CN103018732B - MIMO (multi-input multi-output) radar waveform synthesis method based on space-time joint optimization - Google Patents

Abstract

The invention discloses an MIMO (multi-input multi-output) radar waveform synthesis method based on space-time joint optimization. The method mainly solves the problem that existing methods are poor in autocorrelation property of air domain composite signals under the condition of guarantee of space power distribution of transmitted waveforms. The method includes the steps: determining a correlation matrix of a transmitted waveform according to actual demands; generating an initial constant modulus waveform matrix; determining an interested observation azimuth angle, namely an azimuth angle needing improvement of the autocorrelation property; designing a constant modulus waveform phase matrix by means of sequential quadratic programming; and synthesizing a constant modulus waveform matrix according to the phase matrix. The air domain property of the transmitted waveforms and the time domain autocorrelation property of specific direction signals are considered during waveform design, the synthesized waveforms are in expected space power distribution and have fine time domain autocorrelation property in the interested direction, and the method can be used for waveform design of MIMO radar in stages of target detection and tracking.

Description

The MIMO radar waveform synthetic method of optimizing based on space-time joint

Technical field

The invention belongs to Radar Technology field, relate to the synthetic of radar waveform, can be used for the Waveform Design of MIMO radar at target detection and tracking phase, to meet engineering desired properties.

Background technology

Multiple-input and multiple-output MIMO radar is a kind of emerging active detection technology, has now become a study hotspot in Radar Technology field.According to the arrangement of antenna, MIMO radar can be divided into distributed MIMO radar and centralized MIMO radar two classes.Wherein the feature of centralized MIMO radar is that array element distance is less, has the ability that freely designs every slave antenna waveform, i.e. waveform diversity.Compared with phased-array radar, the degree of freedom of centralized MIMO radar has improved, and this makes MIMO radar have more superiority, as better parameter resolving ability, transmitting pattern designed capacity etc. more flexibly.

At present, the Waveform Design of MIMO radar mainly comprises the aspect such as Waveform Design of orthogonal waveforms design, particular transmission directional diagram.Wherein, orthogonal waveforms design is mainly for the detection of target; The Waveform Design of particular transmission directional diagram, mainly for the tracking of target, solves the dimensional energy assignment problem of radar system.

Design for orthogonal waveforms, mainly the orthogonality based on signal between array element designs transmitted waveform at present, as [Deng H..Polyphase Code Design for Orthogonal Netted Radar Systems.IEEE Trans.on Signal Processing.2004, Vol.52 (11) .3126-3135.].Although adopt the waveform that this type of mode designs can ensure that between array element, signal has good orthogonality, the pulse pressure characteristic of space composite signal is poor, is unfavorable for weak target detection.For the Waveform Design of particular transmission directional diagram, current method mainly comprises two steps: signal correlation matrix optimization and transmitted waveform are comprehensive.Wherein signal correlation matrix optimization, the comparatively effective method of delivering on international publication is positive semidefinite law of planning (the Semi-defined programming that Stoica Petre and Li Jian propose, SDP), see [Stoica P., Li J., XieY..On probing signal design for MIMO radar.IEEE Trans.on Signal Processing.2007, Vol.55 (8) .4151-4161], the method under minimum mean square error criterion, obtains the signal correlation matrix of global optimum according to given transmitting pattern.Comprehensive for transmitted waveform, effective method is round-robin algorithm (Cyclic Algorithm at present, CA), see [Stoica P., Li J., ZhuX..Waveform Synthesis for Diversity-Based Transmit Beampattern Design.IEEE Trans.on Signal Processing.2008, Vol.56 (6) .2593-2598].This algorithm, in the situation that meeting signal and being permanent mould, stresses to consider the approximation problem of transmitting pattern, and there is no to consider the correlation properties of " space composite signal " or " echoed signal ".

In reality, for radar system, not only wish to transmit to there is constant modulus property, and should there is following characteristic:

1) transmit waveform should have expectation spatial power distribute, the transmitting pattern that formed will approach the transmitting pattern of expectation.

2) space composite signal or echoed signal have good pulse pressure characteristic, and the time domain autocorrelation peak sidelobe level of echoed signal is low.

