CN105182293B - Based on relatively prime array MIMO radar DOA and DOD methods of estimation - Google Patents
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Abstract
The invention discloses one kind based on relatively prime array MIMO radar DOA and DOD methods of estimation, mainly solve the problems, such as that the low and recognizable number of source of MIMO radar system target reconnaissance accuracy is few in the prior art.The step of present invention is realized is as follows, and (1) sets up relatively prime Array Model；(2) array received data are obtained；(3) computing array receives vector；(4) estimate covariance matrix；(5) MUSIC power spectrum charts are drawn and estimates DOA and DOD values.The method that the present invention is combined using relatively prime array with MIMO radar system, hence it is evident that improve target reconnaissance accuracy and recognizable information source number.Can be used to realize carrying out target reconnaissance and passive location to aircraft, Ship Motion target by radar.
Description
Technical Field
The invention belongs to the technical field of communication, and further relates to a multi-Input multi-Output (MIMO) radar system Direction of Arrival (DOA) and target emission angle (DOD) joint estimation method based on a co-prime array in the technical field of radar. The invention realizes the target reconnaissance and passive positioning of the moving targets of the aircraft and the ships through the radar.
Background
The estimation of DOA and DOD of signals is an important branch of the array signal processing field, which means that space acoustic signals and electromagnetic signals are received by an antenna array in an induction mode, and then the direction of a signal source is rapidly and accurately estimated by using a modern signal processing method, so that the method has important application value in the fields of radar, sonar, wireless communication and the like. With the continuous progress of science and technology, there are higher and higher requirements on the accuracy and resolution of the estimation of the signal direction of arrival.
The MIMO radar transmits different waveform signals using a plurality of antennas and then receives echo signals using a plurality of antennas. The DOA and DOD estimation of the MIMO radar has the following advantages: the virtual aperture is expanded by using a matched filtering technology, so that the estimation precision of DOA and DOD is improved; the matched filtered virtual array estimates more targets than a conventional phased array radar; waveform diversity of the transmitted signal can be utilized to increase flexibility of the transmit beam design, thereby improving the accuracy of the DOA and DOD estimates.
Piya Pal et al, in their published paper, "Coprime Sampling and the MUSIC algorithm" ("Digital signal processing work and IEEE signal processing acquisition work", pp.289-294,2011.) discloses a method for estimating DOA based on a relatively prime array. The method firstly constructs a non-uniform co-prime array which is divided into two uniform sub-arrays, and the values of the array element intervals of the sub-arrays are co-prime. Then, the covariance matrix formed by the signals received by the array is rearranged, smoothed, and the like. And finally, performing MUSIC algorithm estimation to finally obtain DOA information. The method has the capability of estimating the number of signals which is more than the number of array elements, but the method still has the defect that the method can only estimate the one-dimensional DOA value of the common array radar and cannot be used for estimating the two-dimensional angle value in the MIMO array radar system.
The patent of Shenzhen research institute of Shenzhen university of Harbin Industrial university (patent application No. CN201410409417.3, publication No. CN104215947A) discloses a bistatic MIMO radar angle estimation method. The method utilizes a least square SLS method to carry out combined estimation on a target departure angle DOD and a direction of arrival angle DOA. Firstly, a rotational invariance equation is solved by using a structural least square method, and then the estimation error of the signal subspace is iteratively minimized, so that the estimation precision of the signal subspace is improved. However, the method still has the defects that the method adopts the typical linear uniform array, the estimated signal number is lower than the array element number, and the target number is too many to be identified, so that the target capture fails.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a method for estimating DOA and DOD of an MIMO radar based on a co-prime array. The invention provides a method for estimating DOA and DOD values by using a co-prime array as a signal receiving and transmitting array, which improves the target reconnaissance accuracy and the number of identifiable information sources so as to solve the problem of small number of identifiable information sources of an MIMO radar system in the prior art.
The basic idea of the invention is as follows: establishing a co-prime array model, obtaining array receiving data, calculating an array receiving vector, estimating a covariance matrix, and drawing MUSIC power spectrogram estimation DOA and DOD values.
