CN101902432B - Method for establishing and optimizing fully-complementary sequence in orthogonal MIMO radar system - Google Patents

Abstract

The invention discloses a method for establishing and optimizing a fully-complementary sequence in an orthogonal MIMO radar system, which is used in the orthogonal MIMO radar system. The method comprises the following steps of: firstly, setting an iteration number and an initial complementary sequence, and establishing the fully-complementary sequence by adopting an iteration method; secondly, selecting a suitable full-complementary sequence as a transmission signal according to antenna data in the orthogonal MIMO radar system; and finally, optimizing the selected full-complementary sequence according to clutter characteristics in the orthogonal MIMO radar system, and using the optimized full-complementary sequence as the final transmission signal. The method adopts the full-complementary sequence to construct orthogonal MIMO radar transmission signals, and finds the transmission signal capable of making mutual information amount be the largest through optimization so as to improve the mutual information amount.

Description

Fully-complementary sequence makes up and optimization method in a kind of orthogonal MIMO radar system

Technical field

The invention belongs to the Radar Technology field, the structure and the optimization method of fully-complementary sequence in particularly a kind of orthogonal MIMO radar.

Background technology

Multiple-input and multiple-output (MIMO; Multiple-Input Multiple-Output) technology is at first invented by the AT&T Labs the nineties in 20th century at wireless communication field, and mimo wireless communication is divided into the technology of utilizing Space Time Coding to improve signal to noise ratio and sends two kinds of main modes of technology that different information improve transmission rate simultaneously with many antennas.Along with the research of MIMO communication system, people have proposed the notion of MIMO radar again.

The notion of orthogonal MIMO radar is proposed by the Lincoln laboratory at first; The orthogonal MIMO radar is at the mutually orthogonal waveform of transmitting terminal emission; Compare with traditional phased array radar, have good advantages at aspects such as wide search wave beam formation, low probability of intercept (LPI), clutter inhibition.

The orthogonal MIMO radar has above-mentioned many advantages; Since coming out, just received the common concern of Chinese scholars; For this New System radar of orthogonal MIMO radar; Because the mutually orthogonal waveform collection of each transmission antennas transmit, receiving terminal recovers each component that transmits through matched filter processing, and the design that therefore transmits has directly influenced the systematic function of MIMO radar.In order to suppress to disturb and improve multiple target resolution, have good correlation function between requiring to transmit, preferably satisfy complete quadrature, promptly the non-periodic autocorrelation function secondary lobe is that zero-sum cross-correlation function aperiodic main lobe and secondary lobe are zero.The MIMO radar mainly adopts quadrature polyphase code and orthogonal frequency coding at present; Though the correlation function of above-mentioned two types of codings has lower side lobe performance; But still can not satisfy the complete quadrature between transmitting; Theoretical research shows that it is non-existent satisfying completely orthogonal sequence in traditional solid size field.Because fully-complementary sequence is made up of a plurality of subsequences; And between the subsequence relation of quadrature; Just in time coincide, thereby a new research direction has been opened up in the selection that appears as the orthogonal MIMO radar signal of fully-complementary sequence with the many signals and the orthogonality of the requirement of orthogonal MIMO radar.

Mutual information is important in an orthogonal MIMO theory system index, and the mutual information of system is big more, and the useful information amount of from system, extracting is also just many more.Because the complex characteristics of orthogonal MIMO Radar channel; Different clutter types can change the size of mutual information; In order to improve mutual information, we can improve the characteristic of channel from the angle of signal, promptly are optimized processing to transmitting to obtain optimum systematic function.

Summary of the invention

The invention provides fully-complementary sequence structure and optimization method in a kind of orthogonal MIMO radar system; Purpose is adopting fully-complementary sequence to construct aspect the orthogonal MIMO radar emission signal; And the fully-complementary sequence of being constructed has been realized the raising of channel capacity through optimizing.

