Multipath high-order qam signal direct positioning method based on dual atomic norm minimization

Abstract

The application discloses a kind of based on dual atomic norm minimization multipath high-order QAM signal direct positioning method, first, construct distributed multi-sensor array positioning model under multipath environment, receive signal is obtained;Second, the simplified fourth-order cumulant of each sensor array received signal is calculated, and it is extended to obtain virtual signal;Then, respectively construct semi-positive definite constraint problem, and the dual vector is solved to obtain;Finally, all dual vectors are combined to construct cost function and directly search emitter position, and the position estimation value is obtained.The kind of direct positioning method based on dual atomic norm minimization multipath high-order QAM signal that the application designs can effectively locate emitter.In addition, the method makes full use of the characteristics of high-order QAM signal, can extend array aperture, estimates more emitters.The positioning performance of the application is superior to the traditional spatial smoothing subspace data fusion direct positioning method and discrete fourier transform direct positioning method.

Description

Technical Field

[0001] This invention relates to the field of wireless positioning technology, and in particular to a direct positioning method for multipath high-order QAM signals based on the minimization of dual atom norms. Background Technology

[0002] In modern communication systems, QAM (Quadrature Amplitude Modulation) signals play a crucial role. With the rapid development of communication technology, the requirements for data transmission rates and spectral efficiency are becoming increasingly stringent. QAM, with its superior ability to achieve high-speed data transmission within limited bandwidth, has become the preferred modulation scheme for many communication standards. By simultaneously modulating the amplitude and phase of the carrier wave, QAM can transmit multiple bits of information within one symbol period. For example, in higher-order QAM modulation, such as 64-QAM and 256-QAM, each symbol can carry 6 bits, 8 bits, or even more of information, greatly improving spectral efficiency. This characteristic has led to the widespread application of QAM in high-speed wireless communication systems such as 5G mobile communication and Wi-Fi.

[0003] Radio positioning technology plays a crucial role in many fields such as modern communication, navigation, surveillance, and security. Traditional radio positioning methods mainly include indirect positioning techniques based on ranging, angle of arrival (AoA), and time of arrival (ToA). The implementation of these techniques relies on the accurate measurement of signal propagation characteristics and subsequent calculation processes. However, in complex environments with significant multipath effects, signals undergo reflection, scattering, and diffraction, which greatly degrades the performance of the aforementioned indirect positioning methods, making it difficult to reliably guarantee positioning accuracy.

[0004] To effectively address the challenges posed by multipath effects, direct localization (DLT) technology has attracted significant attention in recent years. This technology extracts the signal source location information directly from the received signal without deducing signal propagation characteristics through intermediate steps. However, current DLT methods suffer from several problems when handling multipath environments: firstly, these methods recover the target signal at the cost of reduced array aperture, leading to a decrease in the number of estimable radiation sources; secondly, these methods often struggle to fully extract useful information from high-order QAM signals from multipath sources, thus limiting the improvement of localization accuracy.

[0005] Dual atom norm minimization techniques have shown great potential in signal processing. This technique can efficiently utilize the sparsity and structured characteristics of signals to recover target signals from observational data, significantly enhancing the robustness and accuracy of signal processing. However, how to effectively integrate dual atom norm minimization techniques in multipath environments remains a challenge and difficulty in the current technological development process.

[0006] In view of this, the present invention proposes a direct localization method for high-order QAM signals in multipath environments based on minimizing the dual atom norm, aiming to solve the above-mentioned technical problems and improve the localization accuracy and reliability of high-order QAM signals in multipath environments. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to address the deficiencies mentioned in the background art by providing a direct localization method for multipath high-order QAM signals based on the minimization of dual atom norms.

[0008] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0009] The direct localization method for multipath high-order QAM signals based on dual atom norm minimization is characterized by the following steps:

[0010] Step 1) Construct a distributed multi-sensor array localization model under multipath environment and obtain the received signal r. l (t);

[0011] The distributed multi-sensor array localization model is used to locate K far-field QAM radiation sources with unknown locations. It includes L sensor arrays with known locations, each equipped with an M-element uniform linear array arranged horizontally along the x-axis with a spacing of d. The center position vector of the l-th sensor array is represented as... These represent its x-coordinate and y-coordinate, respectively;

