CN109613475B - Self-adaptive optimization co-prime matrix arrangement method and target DOA estimation method - Google Patents
Self-adaptive optimization co-prime matrix arrangement method and target DOA estimation method Download PDFInfo
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- CN109613475B CN109613475B CN201910122620.5A CN201910122620A CN109613475B CN 109613475 B CN109613475 B CN 109613475B CN 201910122620 A CN201910122620 A CN 201910122620A CN 109613475 B CN109613475 B CN 109613475B
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Abstract
The invention discloses a configuration method of a self-adaptive optimization co-prime matrix and a target DOA estimation method, which comprises the following steps of 1: reversing the position of any subarray in the co-prime matrix, namely reversing the coordinate position from a positive axis to a negative axis; and 2, step: translating the inverted subarray in the step 1, wherein the translation factor is obtained as FA through an optimization equation; the self-adaptive optimization co-prime matrix arrangement algorithm is simple, convenient and feasible, and has stronger universality; the optimal arrangement mode does not need to be recalculated aiming at the co-prime arrays with different unit numbers; compared with the traditional differential co-prime array, the differential co-prime array obtained by the invention has more continuous unit numbers and larger aperture numbers, is used in the fields of communication, imaging, positioning and the like, and can obtain better information processing effect on the premise of not increasing the unit numbers.
Description
Technical Field
The invention relates to the field of antennas, in particular to an arrangement method of a self-adaptive optimization co-prime array and a target DOA estimation method of a differential co-prime array generated based on the co-prime array.
Background
Antenna arrays are widely studied as signal transmitting and receiving devices in many fields such as communications, imaging, positioning, and the like. How to realize as large an aperture as possible with a limited array element is a technical challenge in the field of antennas. The traditional N-element antenna array can detect N-1 targets at most due to limited aperture; to solve this problem, a co-prime matrix is proposed. Although the differential co-prime array generated by the co-prime array has a larger aperture than the conventional co-prime array or the linear array, the degree of freedom is higher than that of the conventional array, so that the signal receiving capability and the signal detection capability are further obviously improved. However, the number of consecutive elements is still not fully excavated, i.e. the degree of freedom does not reach the maximum achievable, and the problem of holes is not radically reduced. In addition, the existing method for reducing holes, namely improving the degree of freedom, is complex in operation and large in calculation amount, needs to calculate an optimized arrangement mode again aiming at a co-prime matrix composed of different co-prime numbers, and is seriously insufficient in operability.
Disclosure of Invention
The invention provides an arrangement method of a self-adaptive optimization co-prime matrix, which is simple to operate and high in degree of freedom, and does not need to recalculate optimal arrangement aiming at co-prime matrices with different cell numbers, and a method for using a differential co-prime matrix obtained by the co-prime matrix in target DOA estimation.
The technical scheme adopted by the invention is as follows: a self-adaptive optimization co-prime matrix arrangement method comprises the following steps:
step 1: reversing the position of any subarray in the co-prime matrix, namely reversing the coordinate position from a positive axis to a negative axis;
and 2, step: and (4) translating the inverted subarray obtained in the step (1) to obtain an optimized co-prime matrix, wherein the translation factor is FA.
Further, the translation factor FA is as follows:
in the formula: a. The dis Is a position matrix of the sub-array A, B dis For the position matrix of subarray B, the function g (a, B) is the continuous maximum in the difference of matrices a and B.
A difference co-prime matrix based DOA estimation method comprises the following steps:
s1: obtaining an optimized differential co-prime array according to the optimized co-prime array obtained in the step 2, and taking the differential co-prime array as a receiving and transmitting antenna array;
s2: transmitting a detection pulse by adopting the receiving and transmitting antenna array in the step S1, and receiving an echo signal of a target after the echo signal is reflected by the space target;
s3: performing matrixing processing on the echo signals obtained in the step S2;
s4: and calculating DOAs from different path targets by using a Capon method to complete the estimation of the target DOA.
The method has the beneficial effects that:
(1) The self-adaptive optimization co-prime matrix arrangement algorithm is simple, convenient and feasible, and has stronger universality; the optimal arrangement mode does not need to be recalculated aiming at the co-prime arrays with different unit numbers;
(2) Compared with the differential co-prime array obtained by the traditional co-prime array, the differential co-prime array generated by the invention has more continuous unit numbers and larger aperture number, is used in the fields of communication, imaging, positioning and the like, and can obtain better information processing effect on the premise of not increasing the unit number;
(3) The target DOA estimation method can obviously improve the positioning accuracy and resolution of the DOA and reduce side lobes.
