A two-dimensional DOA estimation method based on a four-element rectangular antenna array

Abstract

The application improves a two-dimensional DOA estimation method based on a four-element rectangular antenna array, comprising: step 1, receiving a target signal by using the four-element rectangular antenna array, and calculating a cross-correlation vector of a preamble sequence in the target signal and a corresponding local preamble sequence; step 2, establishing a space rectangular coordinate system according to the four-element rectangular antenna array, and constructing a steering vector of the preamble sequence in the target signal in the space rectangular coordinate system, estimating an angle between the target signal DOA and each coordinate axis of the space rectangular coordinate system, making the steering vector and the cross-correlation vector best in matching degree, and obtaining an estimation result of the target signal DOA. The application uses the estimation method of the preamble sequence, is higher in accuracy, provides higher gain with longer preamble sequence, and is better in DOA estimation effect.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of wireless communication, and particularly relates to a two-dimensional DOA tracking estimation method based on a four-element rectangular antenna array. BACKGROUND

[0002] With the development of the wireless communication industry, people have higher and higher demand for information transmission in motion. As an important part of array signal processing, direction of arrival (DOA) estimation can identify the direction of a target signal through analysis and processing of characteristic information of a received signal. Through the knowledge of the target direction, an array antenna can form a high-gain beam in the target direction through beamforming (BF) technology, thereby bringing gain to a communication link.

[0003] After years of development, there are many DOA estimation algorithms. In 1969, Capon proposed a Capon algorithm based on optimal spatial filtering to realize DOA estimation by compressing the power of undesired signals. R. Schmidt proposed a MUSIC algorithm in IEEE Transactions on Antennas and Propagation, vol. 34, no. 3, pp. 276-280, which utilizes the orthogonality of the signal subspace and the noise subspace to obtain the signal source by performing eigenvalue decomposition on the covariance matrix of the received signal and searching for spectral peaks. However, this algorithm needs to perform a large number of matrix inversion operations, and its performance is also restricted by the search interval in practical applications. Later, B. D. Rao and K. V. S. Hari proposed a Root-MUSIC method in IEEE Transactions on Acoustics, vol. 37, no. 12, pp. 1939-1949, which reduces the computational complexity while improving the performance in low signal-to-noise ratio conditions. However, the MUSIC method and the Root-MUSIC method do not utilize known pilot information, and their performance is greatly affected in the case of a small number of snapshots. SUMMARY

[0004] The application aims to solve the problems of large search range, long calculation time, large resource consumption and poor effect of existing two-dimensional DOA estimation methods, and proposes a two-dimensional DOA estimation method based on a four-element rectangular antenna array, which can realize accurate and rapid tracking estimation of the direction of arrival of a target signal.

[0005] The application is implemented through the following technical solutions:

[0006] A two-dimensional DOA estimation method based on a four-element rectangular antenna array, comprising:

[0007] Step 1, receiving target signal by using a four-element rectangular antenna array, and calculating a cross-correlation vector of a preamble sequence in the target signal and a corresponding local preamble sequence;

[0008] Step 2, establishing a spatial rectangular coordinate system according to the four-element rectangular antenna array, and constructing a steering vector of the preamble sequence in the target signal in the spatial rectangular coordinate system, and estimating an angle between the target signal DOA and each coordinate axis of the spatial rectangular coordinate system, so that the steering vector and the cross-correlation vector are best matched, and an estimation result of the target signal DOA is obtained.

[0009] Preferably, step 2 specifically comprises:

[0010] Step 2.1, establishing the spatial rectangular coordinate system, the position of the four-element rectangular antenna array being a first quadrant of an XOY plane of the spatial rectangular coordinate system, and the position of a reference element in the four-element rectangular antenna array coinciding with an origin of the spatial rectangular coordinate system; the distance between elements on an X-axis of the four-element rectangular antenna array being d x , and the distance between elements in a Y-axis direction being d y ;

[0011] Step 2.2, setting the angle between the target signal DOA and the X-axis of the spatial rectangular coordinate system as α, the angle between the target signal DOA and the Y-axis of the spatial rectangular coordinate system as β, and the angle between the target signal DOA and the Z-axis of the spatial rectangular coordinate system as γ, and constructing the steering vector as wherein λ is a wavelength, and j is an imaginary unit;

[0012] Step 2.3, solving the angles α, β and γ so that the steering vector and the cross-correlation vector are best matched, and obtaining the estimation result of the target signal DOA.

