CN102967852B - Method for generating multi-input multi-output over-horizon (MIMO-OTH) radar waveforms based on digital signal processor (DSP) sequences - Google Patents

Abstract

The invention discloses a method for generating multi-input multi-output over-the-horizon (MIMO-OTH) radar waveforms based on digital signal processor (DSP) sequences, belonging to the technical field of MIMO-OTH radar and aiming to generate emission signals for an MIMO-OTH radar system. According to the technical problems that an MIMO-OTH radar has a narrower working frequency range and strong out-of-band interference, the method is characterized in that emission waveforms are constructed based on the DPS sequence and the waveform of each emission antenna is generated by conducting weighing summation on the same group of DPS sequences by adopting a group of different weights, therefore, waveforms of different emission antennas can be either orthorhombic or correlated with each other. In a circumstance that the total energy emitted by radar and other working parameters are constant, the detection probability of the MIMO-OTH radar system can be improved in a way of optimizing preset waveform weight parameters; and by adopting the method disclosed by the invention, the MIMO-OTH radar system achieves a good detection performance.

Description

MIMO-OTH radar waveform generation method based on DPS sequence

Technical field

The invention belongs to Radar Technology field, relate in particular to a kind of MIMO-OTH radar waveform generation method based on DPS sequence.

Background technology

Sky-wave beyond visual range (OTH) radar, it is a kind of radar system with overlength distance target detection and acquisition of information, the target of its detection normally unknown with non-cooperation, it utilize ionosphere to electromagnetic reflection, under look propagation, realize detection and parameter measurement to target.Multiple-input and multiple-output (MIMO) radar, a kind of radar system with multiple-input and multiple-output characteristic, for phased-array radar, the each emitting antenna of MIMO radar can be launched different waveform arbitrarily, has the benefit of waveform diversity.

In recent years along with MIMO radar research progressively deeply, being also applied in radar system of the advantage of MIMO.MIMO system is called to MIMO-OTH radar for the system of OTH radar.MIMO radar is divided into and splits antenna and put altogether two kinds, antenna, and the interval that the former puts by its antenna is compared with obtaining greatly spatial reuse gain, and the latter is by the different radar waveform acquisition wave shape gain of transmitting.For the ease of directly adopt the mode of MIMO in existing radar system, substantially launch based on putting altogether antenna MIMO radar about the realization of MIMO-OTH radar at present.

In MIMO-OTH radar system, the existing waveform generating mode adopting mainly can be divided into two kinds: a kind of is basic MIMO orthogonal waveforms, as Frequency Hopping Signal, and linear FM signal etc.For example, the people such as Frazer have used the linear frequency modulation continuous wave (LFMCW) of time interleaving in the experiment of MIMO-OTH radar, but these orthogonal waveforms are not for Radar Design; Another kind is that the people such as Jeffrey Krolik are in the time of research Radar Sea Area Objects test problems, change for sea-surface target the slow time MIMO(SLO-MO that characteristic provides slowly) signal, the train of impulses that its each antenna transmission signal obtains by same pulse repetition training draws through phase encoding.SLO-MO waveform can obtain (with respect to AWG (Arbitrary Waveform Generator)) by the signal generator of a low cost, but it does not do and optimize waveform itself.

Discrete prolate-spheroidal (DPS) sequence is the orthogonal sequence that has better selectivity characteristic and be with limit characteristic by a group, and its shape and number are determined by bandwidth and pulsewidth, and this organizes between sequence separate.In the pulse that to suppose a pulsewidth be T, with sample frequency f _sto signal v (t) sampling, obtain the discrete series v (n) that a length is N.If pulsewidth N → ∞, signal is the signal of a band limit, and the discrete time Fourier transform V (F) of sequence v (n) is limited in [W, W] bandwidth range, wherein W≤12.And in the time that N is a finite value, V (F) is strictly limited in [W, W].Research and propose, by maximizing the energy of signal in time limit and band limit, can obtaining one group, to meet pulsewidth be N simultaneously, and bandwidth is the sequence of [W, W], meet the characteristic of time limit and band limit simultaneously, this group sequence is called as DPS sequence, wherein k (k=1,2,, N) and DPS sequence table after individual normalization is shown: v _k(n; N, W), n=1,2 ..., N, this N DPS sequence all has mutually orthogonal characteristic in time domain He in frequency,

$\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{v}_k(n;N,W)v_{k^{\′}}(n;N,W)=\left\{\begin{array}{cc}1& k=k^{\′}\\ 0& k\≠k^{\′}\end{array}\right.$

And front 2NW DPS sequence can form one group of orthogonal basis.DPS sequence with and produce principle communication and radar on can be widely used, be necessary to propose a kind of MIMO-OTH radar wave generation method based on DPS sequence.