The structure of fully-complementary sequence and optimization method in a kind of orthogonal MIMO radar system specifically may further comprise the steps:

Step 1, according to the demand of actual orthogonal MIMO radar, be provided for the iterations r that fully-complementary sequence makes up, require constructed complementary series number 2 ^R+1Be greater than or equal number of transmit antennas in the orthogonal MIMO radar system; Wherein, r is the integer greater than 0;

The number of phases of step 2, setting fully-complementary sequence is provided with initial complementary series { A ₀, B ₀, A in the set initial complementary series ₀With B ₀Complementary;

Step 3, employing iterative method make up fully-complementary sequence;

Described iterative method is the process of a recurrence, by { A ₀, B ₀Can construct two pairs of fully-complementary sequences: { A ₀B ₀A ₀-B ₀And

With

Again will be wherein each fully-complementary sequence proceed iteration and go down iteration r time;

Step 4, according to antenna data in the orthogonal MIMO radar system, select fully-complementary sequence; The fully-complementary sequence number of said selection is identical with number of transmit antennas;

Step 5, the fully-complementary sequence of step 4 being chosen according to noise performance in the orthogonal MIMO radar system are optimized;

According to following channel capacity formula fully-complementary sequence is optimized:

$I(h;y)=N\·\lg [\det (E_{2L}+{\mathrm{\δ}}_h^2{P}^{-\frac{1}{2}}{\mathrm{SS}}^H{P}^{-\frac{1}{2}})$

$=N\·\lg \left[\det (E_M+{\mathrm{\δ}}_h^2{S}^H{P}^{-1}S)\right]$

Wherein, I (h; Y) expression mutual information, h representes channel matrix,

y ₁... y _NBe respectively the 1st to N the echo that receiver receives, N is the reception antenna number, and T representes the transposition computing; E is a unit matrix; Subscript H representes conjugate transpose; P is the distribution matrix of noise signal v; L representes the code element number of sequence, equals the sub-sequence length of complementary series;

The variance yields of expression channel; M is the number of transmit antennas of orthogonal MIMO radar;

The matrix S that is made up of fully-complementary sequence is:

Wherein

{ S _Am, S _BmBe the complementary series of choosing in the step 4,1≤m≤M;

When noise signal v is relevant, according to (ψ S) ^HP ^-1(ψ S)=S ^H(ψ ^HP ^-1ψ) S=Λ, the ψ S that obtains are the fully-complementary sequence matrixes after optimizing;

That wherein, hints obliquely at matrix ψ asks method following:

Because matrix P is a positive definite matrix, can decompose as follows clutter matrix P:

${\mathrm{\ψ}}^H{P}^{-1}\mathrm{\ψ}={\mathrm{\δ}}_v^{-2}E$

Then: $P^{-1}={\mathrm{\δ}}_v^{-2}{\left({\mathrm{\ψ}}^H\right)}^{-1}E{\mathrm{\ψ}}^{-1}$

That is: $P={\mathrm{\δ}}_v^2\mathrm{\ψ}{\mathrm{\ψ}}^H$

When noise signal v is white Gaussian noise,

arranged according to then S be exactly the fully-complementary sequence matrix after optimizing; Wherein

representes the variance yields of noise signal, and Λ is a diagonal matrix; With the fully-complementary sequence matrix S after optimizing as transmitting in the orthogonal MIMO radar.

Advantage of the present invention and good effect are:

(1) to utilize alternative manner to construct number abundant in the present invention, and the sufficiently long fully-complementary sequence of code length can satisfy the application of actual orthogonal MIMO radar system fully;

(2) different distributions of pair of orthogonal MIMO radar clutter of the present invention has been carried out optimum processing to transmitting, and the Optimal Signals that obtains has enlarged mutual information, has improved systematic function.

Description of drawings

Fig. 1 is the flow chart of steps of fully-complementary sequence structure of the present invention and optimization method;

Fig. 2 is the sketch map that fully-complementary sequence makes up in the step 2 of the present invention;

Fig. 3 is that the present invention optimizes the back signal and the former mutual information that transmits compares sketch map.

Embodiment

To combine accompanying drawing and embodiment that the present invention is done further detailed description below.

Fully-complementary sequence structure and optimization method are realized through following steps in the orthogonal MIMO radar system provided by the invention, and be as shown in Figure 1:

Step 1, iterations r is set.Choosing iterations in the embodiment of the invention is 3.According to the demand of actual orthogonal MIMO radar, sequence length can not be oversize can not be too short, oversize complexity height a bit, having lacked very much systematic function can be a little bit poorer, general iterations is between 3～5.Require constructed complementary series number 2 ^R+1Be greater than or equal number of transmit antennas in the orthogonal MIMO radar system.

