Four-order layered array design method based on four-order cumulant

Abstract

The invention discloses a fourth-order layered array design method based on a fourth-order cumulant, and the method comprises the steps: constructing a first sub-array, and generating a second-order sum common array and a second-order difference common array based on the first sub-array; judging whether the first sub-array meets the condition that the second-order sum common array and the second-order difference common array have no hole, if so, entering the next step, and if not, returning to reconstruct the first sub-array; generating a second sub-array based on the second order and the common array; according to the first sub-array and the second sub-array, calculating to obtain two three-order difference common arrays; generating a third sub-array based on the two three-order difference common arrays; and obtaining a union set of the first sub-array, the second sub-array and the third sub-array to obtain a fourth-order layered array. The degree of freedom of the obtained array structure can be enhanced, and the mutual coupling effect between the sensors can be reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of array signal, in particular to a fourth-order layered array design method based on fourth-order cumulant. BACKGROUND

[0002] In the field of array signal processing and target positioning, sparse array is widely used in high-resolution direction of arrival estimation due to its high degree of freedom and large virtual aperture with limited number of sensors. In particular, the sparse array design method based on fourth-order difference co-array is proposed in recent years, which effectively improves the robustness of signal detection and parameter estimation by utilizing high-order statistical characteristics to suppress Gaussian noise interference.

[0003] However, the existing sparse array design based on fourth-order difference co-array is based on a fourth-order difference co-array expression, which limits the growth of the degree of freedom of the sparse array. In addition, the existing sparse array design based on fourth-order difference co-array is designed to further increase the degree of freedom, while ignoring the mutual coupling effect between sensors in the array, but in actual application, the mutual coupling effect between sensors will cause the performance of angle of arrival estimation to decrease.

[0004] Therefore, in order to solve the above problems, a fourth-order layered array design method based on fourth-order cumulant is needed, which can not only enhance the degree of freedom, but also reduce the mutual coupling effect between sensors. SUMMARY

[0005] Therefore, the purpose of the present application is to overcome the defects in the prior art and provide a fourth-order layered array design method based on fourth-order cumulant, which can not only enhance the degree of freedom, but also reduce the mutual coupling effect between sensors.

[0006] The fourth-order layered array design method based on fourth-order cumulant of the present application comprises the following steps:

[0007] Construct a first sub-array, and generate a second-order sum co-array and a second-order difference co-array based on the first sub-array;

[0008] Determine whether the first sub-array satisfies the condition that the second-order sum co-array and the second-order difference co-array have no holes, if yes, proceed to the next step, if not, return to reconstruct the first sub-array;

[0009] Generate a second sub-array based on the second-order sum co-array;

[0010] Calculate two kinds of third-order difference co-arrays according to the first sub-array and the second sub-array;

[0011] Generate a third sub-array based on the two kinds of third-order difference co-arrays;

[0012] The union of the first subarray, the second subarray and the third subarray is a fourth-order hierarchical array.

[0013] Further, the second-order sum and co-array is determined according to the following formula and the second-order difference co-array is determined according to the following formula :

[0014] ;

[0015] ;

[0016] wherein, is the first subarray, is the second subarray, and are elements of the first subarray; denotes the maximum value of the continuous part starting from 0 in the second-order sum and co-array ; denotes the maximum value of the continuous part starting from to in the second-order difference co-array .

[0017] Further, the conditions for making the second-order sum and co-array and the second-order difference co-array hole-free include , and ; wherein, denotes the maximum element of the first subarray .

[0018] Further, the second subarray is determined according to the following formula

[0019] ;

[0020] wherein, ; ; is the number of sensors of the second subarray .

[0021] Further, the two third-order difference co-arrays include the third-order difference co-array and the third-order difference co-array ;

[0022] wherein, ; ; denotes the maximum value of the continuous part starting from 0 in the third-order difference co-array ; denotes the maximum value of the continuous part starting from 0 in the third-order difference co-array ; is the second subarray The elements of the set.

