A Filled Augmented Coprime MIMO Radar for DOA Estimation and Its Applications

Abstract

This invention provides a filled augmented coprime MIMO radar and its application for DOA estimation, relating to the field of array antenna layout. The MIMO radar uses a filled augmented coprime array structure with the same number of elements as the transceiver array, where M and N are coprime numbers, M is the number of elements on the positive x-axis, and Q is the number of elements on the positive x-axis. A spreading factor is introduced to further increase the antenna aperture. This invention's MIMO radar uses a filled augmented coprime array as the transceiver array, effectively avoiding the mutual coupling effects caused by inter-array crossover. Furthermore, the introduction of a spreading factor not only expands the antenna aperture and improves resolution, but also further reduces the influence of mutual coupling and obtains more virtual elements, greatly increasing the degree of freedom in DOA estimation.

Description

Technical Field

[0001] This invention relates to the field of array antenna layout, and more particularly to a filled augmented coprime MIMO radar for DOA estimation and its applications. Background Technology

[0002] Multiple-Input Multiple-Output (MIMO) radar is a novel radar technology, first proposed by Lincoln Laboratory in 2003. The key feature of MIMO radar technology is that both the transmitting and receiving arrays are equipped with multiple antennas for signal transmission and far-field signal reception, respectively. It is classified into monostatic MIMO radar and bistatic MIMO radar based on whether the transmitting and receiving elements are located in the same position. MIMO radar offers significant improvements in spatial resolution, degrees of freedom (DOF), and parameter identifiability.

[0003] Currently, the design of sparse MIMO array structures has attracted widespread attention. Their element spacing breaks through the half-wavelength limitation, allowing for the expansion of the array aperture. Furthermore, based on virtualized spatial smoothing-like DOA estimation methods, a difference co-array of sum co-array (DCSC), i.e., a virtual array, is generated, which can significantly improve DOA estimation performance and increase the number of identifiable targets. However, existing MIMO array structures have low degrees of freedom and poor anti-coupling properties. Summary of the Invention

[0004] Purpose of the invention: This invention aims to provide a filled augmented coprime MIMO radar for DOA estimation, which aims to provide lower mutual coupling, higher degrees of freedom and better angle estimation performance compared with other types of MIMO radars with the same total number of array elements. It can be applied to wireless communication, sonar, positioning and other fields.

[0005] To achieve the above technical objectives, this invention proposes a filled augmented coprime MIMO radar for DOA estimation, comprising a transmit array and a receive array, wherein:

[0006] Both the transmitting array and the receiving array adopt a filled augmented coprime array (SACA) structure. The SACA structure is composed of a first subarray, a second subarray, and a third subarray. The first subarray and the second subarray constitute an augmented coprime array (ACA) structure. The third subarray is arranged along the negative half-axis and is used to fill the holes in the ACA structure. The array parameters of the SACA structure include coprime integers M, N and Q, where M and N are coprime, and Q represents the number of array elements set in the negative half-axis direction; The transmitting array and the receiving array are combined to form a virtual array structure for direction-of-arrival (DOA) estimation.

[0007] As a preferred embodiment, both the transmitting array and the receiving array have an array element number equal to... The SACA structure, in which M and N are coprime numbers. Q is the number of array elements on the positive half of the x-axis, and Q is the number of array elements on the negative half of the x-axis.

[0008] As a preferred embodiment, the set of element positions of the transmitting array satisfies ,in , , These represent the positions of the array elements corresponding to the first, second, and third subarrays, respectively.

[0009] As a preferred embodiment, the positions of the array elements corresponding to the first subarray, the second subarray, and the third subarray satisfy the following relationship:

[0010]

[0011]

[0012] in The unit element spacing, The carrier wavelength.

[0013] As a preferred embodiment, the set of element positions of the receiving array is as follows: ,in For expansion factor, .

[0014] As a preferred solution, this MIMO radar achieves continuous virtual array element range. ; in ; The final continuous degrees of freedom obtained are: .

[0015] Compared with the prior art, the present invention has the following beneficial effects: (1) Using a filled augmented coprime array as the transceiver array results in lower element mutual coupling and a larger antenna aperture.

[0016] (2) By introducing an expansion factor, the aperture of the antenna is further expanded, resulting in more virtual array elements.

[0017] It can achieve better DOA estimation performance.

[0018] (3) It can achieve better DOA estimation performance. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the SACA transceiver array and its DCA structure according to the present invention.

[0020] Figure 2 This is a schematic diagram of the ACA hole structure.

[0021] Figure 3 A comparison diagram of SACA and its DCA with different structures.

[0022] Figure 4 A comparison diagram of the degrees of freedom for different MIMO radars.