[0013] Further, step 2.3 specifically comprises:

[0014] Designing a target function:

[0015] Q = |a H p

[0016] wherein p is the cross-correlation vector, p = [p0, p1, p2, p3] T , p0, p1, p2 and p3 are cross-correlation values of each element in the four-element rectangular antenna array;

[0017] Setting a priori direction of the target signal as (α p , β p , γ p ), and the angle deviation between the target signal DOA and the a priori direction being not more than a preset m p , and obtaining an optimization problem about the angles between the target signal DOA and the coordinate axes as:

[0018]

[0019] Solving the optimization problem, an estimation result of the target signal DOA is obtained.

[0020] Further, solving the optimization problem, the specific method comprises:

[0021] Step 2.3.1, in the constraint condition of the optimization problem, a set of initial values α0, β0, γ0 satisfying the constraint condition is selected at random, and a steering vector is obtained. The value of the objective function at this time is calculated.

[0022] Step 2.3.2, let α = α0, and the constraint condition is obtained.

[0023]

[0024] The second inequality is taken as an equation to obtain a straight line equation about cosβ and cosγ, and the first circle equation is combined to obtain a quadratic equation about cosβ; if the quadratic equation has real solutions, the value range [b1, b2] of the variable cosβ is obtained, b1 and b2 are real roots of the quadratic equation, and step 2.3.3 is executed; if the quadratic equation has no real solutions, the initial values α0, β0, γ0 are reselected in step 2.3.1;

[0025] Step 2.3.3, the objective function is Wherein When α = α0, φ2 that maximizes Q is obtained, and after deblurring, a local optimal solution cosβ of cosβ is obtained. * , and a local optimal solution β of β is obtained. * ;

[0026] Step 2.3.4, according to β * , a local optimal solution α * of α is obtained, and according to α * , β * , γ* is obtained from the constraint condition, and the value of the objective function Q * = | (a * ) H p| is obtained.

[0027] Step 2.3.5, calculate ε = Q * -Q0;

[0028] Step 2.3.6, if ε > threshold, wherein threshold is a pre-set precision value, let α0 = α * , β0 = β * , γ0 = γ * , and recalculate Return to step 2.3.2, otherwise, go to step 2.3.7.

[0029] Step 2.3.7, record α * ,β * ,γ * Q * As a set of suboptimal solutions, this set of suboptimal solutions serves as the estimation result of the target signal DOA.

[0030] Furthermore, in step 2.3.3, the local optimal solution for cosβ is obtained. * The specific method is as follows:

[0031] First, based on the given α = α0, find the ideal optimal value of φ2. Set another objective function m represents the possible multiple solutions, and the optimization objective is set as... Solving for the actual optimal value The constraints to be satisfied are:

[0032]

[0033] Furthermore, in step 2.3.3, the actual optimal value The solution method is as follows: traverse the values ​​of m within the range of values ​​described by the constraints, and within the range described by the constraints... Within the range of values, select the one that minimizes Q1. If there are multiple candidate solutions... To ensure that the minimum value of Q1 is the same, select the candidate solution that is closest to the prior direction. As the final solution, i represents the index of multiple candidate solutions. This completes the solution fuzziness and yields the actual optimal value. We obtain the local optimal solution for cosβ, i.e., cosβ * This leads to the local optimal solution β. * .

[0034] Furthermore, in step 2.3.4, according to β * Find the local optimal solution α. * Specifically:

[0035] objective function in When β = β * When φ1 that maximizes Q is found, and after unfuzzing, the local optimal solution cosα is obtained. * The local optimal solution α is obtained. * .

[0036] Furthermore, it also includes:

[0037] Step 2.3.8, change the value of a0 in step 2.3.1, repeat steps 2.3.1 to 2.3.7 multiple times to obtain multiple sets of suboptimal solutions, select Q from the multiple sets of suboptimal solutions * The maximum set of solutions is taken as the final solution, and the final solution is taken as the estimation result of the target signal DOA.

[0038] Compared with the prior art, the present application has the following beneficial effects:

[0039] The signal in a general communication system often adds a preamble sequence for synchronization and channel estimation, etc. The present application utilizes the preamble sequence in wireless communication for DOA estimation, that is, the present application utilizes the correlation of the preamble sequence and the corresponding known local preamble sequence to obtain a coherent gain. Compared with other DOA estimation methods, the estimation method using the preamble sequence in the present application has higher accuracy. The longer the preamble sequence, the higher the gain provided, and the better the effect of DOA estimation.