Summary of the invention

In view of this, goal of the invention of the present invention is: the working frequency range for MIMO-OTH radar system is narrower, and the larger technical matters of the outer interference of band, and a kind of MIMO-OTH radar waveform generation method based on DPS sequence is provided.

MIMO-OTH radar waveform generation method based on DPS sequence of the present invention, comprises the following steps:

Step S1, according to frequency span B, pulse width T, sample frequency f _s, determine sampling number N in the relative band width W of radar work and pulse, produce corresponding DPS sequence according to sampling number N in described relative band width W, pulse;

Step S2, the one group of DPS sequence producing according to step S1, in the mode of weighted sum, the radar waveform s of m emitting antenna of structure _m(n; d _m):

$s_m(n;d_m)=\underset{k=1}{\overset{2\mathrm{NW}}{\mathrm{\Σ}}}{d}_k^m{v}_k(n;N,W),n=1,...,N$

Wherein, described v _k(n; N, W) k normalized DPS sequence of expression, waveform weights coefficient

and

represent m k the DPS sequence weights coefficient transmitting, waveform weighting parameter constraint condition is: d _mnorm be not more than radar emission gross energy E ₀, i.e. d _m ^hd _m≤ E ₀;

Step S3, based on any one group waveform weights coefficient that meets described waveform weighting parameter constraint condition, transmitted waveform s _m(n; d _m);

Step S4, receive described transmitted waveform s _m(n; d _m) after ionosphere and target reflection, comprise extra large clutter x _cechoed signal r with noise z ₀, obtain described echoed signal r ₀statistical property

Step S5, according to radar running parameter, echoed signal r ₀statistical property

to waveform weights coefficient d _mbe optimized:

Step S501, is configured to optimize waveform weights coefficient d _mmatrix

Wherein, wherein, matrix

it is matrix associate matrix, described in

obtain according to sampling number N in frequency span W, pulse and DPS sequence, wherein Ψ (n) is about M v ^h(n) block diagonal matrix, v (n)=[v ₁(n; N, W) ..., v _2NW(n; N, W)] ^t, described M represents the number of emitting antenna;

Matrix it is matrix A _tassociate matrix, described matrix A _tfor about N diag{a _t(θ _t) block diagonal matrix, diag{a _t(θ _t) represent about a _t(θ _t) diagonal matrix, described a _t(θ _t) expression transmitting steering vector, θ _trepresent the angle of target with respect to emission array;

Matrix

it is matrix A _rassociate matrix, described matrix A _rfor about N a _r(θ _r) block diagonal matrix, described a _r(θ _r) represent to receive steering vector, θ r represents the angle of target with respect to receiving array;

Matrix

matrix Q ₁associate matrix, described matrix Q ₁for individual about N

block diagonal matrix, described in

for vectorial q ₁transposition, vectorial q ₁represent the covariance R of target reflection factor vector _αeigenvalue λ ₁the proper vector of corresponding orthonomalization, wherein R _α=λ ₁q ₁q ₁ ^h, described q ₁ ^hfor vectorial q ₁associate matrix;

Step S502, based on matrix Φ and radar emission gross energy E ₀, to waveform weights coefficient d _mbe optimized:

Step S502-1, waveform of initialization weights coefficient d _m;

Step S502-2, gets

for order matrix Φ obtains eigenvalue of maximum characteristic of correspondence vector;

Step S502-3, error of calculation value

Step S502-4, get interim optimum waveform weights coefficient d ' _mfor:

Step S502-5, whether error in judgement value ε is not more than 1e-10dB, if so, makes d _m=d ' _m, enter step S6; If not, make d _m=d ' _m, return to step S502-2;

Step S6, based on step S5 optimize after waveform weights coefficient d _mwith the waveform s based on DPS sequence _m(n; d _m), generate the radar waveform of each emitting antenna.

