoms coordinate k of restructuring matrix, and solve the maximal value of x;

Second step, obtains corresponding element matrix, and utilizes least square method to solve described corresponding element matrix equation;

3rd step, upgrades surplus, enters second time iteration, repeats the process of the first step to the 3rd step;

4th step, obtains institute's maximizing, iteration ends after several iteration.

4. method according to claim 2, it is characterized in that, the switch process of described radar signal is as follows:

Step one, the radar signal of described reception is its duration of pulse T ₀=1us, pulse-recurrence time PRT=8T ₀, priori bandwidth information B=64MHz and target are counted S=8; Chirp Design of Signal for mixing is as follows: getting duration of chirp consistent with input signal is T ₀=1us, and get its frequency modulation rate and equal K ₀=B/T=6.4 × 10 ¹³, i.e. C ₀=exp (j2 π K ₀t ²);

Step 2, is expressed as the process mathematic(al) representation of original signal and the mixing of chirp signal: y ₁=C ₁x; Wherein C ₁diagonal entry be C ₀repeat displacement, be full of the whole burst length, namely all the other elements are 0;

Step 3, supposes lack sampling original signal being carried out to 1/4, then whole lack sampling result is by the simply constructed low-pass filter H of the mode of adjacent 4 element overlaid

By obtaining the undersampled signal of 1/4 after low-pass filter be:

y′ ₁＝Hy ₁＝HC ₁x

Step 4, according to orthogonal matching pursuit (orthogonalmatchingpursuit, the OMP) algorithm of compressed sensing, by undersampled signal y ' ₁reconstruct original radar signal and obtain x ₁;

Step 5, is set to 2K by the frequency modulation rate of the chirp signal being used for mixing in step one ₀=1.32 × 10 ¹⁴,

Step 6, repeats step one to the process of step 4 based on the chirp signal after amendment frequency modulation rate, obtains the second reconstruct radar signal x ₂;

Step 7, by described first reconstruct radar signal x ₁with described second reconstruct radar signal x ₂average addition, i.e. x'=(x ₁+ x ₂)/2, by adopting the mode of peak-peak search, obtain the maximum multiple peak and the energy value that reconstruct radar signal, thus the reconstruct of realize target radar signal.

5. for realizing a system for claim 1 method, it is characterized in that, described analog information converting system is made up of two groups of AIC random demodulation systems based on chirp mixing and totalizer; The signal input port of described two groups of AIC random demodulation systems is the input end of analog signal mouth of described analog information converting system, for receiving same simulating signal; The signal output port of described two groups of AIC random demodulation systems is connected with two signal input ports of totalizer respectively; The signal output port of described totalizer is the signal output port of described analog information converting system, for exporting reconfiguration information signal;

Described two groups of AIC random demodulation systems based on chirp mixing are used for the conversion of described simulating signal and reconstruct; Described totalizer is used for described first reconstruction signal x ₁with described second reconstruction signal x ₂superposition.

6. system according to claim 5, it is characterized in that, the described AIC random demodulation system based on chirp mixing comprises: chirp detuner (1), low-pass filter (2), low speed ADC (3), compression reconfiguration module (4); The signal input port (a) of described chirp detuner (1) is the signal input port of described AIC random demodulation system, chirp signal input port (b) of described chirp detuner (1) receives chirp sequence, and mixed frequency signal output port (c) of described chirp detuner (1) is connected with the signal input port of low-pass filter (2); The signal output port of described low-pass filter (2) is connected with the signal input port of described low speed ADC (3); The signal output port of described low speed ADC (3) is connected with the signal input port of described compression reconfiguration module (4); The described signal output port of compression reconfiguration module (4) is connected with one of signal input port of totalizer;

Described chirp regulator (1), for the mixing of chirp signal and simulating signal x (t), obtains mixed frequency signal; Described low-pass filter (2) is for the high-frequency interferencing signal in mixed frequency signal described in filtering; Described low speed ADC (3), for the lack sampling of simulating signal, obtains undersampled signal; Described compression reconfiguration module (4), for implementing the orthogonal matching algorithm of compressed sensing to described undersampled signal, obtains reconstruction signal.

7. system according to claim 6, it is characterized in that, described simulating signal to be converted is radar signal.