[0040] Further, the method of the present application takes the DOA range of the target signal as a constraint condition and iteratively estimates the two-dimensional spatial angle. Under the same prior condition, the method can realize fast tracking estimation of the target direction. Unlike the method of searching for a peak value in a certain spatial angle range in the literature, the iterative calculation can greatly reduce the operation amount of two-dimensional search. BRIEF DESCRIPTION OF DRAWINGS

[0041] Figure 1 The arrangement of the four-element rectangular antenna array used in the simulation example of the present application.

[0042] Figure 2 The complementary cumulative distribution function (CCDF) graph of the DOA estimation error using the method of the present application and the MUSIC method under the same received signal-to-noise ratio is compared. The simulation conditions are set as follows: the distance between adjacent antenna elements d x = d y = 0.0336 m, the carrier frequency f = 35 GHz. The incoming wave direction is within a conical region centered at an angle of 85.02° with the X-axis, 81.35° with the Y-axis, and 10° with the Z-axis, with a maximum deviation angle m p = 4°. The prior direction a p = 85.02°, b p = 81.35°, and g p = 10°. The received known pilot sequence length is 254 points, and the received signal-to-noise ratio is -10 dB. In addition, the precision in iteration is threshold = 0.01.

[0043] Figure 3The CCDF (complementary cumulative distribution function) graph of the maximum likelihood estimation error based on the pilot is compared under different iteration initial value numbers, and the simulation conditions are the same as Figure 2 .

[0044] Figure 4 The flowchart of the method of the application is shown in the figure. DETAILED DESCRIPTION

[0045] In order to further understand the application, the application is described below in combination with examples, which are only used to further explain the features and advantages of the application, and are not used to limit the claims of the application.

[0046] The overall idea of the two-dimensional DOA estimation method based on the four-element rectangular antenna array of the application is as follows: the correlation of the received signal (the preamble sequence) of the four-element rectangular array antenna and the local preamble sequence is calculated, the phase information and the initial condition are used for calculation, and finally the DOA estimation result of the target signal is obtained.

[0047] As shown in Figure 1 , the antenna array plane used in the present example is a rectangular antenna array composed of 2x2 antenna elements, and the distances between the adjacent antenna elements along the X-axis direction and the Y-axis direction are d x ,d y , the carrier frequency is f, and the wavelength is , where c is the speed of light. The target signal wave direction is within a conical region with the X-axis angle α p , and the Y-axis angle β p as the center, and the maximum deviation angle is m p . The precision threshold in iteration satisfies threshold>0.

[0048] The method of the application can obtain the estimation of the target signal wave direction according to the received signal of the four-element rectangular antenna array, and the flowchart of the method of the application is shown in Figure 4 , which includes the following steps:

[0049] Step 1: at the receiving end, the target signal transmitted by the transmitting end is received by the four-element rectangular antenna array, and the target signal contains a preamble sequence, and the preamble sequence is calculated with the corresponding local known preamble sequence to obtain a cross-correlation vector p, p=[p0, p1, p2, p3] T , and the elements in the cross-correlation vector are the cross-correlation values of each element.

[0050] Step 2: estimate the angle between the target signal DOA and the coordinate axes of the spatial rectangular coordinate system, so that the direction vector of the preamble sequence in the target signal matches the cross-correlation vector p to the best extent, and the target signal DOA estimation result is obtained.

[0051] Step 2 specifically includes:

[0052] Step 2.1, a space rectangular coordinate system is established, the position of the four-element rectangular antenna array is the first quadrant of the XOY plane, the position of the reference array element coincides with the origin, the distances between the array elements in the X-axis and Y-axis directions of the four-element rectangular antenna array are d x ,d y .

[0053] Step 2.2, assuming that the angle between the target signal DOA and the X-axis of the space rectangular coordinate system is α, the angle between the target signal DOA and the Y-axis is β, and the angle between the target signal DOA and the Z-axis is γ, a 4x1-dimensional steering vector of the target signal incident to the four-element rectangular antenna array is constructed, which is denoted as where λ is the wavelength, and j is the imaginary unit.

[0054] Step 2.3, the angles α, β, and γ between the target signal DOA and the coordinate axes are solved, so that the steering vector in step 2.2 and the received cross-correlation vector are best matched, and the target signal DOA estimation result is obtained.