[0012] The position vector of the kth radiation source is represented as: The x-coordinate represents the location of the k-th radiation source. The ordinate represents the location of the k-th radiation source; let the k-th radiation source reach the l-th sensor array after multiple reflections, including a line-of-sight path and V. l,k There are several different non-line-of-sight paths; the angle of arrival of the line-of-sight path from the k-th radiation source to the l-th sensor array is denoted as... Among them, logical expressions The value is 1 when true and 0 otherwise, arctan(·) ∈ (-π / 2, π / 2). Used to eliminate the ambiguity of arctan(y / x) = arctan(-y / (-x)); the angle of arrival of the v-th non-line-of-sight path from the k-th radiation source to the l-th sensor array is denoted as θ. l,k,v , v∈<1,V l,k >, <1,V l,k > indicates that it is greater than or equal to 1 and less than or equal to V. l,k The set of integers;

[0013] The received signal of the l-th sensor array at time t is t∈<1,T>, where T is the number of quicks; s k (t) represents the QAM signal with non-zero kurtosis emitted by the k-th radiation source at time t; n l (t) is the additive white Gaussian noise vector of the l-th sensor array, and its covariance is I M Describes an M-dimensional identity matrix. Indicates noise power; α l,k,v Let represent the fading coefficient of the v-th non-line-of-sight path from the k-th radiation source to the l-th sensor array; the steering vector a(θ) for a given θ, its i-th element Where λ represents the signal carrier wavelength, and j is the imaginary unit;

[0014] Step 2), calculate the simplified fourth-order cumulant z of the received signals from each sensor array. l And expand it to obtain a virtual signal.

[0015] The simplified fourth-order cumulant of the received signal from the l-th sensor array is expressed as:

[0016]

[0017] in, Describing mathematical expectation, e i Let n represent a vector whose i-th element is 1 and all other elements are 0. l r l s k They are n l (t), r l (t), s k The simplified form of (t);

[0018] Then it is expanded to obtain a virtual signal. in:

[0019] Diagonal matrix Λ = diag{1, 1 / 2, ..., 1 / M, 1 / (M-1), ..., 1};

[0020] matrix 0 M×(M-1) Represents an M×(M-1) dimensional zero matrix;

[0021] vec{·} denotes the vectorization operator, Toep(z l ) indicates based on vector z l Construct a Toplitz matrix;

[0022] Vandermonde matrix Bl The columns are composed of 2M-1 dimensional vectors. Composition; b(θ) for a given θ, its i-th element is

[0023] It is a virtual transmission signal;

[0024] Step 3) Construct semi-positive definite constrained problems and solve them to obtain the dual vector q. l ;

[0025] Step 3.1), use atomic norms for sparse representation. Define a set of atoms The angle of arrival estimation of the radiation source can then be expressed as an atomic norm minimization problem: in, Represents a set of atoms The overcomplete dictionary constituted Represents a sparse vector;

[0026] Step 3.2) yields the dual problem of minimizing the atomic norm as follows: Where, q l The vector represents the dual vector, and the superscript H indicates the conjugate transpose, ‖·‖ ∞ Represents the infinite norm;

[0027] Step 3.3) The dual problem of minimizing the atomic norm is expressed as a positive semidefinite program as follows:

[0028] Where H l It is an Hermitian matrix;

[0029] Step 3.4): Solve the positive semidefinite programming problem using the convex optimization toolbox to obtain the dual vector q. l ;

[0030] Step 4): Construct a cost function by combining all dual vectors, and search for the estimated location of the radiation source;

[0031] Step 4.1), using the dual vector q l Construct cost function Where p represents the position vector, θ l (p) represents the angle of arrival of the line-of-sight path from p to the l-th sensor array. |·| represents the modulus of a complex number;

[0032] Step 4.2) Perform a spectral peak search on the cost function to obtain the coordinates corresponding to the peaks, which are the estimated results of the radiation source location.

[0033] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0034] This invention can fully utilize the sparsity and structured characteristics of signals to better recover target signals from observation data, expand array aperture, suppress multipath effects, and increase available degrees of freedom. Its position estimation accuracy is better than the traditional SSP-SDF direct positioning method and DFT direct positioning method, and no additional parameter pairing process is required. Attached Figure Description

[0035] Figure 1 This is a flowchart of the present invention;

[0036] Figure 2 This is a scenario diagram for joint localization using a distributed multi-sensor array in a multipath environment.

[0037] Figure 3 This diagram illustrates the available degrees of freedom for the present invention and traditional positioning methods under different numbers of sensors;

[0038] Figure 4 This is a schematic diagram illustrating the root mean square error performance of the present invention and traditional positioning methods under different signal-to-noise ratios;

[0039] Figure 5 This diagram illustrates the root mean square error performance of the present invention and traditional positioning methods under different snapshot numbers. Detailed Implementation

[0040] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings:

[0041] This invention can be implemented in many different forms and should not be considered limited to the embodiments described herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully express the scope of the invention to those skilled in the art. In the drawings, components are enlarged for clarity.