In sum, owing to having adopted technique scheme, the invention has the beneficial effects as follows: owing to having adopted discrete prolate-spheroidal (DPS) sequence with good band limit characteristic to construct the radar waveform of emitting antenna, and the radar waveform of each emitting antenna adopts respectively a different set of waveform weights coefficient d _mto same group of DPS sequence, weighted sum draws, this makes between the radar waveform of different transmit antennas can be both orthogonal also can being correlated with; Based on certain in the situation that, constructing the principle of waveform in gross energy and other parameters by maximizing the detection probability of MIMO-OTH radar system, the present invention is by waveform weights coefficient d _mconstraint qualification and setting limit, make radar waveform that the present invention generates compare the conventional linear frequency modulation of MIMO-OHT radar system (LFM) waveform and there is more excellent detection performance.

Brief description of the drawings

Examples of the present invention will be described by way of reference to the accompanying drawings, wherein:

Fig. 1 is that the present invention is real part and the imaginary part of the waveform of 4 generations in number of transmit antennas;

Fig. 2 is under different transmit antennas number, optimization waveform and the FS LFM(frequency expansion linear frequency modulation based on DPS sequence of the present invention) the ROC curve map of waveform.

Embodiment

Disclosed all features in this instructions, or step in disclosed all methods or process, except mutually exclusive feature and/or step, all can combine by any way.

Disclosed arbitrary feature in this instructions (comprising any accessory claim, summary and accompanying drawing), unless narration especially all can be replaced by other equivalences or the alternative features with similar object.,, unless narration especially, each feature is an example in a series of equivalences or similar characteristics.

If MIMO-OTH radar system number of transmit antennas is M, receiving antenna number is L.

Step S101, according to selected frequency span B, pulse width T, sample frequency f _s, determine sampling number N in the relative band width W of radar work and pulse, produce corresponding DPS sequence according to sampling number N in described relative band width W and pulse;

Step S201, the waveform of the transmitting of each emitting antenna is made up of with different weights weighted sums front 2NW DPS sequence respectively, and the radar waveform of m antenna transmission is constructed to s _m(n; d _m):

$s_m(n;d_m)=\underset{k=1}{\overset{2\mathrm{NW}}{\mathrm{\Σ}}}{d}_k^m{v}_k(n;N,W)=v^H\left(n\right)d_m,m=1,...,M,n=1,...,N---\left(1\right)$

Wherein v (n)=[v ₁(n; N, W) ..., v _2NW(n; N, W)] ^t, and v _k(n; N, W) expression k (k=1,2 ..., 2NW) and individual normalized DPS sequence, vH (n) is the conjugate transpose of v (n), waveform weights coefficient

represent m k the DPS sequence weights coefficient transmitting, and d _mmeet waveform weighting parameter constraint condition: d _m ^hd _m≤ E ₀, d _m ^hd _mconjugate transpose.

Step S301, based on any one group waveform weights coefficient d that meets above-mentioned waveform weighting parameter constraint condition _m, according to the radar waveform s of formula (1) structure emitting antenna m _m(n; d _m), and launch this waveform signal.

Step S401, the transmitted waveform of the each reception array element receiving step S301 by MIMO-OTH radar system comprises extra large clutter x after ionosphere and target reflection _cechoed signal r with noise z ₀, and calculate this echoed signal r ₀statistical property

in this embodiment, can obtain by following method, also can obtain all and can realize by existing other modes:

$C_0^{-1}={(R_c+R_z)}^{-1}---\left(2\right)$

In formula (2), R _crepresent extra large clutter x _ccovariance,

symbol E{} represents the variable in bracket to average,

x _cconjugate transpose, and symbol

represent Kronecker (Kronecker) product, vectorial a _r(θ _r) represent that target is with respect to receiving array angle θ _rreception steering vector,

wherein φ _r=2 π d _tsin θ _t/ λ represents the space quadrature between adjacent transmission array element, θ _tfor target is with respect to the angle of emission array, d _tfor array element distance, λ is wavelength.H _cthe matrix being made up of the clutter impulse response vector in observation time, is the matrix of N × MN dimension, and N is sampling number in pulse, and M is MIMO-OTH radar system number of transmit antennas:

Wherein, h ^t _c(n) be h _c(n) transposition,

represent the clutter impulse response vector in n moment, vectorial p=[p ^t(1) ..., p ^t(N)] ^t, represent in observation time that each transmitted waveform is at the signal that closes at target place, wherein p (n)=s (n) ⊙ a _t(θ _t) ≡] p ₁(n) ..., p _m(n)] ^t, the waveform of sampled point in n the pulse that s (n) obtains based on formula (1), a _t(θ _t) represent that target is with respect to the angle θ of emission array _ttransmitting steering vector.

