Low complexity spectral peak searching method based on multi-ap cooperation

Abstract

The application discloses a low-complexity spectrum peak searching method based on multi-AP cooperation, belongs to the field of signal processing, and is applied to signal level fusion problems of multi-AP cooperation in a sensing-integrated scene. The method decomposes a high-complexity matching filtering problem into two sub-problems of position estimation and speed estimation, firstly performs coarse searching on the matching filtering result by setting a grid to determine an initial iteration point of the gradient method, then updates the spatial coordinates by using the gradient ascent method, sets an adaptive adjustment step, and obtains a peak value result of the spatial spectrum. By proving the approximate convexity of the received signal after the matching filtering, the target function can be adapted to the gradient-based algorithm near the peak value, and the method of the application can greatly reduce the calculation complexity without sacrificing the sensing accuracy.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and in particular to a low-complexity spectral peak search method based on multi-AP cooperation. Background Technology

[0002] With the development trend of integrated sensing, the collaborative signal processing among multiple access points (APs) is becoming increasingly important. Traditional signal processing methods face the challenge of high computational complexity when dealing with signal-level fusion problems involving multiple APs. For example, the highly complex matched filtering problem leads to low signal processing efficiency, making it difficult to quickly acquire target position and velocity information while maintaining sensing accuracy. In practical applications, such as real-time positioning and velocity measurement of UAVs in low-altitude sensing networks, the complex calculation process can cause processing delays, affecting the system's real-time performance and accuracy.

[0003] Currently, research on multi-AP signal-level fusion is deepening, but existing methods often require a trade-off between computational complexity and sensing accuracy. Some methods employ complex algorithms to improve sensing accuracy, resulting in huge computational loads and excessive hardware requirements; while some low-complexity methods struggle to guarantee sufficient sensing accuracy, failing to meet practical application needs. Therefore, developing a multi-AP signal-level fusion method that can reduce computational complexity without sacrificing sensing accuracy is of significant practical importance. Summary of the Invention

[0004] This invention provides a low-complexity spectral peak search method based on multi-AP cooperation, which significantly reduces computational complexity without reducing sensing accuracy, and achieves efficient and accurate estimation of target position and velocity. It solves the problem of high computational complexity of traditional matched filtering methods in multi-AP cooperation in the context of integrated sensing.

[0005] This invention provides a low-complexity spectral peak search method based on multi-AP cooperation, comprising the following steps:

[0006] Step 1: Convert the received signal in the time-frequency domain to the time-delay Doppler domain by matched filtering, and apply the back projection method to map the received signal in the time-delay Doppler domain to the coordinate position space and coordinate velocity space domain.

[0007] Step 2: Establish an optimization objective function based on the multivariate optimization problem obtained through matched filtering and back projection methods, and decouple the objective function into two sub-optimization problems concerning the target position and the target velocity;

[0008] Step 3: For the two sub-optimization problems, set grid points for the objective function, and perform a coarse peak search by traversing the grid to obtain a coarse estimate.

[0009] Step 4: Using the coarse estimate as the initial value for the gradient method, perform iterative optimization along the gradient direction within the local coordinate range to obtain the target position and target velocity estimation results under signal-level fusion.

[0010] Optionally, in one embodiment of the present invention, step 1 specifically includes:

[0011] Construct a sensing signal model, where the echo signal received by the r-th access node from the t-th access node at the k-th subcarrier and the l-th symbol is represented as y. r,t (k,l), where k=1,…,K, l=1,…,L, through matched filtering, the received signal is converted from the time-frequency domain to the time-delay Doppler domain. This process can be expressed as:

[0012]

[0013] Where τ and ω are indices of the time-delay Doppler domain;

[0014] The process of mapping the received signal from the time-delay Doppler domain to the spatial coordinate domain, represented by the back projection, is as follows:

[0015] τ r,t (x,y,z)=(d r (x,y,z)+d t (x,y,z))KΔf / c,

[0016]

[0017] For the AP transmit / receive pair labeled r and t, τ r,t (x,y,z) are the target time delay variables, ω r,t (v x ,v y ,v z ) represents the target Doppler velocity variable. Let x represent the distances from the target to the receiving base station and the transmitting base station, respectively, and let Δf and c represent the subcarrier spacing and the speed of light, respectively. r y r , z r (x) represents the three-dimensional coordinates of the receiving AP. t y t , z t (v) represents the three-dimensional coordinates of the transmitting AP. x ,v y ,v z ) represent the target's three-dimensional velocity components, T p λ represents the symbol period and wavelength.