Above-mentioned existing waveform design method has only ensured that the spatial power of transmitted waveform distributes, and do not consider the autocorrelation performance of space composite signal or echoed signal, may cause the signal after pulse pressure to there is higher peak sidelobe, be unfavorable for weak target detection.

Summary of the invention

The object of the invention is to the deficiency for above-mentioned prior art, a kind of MIMO radar waveform synthetic method of optimizing based on space-time joint is proposed, to ensure that waveform can approach desired orientation figure, and improve the time domain autocorrelation performance of echoed signal, and then improve follow-up target detection performance.

For achieving the above object, MIMO radar waveform synthetic method of the present invention, comprises the steps:

(1) determine the correlation matrix R of transmitted waveform, wherein R is the Hermitian positive semidefinite matrix of M dimension, and M represents to launch element number of array;

(2) produce at random the initial permanent mould waveform matrix X that L × M ties up ⁰, wherein L represents the code length transmitting;

(3) determine interested observed azimuth

be the position angle that autocorrelation performance need to improve, wherein I represents the total number of interested observed azimuth;

(4) according to correlation matrix R, initial permanent mould waveform matrix X ⁰, the phasing matrix Φ that design dimension is L × M:

(4a) set up the following Optimized model of phasing matrix Φ:

$\underset{\mathrm{\Φ}}{\min }\max \left\{\underset{{\left\{{\mathrm{\α}}_i\right\}}_{i=1}^I}{\underset{k=1,...,L-1}{\max }}\right[\left|f(\mathrm{\Φ},{\mathrm{\α}}_i,k)\right|],\underset{p=1,...,M-1}{\underset{q=p+1,...,M}{\max }}[\mathrm{\μ}|g(\mathrm{\Φ},p,q)-R_{\mathrm{pq}}|\left]\right\},$

Wherein, g (Φ, p, q) be p that phasing matrix Φ is corresponding with the related coefficient of q array element waveform, R _pqthe capable q column element of p that represents correlation matrix R, μ represents that directional diagram approaches weight, || represent plural mould value or absolute value of a real number; F (Φ, α _i, be k) that waveform that phasing matrix Φ is corresponding is at α _ithe normalized autocorrelation functions value at k delay positions place in direction, is expressed as:

$f(\mathrm{\Φ},{\mathrm{\α}}_i,k)=\frac{1}{L}\left|a^H\left({\mathrm{\α}}_i\right){\left[\exp \left(\mathrm{j\Φ}\right)\right]}^H{J}_k\exp \left(\mathrm{j\Φ}\right)a\left({\mathrm{\α}}_i\right)\right|/\left[a^H\left({\mathrm{\α}}_i\right)\mathrm{Ra}\left({\mathrm{\α}}_i\right)\right]$

Wherein a (α _i) expression α _ithe steering vector of direction, i=1 ..., I, exp (j Φ) represents the permanent modular matrix forming taking each element in phasing matrix Φ as phase place, and symbol j represents imaginary unit, and symbol exp () represents the exponential function taking natural logarithm e the end of as, J _krepresent the excursion matrix of L × L dimension, k=1 ..., L-1, () ^hrepresent conjugate transpose;

(4b) utilize the mathematical model in seqential quadratic programming solution procedure (4a), obtain phasing matrix Φ;

(5) according to phasing matrix Φ, synthetic permanent mould waveform matrix X=[x ₁, x ₂... x _m], this perseverance mould waveform matrix X is final synthetic MIMO radar waveform, wherein, and vector x _m=[x _1m..., x _lm] ^tthe m row of representing matrix X,

represent the capable m column element of l of phasing matrix Φ, l=1 ..., L, m=1 ..., M, () ^trepresent transposition.

The present invention has the following advantages:

1) the present invention, due to orthogonal Waveform Design and the Waveform Design with specific direction figure have been set up to unified model, therefore can adopt unified signal processing mode at receiving end, and then reduce system complexity;

2) the present invention is owing to having considered the spatial domain characteristic of waveform and the time domain specification of direction signal interested in transmitted waveform design process simultaneously, the waveform of synthesized not only can approach the directional diagram of expectation, and upwards has good time domain autocorrelation performance in interested parties.