(1) Establishing a co-prime array model:
(1a) 2P + Q-1 antenna receivers are used for forming a co-prime array, wherein P, Q respectively represents two co-prime numbers, and the value range is Q > P ≥ 2;
(1b) taking each antenna receiver as an array element;
(1c) the electromagnetic signals are incident to the co-prime array;
(2) acquiring array receiving data:
using a co-prime array antenna receiver to perform snapshot sampling and matched filtering operations on the space target electromagnetic signal to obtain a co-prime array output signal;
(3) calculating an array reception vector:
(3a) for array output signals obtained after each snapshot sampling and matched filtering operation, a co-prime matrix is constructed as follows:
wherein, Y [ l ]]Representing a co-prime matrix, x, constructed from the array output signals after snapshot sampling and matched filtering operationsz,m[l]The fast beat signal acquisition method comprises the steps that signals transmitted by an mth array element received by the zth array element are represented, the value range of M is 0,1,.
(3b) Dividing all array elements at intervals of d, judging whether array elements exist in a division point, if so, representing the position information corresponding to the array elements as 1, otherwise, representing the position information corresponding to the array elements as 0, wherein d is more than 0 and less than or equal to lambda/2, and lambda represents the wavelength of an electromagnetic signal incident to a co-prime array;
(3c) constructing a vector of [ (2P-1) Q +1 ]. times.1 dimension, wherein P, Q respectively represents two relatively prime numbers, and the value range is Q & gtP & gtmore than or equal to 2;
(3d) sequentially putting the position information corresponding to the array elements of the relatively prime array into [ (2P-1) Q +1] × 1-dimensional vectors according to the sequence from the first array element to the last array element, wherein P, Q respectively represents two relatively prime numbers, the value range of Q is more than P and is more than or equal to 2, and the array position vector is obtained;
(3e) the array element position vector is calculated according to the following formula:
ω(n)＝(ν*v-)(n)
where ω (n) represents an array element position vector, n represents the sequence number of an element in the array element position vector ω (n), v represents an array position vector, a represents a convolution operation, v represents a convolution operation-Representing an inverted array position vector obtained by performing inverted sequence arrangement operation on the array position vector v;
(3f) selecting elements with the element serial number of zeta and the value of nonzero from the array element position vector omega (n) to construct a redundancy-free array element position vectorZeta ranges from-1, -2, ·, - (2P-1) Q and P, Q to represent two relatively prime numbers, wherein Q is larger than P and is larger than or equal to 2, and r represents a position vector of an array element without redundancyThe sequence number of the middle element, r, is 1,2, G represents the position vector of the non-redundant array elementLength of (d);
(3g) calculating the data received by each array element in the redundancy-free array element position vector according to the following formula:
yr＝Yi(l)×Yj H(l)/L
wherein, yrRepresenting a redundancy-free array element position vectorThe received data of the r-th array element, r represents the position vector of the non-redundant array elementThe sequence number of the middle element, r, is 1,2, G represents the position vector of the non-redundant array elementLength of (2), Yi(l) I-th row, Y, representing a co-prime matrixj(l) J-th row of the co-prime matrix (·)HDenotes a conjugate transpose operation, i, j denotes thatIn any group of integer pairs of conditions, i is greater than or equal to 0 and less than or equal to 2P-1, j is greater than or equal to 0 and less than or equal to Q-1, P, Q respectively represent two coprime numbers, the range of Q is greater than P and greater than or equal to 2, and L represents a fast beat number;
(3h) constructing an array receiving vector corresponding to the position vector of the redundancy-free array element according to the following formula:
y＝[y1,y2,…,yr,…,yG]
wherein y represents a non-redundant array element position vectorCorresponding array receive vector, yrRepresenting a redundancy-free array element position vectorThe value range of r is 1, 2. G, G represents the position vector of the redundancy-free array elementLength of (d);
(4) estimating a covariance matrix:
the covariance matrix of the array received vector is estimated as follows:
wherein,the covariance matrix of array receiving vector is shown, L is 1,2 … L, L is fast beat number, ∑ is summation operation, y is no redundant array element position vectorThe corresponding array receives the vector, H represents the conjugate transpose operation;
(5) drawing a multi-signal classification method MUSIC power spectrogram estimation direction of arrival (DOA) and target emission angle (DOD):
(5a) setting the range of the arrival direction angle of the target electromagnetic signal as an x-axis coordinate, setting the range of the target emission angle of the target electromagnetic signal as a y-axis coordinate, calculating the power value of the target electromagnetic signal by adopting a multi-signal classification method MUSIC, and setting the power value of the target electromagnetic signal as a z-axis coordinate; drawing power value points according to the coordinate values of an x axis, a y axis and a z axis, and connecting the power values to obtain a multi-signal classification method MUSIC power spectrogram;
(5b) sequencing power values of the power spectrogram from large to small, and sequentially extracting first K spectral peaks, wherein K represents the number of target electromagnetic signals incident to a co-prime array;
(5c) and taking the x-axis coordinate value corresponding to the peak point of the first K spectral peaks as the DOA value of the direction of arrival angle of the target, and taking the y-axis coordinate value corresponding to the peak point of the first K spectral peaks as the DOD value of the target emission angle of the target.