The number of phases of step 2, setting fully-complementary sequence is provided with initial complementary series { A ₀, B ₀, A in the selected initial complementary series ₀With B ₀Complementary.The number of phases of choosing fully-complementary sequence in the embodiment of the invention is the structure that 5 initial complementary series is explained fully-complementary sequence: A ₀=(1i-i-1i), B ₀=(111i-i).In practical application, the number of phases of fully-complementary sequence generally is set at 2 or 4.The number of phases of fully-complementary sequence is the same with the initial complementary series number of phases.

Initial complementary series according to selected can obtain: the length L of initial complementary series ₀=5; Initial complementary series number of phases P_n=4; The length L that needs the fully-complementary sequence of structure _r=L ₀* 2 ^r=40, this length is meant the sub-sequence length of each complementary series.

Step 3, employing iterative method make up fully-complementary sequence.

Described iterative method is the process of a recurrence, by { A ₀, B ₀Can construct two pairs of fully-complementary sequences: { A ₀B ₀A ₀-B ₀And

With

Wherein, { A ₀B ₀A ₀-B ₀With

It is complementary fully,

With Complementary fully.In like manner, again will be wherein each fully-complementary sequence proceed iteration and go down, iteration r time, the number of the fully-complementary sequence that constructs are 2 ^r, the number of complementary series is 2 ^R+1, the length L of fully-complementary sequence _r=L ₀* 2 ^rIf initial complementary series number of phases P_n＞2 then need conjugation to handle in building process, building process is as shown in Figure 2, wherein

Expression B ₀The opposite sequence of sequence,

Expression B ₀Conjugation.

As shown in Figure 2, iteration once, by { A ₀, B ₀Construct { A ₁, B ₁, { A ₁', B ' ₁, { (AA) ₁, (BB) ₁, { (AA) ₁', (AA) ' ₁, wherein, { A ₁, B ₁Be { A ₀B ₀A ₀-B ₀, { A ₁', B ' ₁Do

{ (AA) ₁, (BB) ₁Do

{ (AA) ₁', (BB) ' ₁Do

Iteration for the second time, with { A ₁, B ₁Be example, construct { A ₂, B ₂, { A ₂', B ' ₂, { (AA) ₂, (BB) ₂, { (AA) ₂', (BB) ' ₂, wherein, { A ₂, B ₂Be { A ₁B ₁A ₁-B ₁, { A ₂', B ' ₂Do

{ (AA) ₂, (BB) ₂Do

{ (AA) ₂', (BB) ' ₂Do

Iteration for the third time, with { A ₂, B ₂Be example, construct { A ₃, B ₃, { A ₃', B ' ₃, { (AA) ₃, (BB) ₃, { (AA) ₃', (BB) ' ₃, wherein, { A ₃, B ₃Be { A ₂B ₂A ₂-B ₂, { A ₃', B ' ₃Do { (AA) ₃, (BB) ₃Do

{ (AA) ₃', (BB) ' ₃Do

In like manner, can carry out r time iteration.

The constructed fully-complementary sequence that goes out is a quadrature.Specify as follows:

The a pair of fully-complementary sequence that constructs through the r rank is { A _r, B _rAnd A ' _r, B ' _r, as satisfying

With

Wherein * representes related operation, proves that then sequence is a fully-complementary sequence, is quadrature, forms one type of fully-complementary sequence collection by these sequences of same length.

Iteration is 3 times in the embodiment of the invention, and the fully-complementary sequence collection that constructs comprises 8 pairs of fully-complementary sequences, i.e. 16 complementary seriess, and each complementary series comprises two sub-sequence, and each sub-sequence length is 40, and a pair of fully-complementary sequence wherein is:

Wherein,

Can verify that thus constructed sequence is a fully-complementary sequence.

Step 4, according to antenna data in the orthogonal MIMO radar system, select suitable fully-complementary sequence.According to the number of transmitting antenna, require to construct complementary series number 2 ^R+1Be greater than or equal number of transmit antennas, from 2 ^R+1Choose complementary series number in the middle of the individual complementary series with the transmitting antenna similar number.

Number of transmit antennas is 2 in the embodiment of the invention, 2 of reception antenna data bit.Choose following fully-complementary sequence as transmitting:

Step 5, the fully-complementary sequence of step 4 being chosen according to noise performance in the orthogonal MIMO radar system are optimized.