Brief description of the drawings

Fig. 1 is main flow chart of the present invention;

Fig. 2 is the directional diagram of emulation orthogonal waveforms of the present invention;

Fig. 3 is the upwards autocorrelation sequence figure of signal of emulation interested parties of the present invention;

Fig. 4 is the directional diagram of emulation broad beam waveform of the present invention;

Fig. 5 is the upwards autocorrelation sequence figure of signal of emulation interested parties of the present invention;

Fig. 6 is the directional diagram of emulation multi-beam waveform of the present invention;

Fig. 7 is the autocorrelation sequence figure of signal in simulation objectives direction of the present invention.

Embodiment

With reference to Fig. 1, the specific implementation step of the present embodiment is as follows:

Step 1, determines the correlation matrix of transmitted waveform.

According to different waveform needs, determine the correlation matrix of transmitted waveform according to following two kinds of modes:

The first, for orthogonal waveforms design, the correlation matrix of transmitted waveform is defined as R=I _m, wherein I _mthe unit matrix that represents M dimension, M represents to launch array number;

The second, for the Waveform Design of particular transmission directional diagram, adopts protruding optimization tool bag cvx to solve following transmitting pattern Matching Model, obtains the correlation matrix R of transmitted waveform:

$\underset{\mathrm{\α},R}{\min }\underset{n=1}{\overset{N_s}{\mathrm{\Σ}}}{\mathrm{\ω}}_n{[\mathrm{\αD}\left({\mathrm{\θ}}_n\right)-a^H\left({\mathrm{\θ}}_n\right)\mathrm{Ra}\left({\mathrm{\θ}}_n\right)]}^2$

s.t.R _mm=1,m=1,…,M

R≥0

Wherein ω _nbe n azimuth angle theta _nthe weight at place, a (θ _n) be θ _nthe steering vector at place, n=1 ..., N _s, N _sfor spatial sampling is counted, α is scale factor, R _mmfor m the diagonal element of transmitted waveform correlation matrix R, () ^hrepresent conjugate transpose, D (θ _n) be the transmitting pattern of expectation, be expressed as:

Wherein F ₁(θ _n) be the expectation transmitting pattern of target tracking stage, be expressed as:

Wherein θ _nrepresent discrete azimuth angle, β _v>=0 represents weights, P _v(θ _n) represent that traditional phased-array radar points to target direction

time wave beam, Ω _vrepresent P _v(θ _n) main lobe region, n=1 ..., N _s, v=1 ... V, V is target number;

F ₂(θ _n) be the expectation transmitting pattern in zonule target search stage, be expressed as:

Wherein δ represents half beam width, θ ₀represent beam position, θ _nrepresent discrete azimuth angle, n=1 ..., N _s.

Step 2, produces initial permanent mould waveform matrix.

Adopt random fashion to produce the permanent mould waveform matrix that a L × M ties up, as initial permanent mould waveform matrix X ⁰,

The concrete form of initial permanent mould waveform matrix is

$X^0=[x_1^0,x_{2,...}^0{x}_M^0],$

Wherein, vector

initial permanent mould waveform matrix X ⁰m row, represent the waveform of m array element, wherein

initial waveform matrix X ⁰the capable m column element of l, l=1 ..., L, m=1 ..., M, () ^trepresent transposition, || represent plural mould value, L represents code length.

Step 3, determines interested observed azimuth, the position angle that autocorrelation performance need to improve.