Compared with the prior art, the invention has the following advantages:
firstly, the method for simultaneously solving the DOA and the DOD based on the direction of arrival and the target emission angle is adopted, so that the defect that the co-prime array in the prior art can only be used for estimating the one-dimensional DOA value of the common array radar and can not be used for estimating the two-dimensional angle value in the MIMO array radar system is overcome, and the method has the advantage of higher target reconnaissance accuracy.
Secondly, the method of combining the co-prime array model and the MIMO radar system is adopted, so that the defect that the estimated signal number is lower than the array element number due to the fact that a typical linear uniform array is adopted in the prior art is overcome, and the method has the advantage that the number of the information sources which can be identified by the array is large under the condition that the array element number is the same.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of a relatively prime array structure according to the present invention;
FIG. 3 is a vector diagram of the position of the array element of the co-prime array when P is 2 and Q is 3 in the present invention;
fig. 4 is a MUSIC power spectrum graph drawn in a simulation experiment of the present invention.
Detailed Description
The present invention is described in further detail below with reference to the attached drawing figures.
Referring to fig. 1, the specific steps of the present invention are as follows.
Step 1, establishing a co-prime array model.
2P + Q-1 antenna receivers are used to form a co-prime array, wherein P, Q represents two co-prime numbers with the value range of Q > P ≧ 2.
Each antenna receiver is used as an array element.
An electromagnetic signal is incident on the co-prime array.
The method for constructing the co-prime array model comprises the following specific steps:
referring to fig. 2, a constructed co-prime array model in the embodiment of the invention forms a linear array 1 with uniform array element spacing by using Q antenna receivers, forms a linear array 2 with uniform array element spacing by using 2P-1 antenna receivers, wherein the array element spacing of the linear array 1 is Pd, the array element spacing of the linear array 2 is Qd, P, Q respectively represents two co-prime numbers, the value range of Q is more than P and is more than or equal to 2, the value range of d is more than 0 and is less than or equal to λ/2, and λ represents the wavelength of an electromagnetic signal incident to the co-prime array.
The first array element of the linear array 1 is set to array element 0 of the co-prime array.
2P-1 array elements in the linear array 2 are sequentially placed in positions with the interval distance Qd,2Qd, … and (2P-1) Qd from the array element 0 to obtain a co-prime array, wherein P, Q respectively represents two co-prime numbers, the value range of Q is more than P and more than or equal to 2, the value range of d is more than 0 and less than or equal to lambda/2, and lambda represents the wavelength of an electromagnetic signal incident to the co-prime array.
From the first array element to the last array element of the co-prime array, the array elements are named as array element 0, array element 1, … … and array element 2P + Q-2 in sequence, wherein P, Q respectively represents two co-prime numbers, and the value range is Q & gtP & gt2.
Because Q is more than P and is more than or equal to 2, the first array element of the linear array 2 is certainly behind the 2 nd array element of the linear array 1, and the linear array 2 is inserted in the linear array 1. Theoretically, when the length of the array is large, the linear array 1 and the linear array 2 may overlap in a far place, and since the selection of P, Q is relatively prime and the length of the linear array 1 and the linear array 2 is limited, in the present invention, the linear array 1 and the linear array 2 are not overlapped, all the array elements of the linear array 2 are sequentially inserted into the linear array 1, and the linear array 1 and the linear array 2 are on the same line.