Drawings
FIG. 1 is a diagram of a conventional co-prime array and sub-array.
FIG. 2 shows a graph of M c ＝3，N c And when =8, the layout of the traditional differential co-prime array generated by the traditional co-prime array is schematic.
FIG. 3 is a flowchart of the method for optimizing co-prime matrix arrangement according to the present invention.
Fig. 4 is a schematic diagram of the optimized co-prime matrix and its sub-matrices in the present invention.
FIG. 5 shows a graph of M c ＝3，N c And when =8, the arrangement of the optimized differential co-prime array generated by the optimized co-prime array of the present invention is schematically illustrated.
Fig. 6 is a power spectrum containing DOA information based on a conventional differential co-prime array and an optimized differential co-prime array.
Fig. 7 is an enlarged schematic view of fig. 6.
Detailed Description
The invention is further described with reference to the following figures and specific examples.
A self-adaptive optimization co-prime matrix arrangement method comprises the following steps:
step 1: reversing the position of any subarray in the co-prime matrix, namely reversing the coordinate position from a positive axis to a negative axis;
step 2: and (3) translating the sub-array inverted in the step (1) to obtain an optimized co-prime array, wherein the translation factor is FA.
Assuming that the position of any one subarray A in the co-prime array is reversed to obtain an optimized co-prime array subarray A; and forming a new co-prime array by the optimized co-prime subarray A and the subarray B in the original co-prime array, and obtaining an optimized differential co-prime array by using the new co-prime array.
The translation factor FA is as follows:
in the formula: a. The dis Is a position matrix of the sub-array A, B dis For the position matrix of subarray B, the function g (a, B) is the continuous maximum in the difference of matrices a and B.
Selecting two natural numbers M of any coprime c And N c According to the traditional co-prime array arrangement, the number of array units is N =2M c +N c -1; if the array is not operated any more with an effective aperture number of N, the maximum number of targets that can be detected is N-1. In order to obtain a larger aperture, a conventional co-prime array needs to be deformed to realize a virtual uniform line array having more continuous elements. Therefore, a larger aperture can be obtained. The array formed by this deformation operation is called a differential co-prime array. Corresponding array element position is S DCA ＝{±(n c M c d-m c N c d) Wherein (1. Ltoreq. N) c ≤N c -1)，(1≤m c ≤2M c -1). The differential co-prime array generated in the mode has limited number of continuous units, namely, the degree of freedom is limited or more holes appear.
In order to solve the problems in the prior art, the position of any sub-array of the traditional co-prime array is inverted, namely the coordinate position is inverted from a positive axis to a negative axis; and translating the inverted subarray by the translation factor of FA.
The FA is obtained by solving the maximum continuous value of the distance difference matrices of the two sub-matrices, and the physical meaning of the maximum continuous value of the distance difference matrix is the maximum continuous unit number of the differential co-prime matrix.
The specific process is as follows:
taking the number of two sub-array units of the co-prime array as M c And N c Suppose M c ＜N c . At this time, the number of co-prime array cells obtained by the conventional method is N =2M c +N c -1. If the array is not operated any more with an effective aperture number of N, the maximum number of targets that can be detected is N-1. The corresponding co-prime matrix arrangement is shown in FIG. 1, with sub-matrix A at a position of [0 c ,2M c ,…,(N c -1)M c ]d, the position of the subarray B is [0 c ,2N c ,…,(2M c -1)N c ]d and d is a half wavelength of the working center frequency of the antenna. The degree of freedom of the differential co-prime matrix generated in this way is at least 2M c N c +1, e.g. when M c ＝3，N c =8, the position arrangement of the corresponding differential co-prime matrix unit is shown in fig. 2. It can be seen that the number of consecutive units is 26 × 2+1=53, i.e. the degree of freedom is 53 and greater than 2M c N c +1= 49. The difference co-prime array has 4M c N c -2N c +1=81 apertures contain 14 holes, indicated by the dark grey circles in fig. 2. Therefore, the number of effective apertures that can be realized by using a differential co-prime array generated in a conventional manner is 81-14= 67.