According to different waveforms, set as follows interested observed azimuth

(3.1), for orthogonal waveforms, set interested observed azimuth and be:

${\mathrm{\α}}_i=\frac{180}{\mathrm{\π}}\arcsin (-1+2\mathrm{\Δf}(i-1)),i=1,...,I$

Wherein arc sin represents arcsin function, normalization spatial frequency interval

the total number of interested observed azimuth is I=4M+1;

(3.2), for broad beam waveform, set interested observed azimuth and be:

${\mathrm{\α}}_i=\frac{180}{\mathrm{\π}}\arcsin [\sin ({\mathrm{\θ}}_0-\mathrm{\δ})+2\mathrm{\Δf}(i-1)],i=1,...,I$

Wherein δ represents half beam width, θ ₀represent beam position, normalization spatial frequency interval

the total number of interested observed azimuth is

represent to be not less than 4Mcos θ ₀the smallest positive integral of sin δ;

(3.3), for multi-beam waveform, set interested observed azimuth and be:

Wherein γ represents half-power beam width, and symbol rem (i, 3) represents that i is to 3 complementations, symbol

represent to be not less than the smallest positive integral of i/3,

represent the

individual target direction, the total number of interested observed azimuth is I=3V, V represents target number.

Step 4, utilizes seqential quadratic programming to design the phasing matrix of permanent mould waveform.

(4.1) set up the Optimized model of phasing matrix Φ:

If the phasing matrix of L × M dimension is Φ, the element of the capable m row of its l is

l=1 ..., L, m=1 ..., M,

the phase place that represents the capable m column element of permanent mould waveform matrix X l to be designed, the Optimized model of setting up phasing matrix Φ is as follows:

$\underset{\mathrm{\Φ}}{\min }\max \left\{\underset{{\left\{{\mathrm{\α}}_i\right\}}_{i=1}^I}{\underset{k=1,...,L-1}{\max }}\right[\left|f(\mathrm{\Φ},{\mathrm{\α}}_i,k)\right|],\underset{p=1,...,M-1}{\underset{q=p+1,...,M}{\max }}[\mathrm{\μ}|g(\mathrm{\Φ},p,q)-R_{\mathrm{pq}}|\left]\right\},$

Wherein R _pqthe capable q column element of p that represents correlation matrix R, μ represents that directional diagram approaches weight, || represent plural mould value or absolute value of a real number; F (Φ, α _i, be k) that waveform that phasing matrix Φ is corresponding is at α _ithe normalized autocorrelation functions value at k delay positions place in direction, is expressed as:

$f(\mathrm{\Φ},{\mathrm{\α}}_i,k)=\frac{1}{L}\left|a^H\left({\mathrm{\α}}_i\right){\left[\exp \left(\mathrm{j\Φ}\right)\right]}^H{J}_k\exp \left(\mathrm{j\Φ}\right)a\left({\mathrm{\α}}_i\right)\right|/\left[a^H\left({\mathrm{\α}}_i\right)\mathrm{Ra}\left({\mathrm{\α}}_i\right)\right],$

Wherein a (α _i) expression α _ithe steering vector of direction, exp (j Φ) represents the permanent modular matrix forming taking each element in phasing matrix Φ as phase place, the capable m column element of its l is

l=1 ..., L, m=1 ..., M, J _kfor the excursion matrix of L × L dimension, be expressed as:

$J_k=\left[\begin{array}{cc}{0}_{(L-k)\×k}& I_{L-k}\\ 0_{k\×k}& 0_{k\×(L-k)}\end{array}\right],k=1,...,L-1,$

Wherein I _l-kfor the unit matrix of L-k dimension, 0 represents complete zero gust; G (Φ, p, q) be p that phasing matrix Φ is corresponding with the related coefficient of q array element waveform, be expressed as:

In formula

with

represent respectively p row and the q row of phasing matrix Φ,

represent the waveform of p the array element that phasing matrix Φ is corresponding,

represent the waveform of q the array element that phasing matrix Φ is corresponding, p=1 ..., M-1, q=p+1 ..., M;

(4.2) with initial permanent mould waveform matrix X ⁰phasing matrix Φ ⁰for initial solution, utilize the mathematical model in seqential quadratic programming solution procedure (4.1), obtain phasing matrix Φ;

Wherein initial solution Φ ⁰in element be initial permanent mould waveform matrix X ⁰the phase place of middle element, seqential quadratic programming is shown in [Antoniou A., Lu W., Practical Optimization Algorithm and Engineering Applications, Springer, 2007.].

Step 5, synthetic permanent mould waveform matrix.