And 2, acquiring array receiving data.
And carrying out snapshot sampling and matched filtering operation on the space target electromagnetic signal by using a co-prime array antenna receiver to obtain a co-prime array output signal.
And 3, calculating an array receiving vector.
For array output signals obtained after each snapshot sampling and matched filtering operation, a co-prime matrix is constructed as follows:
wherein, Y [ l ]]Representing a co-prime matrix, x, constructed from the array output signals after snapshot sampling and matched filtering operationsz,m[l]Represents Y [ l ]]Any element in, xz,m[l]The fast beat array comprises an M-th array element, M and N, wherein the M ranges from 0 to 1, the temperature is high, the M and the z represent the number of the array elements transmitted by the co-prime array, the M ranges from 2P + Q-1, the N represents the number of the array elements received by the co-prime array, the N ranges from 2P + Q-1, P, Q represents two co-prime numbers, the Q ranges from more than P and more than or equal to 2, the L ranges from 1 to 2 … L, and the L represents the fast beat number.
And dividing all array elements at intervals of the length of d, judging whether array elements exist in the division points, if so, representing the position information corresponding to the array elements as 1, otherwise, representing the position information corresponding to the array elements as 0, wherein the value range of d is more than 0 and less than or equal to lambda/2, and lambda represents the wavelength of the electromagnetic signals incident to the co-prime array.
A vector of [ (2P-1) Q +1 ]. times.1 dimension is constructed, wherein P, Q represents two relatively prime numbers, and the value range is Q & gtP & gt2.
And sequentially putting the position information corresponding to the array elements of the relatively prime array into [ (2P-1) Q +1] × 1-dimensional vectors according to the sequence from the first array element to the last array element, wherein P, Q respectively represents two relatively prime numbers, and the value range is Q & gtP & gtmore than or equal to 2, so as to obtain the array position vector.
The array element position vector is calculated according to the following formula:
ω(n)＝(ν*v-)(n)
where ω (n) represents an array element position vector, n represents the sequence number of an element in the array element position vector ω (n), v represents an array position vector, a represents a convolution operation, v represents a convolution operation-The method comprises the following steps of representing an inverted sequence array position vector obtained after the inverted sequence arrangement operation is carried out on the array position vector v, wherein all possible values of an element serial number n in the array element position vector are as follows:
-(2P-1)Q,-(2P-1)Q+1,...,(2P-1)Q-1,(2P-1)Q
wherein P, Q represents two relatively prime numbers, and the value range is Q > P ≧ 2.
The value of the array element position vector ω (n) in the embodiment of the present invention is as shown in fig. 3, where fig. 3 shows the array element position vector ω (n) obtained when the co-prime array P is 2 and Q is 3, the abscissa of fig. 3 shows the array element position vector ω (n), and the ordinate shows the number of times of repetition of the array element position.
Selecting an element with the element serial number of zeta and the value of nonzero from the array element position vector omega (n) to form a redundancy-free array element position vectorZeta has a value range of-1, -2., - (2P-1) Q, P, Q, wherein the value range of Zeta is Q & gtP & gtmore than or equal to 2, and r represents a position vector of a non-redundant array elementThe serial number of the middle element, r, is 1,2The reason why no other element is selected in the array element position vector ω (n) is that the received signal when ζ is 0 contains noise information, the received signal when ζ is in a range of 1, 2., (2P-1) Q and the received signal when ζ is in a range of-1, -2., (2P-1) Q are conjugate to each other, and the estimation accuracy of the angle cannot be increased, and if the array element received vector ω (n) is as shown in fig. 3, when the cross-prime array P is 2 and Q is 3, the redundant array element position vector is not selected
Calculating the data received by each array element in the redundancy-free array element position vector according to the following formula:
yr＝Yi(l)×Yj H(l)/L
wherein, yrRepresenting a redundancy-free array element position vectorThe received data of the r-th array element, r represents the position vector of the non-redundant array elementThe serial number of the middle element, r, is 1,2Length of (2), Yi(l) I-th row, Y, representing a co-prime matrixj(l) J-th row of the co-prime matrix (·)HDenotes a conjugate transpose operation, i, j denotes thatConditionI is more than or equal to 0 and less than or equal to 2P-1, j is more than or equal to 0 and less than or equal to Q-1, P, Q represents two coprime numbers, the value range of Q is more than or equal to P and more than or equal to 2, and L represents the fast beat number.