R _zrepresent the covariance of noise z, symbol E{} represents the variable in bracket to average, wherein z=[z ₁(1) ..., z _l(1) ..., z ₁(N) ..., z _l(N)] ^tfor noise vector, for noise power.

Step S501, is configured to optimize waveform weights coefficient d _mmatrix

Wherein, matrix

it is matrix A _tassociate matrix, described matrix A _tfor about N diag{a _t(θ _t) block diagonal matrix, diag{a _t(θ _t) represent about a _t(θ _t) diagonal matrix, described a _t(θ _t) expression transmitting steering vector, θ _trepresent the angle of target with respect to emission array, can be expressed as:

A _t=Diag{diag{a _t(θ _t) ..., diag{a _t(θ _t), symbol Diag{} and diag{} represent respectively block diagonal matrix and diagonal matrix, in above formula, comprise altogether N diag{a _t(θ _t);

Matrix

it is matrix A _rassociate matrix, described matrix A _rfor about N a _r(θ _r) block diagonal matrix, described a _r(θ _r) expression reception steering vector, θ _rrepresent the angle of target with respect to receiving array, can be expressed as:

A _r=Diag{a _r(θ _r) ..., a _r(θ _r), N a altogether _r(θ _r);

Matrix

n altogether

, wherein i=1 ..., M _low, and q _ithe covariance R by target reflection factor vector _αdecomposition obtains,

wherein, M _lowrepresent R _αorder, constant λ _ifor R _αthe eigenwert that i is large, and

be the column vector of M × 1 row, represent corresponding λ _ithe proper vector of orthonomalization, because of the covariance R of target reflection factor vector _αfor prior art, concrete computation process is not described in detail herein.

Matrix

matrix Q ₁associate matrix, according to above-mentioned Q _iobtain Q ₁;

Step S502, based on matrix Φ and radar emission gross energy E ₀, according to the following step to waveform weights coefficient d _mbe optimized processing:

Step S502-a, waveform of initialization weights coefficient d _m, can be set as meeting the arbitrary value of waveform weighting parameter constraint condition;

Step S502-b, gets

for order matrix Φ obtains eigenvalue of maximum characteristic of correspondence vector;

Step S502-c, error of calculation value

Step S502-d, get interim optimum waveform weights coefficient d ' _mfor:

Step S502-e, whether ε is enough little for error in judgement value, judges ε≤1e-10dB, if so, makes d _m=d ' _m, enter step S601; If not, make d _m=d ' _m, return to step S502-b;

Step S601, the waveform weights coefficient d after optimizing based on step S502 _mwith the waveform s based on DPS sequence _m(n; d _m), generate the radar waveform of each emitting antenna.

Embodiment 1

If the carrier frequency f of MIMO-OTH radar system _c=10MHz, bandwidth B=1500Hz, waveform (pulse signal) the base-band signal frequency scope that transmits is | f|≤750Hz, due to the factor producing in propagating and realizing, as ionospheric reflection characteristic and external interference etc., establishes the sample frequency f of signal _s=1875Hz, by relative signal frequency range [W, W], obtains W=B (2f _s)=0.4.Spendable working frequency range is, f ₀-B/2≤f≤f ₀+ B2, wherein f ₀frequency centered by=10MHz, establishes the pulsewidth T=16ms of signal, and therefore the sampling number in pulse is N=Tf _s=30.Target is 30 ° with respect to the angle of emission array and receiving array, i.e. θ _t=θ _r=30 °, transmitting gross energy E ₀=4, the number (number of transmit antennas) of transmitting array element is M=4, and the number (receiving antenna number) that receives array element is L=2.Obtain the radar waveform based on DPS sequence of the present invention according to step S101-601, with reference to Fig. 1, be followed successively by real part and the imaginary part figure of the transmitted waveform of each emitting antenna from sitting on the right side.