According to phasing matrix Φ, synthetic permanent mould waveform matrix: X=[x ₁, x ₂... x _m], this perseverance mould waveform matrix X is final synthetic MIMO radar waveform, wherein, and vector x _m=[x _1m..., x _lm] ^tthe m row of representing matrix X,

represent the capable m column element of l of phasing matrix Φ, l=1 ..., L, m=1 ..., M.

Effect of the present invention further illustrates by following simulation comparison test:

1. simulated conditions:

Suppose that MIMO radar system is made up of even linear array, array element distance is half-wavelength, transmitter, phase coded signal.

2. emulation content

Emulation 1, establishes array number M=5, and code length is L=50, and directional diagram approaches weight and is taken as μ=2, and orthogonal Waveform Design is carried out to emulation, directional diagram corresponding to the orthogonal waveforms of synthesized as shown in Figure 2, at interested parties autocorrelation sequence upwards as shown in Figure 3.

Emulation 2, establishes array number M=16, and code length is L=100, and beam position is θ ₀=0 °, half beam width is δ=20 °, and directional diagram approaches weight and is taken as μ=2, and broad beam Waveform Design is carried out to emulation, directional diagram corresponding to the broad beam waveform of synthesized as shown in Figure 4, at interested parties autocorrelation sequence upwards as shown in Figure 5.

Emulation 3, if array number M=16, code length is L=100, beam position is for being respectively-40 °, 0 ° and 40 °, directional diagram approaches weight and is taken as μ=2, and multi-beam Waveform Design is carried out to emulation, directional diagram corresponding to the multi-beam waveform of synthesized as shown in Figure 6, at interested parties autocorrelation sequence upwards as shown in Figure 7.

3. analysis of simulation result:

As can be seen from Figure 2, the power that the orthogonal waveforms that adopts the present invention to design has omnidirectional distributes, very approaching with the directional diagram of expecting.

As can be seen from Figure 3, adopt the orthogonal waveforms of the present invention's design less at interested parties autocorrelation peak secondary lobe upwards, only have-22dB.

As can be seen from Figure 4, adopt the broad beam waveform of the present invention's design to form main lobe between [20 °, 20 °], with optimum correlation matrix, the directional diagram that designed transmitted waveform correlation matrix forms is very approaching.

As can be seen from Figure 5, the autocorrelation peak secondary lobe of the broad beam waveform of employing the present invention design in [20 °, 20 °] direction is less, only has-21.5dB.

As can be seen from Figure 6, adopt the multi-beam waveform of the present invention design at-40 °, 0 °, in 40 ° of directions, form 3 main lobes, and with optimum correlation matrix, the directional diagram that designed transmitted waveform correlation matrix forms is very approaching.

As can be seen from Figure 7, upwards autocorrelation peak secondary lobe is less in interested parties for the multi-beam waveform that adopts the present invention to design, and only has-22.2dB.

Claims (3)

1. a MIMO radar waveform synthetic method of optimizing based on space-time joint, comprises the steps:

(1) determine the correlation matrix R of transmitted waveform, wherein R is the Hermitian positive semidefinite matrix of M dimension, and M represents to launch element number of array;

(2) produce at random the initial permanent mould waveform matrix X that L × M ties up ⁰, wherein L represents the code length transmitting;

(3) determine interested observed azimuth

be the position angle that autocorrelation performance need to improve, wherein I represents the total number of interested observed azimuth;

(4) according to correlation matrix R, initial permanent mould waveform matrix X ⁰, the phasing matrix Φ that design dimension is L × M:

(4a) set up the following Optimized model of phasing matrix Φ:

$\underset{\mathrm{\Φ}}{\min }\max \left\{\underset{\underset{{\left\{{\mathrm{\α}}_i\right\}}_{i=1}^I}{k=1,...,L-1}}{\max }\right[\left|f(\mathrm{\Φ},{\mathrm{\α}}_i,k)\right|],\underset{\underset{p=1,...,M-1}{q=p+1,...,M}}{\max }[\mathrm{\μ}|g(\mathrm{\Φ},p,q)-R_{\mathrm{pq}}|\left]\right\},$