Constructing an array receiving vector corresponding to the position vector of the redundancy-free array element according to the following formula:
y＝[y1,y2,…,yr,…,yG]
wherein y represents a non-redundant array element position vectorCorresponding array receive vector, yrRepresenting a redundancy-free array element position vectorThe value range of r is 1,2, … G, G represents the received data of the middle r array elementLength of (d).
And 4, estimating a covariance matrix.
The covariance matrix of the array received vector is estimated as follows:
wherein,the covariance matrix of array receiving vector is shown, L is 1,2 … L, L is fast beat number, ∑ is summation operation, y is no redundant array element position vectorThe corresponding array receives the vector, H denotes the conjugate transpose operation.
And 5, drawing MUSIC power spectrogram estimation DOA and DOD values.
Setting the range of the arrival direction angle of the target electromagnetic signal as an x-axis coordinate, setting the range of the target emission angle of the target electromagnetic signal as a y-axis coordinate, calculating the power value of the target electromagnetic signal by adopting a multi-signal classification method MUSIC, and setting the power value of the target electromagnetic signal as a z-axis coordinate; drawing power value points by using the coordinate values of an x axis, a y axis and a z axis, and connecting the power values to obtain a multi-signal classification method MUSIC power spectrogram, wherein the range of the arrival direction angle of the target electromagnetic signal is-90 degrees, and the range of the target emission angle of the target electromagnetic signal is-90 degrees.
The specific steps for obtaining the power value of the MUSIC spatial spectrum by the multiple signal classification method are as follows:
first, a co-prime array manifold F is defined, which is a (2PQ +1) x 1-dimensional vector, P, Q representing two co-prime numbers with the range Q > P ≧ 2.
Next, each element in the coprime array manifold F is calculated according to the following formula:
wherein, F () represents the first element in the relatively prime array manifold F, the value range of which is 1, 2.. ξ represents the length of F (),to representThe (c) th element of (a),representing the emission array versus the target emission angleThe vector of responses of the signals of (a),representing the target emission angle of the co-prime array emission signal,is expressed asαk m-1Represents the m-th transmitting array element to the target transmitting angle asM is in the range of 0,1, where M represents the number of transmitting array elements in the MIMO radar system, αkIs calculated asdtRepresenting the spacing between the emitting arrays, λ representing the wavelength of the electromagnetic signal incident on the co-prime array, αrj(θk) Representation αr(θk) α th element of (1)r(θk) Representing the receiving array by a direction of arrival angle thetakOf the signal response vector of thetakIndicating the direction of arrival of the co-prime array received signal, αr(θk) Is expressed as αr(θk)＝[1,βk,…,βk n-1,…,βk N-1]T，βk n-1The direction angle of arrival of the nth receiving array element pair is represented as thetakN, N represents the number of receiving array elements in the MIMO radar system, βkIs calculated asdrRepresenting the spacing between the receiving arrays, λ representing the wavelength of the electromagnetic signal incident on the co-prime array, i, j representing the condition being satisfiedI is greater than or equal to 0 and less than or equal to 2P-1, j is greater than or equal to 0 and less than or equal to Q-1, and P, Q represents two coprime numbers, wherein the range of Q is greater than P and greater than or equal to 2.
And finally, calculating the power value of the MUSIC spatial spectrum by the multiple signal classification method according to the following formula:
wherein f isco_musicRepresenting the power value of the MUSIC space spectrum by a multiple signal classification method, F representing the coprime array manifold, H representing the matrix conjugate transpose operation, EnCovariance matrix representing vectors of data received from arrayAnd after singular value decomposition, a noise subspace is formed by eigenvectors corresponding to the small eigenvalues.
And searching the first K spectral peaks with larger power from the power spectrogram in a sequence from high to low, wherein K represents the number of target electromagnetic signals incident to the co-prime array.