[0023] Figure 5 A comparison graph showing the variation of RMSE with SNR for different MIMO radars.

[0024] Figure 6 A comparison chart showing the variation of RMSE with the number of snapshots for different MIMO radars.

[0025] Figure 7 A comparison graph showing the variation of RMSE with coupling coefficient for different MIMO radars. Detailed Implementation

[0026] In the following description, numerous specific details are set forth in order to provide a more thorough understanding of the invention. However, it will be apparent to those skilled in the art that the invention can be practiced without one or more of these details. In other instances, certain technical features well-known in the art have not been described in order to avoid obscuring the invention.

[0027] The following examples illustrate the specific design concept of the filled augmented coprime MIMO radar for DOA estimation according to the present invention.

[0028] I. Data Model Consider a monostatic MIMO radar with M elements in its transmit array and N elements in its receive array, and the sets of their element positions are as follows: , ,in, Represents the spacing between unit array elements. Let be the wavelength of the incident signal. Assume there are K narrowband far-field uncorrelated sources in space, with incident angles of . The received signal model can then be expressed as:

[0029] in, Represents the Khatri-Rao product. , These represent the direction matrices of the receiving array and the transmitting array, respectively. These are orthogonal signals emitted by the radar. With zero mean and variance Additive white Gaussian noise, These represent the steering vectors of the transceiver array, which can be specifically expressed as:

[0030]

[0031] Equation (1) can be rewritten as:

[0032] in, , Represents the Kronecker product, a matrix The virtual array element positions are represented by a second-order sum array of the transceiver array. In this embodiment, a MIMO radar structure with shared transceiver is considered. Therefore... Then the covariance matrix of the received signal can be expressed as:

[0033] in, , , Representing signal power, in practice, this embodiment often uses L snapshots to approximate the estimation. :

[0034] right Vectorization yields:

[0035] physical array The generated difference co-array (DCA) is symmetric, defined as the distinct differences between all elements of the array, expressed by the formula:

[0036] In equation (7), the virtual array element flow matrix is ​​obtained through vectorized covariance matrix operations. The corresponding set of virtual array element positions is a sum-difference joint array. Specifically, it is expressed as:

[0037]

[0038]

[0039] in Let f(x) represent the difference arrays of the transmitting array and the receiving array, respectively. As can be seen from equation (9), the virtual array element position set of the MIMO radar is obtained by calculating the transmitting and receiving arrays and the difference array.

[0040] In practical engineering, mutual coupling effects often exist between antennas, which can reduce DOA estimation performance. The signal model given in Equation (1) ignores the mutual coupling effect between adjacent sensors and introduces a mutual coupling matrix. Then, the signal model can be represented as:

[0041] Mutual coupling matrix The elements in can be specifically represented as:

[0042] in, or , representing the spacing between physical array elements, Representation matrix The element value in the i-th row and j-th column satisfies B represents the maximum element spacing considering mutual coupling effects. Beyond this distance, the mutual coupling effect between elements is ignored in this embodiment. In this embodiment, B=100 is assumed, and the joint mutual coupling coefficient matrix of the receiving array and the transmitting array is... ,in, and These represent the mutual coupling matrices of the transmitting array and the receiving array, respectively. Assume... , ,in, This represents the intensity of mutual coupling between array elements at a unit spacing.

[0043] II. Polynomial Representation Transmitter Array DCA The polynomial representation of is:

[0044] in, The binary expression for the transmit array DCA is defined as follows:

[0045] Similarly, this embodiment can construct a corresponding polynomial for the receiver DCA. According to equation (12), the DCSC of a sparse MIMO system can be modeled by the following polynomial:

[0046] in Let represent the polynomial of the receiving array DCA. From equation (14), it can be seen that DCSC can be considered as a replication-shift process: one DCA acts as the primary array, while the other DCA replicates and shifts the primary array (PA). Without loss of generality, in this embodiment, the transmitting and receiving DCA are selected as the primary array and the replica and shift array (DSA), respectively. Subsequently, the minimum element spacing of PA and DSA is 1 and 1, respectively. Both have P array elements. Therefore, RSA will replicate PA P times, and periodically... Perform the shift.

[0047] III. Filling the Augmented Coprime Matrix To fill the holes in the Augmented Coprime Array (ACA), this embodiment adds a subarray to the negative half-axis of the ACA, forming a longer continuous DCA, thus designing a new sparse array called the SACA-filled Augmented Coprime Array. The proposed array can effectively improve the array's Uniform Degree of Freedom (uDOF). The specific set of SACA locations is given by the following formula:

[0048] in All are positive integers. Coprime. (Assume) SACA consists of three subarrays. The first and second subarrays form ACA; the third subarray extends from the reference sensor towards the negative axis and contains Q sensors with an element spacing of [missing information]. A uniform linear array; since the positions of each subarray coincide only at the origin, the total number of SACA array elements is... .