[0023] Further, the third sub-array is determined according to the following formula :

[0024] ;

[0025] wherein, ; ; is the number of sensors of the third sub-array .

[0026] The beneficial effects of the present application are: the fourth-order hierarchical array design method based on fourth-order cumulants disclosed in the present application generates a second-order sum array and a second-order difference array based on a first sub-array, generates a second sub-array, calculates two third-order difference arrays based on the first sub-array and the second sub-array, generates a third sub-array based on the structure relationship of the two third-order difference arrays, and finally combines the three sub-arrays to form a fourth-order hierarchical array with a hierarchical progressive feature; the present application realizes high-degree expansion while maintaining a limited number of array elements through multi-level differential and hierarchical structure design, effectively reduces the mutual coupling effect between sensors, and thus improves the resolution and robustness of the sparse array in angle of arrival estimation. BRIEF DESCRIPTION OF DRAWINGS

[0027] The present application will be further described below in conjunction with the accompanying drawings and examples:

[0028] Figure 1 The present application is a fourth-order hierarchical array design method principle flowchart. DETAILED DESCRIPTION

[0029] The present application will be further described below in conjunction with the accompanying drawings and examples:

[0030] The present application discloses a fourth-order hierarchical array design method based on fourth-order cumulants, comprising the following steps:

[0031] Constructing a first sub-array and generating a second-order sum array and a second-order difference array based on the first sub-array;

[0032] Determining whether the first sub-array satisfies the condition that the second-order sum array and the second-order difference array are hole-free, if yes, proceeding to the next step, if not, returning to reconstruct the first sub-array;

[0033] Generating a second sub-array based on the second-order sum array;

[0034] Calculating two third-order difference arrays based on the first sub-array and the second sub-array;

[0035] Generating a third sub-array based on the two third-order difference arrays;

[0036] The union of the first sub-array, the second sub-array and the third sub-array is a four-order hierarchical array.

[0037] The present application obtains the first sub-array of any generator by input The corresponding second sub-array is calculated And the third sub-array Then the union of the first sub-array The second sub-array And the third sub-array Obtains a four-order hierarchical array .

[0038] In this embodiment, the four-order hierarchical array design method of the present application specifically includes the following steps:

[0039] Step 1: The input parameters are the first sub-array generator , and the sensor numbers of the second sub-array And the third sub-array And ;

[0040] Step 2: According to the input parameters, the maximum elements in the second-order sum co-array And the maximum elements in the second-order difference co-array Are calculated respectively ;

[0041] Wherein, Represents the maximum value of the continuous part from 0 in the second-order sum co-array , and the second-order sum co-array ; And Are elements of the first sub-array ; Represents the maximum value of the continuous part from To In the second-order difference co-array , and the second-order difference co-array ;

[0042] Step 3: Verify whether the first sub-array Satisfies the condition that the second-order difference co-array And the second-order sum co-array Have no holes, if it satisfies, proceed to step 4, if it does not satisfy, return to step 1 to input a new generator first sub-array , and start from step 1 to execute again; wherein the condition of no holes includes:

[0043] , ,​​ ;in, Indicates the first subarray The largest element.

[0044] Step 4: Based on the results obtained in Step 2 The second subarray is calculated. The first element Second subarray Inter-element spacing This leads to the second subarray. ;

[0045] in, , ; ;

[0046] Step 5: Based on the first subarray Second subarray The largest element of the two third-order difference comatrices was calculated. and ;

[0047] in, This represents the first type of third-order difference comatrix. The maximum value of the continuous part starting from 0, the first type of third-order difference comatrix , Indicates from the second subarray Take any number from the first subarray and... The set of all possible combinations obtained by taking the sum and difference of any two numbers in the set;

[0048] This represents the second type of third-order difference comatrix. The maximum value of the continuous part starting from 0, the second type of third-order difference comatrix , Indicates from the second subarray Take any number from the first subarray and... The set of all possible outcomes obtained by taking the difference between any two numbers;

[0049] Step 6: According to , , Number of second sub-array sensors The third subarray is calculated. The first element and the third subarray Inter-element spacing This leads to the third subarray. ;

[0050] in, ; ;

[0051] .