The method of the invention is provided in order to obtain the number of continuous units, namely the degree of freedom and the number of effective apertures, as much as possible on the premise of not increasing the number of array units. Inverting a sub-array, e.g. A, in the co-prime array to obtain a new position [ - (N) c -1)M c ,…,-2M c ,-M c ,0]d; from conventional max ((N) by transforming the maximum position of the cell c -1)M c d,(2M c -1)N c d) I.e. from (N) c -1)M c d，(2M c -1)N c d taking the maximum value to become [ (N) c -1)M c +(2M c -1)N c ]d. It can be seen that [ (N) c -1)M c +(2M c -1)N c ]d is always greater than max ((N) c -1)M c d,(2M c -1)N c d) In that respect Thus, it is possible to provideThe maximum position of the unit of the differential co-prime array generated by the reversed co-prime array is constantly larger than that of the unit of the differential co-prime array generated by the traditional method.
However, the problem of the optimal number of the continuous units cannot be solved by simple inversion, so that a universal method for optimizing the translation factor FA is provided. The specific method comprises the following steps:
in the formula: a. The dis Is a position matrix of the sub-array A, B dis As the position matrix of subarray B, the function g (a, B) is the continuous maximum in the difference of matrices a and B; in the invention, a = -A dis + FAd, the original co-prime subarray A is replaced after the inversion translation transformation of the subarray A, and the subarray B does not do any operation. Therefore, the method only needs to transform one subarray, and is simple and convenient. In addition, the result obtained by the optimization equation is the optimal translation factor FA of the co-prime matrix corresponding to the differential co-prime matrix with the largest number of continuous units.
The FA optimization process is as shown in fig. 3, and for the co-prime matrix with the set number of cells, a value range of the translation factor FA is set, which can be very large, and the step length can be very small; the FA value range and the step length are determined according to the actual application scene; using the initial value of FA to obtain a difference co-prime matrix, the obtained number of continuous elements is Q 1 The second value of FA obtains a differential co-prime matrix by the same method, and the obtained number of continuous units is Q 2 (ii) a Comparison Q 1 And Q 2 Is of a magnitude of (Q) 1 ＜Q 2 If the initial value is not the optimal solution, namely the optimal translation factor number FA, the initial value of the FA value range is excluded, the second value is set as the initial value, the corresponding difference co-prime matrix is obtained, the number of continuous units is calculated and obtained, and the number is defined as Q 1 Changing the third value of the original value range into the second value of the new value range, and calculating to obtain a corresponding differential co-prime matrix and the number of continuous units, which are defined as Q 2 . Then the same as discussed above until the maximum Q is found 2 And the corresponding translation factor FA is the optimal value of FA. If Q 1 ＜Q 2 If the difference is not true, the number of the continuous units of the difference co-prime matrix obtained by the initial value is more than that of the continuous units of the difference co-prime matrix obtained by the second value, the third value replaces the second value in the original value range, and the corresponding difference co-prime matrix and the number of the continuous units are calculated and obtained and are defined as Q 2 Then compare Q 1 And Q 2 Repeating the steps, and still obtaining Q after traversing all values 1 ＜Q 2 It is not true. The optimal solution with the initial value as the translation factor FA is illustrated.
In general Q 1 ＜Q 2 And if the translation factor FA cannot be established constantly or not, the corresponding processing mode needs to be selected after judgment to obtain the optimal solution of the translation factor FA. The co-prime subarray a after inversion is translated as shown in fig. 4. And calculating the position difference of the new subarray A and the atom array B to obtain a new differential co-prime array, wherein the array is the optimally arranged differential co-prime array, and the number of continuous units of the array is the largest. Also with M c ＝3，N c For example, =8, the optimal translation factor FA =8 obtained by the above method, and the corresponding differential co-prime matrix distribution is shown in fig. 5. It can be seen that the number of consecutive units is 39 × 2+1=79, i.e. the degree of freedom is 79, which is greater than 53 obtained by the conventional method. In addition, the differential co-prime matrix has a total of 107 apertures containing 14 holes, as indicated by the dark gray circles in FIG. 5. The effective number of apertures is 93. Under the condition of not changing the number of the co-prime array units, compared with the traditional differential co-prime array, the optimized differential co-prime array generated by the method increases the number, the degree of freedom and the effective aperture number of continuous units.