Number according to orthogonal MIMO radar system transmitting antenna and reception antenna; Choose the fully-complementary sequence that makes up in the step 3 suitably; According to the type of clutter in the real system, be foundation with the maximize channel capacity, the fully-complementary sequence of launching is optimized processing.

The clutter distribution matrix P of orthogonal MIMO radar system in the embodiment of the invention _{K, q}=0.4 ^{| k-q|}, k, q be the capable ordinal sum row ordinal number of representing matrix P respectively; Embodiment P is 2L rank matrixes, and then k, the equal value of q are 1 here ..., 2L.I.e.

Because the number of transmit antennas of orthogonal MIMO radar is M, the fully-complementary sequence that then makes up from step 3 is concentrated and is chosen M to complementary series { A _m, B _m(m=1 ..., M) as transmitting S, that is:

Wherein,

{ S _Am, S _BmBe the complementary series of choosing in the step 4,1≤m≤M; T representes the transposition computing, sets reception antenna number N simultaneously, orthogonal MIMO Radar channel parameter h _n=[h _N1..., h _NM] ^T, v _nExpression clutter item, then n the echo y that receiver receives _nFor:

y _n＝Sh _n+v _n n＝1，…，N (2)

The signal that each antenna is received makes up,

simultaneously

X represent the signal combination of all antennas; Channel matrix then

y＝Xh+v (3)

V representes the clutter noise matrix;

formula (3) can get the orthogonal MIMO radar system capacity C according to this formula to be for the orthogonal MIMO radar system emission receives equation:

C＝max{I(h；y)}＝max{H(y)-H(y|h)}(4)

Wherein, I (h; Y) be mutual information, H (y) is the entropy of matrix y, and H (y|h) is the conditional entropy of y under the given h, because the independence of h and y, then formula (4) can be write as:

I(h；y)＝H(y)-H(v|h)＝H(y)-H(v)(5)

H (is the entropy of noise matrix v v), supposes that channel matrix h obeys average E (h)=0, variance

Distribution,

The variance yields of expression channel, E _NMExpression E is NM rank matrixes, the variance of definition v

L representes the code element number of sequence, the just sub-sequence length of complementary series; Shannon's theorems according to communication theory can get:

$H\left(y\right)=\lg \left[\det ({\mathrm{\δ}}_h^2\·{\mathrm{XX}}^H+\mathrm{\Σ})\right]---\left(6\right)$

H(v)＝lg[det(∑)](7)

$I(h;y)=H\left(y\right)-H\left(v\right)=\lg \left[\det (E_{2\mathrm{NL}}+{\mathrm{\δ}}_h^2{\mathrm{\Σ}}^{-1}{\mathrm{XX}}^H)\right]---\left(8\right)$

The objective of the invention is to find the X that transmits that can make mutual information maximum; Because so S (i.e. the fully-complementary sequence of emission) is determining X, formula (8) can be write as :

$I(h;y)=N\·\lg \left[\det (E_{2L}+{\mathrm{\δ}}_h^2{P}^{-1/2}{\mathrm{SS}}^H{P}^{-1/2})\right]$ (9)

$=N\·\lg \left[\det (E_M+{\mathrm{\δ}}_h^2{S}^H{P}^{-1}S)\right]$

When noise signal v is white Gaussian noise;

E is a unit matrix, at this moment

$S^H{P}^{-1}S={\left(P^{-1/2}S\right)}^H\left(P^{-1/2}S\right)={\mathrm{\δ}}_v^{2}E=\mathrm{\Λ}---\left(10\right)$

Be S ^HP ^-1S is a diagonal matrix, at this moment I (h; Y) obtain maximum, this moment, fully-complementary sequence was optimal sequence, and when noise signal v was relevant, we need transform ψ S to the S that transmits, and make (ψ S) ^HP ^-1(ψ S) is diagonal matrix, improves channel capacity:

(ψS) ^HP ^-1(ψS)＝S ^H(ψ ^HP ^-1ψ)S＝Λ(11)

At this moment, ψ S is the sequence after the optimization.

That hints obliquely at matrix ψ asks method following:

Because matrix P is a positive definite matrix, can decompose as follows clutter matrix P:

${\mathrm{\ψ}}^H{P}^{-1}\mathrm{\ψ}={\mathrm{\δ}}_v^{-2}E---\left(12\right)$

Then further can obtain formula (13):

$P^{-1}={\mathrm{\δ}}_v^{-2}{\left({\mathrm{\ψ}}^H\right)}^{-1}E{\mathrm{\ψ}}^{-1}---\left(13\right)$

Further obtain formula (14) again:

$P={\mathrm{\δ}}_v^2\mathrm{\ψ}{\mathrm{\ψ}}^H---\left(14\right)$

Calculate ψ from formula (14) according to concrete clutter distribution matrix.