[0055] Step 2.3 is specifically:

[0056] Design the objective function:

[0057] Q = |a H p|

[0058] When the objective function Q is maximum, the matching degree of the steering vector and the cross-correlation vector is best, and at the same time, it is also necessary to ensure that the solution result is within the range of the target signal DOA. Assuming that the prior direction of the target signal is (α p ,β p ,γ p ), the angle deviation between the target signal DOA and the prior direction is not more than m p , and m p can be specified in advance, so the optimization problem about the angles between the target signal DOA and the coordinate axes is:

[0059]

[0060] Solving the optimization problem can obtain the DOA estimation result.

[0061] In step 2.3, the steps of solving the DOA estimation result specifically include:

[0062] Step 2.3.1, in the constraint condition of step 2.3, a set of initial values α0, β0, and γ0 satisfying the constraint condition is arbitrarily selected, and the steering vector The value of the objective function at this time is calculated

[0063] Step 2.3.2, according to step 2.3, α = α0 is obtained, and the constraint condition is

[0064]

[0065] Taking the equality sign of the second inequality yields the equation of the line in terms of cosβ and cosγ. Combining this equation with the first circle equation, we obtain a quadratic equation in terms of cosβ. If this quadratic equation has real solutions, we can find the range of values ​​for the variable cosβ [b1, b2], where b1 and b2 are the real roots of the quadratic equation, and proceed to step 2.3.3. If there are no real solutions, we stop the iteration and return to step 2.3.1 to reselect initial values ​​α0, β0, γ0.

[0066] Step 2.3.3, Objective Function in When α = α0, φ2 that maximizes Q can be obtained. After unfuzzing, the local optimum of cosβ is obtained, i.e., cosβ * The specific method is to first determine the ideal optimal value of φ2 based on the known α = α0. To obtain a result that most closely approximates the true incident direction of the target signal, another objective function is set. m represents the possible multiple solutions, and the optimization objective is set as... Solving for the actual optimal value The constraints that need to be satisfied are:

[0067]

[0068] Actual optimal value The solution method is as follows: traverse the values ​​of m within the range of the second constraint, and within the range described by the first constraint. Within the range of values, select the one that minimizes Q1. If there are multiple candidate solutions... To ensure that the minimum value of Q1 is the same, select the solution that is closest to the prior direction of the target signal. As the final solution, 'i' represents the index of the multiple candidate solutions. This completes the solution fuzziness. We obtain the local optimal solution for cosβ, i.e., cosβ * Thus, the local optimal solution β is obtained. * .

[0069] Step 2.3.4, given β * In the same case as steps 2.3.2 to 2.3.3, the local optimal solution α for this round can be obtained. * Then, based on the constraints according to α * ,β * Find γ * Thus, the objective function value Q is obtained. * =|(a * ) Hp|.

[0070] Step 2.3.5, calculate ε = Q * - Q0.

[0071] Step 2.3.6, if ε > threshold, wherein threshold is a preset precision value, then let α0 = α * , β0 = β * , γ0 = γ * , recalculate Return to step 2.3.2, otherwise go to step 2.3.7; wherein threshold is a real number greater than 0.

[0072] Step 2.3.7, record α * , β * , γ * , Q * as a set of suboptimal solutions.

[0073] Step 2.3.8, change the value of α0 in step 2.3.1, repeat steps 2.3.1 to 2.3.7 multiple times to obtain multiple sets of suboptimal solutions, and select the set of solutions with the maximum Q * as the final solution, that is, obtain the DOA estimation result.

[0074] The antenna array used in the application is a common four-element rectangular antenna array, and other irregular antenna arrays can be equivalent to a four-element rectangular antenna array by dividing sub-arrays and virtual reference elements.

[0075] As can be seen from Figure 2 , compared with the error complementary cumulative distribution curve estimated by the MUSIC method, the probability of large error using the method of the application is lower, and the performance is better. As can be seen from Figure 3 , the performance curve obtained by the method is very close to the performance curve obtained by two-dimensional search using the steering vector, that is, the method has the same performance as the maximum likelihood estimation method based on two-dimensional search, but reduces the operation time. Therefore, the method uses iterative processing, greatly reduces the operation time under the premise of ensuring performance.

[0076] At this point, both the technical scheme and the simulation results can verify the effective role of the method of the application in DOA estimation.