And taking the x-axis coordinate value corresponding to the peak point of the first K spectral peaks as the DOA value of the direction of arrival angle of the target, and taking the y-axis coordinate value corresponding to the peak point of the first K spectral peaks as the DOD value of the target emission angle of the target.
The effect of the present invention will be further described with reference to the simulation diagram.
1. Simulation conditions are as follows:
the simulation of the present invention was performed in the software environment of MATLAB R2014 a.
2. Simulation content:
the simulation experiment of the invention utilizes 9 antenna receivers to form a co-prime array, wherein the array element spacing of a linear array 1 in the co-prime array is 3d, the array element spacing of a linear array 2 is 4d, d is half of the wavelength of an incident electromagnetic signal, the sampling fast beat number is 500, the angle range of a target electromagnetic signal arrival direction angle DOA observation airspace is [ -90 degrees, 90 degrees ], the space grid division interval is 1 degree, the angle range of a target electromagnetic signal target emission angle DOD observation airspace is [ -90 degrees, 90 degrees ], the space grid division interval is 1 degree, the number of transmitting elements and the number of receiving elements in a multi-input and output MIMO radar system are both 9, the number of target electromagnetic signals incident to the co-prime array is 12, the transmission angle and the receiving angle of the target electromagnetic signals are (-60 degrees, -50 degrees, -40 degrees, -40 °, -30 °, -20 °,0 ° (0 °,10 °) (10 °,20 °) (20 °,30 ° (30 °,40 °) (40 °,50 °,60 ° (60 °,70 °), signal-to-noise ratio is 10 db.
3. Simulation effect analysis:
fig. 4 is a power spectrum of a multiple signal classification method MUSIC drawn in a simulation experiment of the present invention, in which an x coordinate in fig. 4 represents a direction-of-arrival angle range of a target electromagnetic signal, a y coordinate represents a target emission angle range of the target electromagnetic signal, a z coordinate represents a target electromagnetic signal power value calculated by using the multiple signal classification method MUSIC, and fig. 4 represents a situation in which the target electromagnetic signal power value calculated by using the multiple signal classification method MUSIC varies with the direction-of-arrival angle range and the target emission angle range.
As can be seen from fig. 4, the direction of arrival angle and the target emission angle of the target electromagnetic signal have a large influence on the power value of the target electromagnetic signal calculated by the multi-signal classification method MUSIC, the x-axis coordinate value corresponding to the peak point of the spectral peak with a large power value is used as the direction of arrival angle DOA value of the target, and the y-axis coordinate value corresponding to the peak point of the spectral peak with a large power value is used as the target emission angle DOD value of the target. Under the condition that the number of array elements of a linear array 1 of the co-prime array is 4 and the number of array elements of a linear array 2 is 5, the invention can estimate 12 signal sources at most, which is more than 8 signal sources recognizable by the traditional uniform array. Obviously, the method improves the accuracy of target reconnaissance and the number of identifiable information sources, is higher than that of the MIMO radar target positioning method in the prior art, and shows outstanding performance on multi-target identification.
Claims (6)
1. A mutual prime array MIMO radar DOA and DOD estimation method comprises the following steps:
(1) establishing a co-prime array model:
(1a) 2P + Q-1 antenna receivers are used for forming a co-prime array, wherein P, Q respectively represents two co-prime numbers, and the value range is Q > P ≥ 2;
(1b) taking each antenna receiver as an array element;
(1c) the electromagnetic signals are incident to the co-prime array;
(2) acquiring array receiving data:
using a co-prime array antenna receiver to perform snapshot sampling and matched filtering operations on the space target electromagnetic signal to obtain a co-prime array output signal;
(3) calculating an array reception vector:
(3a) for array output signals obtained after each snapshot sampling and matched filtering operation, a co-prime matrix is constructed as follows:
wherein, Y [ l ]]Representing a co-prime matrix, x, constructed from the array output signals after snapshot sampling and matched filtering operationsz,m[l]The fast beat signal acquisition method comprises the steps that signals transmitted by an mth array element received by the zth array element are represented, the value range of M is 0,1,.