[0042] like Figure 1 As shown, this invention discloses a direct localization method for multipath high-order QAM signals based on dual atom norm minimization, specifically including the following steps:

[0043] Step 1) Construct a distributed multi-sensor array localization model under multipath environment and obtain the received signal r. l (t).

[0044] like Figure 2 As shown, the distributed multi-sensor array localization model is used to locate K far-field QAM radiation sources with unknown locations. It includes L sensor arrays with known locations, each equipped with an M-element uniform linear array arranged horizontally along the x-axis with a spacing of d. The position vector of the k-th radiation source is represented as... The superscript T denotes matrix transpose. The x-coordinate represents the location of the k-th radiation source. The ordinate of the k-th radiation source's position is represented by the vector of the center position of the l-th sensor array. and Let x and y represent the x and y coordinates, respectively. We assume that the k-th radiation source reaches the l-th sensor array after multiple reflections, containing a line-of-sight (LoS) path and V. l,k There are three distinct non-line-of-sight (NLoS) paths. The angle of arrival (AoA) of the LoS from the k-th radiation source to the l-th sensor array is denoted as...

[0045]

[0046] Where the logical expression The value is 1 when it is true, and 0 otherwise. arctan(·) ∈ (-π / 2, π / 2). Used to eliminate the ambiguity of arctan(y / x) = arctan(-y / (-x)).

[0047] The AoA of the v-th NLoS from the k-th radiation source to the l-th sensor array is denoted as θ. l,k,v ,v∈<1,V l,k >, where <1,V l,k > indicates that it is greater than or equal to 1 and less than or equal to V. l,k A set of integers.

[0048] The received signal of the l-th sensor array at time t (t∈<1,T>, where T is the number of snapshots) is

[0049]

[0050] Among them, s k (t) represents the QAM signal with non-zero kurtosis emitted by the k-th radiation source at time t, n l (t) is the additive white Gaussian noise vector of the l-th sensor array, and its covariance is I M Describes an M-dimensional identity matrix. Represents noise power, α l,k,v Let v represent the fading coefficient of the v-th non-line-of-sight path from the k-th radiation source to the l-th sensor array. For a given θ, the i-th element of the steering vector a(θ) has the following form:

[0051] Where λ represents the signal carrier wavelength, and j is the imaginary unit.

[0052] Step 2), calculate the simplified fourth-order cumulant z of the received signals from each sensor array. l And expand it to obtain a virtual signal.

[0053] The simplified fourth-order cumulant of the received signal from the l-th sensor array can be expressed as:

[0054]

[0055] in, Describing mathematical expectation, e i Let n represent a vector whose i-th element is 1 and all other elements are 0. l r l s k They are n l (t(、r l (t), s k The simplified form of (t).

[0056] Then, by expanding it, a virtual signal can be obtained. Where, the diagonal matrix Λ = diag{1, 1 / 2, ..., 1 / M, 1 / (M-1), ..., 1}, the matrix

[0057] 0 M×(M-1) Let T represent an M×(M-1) dimensional zero matrix, where the superscript T denotes the matrix transpose. vec{·} denotes the vectorization operator, Toep(z l ) indicates based on vector z l Construct a Topelitz matrix and a Vandermonde matrix B. l The columns are composed of 2M-1 dimensional vectors. The composition, b(θ), for a given θ, has the following form for its i-th element: It can be viewed as a virtual transmission signal.

[0058] Step 3) Construct semi-positive definite constrained problems and solve them to obtain the dual vector q. l .

[0059] The virtual received signal obtained in step 2 Sparse representation can be achieved using atomic norms. Define a set of atoms. The AoA estimation of the radiation source can then be expressed as the following atomic norm minimization problem:

[0060]

[0061] in Represents a set of atoms The overcomplete dictionary constituted This represents a sparse vector.

[0062] The dual problem of minimizing the atomic norm is:

[0063]

[0064] Where, q l The vector represents the dual vector, and the superscript H indicates the conjugate transpose, ‖·‖ ∞ It represents the infinite norm.

[0065] The dual problem of minimizing the atomic norm can be represented as a positive semidefinite program:

[0066] Where H l It is an Hermitian matrix;

[0067] The above positive semidefinite programming problem can be solved using the convex optimization toolbox, yielding the dual vector q. l .

[0068] Step 4) Construct a cost function by combining all dual vectors and search for the estimated location of the radiation source.