Claims

1. A two-dimensional DOA estimation method based on a four-element rectangular antenna array, characterized in that, The method comprises the following steps: Step 1, receiving a target signal by using a four-element rectangular antenna array, and calculating a cross-correlation vector of a preamble sequence in the target signal and a corresponding local preamble sequence; Step 2, establishing a spatial rectangular coordinate system according to the four-element rectangular antenna array, constructing a steering vector of the preamble sequence in the target signal in the spatial rectangular coordinate system, estimating an angle between a DOA of the target signal and each coordinate axis of the spatial rectangular coordinate system, and making the steering vector and the cross-correlation vector best matched to obtain an estimation result of the DOA of the target signal; Step 2 specifically comprises: Step 2.1, a space rectangular coordinate system is established, the position of the four-element rectangular antenna array is the first quadrant of the XOY plane of the space rectangular coordinate system, and the position of the reference element in the four-element rectangular antenna array coincides with the origin of the space rectangular coordinate system; the distance between the elements on the X-axis in the four-element rectangular antenna array is , and the distance between the elements in the Y-axis direction is ; Step 2.2, let the target signal DOA and the X axis of the spatial orthogonal coordinate system form an angle of , and the Y axis form an angle of , and the Z axis form an angle of , and the guide vector is constructed as , wherein is the wavelength, is the imaginary unit; Step 2.3, solving the angle The DOA estimation result of the target signal is obtained by matching the steering vector and the cross-correlation vector.

2. The method according to claim 1, wherein, Step 2.3 specifically comprises: designing a target function; wherein is the cross-correlation vector, , are the cross-correlation values of the elements of the quadrature rectangular antenna array, respectively. The prior direction of the target signal is set as The angle deviation between the target signal DOA and the prior direction is not more than a preset The optimization problem about the angle between the target signal DOA and the coordinate axis is obtained as solving the optimization problem to obtain the estimation result of the DOA of the target signal.

3. The method of claim 2, wherein the four-element rectangular antenna array is configured as a 2D DOA estimation method. The specific method for solving the optimization problem comprises: Step 2.3.1, in the constraint condition of the optimization problem, an initial value set satisfying the constraint condition is selected at random , the guide vector , the value of the objective function at this time is calculated ; Step 2.3.2, let , to obtain constraints Taking the second inequality equal to zero gives a linear equation in and which, together with the first circle equation, gives a quadratic equation in ; if this quadratic equation has real roots, the range of values of the variable is obtained , as the real roots of the quadratic equation, step 2.3.3 is executed; if the quadratic equation has no real roots, step 2.3.1 is returned to and new initial values are chosen. Step 2.3.3, Objective Function ,in , ,when At that time, seek to make The largest After defuzzification, we obtain Local optimal solution ,get Local optimal solution ; Step 2.3.4, according to , the local optimal solution of is obtained by constraint condition according to , and , the objective function value is obtained; Step 2.3.5, calculation ; Step 2.3.6, if wherein is a preset precision value, then let , recalculate , return to Step 2.3.2, otherwise go to Step 2.3.7; Step 2.3.7, logging As a set of suboptimal solutions, the set of suboptimal solutions serves as an estimate of the DOA of the target signal.

4. The method of claim 3, wherein the four-element rectangular antenna array is configured as a 2D DOA estimation method. In step 2.3.3, the local optimum solution of is solved by the specific method of . First, according to the known , the ideal optimal value of is obtained, another objective function is set, indicates that there may be multiple solutions, and the optimization goal is set to , the actual optimal value is obtained by solving, and the constraint condition is satisfied: 。 5. The method according to claim 4, wherein, In step 2.3.3, the actual optimal value is solved by: traversing the value of in the value range described by the constraint condition , selecting the value of that makes the value of minimum in the value range described by the constraint condition as the candidate solution, if there are multiple candidate solutions that make the value of minimum the same, selecting the candidate solution closest to the prior direction as the final solution, i indicating the serial number of multiple candidate solutions, thus completing the solution ambiguity, obtaining the actual optimal value , , obtaining the local optimal solution of , that is , and further obtaining the local optimal solution of .​ 6. The method of claim 3, wherein the four-element rectangular antenna array is configured as a 2D DOA estimation method. In step 2.3.4, a local optimum solution of is obtained, specifically: is obtained, specifically:​ Objective function where , when , find the maximum , , after deblurring, get the local optimal solution of , get the local optimal solution of .

7. The method of claim 3, wherein the four-element rectangular antenna array is configured as a 2D DOA estimation method. The method further comprises: Step 2.3.8, change the steps in step 2.3.

1. The value is obtained by repeating steps 2.3.1 to 2.3.7 multiple times to obtain multiple sets of suboptimal solutions. The solution is then selected from these suboptimal solutions. The largest set of solutions is taken as the final solution, and the final solution is used as the estimation result of the target signal DOA.

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