8. system according to claim 7, it is characterized in that, the process of described orthogonal matching algorithm is:

The first step, first time iteration, find the most matched atoms coordinate k of restructuring matrix, and solve the maximal value of x;

Second step, obtains corresponding element matrix, and utilizes least square method to solve described corresponding element matrix equation;

3rd step, upgrades surplus, enters second time iteration, repeats the process of the first step to the 3rd step;

4th step, obtains institute's maximizing, iteration ends after several iteration.

9. system according to claim 7, it is characterized in that, described analog information converting system is made up of two groups of AIC random demodulation systems based on chirp mixing and totalizer; The signal input port of described two groups of AIC random demodulation systems is the input end of analog signal mouth of described analog information converting system, for receiving same radar signal; The signal output port of described two groups of AIC random demodulation systems is connected with two signal input ports of totalizer respectively; The signal output port of described totalizer is the signal output port of described analog information converting system, for exporting reconfiguration information signal;

Described two groups of AIC random demodulation systems based on chirp mixing are used for the conversion of described radar signal and reconstruct; Described totalizer is used for described first reconstruct radar signal x ₁with the described second heavy radar structure signal x ₂superposition;

10. system according to claim 7, it is characterized in that, the described AIC random demodulation system based on chirp mixing comprises: chirp detuner (1), low-pass filter (2), low speed ADC (3), compression reconfiguration module (4); The signal input port (a) of described chirp detuner (1) is the signal input port of described AIC random demodulation system, chirp signal input port (b) of described chirp detuner (1) receives chirp sequence, and mixed frequency signal output port (c) of described chirp detuner (1) is connected with the signal input port of low-pass filter (2); The signal output port of described low-pass filter (2) is connected with the signal input port of described low speed ADC (3); The signal output port of described low speed ADC (3) is connected with the signal input port of described compression reconfiguration module (4); The described signal output port of compression reconfiguration module (4) is connected with one of signal input port of totalizer;

Described chirp regulator (1) is for chirp signal and radar signal mixing, obtain mixed frequency signal; Described low-pass filter (2) is for the high-frequency interferencing signal in mixed frequency signal described in filtering; Described low speed ADC (3), for the lack sampling of radar signal, obtains undersampled signal; Described compression reconfiguration module (4), for implementing the orthogonal matching algorithm of compressed sensing to described undersampled signal, obtains reconstruction signal;

Above-mentioned module is run, and concrete steps are as follows:

Step one, the radar signal of described reception is its duration of pulse T ₀=1us, pulse-recurrence time PRT=8T ₀, priori bandwidth information B=64MHz and target are counted S=8; Chirp Design of Signal for mixing is as follows: getting duration of chirp consistent with input signal is T ₀=1us, and get its frequency modulation rate and equal K ₀=B/T=6.4 × 10 ¹³, i.e. C ₀=exp (j2 π K ₀t ²);

Step 2, is expressed as the process mathematic(al) representation of original signal and the mixing of chirp signal: y ₁=C ₁x; Wherein C ₁diagonal entry be C ₀repeat displacement, be full of the whole burst length, namely all the other elements are 0;

Step 3, supposes lack sampling original signal being carried out to 1/4, then whole lack sampling result is by the simply constructed low-pass filter H of the mode of adjacent 4 element overlaid

By obtaining the undersampled signal of 1/4 after low-pass filter be:

y′ ₁＝Hy ₁＝HC ₁x

Step 4, according to orthogonal matching pursuit (orthogonalmatchingpursuit, the OMP) algorithm of compressed sensing, by undersampled signal y ' ₁reconstruct original radar signal and obtain x ₁;

Step 5, is set to 2K by the frequency modulation rate of the chirp signal being used for mixing in step one ₀=1.32 × 10 ¹⁴,

Step 6, repeats step one to the process of step 4 based on the chirp signal after amendment frequency modulation rate, obtains the second reconstruct radar signal x ₂;

Step 7, by described first reconstruct radar signal x ₁with described second reconstruct radar signal x ₂average addition, i.e. x'=(x ₁+ x ₂)/2, by adopting the mode of peak-peak search, obtain maximum multiple peak and the energy value of reconstruction signal, thus the reconstruct of realize target signal.