[0069] Using the dual vector obtained in step 3, construct the following cost function:

[0070]

[0071] Where p represents the position vector, θ l (p) represents the AoA of the LoS from p to the l-th sensor array. |·| represents the modulus of a complex number.

[0072] Perform a spectral peak search on the cost function, and the coordinates corresponding to the peaks are the estimated results of the radiation source location.

[0073] The traditional SSP-SDF direct positioning method has less than M-1 spatial degrees of freedom for the same number of array elements, and the subarray length is generally set to M / 2 to ensure performance. The DFT direct positioning method has M-1 spatial degrees of freedom for the same number of array elements. The method of this invention obtains 2M-2 spatial degrees of freedom, which increases the available degrees of freedom. Figure 3 This is a schematic diagram illustrating the variation of available degrees of freedom with the number of sensors in the method described in this invention and traditional positioning methods. The simulation is set with a spatial smoothing subarray length of M / 2. From... Figure 3It can be seen that the method described in this invention has more available degrees of freedom than the traditional SSP-SDF direct positioning method and DFT direct positioning method.

[0074] The performance estimation standard of this invention is the Root Mean Square Error (RMSE), defined as follows:

[0075]

[0076] Among them, M c For the number of Monte Carlo experiments, p represents the estimated location of the k-th radiation source in the i-th experiment. k Let represent the actual location of the k-th radiation source, and ‖·‖ represent the 2-norm. The signal-to-noise ratio (SNR) is defined as...

[0077]

[0078] Figure 4 The performance curves of the root mean square error (RMSE) of the method described in this invention, the traditional SSP-SDF direct localization method, and the DFT direct localization method are shown as a function of signal-to-noise ratio. Simulation conditions are as follows: the positions of the two radiation sources are [(50 m, 850 m), (840 m, 380 m)], and the positions of the four sensor arrays are [(-870 m, -1170 m), (-270 m, -1070 m), (330 m, -970 m), (930 m, -870 m)]. Each sensor array is equipped with a uniform linear array with 14 elements. Each target arriving at the sensor array has one LoS and two NLoS, with AoA of NLoS being θ. 1,1,1 = 0.1865 radians, θ 1,1,2 = 0.6823 radians, θ 1,2,1 = -0.1691 radians, θ 1,2,2 = -0.5078 radians, θ 2,1,1 = 0.4069 radians, θ 2,1,2 = -0.0876 radians, θ 2,2,1 = -0.9305 radians, θ 2,2,2 = -0.4366 radians, θ 3,1,1 = 0.2140 radians, θ 3,1,2 = 0.9440 radians, θ 3,2,1 = -0.3537 radians, θ 3,2,2 = 0.0713 radians, θ 4,1,1 = 0.8067 radians, θ 4,1,2 = 0.1926 radians, θ 4,2,1 = 0.4577 radians, θ 4,2,2= -1.0653 radians, with complex fading coefficients |α 1,1,1 |=0.85,|α 1,1,2 |=0.76,|α 1,2,1 |=0.75,|α 1,2,2 |=0.66,|α 2,1,1 |=0.86,|α 2,1,2 |=0.89,|α 2,2,1 |=0.76,|α 2,2,2 |=0.79,|α 3,1,1 |=0.84,|α 3,1,2 |=0.89,|α 3,2,1 |=0.74,|α 3,2,2 |=0.79,|α 4,1,1 |=0.74,|α 4,1,2 |=0.82,|α 4,2,1 |=0.64,|α 4,2,2 | = 0.72, number of snapshots is 8000, global search range y∈<-1200 m, 1200 m>}, search step size 1 m, 500 simulations, compared with the SSP-SDF direct positioning algorithm where the spatial smoothing subarray length is set to 7, the number of subarrays is 8, the radiation source signal is 256-QAM, the sampling rate is 10 kHz, and the symbol rate is 1 kHz. From Figure 4 It can be seen that the positioning accuracy of the present invention is consistently superior to that of the traditional SSP-SDF direct positioning method and the DFT direct positioning method.

[0079] Figure 5 The performance curves of the root mean square error of the method described in this invention, compared with the traditional SSP-SDF direct positioning method and DFT direct positioning method, are shown as a function of the number of snapshots. Simulation conditions and... Figure 4 Consistent, with a signal-to-noise ratio of -8 dB. From Figure 5 It can be seen that the location estimation performance of the method proposed in this invention is consistently better than that of the traditional SSP-SDF direct localization method and DFT direct localization method.