Wherein, R _pqthe capable q column element of p that represents correlation matrix R, μ represents that directional diagram approaches weight, || represent plural mould value or absolute value of a real number; F (Φ, α _i, be k) that waveform that phasing matrix Φ is corresponding is at α _ithe normalized autocorrelation functions value at k delay positions place in direction, is expressed as:

$f(\mathrm{\Φ},{\mathrm{\α}}_i,k)=\frac{1}{L}\left|a^H\left({\mathrm{\α}}_i\right){\left[\exp \left(\mathrm{j\Φ}\right)\right]}^H{J}_k\exp \left(\mathrm{j\Φ}\right)a\left({\mathrm{\α}}_i\right)\right|/\left[a^H\left({\mathrm{\α}}_i\right)\mathrm{Ra}\left({\mathrm{\α}}_i\right)\right]$

Wherein a (α _i) expression α _ithe steering vector of direction, i=1 ..., I, exp (j Φ) represents the permanent modular matrix forming taking each element in phasing matrix Φ as phase place, and symbol j represents imaginary unit, and symbol exp () represents the exponential function taking natural logarithm e the end of as, J _krepresent the excursion matrix of L × L dimension, k=1 ..., L-1, () ^hrepresent conjugate transpose;

$J_k=\left[\begin{array}{cc}{0}_{(L-k)\×k}& I_{L-k}\\ 0_{k\×k}& 0_{k\×(L-k)}\end{array}\right],$

Wherein I _l-kfor the unit matrix of L-k dimension, 0 represents complete zero gust; G (Φ, p, q) be p that phasing matrix Φ is corresponding with the related coefficient of q array element waveform, be expressed as:

In formula

with

represent respectively p row and the q row of phasing matrix Φ, represent the waveform of p the array element that phasing matrix Φ is corresponding,

represent the waveform of q the array element that phasing matrix Φ is corresponding, p=1 ..., M-1, q=p+1 ..., M;

(4b) utilize the mathematical model in seqential quadratic programming solution procedure (4a), obtain phasing matrix Φ;

(5) according to phasing matrix Φ, synthetic permanent mould waveform matrix X=[x ₁, x ₂... x _m], this perseverance mould waveform matrix X is final synthetic MIMO radar waveform, wherein, and vector x _m=[x _1m..., x _lm] ^tthe m row of representing matrix X,

represent the capable m column element of l of phasing matrix Φ, l=1 ..., L, m=1 ..., M, () ^trepresent transposition.

2. MIMO radar waveform synthetic method according to claim 1, the wherein correlation matrix R of the definite transmitted waveform described in step (1), comprises two kinds of modes:

The first, for orthogonal waveforms design, the correlation matrix of transmitted waveform is defined as R=I _m, wherein I _mrepresent the unit matrix of M dimension;

The second, for the Waveform Design of particular transmission directional diagram, adopts the correlation matrix R of transmitting pattern Matching Model design transmitted waveform.

3. MIMO radar waveform synthetic method according to claim 1, the wherein described definite interested observed azimuth of step (3)

to set as follows according to different waveforms:

(3a), for orthogonal waveforms, set interested observed azimuth and be:

${\mathrm{\α}}_i=\frac{180}{\mathrm{\π}}\arcsin (-1+2\mathrm{\Δf}(i-1)),i=1,...,I$

Wherein arcsin represents arcsin function, normalization spatial frequency interval

the total number of interested observed azimuth is I=4M+1;

(3b), for broad beam waveform, set interested observed azimuth and be:

${\mathrm{\α}}_i=\frac{180}{\mathrm{\π}}\arcsin [\sin ({\mathrm{\θ}}_0-\mathrm{\δ})+2\mathrm{\Δf}(i-1)],i=1,...,I$

Wherein δ represents half beam width, θ ₀represent beam position, normalization spatial frequency interval

the total number of interested observed azimuth is

represent to be not less than 4Mcos θ ₀the smallest positive integral of sin δ;

(3c), for multi-beam waveform, set interested observed azimuth and be:

Wherein γ represents half-power beam width, and symbol rem (i, 3) represents that i is to 3 complementations, symbol represent to be not less than the smallest positive integral of i/3, represent the

individual target direction, the total number of interested observed azimuth is I=3V, V represents target number.

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