[0018] Optionally, in one embodiment of the present invention, step 2 specifically includes:

[0019] Combining the received signals in the spatial coordinate domain from all transmit and receive pairs, the optimization objective function is expressed as:

[0020]

[0021] Variables include position coordinates and velocity coordinates

[0022] The target's position and velocity information are determined by solving the following problem:

[0023]

[0024] in, The result of the target location estimation. For the target velocity estimation results, For the target location variable, The target velocity variable;

[0025] Let the phase information of the received signal be ψ. r,t The phase associated with the subcarrier and the phase associated with the symbol are respectively represented as:

[0026]

[0027] in, For single-symbol signal phase information, For single-carrier signal phase information, d r,t ( p ) represents the distance between the two bases of the target. For the target bibase velocity;

[0028] The objective function is then decoupled into two sub-optimization problems, expressed as:

[0029]

[0030] in, and These are the optimization objective functions for position and velocity estimation, respectively. Represents a single-symbol signal. This indicates a single-carrier signal.

[0031] Optionally, in one embodiment of the present invention, step 3 specifically includes:

[0032] For the coordinate space, set the coordinates to be equidistant from points {p0,...,p...} n ,...,p N The original search space subset composed of} One of the grid points p n Represented as:

[0033] p n =(x n ,y n ,z n ) T = (x0+nΔx, y0+nΔy, z0+nΔz) T

[0034] Among them, (x n ,y n ,z n ) T It is a three-dimensional coordinate vector of grid points, where (x0, y0, z0) is the three-dimensional coordinate of the first grid point, and (Δx, Δy, Δz) is the grid spacing in three dimensions;

[0035] The coarse grid search process is equivalent to the following optimization problem:

[0036]

[0037] in, This is the result of a coarse search location estimation. For the coarse search speed estimation result, f1(p) n ) represents the objective function for coarse search location estimation. To estimate the objective function for coarse search speed, For the speed variable during the coarse search process, For the set of coarse grid points, This is the set of coarse grid points for velocity.

[0038] Optionally, in one embodiment of the present invention, step 4 specifically includes:

[0039] The initial value for gradient update is determined by the coarse estimate obtained through coarse grid search. The numerical solution of the partial derivatives of the objective function, calculated using the finite difference method, is approximately expressed as:

[0040]

[0041] Where Δ is an infinitesimal, the accumulated squared gradient variable along the x-axis is defined as:

[0042]

[0043] Among them, the accumulated squared gradient variable S along the y-axis direction y The cumulative squared gradient variable S along the z-axis z Accumulated squared velocity gradient variable along the x-axis Accumulated squared velocity gradient variable along the y-axis The cumulative squared velocity gradient variable along the z-axis Similarly, the gradient update process can be represented as follows:

[0044]

[0045] Where δ is a constant set to avoid the denominator being 0; η represents the learning rate; This represents the position estimation result obtained after the iteration; I represents the iteration number, which is the result of substituting the estimation result into the objective function. The coarse-grid search process is repeated to obtain the initial value for the velocity gradient update iteration. Objective function for velocity estimation The process of calculating the partial derivatives is expressed as follows:

[0046]

[0047] The gradient update process for velocity estimation is expressed as:

[0048]

[0049] This invention presents a low-complexity peak search method based on multi-AP collaboration. It decomposes the high-complexity matched filtering problem into two sub-problems: position estimation and velocity estimation. First, a coarse search is performed on the matched filtering results using a grid to determine the initial iteration point for the gradient method. Then, the spatial coordinates are updated using the gradient ascent method, and an adaptive step size is set to obtain the peak value of the spatial spectrum. By proving the approximate convexity of the received signal after matched filtering, the objective function can be adapted to the gradient-based algorithm near the peak value. This invention significantly reduces the computational complexity of coordinate spatial spectrum peak search in signal-level fusion without sacrificing sensing accuracy. In terms of estimation accuracy, it is comparable to fine-grid traversal search, while its computational speed is faster than existing peak search algorithms.

[0050] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0051] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0052] Figure 1 A flowchart illustrating a low-complexity spectral peak search method based on multi-AP cooperation according to an embodiment of the present invention;

[0053] Figure 2 This is a schematic diagram of a low-complexity spectral peak search method based on multi-AP cooperation according to an embodiment of the present invention;

[0054] Figure 3 This is a graph comparing the position mean square error of the algorithm in this embodiment of the invention with that of other algorithms as a function of signal-to-noise ratio.

[0055] Figure 4 This is a graph comparing the speed mean square error of the algorithm in this embodiment of the invention with that of other algorithms as a function of signal-to-noise ratio.