[0049] It has the following properties: Property 1: For each additional array element, the non-negative continuous hysteresis of DCA increases by M+N.

[0050] Proof: To more clearly illustrate the set of holes The structure, Figure 2 Its specific configuration was shown.

[0051] in As can be seen from the figure, there is a collection of holes. It consists of several triangles, and the positions of the vertices of the triangles are denoted as . If on the negative half-axis of the array Add an array element at that location. The difference matrix between the array elements in the middle and the array elements on the negative half-axis can fill the hole on the upper left side of the triangle, that is:

[0052] From equation (16), we can see that Therefore, on the negative half-axis of the array Adding an element to a point will fill the left hole of the triangle; similarly, the right hole can be filled. If the set... If there are Q array elements, the first unfilled hole appears in the following position:

[0053] If set The number of array elements in the array are respectively and And satisfy Then we have:

[0054] So For each additional array element, the non-negative continuous hysteresis of DCA increases by M+N.

[0055] Property 2: The continuous part of the SACA difference matrix is ,in That is, uDOF is .

[0056] Proof: Since the DCA continuum of ACA is From property 1, we can obtain that If the array elements in the array can fill the holes in its DCA, then:

[0057] Therefore, the uDOF value is:

[0058]

[0059] Property 3: In the total number of array elements Given a given time, the optimal configuration of SACA to maximize its uDOF is:

[0060] Proof: In the total number of array elements Through optimization To maximize the uDOF of SACA, the optimization problem can be modeled as follows:

[0061] because Substituting into equation (22) yields:

[0062] At this point, u is a linear function in two variables N, when When u reaches its maximum value, the problem is transformed into:

[0063] The optimal value is obviously ,at this time , . Figure 3 Displaying the total number of array elements At that time, SACA and its difference matrix under two different configurations, where Figure 3 (a), , Figure 3 (b), The optimal configuration shows that a larger uDOF can be achieved with the optimal configuration.

[0064] IV. Filler-enhanced coprime MIMO radar DCSC can be viewed as a replication and shifting process, where one DCA acts as the PA, and the other replicates and shifts the master array. This is achieved by introducing a spread factor into the transmitter array. DSA replicates the primary array and uses it in conjunction with... The shifts are performed periodically, therefore any sparse array can be directly deployed in a MIMO system to extend its degrees of freedom. Assume its location set is... The continuous part of its difference coma is MIMO radar receiver array location set for Set of launch array locations ,when At that time, the uDOF of the MIMO radar is:

[0065] This invention deploys the proposed SACA at both the transceiver ends of a MIMO radar to obtain SACA-MIMO. Specifically, the expression for the set of positions of its transceiver array is as follows:

[0066] in, These are the sets of locations for the transmit and receive arrays of SACA-MIMO, both of which are based on the proposed SACA structure. It can achieve replication of the primary SACA array. times, and the replication cycle is .

[0067] Property 4: When It can fill hysteresis and voids with a small amount of overlapping hysteresis in adjacent cycles of DCSC.

[0068] Proof: This embodiment first derives the hole structure of SACA, due to the subarray of SACA Spacing Given a uniform linear array with Q elements, the position of the element with the largest self-difference is: If the position of the first unfilled hole is smaller than the position of the first unfilled hole, then the set of hole positions for SACA is the same as that for ACA, i.e.:

[0069] in Since the location of the largest hole in the DCA array will not exceed the location of the largest element in the array, we have:

[0070] because Then we have:

[0071] Simplifying, we get:

[0072] Similar ones Next, this embodiment will use proof by contradiction to prove that when At that time, the DCSC of SACA-MIMO is hole-free. Assuming that holes in later cycles cannot be filled by virtual elements in earlier cycles, meaning that some later holes are located in the same positions as some earlier holes, we have:

[0073] in Substitute Then we have:

[0074] because Then we have:

[0075] Since M and N are coprime integers, and Therefore, there is no set of integers. Equation (33) is satisfied. It can be concluded that the gap in the previous cycle is filled by the lag in the next cycle.

[0076] Will Substituting into equation (25), we can obtain the uDOFs of SACA-MIMO as follows:

[0077] Although there is some overlap in hysteresis between adjacent cycles, SACA-MIMO makes full use of the symmetry between hysteresis and aperture, which increases its degrees of freedom and reduces mutual coupling.

[0078] V. Continuous Degrees of Freedom This section compares the performance of the proposed SACA-MIMO system with other MIMO systems, including NA-MIMO, SAFIS-MIMO, GCA-MIMO, ECA-MIMO, GNA-MIMO, and the proposed SACA-MIMO.