[0080] In summary, analysis of the simulation results demonstrates that the proposed direct localization method using multipath high-order QAM signals based on dual-atom norm minimization can effectively locate targets. Furthermore, this method fully utilizes the sparsity and structured characteristics of the signal, recovering the target signal from the observation data without sacrificing the array aperture, suppressing multipath effects, increasing available degrees of freedom, and improving localization accuracy. Moreover, it eliminates the need for additional parameter pairing processes, achieving higher localization accuracy than traditional SSP-SDF and DFT direct localization methods.

[0081] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0082] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A direct localization method for multipath high-order QAM signals based on minimizing dual atom norms, characterized in that, Includes the following steps: Step 1) Construct a distributed multi-sensor array localization model under multipath environment and obtain the received signal r. l (t); The distributed multi-sensor array localization model is used to locate K far-field QAM radiation sources with unknown locations. It includes L sensor arrays with known locations, each equipped with an M-element uniform linear array arranged horizontally along the x-axis with a spacing of d. The center position vector of the l-th sensor array is represented as... These represent its x-coordinate and y-coordinate, respectively; The position vector of the kth radiation source is represented as: The x-coordinate represents the location of the k-th radiation source. The ordinate represents the location of the k-th radiation source; let the k-th radiation source reach the l-th sensor array after multiple reflections, including a line-of-sight path and V. l,k There are several different non-line-of-sight paths; the angle of arrival of the line-of-sight path from the k-th radiation source to the l-th sensor array is denoted as... Among them, logical expressions The value is 1 when true and 0 otherwise, arctan(·) ∈ (-π / 2, π / 2). Used to eliminate the ambiguity of arctan(y / x) = arctan(-y / (-x)); the angle of arrival of the v-th non-line-of-sight path from the k-th radiation source to the l-th sensor array is denoted as θ. l,k,v , v∈<1,V l,k >, <1,V l,k > indicates that it is greater than or equal to 1 and less than or equal to V. l,k The set of integers; The received signal of the l-th sensor array at time t is T represents the number of snapshots; s k (t) represents the QAM signal with non-zero kurtosis emitted by the k-th radiation source at time t; n l (t) is the additive white Gaussian noise vector of the l-th sensor array, and its covariance is I M Describes an M-dimensional identity matrix. Indicates noise power; α l,k,v Let represent the fading coefficient of the v-th non-line-of-sight path from the k-th radiation source to the l-th sensor array; the steering vector a(θ) for a given θ, its i-th element Where λ represents the signal carrier wavelength, and j is the imaginary unit; Step 2), calculate the simplified fourth-order cumulant z of the received signals from each sensor array. l And expand it to obtain a virtual signal. The simplified fourth-order cumulant of the received signal from the l-th sensor array is expressed as: in, Describing mathematical expectation, e i Let n represent a vector whose i-th element is 1 and all other elements are 0. l r l s k They are n l (t), r l (t), s k The simplified form of (t); Then it is expanded to obtain a virtual signal. in: Diagonal matrix Λ = diag{1, 1 / 2, ..., 1 / M, 1 / (M-1), ..., 1}; matrix 0 M×(M-1) Represents an M×(M-1) dimensional zero matrix; vec{·} denotes the vectorization operator, Toep(z l ) indicates based on vector z l Construct a Toplitz matrix; Vandermonde matrix B l The columns are composed of 2M-1 dimensional vectors. Composition; b(θ) for a given θ, its i-th element is It is a virtual transmission signal; Step 3) Construct semi-positive definite constrained problems and solve them to obtain the dual vector q. l ; Step 3.1), use atomic norms for sparse representation. Define a set of atoms The angle of arrival estimation of the radiation source can then be expressed as an atomic norm minimization problem: in, Represents a set of atoms The overcomplete dictionary constituted Represents a sparse vector; Step 3.2) yields the dual problem of minimizing the atomic norm as follows: Where, q l The vector represents the dual vector, and the superscript H indicates the conjugate transpose, ‖·‖ ∞ Represents the infinite norm; Step 3.3) The dual problem of minimizing the atomic norm is expressed as a positive semidefinite program as follows: Where H l It is an Hermitian matrix; Step 3.4): Solve the positive semidefinite programming problem using the convex optimization toolbox to obtain the dual vector q. l ; Step 4): Construct a cost function by combining all dual vectors, and search for the estimated location of the radiation source; Step 4.1), using the dual vector q l Construct cost function Where p represents the position vector, θ l (p) represents the angle of arrival of the line-of-sight path from p to the l-th sensor array. |·| represents the modulus of a complex number; Step 4.2) Perform a spectral peak search on the cost function to obtain the coordinates corresponding to the peaks, which are the estimated results of the radiation source location.

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