For further comparison, the traditional differential co-prime array and the optimized differential co-prime array are both used as a receiving and transmitting antenna array, and Gaussian modulation pulses with the center frequency of 3.5GHz and the duration of 0.5ns are transmitted as detection pulses. Assuming that the environmental signal-to-noise ratio is-10 dB, the target DOA is respectively 37 degrees, 39 degrees and 41 degrees, the horizontal distance between the space target and the first antenna is 1km, simulating the propagation environment by using a lognormal distribution shadow model, wherein the model realizes different channels according to the different density of obstacles between a signal sending end and a signal receiving end in the environment. The model is widely applied to signal processing, and DOA estimation is carried out by using a traditional Capon algorithm, and the result is shown in FIGS. 6 and 7. Capon is a commonly used beamforming algorithm.
Because the target DOAs are relatively close together, the conventional differential co-prime matrix can only resolve the positions of two DOAs, at 38 ° and 41.5 °, respectively, where 38 ° is the central position of the target DOA at 37 ° and 39 °, with an error of 1 °, and the estimated error of 41.5 ° DOA is 0.5 °. However, the optimized difference co-prime matrix generated by the method provided by the invention can clearly acquire the positions of 3 DOAs at 36.9 degrees, 39.2 degrees and 41 degrees respectively, and the errors are respectively 0.1 degree, 0.2 degree and 0 degree. The positioning accuracy and resolution of the DOA are obviously improved. In the power spectrum containing the DOA information, the waveform obtained by utilizing the optimized differential co-prime matrix is lower than the waveform side lobe obtained by utilizing the traditional differential co-prime matrix, and the DOA is convenient to further identify, so that the co-prime matrix arrangement method provided by the invention can realize the DOA positioning with high precision and low side lobe on the premise of not changing the DOA estimation method.
The arrangement method can effectively increase the number, the degree of freedom and the effective aperture number of the differential co-prime array continuous units. The method is suitable for any co-prime matrix, namely the number of units of which two sub-matrixes are any co-prime, and the optimal arrangement can be obtained only by inputting the number of the units of the two sub-matrixes without repeated calculation. Different from the traditional method which needs different optimization methods for different co-prime arrays, the method increases the universality of the method.
Claims (2)
1. A self-adaptive optimization co-prime array arrangement method is disclosed, wherein the co-prime array is composed of a subarray A and a subarray B, and the method is characterized by comprising the following steps:
step 1: inverting the position of the subarray A in the co-prime array, namely inverting the coordinate position from a positive axis to a negative axis;
and 2, step: translating the subarray A subjected to inversion in the step 1 to obtain an optimized subarray A, and forming an optimized co-prime array by the optimized subarray A and the subarray B of the original co-prime array, wherein the translation factor is FA;
the optimization equation for the translation factor FA is as follows:
in the formula:
is a matrix of the positions of the sub-array a,
is a position matrix, function, of sub-array Bg（a，b) Is a matrixaAndbthe continuous maximum value of the difference of (c),dis a half wavelength of the antenna operating center frequency;
and obtaining the optimal translation factor FA of the co-prime matrix corresponding to the difference co-prime matrix with the maximum number of continuous units according to the result obtained by the optimization equation.
2. A method of estimating DOA of an object using a differential co-prime matrix obtained by the method of claim 1, comprising the steps of:
s1: obtaining an optimized differential co-prime array according to the optimized co-prime array obtained in the step 2, and taking the differential co-prime array as a receiving and transmitting antenna array;
s2: transmitting a detection pulse by adopting the receiving and transmitting antenna array in the step S1, and receiving an echo signal of a target after the echo signal is reflected by the space target;
s3: performing matrixing processing on the echo signals obtained in the step S2;
s4: and calculating DOAs from different path targets by using a Capon method to complete the estimation of the target DOA.
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| CN105182293A (en) * | 2015-08-25 | 2015-12-23 | 西安电子科技大学 | Method for estimating DOA and DOD of MIMO radar based on co-prime array |
| CN106324558A (en) * | 2016-08-30 | 2017-01-11 | 东北大学秦皇岛分校 | Broadband signal DOA estimation method based on co-prime array |
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| CN105182293A (en) * | 2015-08-25 | 2015-12-23 | 西安电子科技大学 | Method for estimating DOA and DOD of MIMO radar based on co-prime array |
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