Embodiment 2

According to setting frequency span B=1500Hz, pulse width T=16ms, sample frequency f _s=1875Hz, determines the relative band width W=B (2f of radar work _s)=0.4, sampling number N=Tf in pulse _s=30, target is with respect to the angle θ of emission array _tangle θ with relative receiving array _rbe 30 °, transmitting gross energy E ₀=4, the number (number of transmit antennas) of transmitting array element is M, is taken as successively 1,2,4,6,8, and the number (receiving antenna number) that receives array element is L=2.Obtain 6 radar waveforms based on DPS sequence according to step S101-601, compared with the FS LFM waveform usual with MIMO-OHT radar system, the present invention has more excellent detection performance, can be shown in Figure 2, and wherein P _fArepresent the false-alarm probability of radar waveform, P _drepresent the monitoring probability of waveform.

The present invention is not limited to aforesaid embodiment.The present invention expands to any new feature or any new combination disclosing in this manual, and the arbitrary new method disclosing or step or any new combination of process.

Claims (1)

1. the MIMO-OTH radar waveform generation method based on DPS sequence, is characterized in that, comprises the following steps:

Step S1, according to frequency span B, pulse width T, sample frequency f _s, determine sampling number N in the relative band width W of radar work and pulse, produce corresponding DPS sequence according to sampling number N in described relative band width W and pulse;

Step S2, the one group of DPS sequence producing according to step S1, in the mode of weighted sum, the radar waveform s of m emitting antenna of structure _m(n; d _m):

$s_m(n;d_m)=\underset{k=1}{\overset{2\mathrm{NW}}{\mathrm{\Σ}}}{d}_k^m{v}_k(n;N,W),n=1,...,N$

Wherein, described v _k(n; N, W) k normalized DPS sequence of expression, waveform weights coefficient

and represent m k the DPS sequence weights coefficient transmitting; Described waveform weights coefficient d _mwaveform weighting parameter constraint condition be: d _mnorm be not more than radar emission gross energy;

Step S3, based on any one group waveform weights coefficient that meets described waveform weighting parameter constraint condition, transmitted waveform s _m(n; d _m);

Step S4, receive described transmitted waveform s _m(n; d _m) after ionosphere and target reflection, comprise extra large clutter x _cechoed signal r with noise z ₀, obtain described echoed signal r ₀statistical property

Step S5, according to radar running parameter, echoed signal r ₀statistical property

to waveform weights coefficient d _mbe optimized:

Step S501, is configured to optimize waveform weights coefficient d _mmatrix

Wherein, matrix

it is matrix

associate matrix, described in obtain according to sampling number N and DPS sequence in relative band width W, pulse, wherein Ψ (n) is about M v ^h(n) block diagonal matrix, v (n)=[v ₁(n; N, W) ..., v _2NW(n; N, W)] ^t, described M represents the number of emitting antenna;

Matrix

it is matrix A _tassociate matrix, described matrix A _tfor about N diag{a _t(θ _t) block diagonal matrix, diag{a _t(θ _t) represent about a _t(θ _t) diagonal matrix, described a _t(θ _t) expression transmitting steering vector, θ _trepresent the angle of target with respect to emission array;

Matrix

it is matrix A _rassociate matrix, described matrix A _rfor about N a _r(θ _r) block diagonal matrix, described a _r(θ _r) expression reception steering vector, θ _rrepresent the angle of target with respect to receiving array;

Matrix

matrix Q ₁associate matrix, described matrix Q ₁for individual about N

block diagonal matrix, described in

for vectorial q ₁transposition, vectorial q ₁represent the covariance R of target reflection factor vector _αeigenvalue λ ₁the proper vector of corresponding orthonomalization, wherein R _α=λ ₁q ₁q ₁ ^h, described vectorial q ₁ ^hfor vectorial q ₁associate matrix;

Step S502, based on matrix Φ and radar emission gross energy E ₀, to waveform weights coefficient d _mbe optimized:

Step S502-1, waveform of initialization weights coefficient d _m;

Step S502-2, gets

for order matrix Φ obtains eigenvalue of maximum characteristic of correspondence vector;

Step S502-3, error of calculation value

Step S502-4, get interim optimum waveform weights coefficient d ' _mfor:

Step S502-5, whether error in judgement value ε is not more than 1e-10dB, if so, makes d _m=d ' _m, enter step S6; If not, make d _m=d ' _m, return to step S502-2;

S6, based on step S5 optimize after waveform weights coefficient d _mwith the waveform s based on DPS sequence _m(n; d _m), generate the radar waveform of each emitting antenna.

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