[0056] Figure 5 This is a comparison curve of the mean square error of the position in the algorithm of this invention and the fine grid traversal as a function of distance from the grid.

[0057] Figure 6 This is a comparison curve of the mean square error of the algorithm and fine grid traversal speed as a function of distance from the grid in this embodiment of the invention;

[0058] Figure 7 This invention provides a comparison of the number of objective function calculations and computation time between the algorithm in this embodiment and other algorithms. Detailed Implementation

[0059] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0060] Figure 1 This is a flowchart illustrating a low-complexity spectral peak search method based on multi-AP collaboration according to an embodiment of the present invention.

[0061] like Figure 1 As shown, this low-complexity spectral peak search method based on multi-AP collaboration includes the following steps:

[0062] Step 1: Convert the received signal in the time-frequency domain to the time-delay Doppler domain by matched filtering, and apply the back projection method to map the received signal in the time-delay Doppler domain to the coordinate position space and coordinate velocity space domain.

[0063] Optionally, in one embodiment of the present invention, step 1 specifically includes:

[0064] Construct a sensing signal model, where the echo signal received by the r-th access node from the t-th access node at the k-th subcarrier and the l-th symbol is represented as y. r,t (k,l), where k=1,…,K, l=1,…,L, through matched filtering, the received signal is converted from the time-frequency domain to the time-delay Doppler domain. This process can be expressed as:

[0065]

[0066] Where τ and ω are indices of the time-delay Doppler domain;

[0067] The process of mapping the received signal from the time-delay Doppler domain to the spatial coordinate domain, represented by the back projection, is as follows:

[0068] τ r,t (x,y,z)=(d r (x,y,z)+d t (x,y,z))KΔf / c,

[0069]

[0070] For the AP transmit / receive pair labeled r and t, τ r,t (x,y,z) are the target time delay variables, ω r,t (v x ,v y ,v z ) represents the target Doppler velocity variable. Let x represent the distances from the target to the receiving base station and the transmitting base station, respectively, and let Δf and c represent the subcarrier spacing and the speed of light, respectively. r y r , z r (x) represents the three-dimensional coordinates of the receiving AP. t y t , z t (v) represents the three-dimensional coordinates of the transmitting AP. x ,v y ,v z ) represent the target's three-dimensional velocity components, T p λ represents the symbol period and wavelength.

[0071] Step 2: Establish an optimization objective function based on the multivariate optimization problem obtained through matched filtering and back projection methods, and decouple the objective function into two sub-optimization problems concerning the target position and the target velocity.

[0072] Optionally, in one embodiment of the present invention, step 2 specifically includes:

[0073] Combining the received signals in the spatial coordinate domain from all transmit and receive pairs, the optimization objective function is expressed as:

[0074]

[0075] Variables include position coordinates and velocity coordinates

[0076] The target's position and velocity information are determined by solving the following problem:

[0077]

[0078] in, The result of the target location estimation. For the target velocity estimation results, For the target location variable, The target velocity variable;

[0079] Let the phase information of the received signal be ψ. r,t The phase associated with the subcarrier and the phase associated with the symbol are respectively represented as:

[0080]

[0081] in, For single-symbol signal phase information, For single-carrier signal phase information, d r,t (p) represents the target bibase distance. For the target bibase velocity;

[0082] The objective function is then decoupled into two sub-optimization problems, expressed as:

[0083]

[0084] in, and These are the optimization objective functions for position and velocity estimation, respectively. Represents a single-symbol signal. This indicates a single-carrier signal.

[0085] Step 3: For the two sub-optimization problems, set grid points for the objective function, and perform a coarse peak search by traversing the grid to obtain a coarse estimate.

[0086] Optionally, in one embodiment of the invention, such as Figure 2 As shown, step 3 specifically includes:

[0087] For the coordinate space, set the coordinates to be equidistant from points {p0,...,p...} n ,...,p N The original search space subset composed of} One of the grid points p n Represented as:

[0088] p n =(x n ,y n ,z n ) T = (x0+nΔx, y0+nΔy, z0+nΔz) T

[0089] Among them, (x n ,y n ,z n ) T It is a three-dimensional coordinate vector of grid points, where (x0, y0, z0) is the three-dimensional coordinate of the first grid point, and (Δx, Δy, Δz) is the grid spacing in three dimensions;

[0090] The coarse grid search process is equivalent to the following optimization problem:

[0091]

[0092] in, This is the result of a coarse search location estimation. For the coarse search speed estimation result, f1(p) n ) represents the objective function for coarse search location estimation. To estimate the objective function for coarse search speed, For the speed variable during the coarse search process, For the set of coarse grid points, This is the set of coarse grid points for velocity.