[0079] Table 1 lists the closed-form expressions for the maximum continuous degrees of freedom achievable by different MIMO radars with a fixed number of array elements. This represents the number of array elements in each subarray of the transceiver array. Figure 4 Comparing the continuous degrees of freedom achievable by different MIMO radars with the same number of array elements, it can be seen that the proposed SACA-MIMO1 and SACA-MIMO2 have higher uDOFs, second only to GNA-MIMO. Although GNA-MIMO has slightly higher degrees of freedom, its structure contains densely arranged array elements, which can cause severe mutual coupling effects. Overall, the proposed array has better DOA estimation performance.

[0080] Table 1 Comparison of continuous degrees of freedom of different MIMO radars

[0081] VI. DOA Estimation Performance To demonstrate that the MIMO array designed in this invention outperforms some existing arrays, the root mean square error (RMSE) is used to measure the performance of DOA estimation. RMSE is defined as follows:

[0082]

[0083] in, Represents the m-th (k-th) source. The DOA estimation results of ( ) times. Assume there are K=11 narrowband uncorrelated sources in space, with incident directions as follows: All MIMO models employ optimal configurations, with a total of 16 array elements in the transmit and receive arrays. Considering the impact of mutual coupling on the array, the coupling coefficient is adjusted. Set it to 0.3. Figure 5 The DOA estimation performance of MIMO radars with different structures was compared under different signal-to-noise ratio conditions, where the number of snapshots L=200. Figure 6 The changes in RMSE with the number of snapshots were compared, with the signal-to-noise ratio (SNR) set to 0 dB. It can be seen that the DOA estimation accuracy of different MIMO radars increases with the increase of both the number of snapshots and the SNR. Under the given conditions of the number of snapshots and SNR, the proposed SACA-MIMO exhibits high estimation performance. Compared with GNA-MIMO, it has a larger element spacing, suppresses mutual coupling effects, and achieves the highest estimation performance.

[0084] To verify the anti-mutual coupling capabilities of different MIMO radars, Figure 7 The relationship between RMSE and coupling coefficient under different MIMO configurations is described. The relationship curve is shown, where the number of snapshots and the signal-to-noise ratio are 200 and 5 dB, respectively. It can be observed that... At that time, GNA-MIMO, due to its dense array elements, is greatly affected by the mutual coupling effect and has low estimation performance. The proposed SACA-MIMO, with its large spacing between array elements, can effectively suppress mutual coupling and achieve high estimation performance even with a large coupling coefficient.

[0085] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A filled augmented coprime MIMO radar for DOA estimation, characterized in that, Includes a transmit array and a receive array, wherein: Both the transmitting array and the receiving array adopt a filled augmented coprime array (SACA) structure. The SACA structure is composed of a first subarray, a second subarray, and a third subarray. The first subarray and the second subarray constitute an augmented coprime array (ACA) structure. The third subarray is arranged along the negative half-axis and is used to fill the holes in the ACA structure. The array parameters of the SACA structure include coprime integers M, N and Q, where M and N are coprime, and Q represents the number of array elements set in the negative half-axis direction; The transmitting array and the receiving array are combined to form a virtual array structure for direction-of-arrival (DOA) estimation.

2. The filled augmented coprime MIMO radar according to claim 1, characterized in that, Both the transmitting array and the receiving array have an array element number equal to [number missing]. The SACA structure, in which M and N are coprime numbers. Q is the number of array elements on the positive half of the x-axis, and Q is the number of array elements on the negative half of the x-axis.

3. The filled augmented coprime MIMO radar according to claim 1, characterized in that, The set of element positions of the transmitting array satisfies ,in , , These represent the positions of the array elements corresponding to the first, second, and third subarrays, respectively.

4. The filled augmented coprime MIMO radar according to claim 3, characterized in that, The positions of the array elements corresponding to the first, second, and third subarrays satisfy the following: in The unit element spacing, The carrier wavelength.

5. The filled augmented coprime MIMO radar according to claim 2, characterized in that, The set of element positions of the receiving array is ,in For expansion factor, .

6. The filled augmented coprime MIMO radar according to claim 5, characterized in that, This MIMO radar achieves continuous virtual element range ; in ; The final continuous degrees of freedom obtained are: 。 7. The application of the filled augmented coprime MIMO radar according to any one of claims 1 to 6 in the field of wireless communication.

8. The application of the filled augmented coprime MIMO radar according to any one of claims 1 to 6 in the field of sonar.

9. The application of the filled augmented coprime MIMO radar according to any one of claims 1 to 6 in the field of positioning.

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