[0052] Seventh step: Finally, the first subarray of the input generator and the second subarray , the third subarray Take the union, that is, the fourth-order hierarchical array .

[0053] In order to better understand the fourth-order hierarchical array design method of the present application, further examples are described as follows:

[0054] First step: the input parameters are the first subarray generator , and the number of sensors of the second subarray and the third subarray are respectively , ;

[0055] Second step: according to the input parameters, the second-order and the sum array The maximum element and the second-order difference coarray The maximum element ;

[0056] Third step: verify that the first subarray of the input generator is the condition that satisfies the generation of the second-order difference coarray and the second-order sum coarray without holes, if it is satisfied, go to the fourth step;

[0057] Fourth step: according to the obtained in the second step, the first element of the second subarray and the interval between its elements are calculated, and then the second subarray is obtained;

[0058] Fifth step: according to the first subarray and the second subarray , the maximum elements of the two third-order difference coarrays and are calculated;

[0059] Sixth step: according to , , and the total number of sensors of the second subarray , the first element of the third subarray and the interval between its elements are calculated, and then the third subarray is obtained;

[0060] ​Step 7: Finally, the first sub-array of the input generator and the calculated second sub-array , the third sub-array The union of the four sub-arrays is the fourth-order hierarchical array .

[0061] Finally, it should be pointed out that the above examples are only used to illustrate the technical solutions of the present application and are not limiting. Although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or replaced equivalently without departing from the spirit and scope of the present application, and all should be covered in the scope of the claims of the present application.

Claims

1. A fourth-order layered array design method based on fourth-order cumulants, characterized by: The method comprises the following steps: constructing a first subarray and generating a second sum coarray and a second difference coarray based on the first subarray; determining whether the first subarray satisfies a condition that the second sum coarray and the second difference coarray are hole-free, if yes, proceeding to the next step, and if not, returning to reconstruct the first subarray; generating a second subarray based on the second sum coarray; calculating two third difference coarrays according to the first subarray and the second subarray; generating a third subarray based on the two third difference coarrays; obtaining a fourth hierarchical array by taking the union of the first subarray, the second subarray and the third subarray.

2. The fourth-order cumulant-based fourth-order hierarchical array design method of claim 1, wherein: The second order and co-array are determined according to the following equations and the second order difference co-array : ； ； in, For the first subarray, and All are first subarrays Element; Represents a second-order summation matrix The maximum value of the continuous segment starting from 0; Represents a second-order difference comatrix Zhong Cong Start to The maximum value of the continuous portion.

3. The fourth-order cumulant-based fourth-order hierarchical array design method of claim 2, wherein: Conditions for making the second-order and co-array and the second-order difference co-array hole-free include , and ; wherein, denotes the largest element of the first sub-array .

4. The fourth-order cumulant-based fourth-order hierarchical array design method of claim 1, wherein: The second sub-array is determined according to the following equation : ； wherein ; ; is the number of sensors of the second sub-array .

5. The fourth-order cumulant-based fourth-order hierarchical array design method of claim 1, wherein: Two third-order difference coarrays include a third-order difference coarray and a third-order difference coarray ; wherein ; ; denotes the third order difference co-array the maximum of the continuous part starting from 0; denotes the third order difference co-array the maximum of the continuous part starting from 0; is an element of the second sub-array .

6. The fourth-order cumulant-based fourth-order hierarchical array design method of claim 5, wherein: The third sub-array is determined according to the following formula : ； wherein ; ; is the number of sensors of the third sub-array .

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