[0093] Step 4: Using the coarse estimate as the initial value for the gradient method, perform iterative optimization along the gradient direction within the local coordinate range to obtain the target position and target velocity estimation results under signal-level fusion.

[0094] Optionally, in one embodiment of the present invention, step 4 specifically includes:

[0095] The initial value for gradient update is determined by the coarse estimate obtained through coarse grid search. The numerical solution of the partial derivatives of the objective function, calculated using the finite difference method, is approximately expressed as:

[0096]

[0097] Where Δ is an infinitesimal, the accumulated squared gradient variable along the x-axis is defined as:

[0098]

[0099] Among them, the accumulated squared gradient variable S along the y-axis direction y The cumulative squared gradient variable S along the z-axis z Accumulated squared velocity gradient variable along the x-axis Accumulated squared velocity gradient variable along the y-axis The cumulative squared velocity gradient variable along the z-axis Similarly, the gradient update process can be represented as follows:

[0100]

[0101] Here, δ is a constant set to avoid the denominator being zero; η represents the learning rate, the position estimation result obtained after the iteration. I represents the number of iterations, where the estimation result is substituted into the objective function. The coarse-grid search process is repeated to obtain the initial value for the velocity gradient update iteration. Objective function for velocity estimation The process of calculating the partial derivatives is expressed as follows:

[0102]

[0103] The gradient update process for velocity estimation is expressed as:

[0104]

[0105] The specific algorithm steps are shown below.

[0106]

[0107] The method of the present invention will be described in detail below through a specific embodiment to verify the performance advantages of the method of the present invention.

[0108] (1) Experimental setup and parameters

[0109] The pseudocode for the algorithm proposed in this invention and the simulation parameters are shown in Table 1.

[0110] Table 1 Simulation Experiment Parameter Settings

[0111]

[0112] (2) Perception accuracy

[0113] Assuming the target's position and velocity parameters are within the range set in Table 1, the signal-to-noise ratio (SNR) is in the range of [-20, 20] dB. Figure 3 and Figure 4 The RMSE results for target position and velocity coordinates are shown under different signal-to-noise ratios. The error of the method proposed in this invention is very close to that of the global traversal method with a search interval of 0.2 m (m / s). Furthermore, the method of this invention can overcome the limitations of fine meshes under high signal-to-noise ratio conditions, achieving smaller errors for off-grid targets. The root mean square error of the target position of the particle swarm optimization algorithm is very close to that of the method of this invention, but the root mean square error of the target velocity is significantly higher.

[0114] Figure 5 and Figure 6With a signal-to-noise ratio (SNR) of 20 dB, the target is set at different distances from the coarse search grid. The maximum spacing of the coarse grid is set to... We are RMSE results are calculated within the specified range. Figure 5 The results show that the RMSE of the traversal search is almost identical at different off-grid locations, while the RMSE results of the method of this invention are all lower than those of the traversal search method. The accuracy of the result of the method of this invention decreases with increasing off-grid distance, but is still better than the traversal grid search. This proves that the simulation experiment appropriately sets the coarse search grid interval, and the constrained coordinates basically ensure that the result converges to the target location.

[0115] This part of the experiment proves that the method of the present invention does not sacrifice the accuracy of target perception.

[0116] (3) Computational complexity

[0117] Figure 7 The average number of computations and runtime for all simulation data are listed. Compared to fine-mesh search, particle swarm optimization reduces computation by an average of 96.85%, while the method of this invention reduces computation by an average of 99.24%. In terms of runtime, particle swarm optimization reduces computation time by 96.36%, while the method of this invention reduces it by 99.12%. The method of this invention significantly reduces the complexity of peak search for multi-AP signal-level fusion, and can better meet the timeliness requirements of target discovery in sensing networks.

[0118] The low-complexity peak search method based on multi-AP cooperation proposed in this invention is applied to the signal-level fusion problem of multi-AP cooperation in a sensor-integrated scenario. It significantly reduces the computational complexity of coordinate space peak search in signal-level fusion, and its estimation accuracy is comparable to fine-grid traversal search, while its computation speed is faster than existing peak search algorithms.

[0119] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0120] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0121] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of preferred embodiments of the invention includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as will be understood by those skilled in the art to which embodiments of the invention pertain.