(3b) Dividing all array elements at intervals of d, judging whether array elements exist in a division point, if so, representing the position information corresponding to the array elements as 1, otherwise, representing the position information corresponding to the array elements as 0, wherein d is more than 0 and less than or equal to lambda/2, and lambda represents the wavelength of an electromagnetic signal incident to a co-prime array;
(3c) constructing a vector of [ (2P-1) Q +1 ]. times.1 dimension, wherein P, Q respectively represents two relatively prime numbers, and the value range is Q & gtP & gtmore than or equal to 2;
(3d) sequentially putting the position information corresponding to the array elements of the relatively prime array into [ (2P-1) Q +1] × 1-dimensional vectors according to the sequence from the first array element to the last array element, wherein P, Q respectively represents two relatively prime numbers, the value range of Q is more than P and is more than or equal to 2, and the array position vector is obtained;
(3e) the array element position vector is calculated according to the following formula:
ω(n)＝(ν*v-)(n)
where ω (n) represents an array element position vector, n represents the sequence number of an element in the array element position vector ω (n), v represents an array position vector, a represents a convolution operation, v represents a convolution operation-Representing an inverted array position vector obtained by performing inverted sequence arrangement operation on the array position vector v;
(3f) selecting elements with the element serial number of zeta and the value of nonzero from the array element position vector omega (n) to construct a redundancy-free array element position vectorZeta ranges from-1, -2, ·, - (2P-1) Q and P, Q to represent two relatively prime numbers, wherein Q is larger than P and is larger than or equal to 2, and r represents a position vector of an array element without redundancyThe sequence number of the middle element, r, is 1,2, G represents the position vector of the non-redundant array elementLength of (d);
(3g) calculating the data received by each array element in the redundancy-free array element position vector according to the following formula:
yr＝Yi(l)×Yj H(l)/L
wherein, yrRepresenting a redundancy-free array element position vectorThe received data of the r-th array element, r represents the position vector of the non-redundant array elementThe sequence number of the middle element, r, is 1,2, G represents the position vector of the non-redundant array elementLength of (2), Yi(l) I-th row, Y, representing a co-prime matrixj(l) J-th row of the co-prime matrix (·)HDenotes a conjugate transpose operation, i, j denotes thatIn any group of integer pairs of conditions, i is greater than or equal to 0 and less than or equal to 2P-1, j is greater than or equal to 0 and less than or equal to Q-1, P, Q respectively represent two coprime numbers, the range of Q is greater than P and greater than or equal to 2, and L represents a fast beat number;
(3h) constructing an array receiving vector corresponding to the position vector of the redundancy-free array element according to the following formula:
y＝[y1,y2,…,yr,…,yG]
wherein y represents a non-redundant array element position vectorCorresponding array receive vector, yrRepresenting a redundancy-free array element position vectorThe value range of r is 1, 2. G, G represents the position vector of the redundancy-free array elementLength of (d);
(4) estimating a covariance matrix:
the covariance matrix of the array received vector is estimated as follows:
wherein,the covariance matrix representing the array received vector, L is 1,2 … L, L represents fast beat number, sigma represents summation operation, and y represents a no-redundancy array element position vectorThe corresponding array receives the vector, H represents the conjugate transpose operation;
(5) drawing a multi-signal classification method MUSIC power spectrogram estimation direction of arrival (DOA) and target emission angle (DOD):
(5a) setting the range of the arrival direction angle of the target electromagnetic signal as an x-axis coordinate, setting the range of the target emission angle of the target electromagnetic signal as a y-axis coordinate, calculating the power value of the target electromagnetic signal by adopting a multi-signal classification method MUSIC, and setting the power value of the target electromagnetic signal as a z-axis coordinate; drawing power value points according to the coordinate values of an x axis, a y axis and a z axis, and connecting the power values to obtain a multi-signal classification method MUSIC power spectrogram;
(5b) sequencing power values of the power spectrogram from large to small, and sequentially extracting first K spectral peaks, wherein K represents the number of target electromagnetic signals incident to a co-prime array;
(5c) and taking the x-axis coordinate value corresponding to the peak point of the first K spectral peaks as the DOA value of the direction of arrival angle of the target, and taking the y-axis coordinate value corresponding to the peak point of the first K spectral peaks as the DOD value of the target emission angle of the target.