Fully-complementary sequence after optimizing is applied in the orthogonal MIMO radar.

Fully-complementary sequence constructed among the present invention is when noise signal v is relevant; Its different-effect that before and after optimizing, is applied in the orthogonal MIMO radar is as shown in Figure 3; Abscissa SCR representes signal to noise ratio; Ordinate is represented mutual information, can see that the fully-complementary sequence that adopts after optimizing than not adopting the fully-complementary sequence of optimizing in application, can improve the mutual information of MIMO radar.

Claims (3)

1. the structure and the optimization method of fully-complementary sequence in the orthogonal MIMO radar is characterized in that this method may further comprise the steps:

Step 1, according to the demand of actual orthogonal MIMO radar, be provided for the iterations r that fully-complementary sequence makes up, require constructed complementary series number 2 ^R+1Be greater than or equal number of transmit antennas in the orthogonal MIMO radar system; Wherein, r is the integer greater than 0;

The number of phases of step 2, setting fully-complementary sequence is provided with initial complementary series { A ₀, B ₀, A in the set initial complementary series ₀With B ₀Complementary;

Step 3, employing iterative method make up fully-complementary sequence;

Described iterative method is the process of a recurrence, by { A ₀, B ₀Construct two pairs of fully-complementary sequences: { A ₀B ₀; A ₀-B ₀And

With

Again will be wherein each fully-complementary sequence proceed iteration and go down iteration r time; Wherein

Expression B ₀The opposite sequence of sequence,

Expression B ₀Conjugation;

Step 4, according to antenna data in the orthogonal MIMO radar system, select fully-complementary sequence; The fully-complementary sequence number of said selection is identical with number of transmit antennas;

Step 5, the fully-complementary sequence of step 4 being chosen according to the noise performance of noise signal v in the orthogonal MIMO radar system are optimized;

According to following mutual information formula fully-complementary sequence is optimized:

$I(h;y)=N\·\lg \left[\det (E_{2L}+{\mathrm{\δ}}_h^2{P}^{-\frac{1}{2}}S{S}^H{P}^{-\frac{1}{2}})\right]$

$=N\·\lg \left[\det (E_M+{\mathrm{\δ}}_h^2{S}^H{P}^{-1}S)\right]$

Wherein, I (h; Y) expression mutual information, h representes channel matrix,

y ₁... Y _NBe respectively the 1st to N the echo that receiver receives, T representes the transposition computing; E is a unit matrix; Subscript H representes conjugate transpose; P is the distribution matrix of noise signal v; L representes the sub-sequence length of complementary series;

The variance yields of expression channel; M is the number of transmit antennas of orthogonal MIMO radar;

The matrix of S for constituting by fully-complementary sequence:

Wherein { S _Am, S _BmBe the complementary series of choosing in the step 4,1≤m≤M;

When noise signal v is relevant, according to (ψ S) ^HP ^-1(ψ S)=S ^H(ψ ^HP ^-1ψ) S=Λ asks for and hints obliquely at matrix ψ, and the ψ S that further obtains again is exactly the fully-complementary sequence matrix after optimizing, with ψ S as transmitting in the orthogonal MIMO radar;

When noise signal v is white Gaussian noise, according to

Have $S^H{P}^{-1}S={\left(P^{-1/2}S\right)}^H\left(P^{-1/2}S\right)={\mathrm{\δ}}_v^{2}E=\mathrm{\Λ};$ Then S is exactly the fully-complementary sequence matrix after optimizing; Wherein

The variance yields of expression noise signal, Λ is a diagonal matrix; With the fully-complementary sequence matrix S after optimizing as transmitting in the orthogonal MIMO radar.

2. the structure and the optimization method of fully-complementary sequence is characterized in that in a kind of orthogonal MIMO radar according to claim 1, and the iterations described in the step 1 is 3～5.

3. the structure and the optimization method of fully-complementary sequence is characterized in that the number of phases of the fully-complementary sequence described in the step 2 is set at 2 or 4 in a kind of orthogonal MIMO radar according to claim 1.

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