Claims

1. A low-complexity spectral peak search method based on multi-AP cooperation, characterized in that, Includes the following steps: Step 1: Convert the received signal in the time-frequency domain to the time-delay Doppler domain by matched filtering, and apply the back projection method to map the received signal in the time-delay Doppler domain to the coordinate position space and coordinate velocity space domain. Step 2: Establish an optimization objective function based on the multivariate optimization problem obtained through matched filtering and back projection methods, and decouple the objective function into two sub-optimization problems concerning the target position and the target velocity; Step 3: For the two sub-optimization problems, set grid points for the objective function, and perform a coarse peak search by traversing the grid to obtain a coarse estimate. Step 4: Using the coarse estimate as the initial value for the gradient method, perform iterative optimization along the gradient direction within the local coordinate range to obtain the target position and target velocity estimation results under signal-level fusion. Step 1 specifically includes: Construct a sensing signal model, where the echo signal received by the r-th access node from the t-th access node at the k-th subcarrier and the l-th symbol is represented as y. r,t (k,l), where k=1,…,K, l=1,…,L, through matched filtering, the received signal is converted from the time-frequency domain to the time-delay Doppler domain. This process can be expressed as: Where τ and ω are indices of the time-delay Doppler domain; The process of mapping the received signal from the time-delay Doppler domain to the spatial coordinate domain, represented by the back projection, is as follows: τ r,t (x,y,z)=(d r (x,y,z)+d t (x,y,z))KΔf / c, For the AP transmit / receive pair labeled r and t, τ r,t (x,y,z) are the target time delay variables, ω r,t (v x ,v y ,v z ) represents the target Doppler velocity variable. Let x represent the distances from the target to the receiving base station and the transmitting base station, respectively, and let Δf and c represent the subcarrier spacing and the speed of light, respectively. r y r , z r () represents the three-dimensional coordinates of the receiving AP. (x t y t , z t (v) represents the three-dimensional coordinates of the transmitting AP. x ,v y ,v z ) represent the target's three-dimensional velocity components, T p λ represents the symbol period and wavelength; Step 2 specifically includes: Combining the received signals in the spatial coordinate domain from all transmit and receive pairs, the optimization objective function is expressed as: Variables include position coordinates and velocity coordinates The target's position and velocity information are determined by solving the following problem: in, The result of the target location estimation. For the target velocity estimation results, For the target location variable, The target velocity variable; Let the phase information of the received signal be ψ. r,t The phase associated with the subcarrier and the phase associated with the symbol are respectively represented as: in, For single-symbol signal phase information, For single-carrier signal phase information, d r,t (p) represents the target bibase distance. For the target bibase velocity; The objective function is then decoupled into two sub-optimization problems, expressed as: in, and These are the optimization objective functions for position and velocity estimation, respectively. Represents a single-symbol signal. Indicates a single-carrier signal; Step 3 specifically includes: For the coordinate space, set the coordinates to be equidistant from points {p0,...,p...} n ,...,p N The original search space subset composed of} One of the grid points p n Represented as: p n =(x n ,y n ,z n ) T =(x0+nΔx,y0+nΔy,z0+nΔz) T Among them, (x n ,y n ,z n ) T It is a three-dimensional coordinate vector of grid points, where (x0, y0, z0) is the three-dimensional coordinate of the first grid point, and (Δx, Δy, Δz) is the grid spacing in three dimensions; The coarse grid search process is equivalent to the following optimization problem: in, This is the result of a coarse search location estimation. For the coarse search speed estimation result, f1(p) n ) represents the objective function for coarse search location estimation. To estimate the objective function for coarse search speed, For the speed variable during the coarse search process, For the set of coarse grid points, For velocity coarse grid point set; Step 4 specifically includes: The initial value for gradient update is determined by the coarse estimate obtained through coarse grid search. The numerical solution of the partial derivatives of the objective function, calculated using the finite difference method, is approximately expressed as: Where Δ is an infinitesimal, the accumulated squared gradient variable along the x-axis is defined as: Among them, the accumulated squared gradient variable S along the y-axis direction y The cumulative squared gradient variable S along the z-axis z Accumulated squared velocity gradient variable along the x-axis Accumulated squared velocity gradient variable along the y-axis The cumulative squared velocity gradient variable along the z-axis Similarly, the gradient update process can be represented as follows: Where δ is a constant set to avoid the denominator being 0; η represents the learning rate; This represents the position estimation result obtained after the iteration; I represents the iteration number, which is the result of substituting the estimation result into the objective function. The coarse-grid search process is repeated to obtain the initial value for the velocity gradient update iteration. Objective function for velocity estimation The process of calculating the partial derivatives is expressed as follows: The gradient update process for velocity estimation is expressed as:

Images