2. The method of claim 1 for estimating DOA and DOD based on a co-prime array MIMO radar, wherein: the method for constructing the co-prime array model in the step (1) comprises the following steps:
the method comprises the following steps that firstly, Q antenna receivers are used for forming a linear array 1 with uniform array element spacing, 2P-1 antenna receivers are used for forming a linear array 2 with uniform array element spacing, the array element spacing of the linear array 1 is Pd, the array element spacing of the linear array 2 is Qd, P, Q respectively represents two co-prime numbers, the value range of Q is more than P and more than or equal to 2, the value range of d is more than 0 and less than or equal to lambda/2, and lambda represents the wavelength of electromagnetic signals incident to the co-prime array;
secondly, setting the first array element of the linear array 1 as an array element 0 of a relatively prime array;
thirdly, sequentially placing 2P-1 array elements of the linear array 2 in positions which are respectively Qd,2Qd, … and (2P-1) Qd away from the array element 0 to obtain a relatively prime array, wherein P, Q respectively represents two relatively prime numbers, the value range of Q is more than P and more than or equal to 2, the value range of d is more than 0 and less than or equal to lambda/2, and lambda represents the wavelength of an electromagnetic signal incident to the relatively prime array;
and fourthly, sequentially naming the array elements as array element 0, array element 1, … … and array element 2P + Q-2 from the first array element to the last array element of the relatively prime array, wherein P, Q respectively represents two relatively prime numbers, and the value range is that Q is more than P and is more than or equal to 2.
3. The method of claim 1 for estimating DOA and DOD based on a co-prime array MIMO radar, wherein: the value range of the element serial number n in the array element position vector ω (n) in the step (3e) is as follows:
-(2P-1)Q,-(2P-1)Q+1,...,(2P-1)Q-1,(2P-1)Q
wherein P, Q respectively represents two relatively prime numbers, and the value range is Q > P ≥ 2.
4. The method of claim 1 for estimating DOA and DOD based on a co-prime array MIMO radar, wherein: the range of the direction of arrival angle of the target electromagnetic signal in the step (5a) is
-90°～90°。
5. The method of claim 1 for estimating DOA and DOD based on a co-prime array MIMO radar, wherein: the target emission angle range of the target electromagnetic signal in the step (5a) is-90 degrees.
6. The method of claim 1 for estimating DOA and DOD based on a co-prime array MIMO radar, wherein: the target electromagnetic signal power value in step (5a) is obtained by:
firstly, defining a co-prime array manifold F, wherein the co-prime array manifold F is a vector of (2PQ +1) multiplied by 1 dimension, P, Q respectively represents two co-prime numbers, and the value range is Q & gtP & gt2;
secondly, each element in the coprime array manifold F is calculated according to the following formula:
wherein, F () represents the first element in the relatively prime array manifold F, the value range is 1, 2.. ξ represents the length of the relatively prime array manifold F,to representThe (c) th element of (a),representing the emission array versus the target emission angleSignal response vector ofThe amount of the compound (A) is,target emission angle representing co-prime array emission signal, αrj(θk) Representation αr(θk) α th element of (1)r(θk) Representing the receiving array by a direction of arrival angle thetakOf the signal response vector of thetakIndicating the direction of arrival angle of the co-prime array received signal, i, j indicating that the condition is satisfiedIn any group of integer pairs, i is greater than or equal to 0 and less than or equal to 2P-1, j is greater than or equal to 0 and less than or equal to Q-1, P, Q respectively represent two relatively prime numbers, and the value range is greater than Q and greater than P and greater than or equal to 2;
thirdly, calculating the target electromagnetic signal power value of the MUSIC space spectrum by the multiple signal classification method according to the following formula:
wherein f isco_musicRepresenting the target electromagnetic signal power value of the MUSIC space spectrum by multiple signal classification method, F representing the cross-prime array manifold, EnCovariance matrix representing vectors of data received from arrayAfter singular value decomposition, small eigenvalue pairs are usedH denotes a matrix conjugate transpose operation, in response to the noise subspace formed by the eigenvectors.
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| US11906651B2 (en) | 2021-02-25 | 2024-02-20 | Nxp B.V. | Radar-based detection using sparse array processing |
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