Low-complexity spectrum peak searching method based on multi-AP cooperation

Abstract

The invention discloses a low-complexity spectrum peak searching method based on multi-AP cooperation, belongs to the field of signal processing, and is applied to the signal level fusion problem of multi-AP cooperation in a communication and sensing integrated scene. According to the method, a high-complexity matched filtering problem is decomposed into two sub-problems of position estimation and speed estimation, firstly, coarse search is carried out on a matched filtering result by setting a grid, and an initial iteration point of a gradient method is determined; and updating the space coordinates by using a gradient ascending method, and setting an adaptive adjustment step length to obtain a peak value result of a spatial spectrum. By proving the approximate convexity of the received signal after matched filtering, the target function can adapt to the gradient-based algorithm near the peak value, and the method can greatly reduce the calculation complexity while not sacrificing the sensing precision.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing, and particularly relates to a low-complexity spectral peak search method based on multi-AP cooperation. Background Art

[0002] In the development trend of integrated communication and sensing, multi-access point (AP) cooperation for signal processing has become increasingly important. Traditional signal processing methods face the problem of high computational complexity when dealing with the signal-level fusion problem of multi-AP cooperation. For example, the high-complexity matched filtering problem makes the signal processing efficiency low, and it is difficult to quickly obtain the position and velocity information of the target while ensuring the sensing accuracy. In practical application scenarios, such as real-time positioning and speed measurement of unmanned aerial vehicles in a low-altitude sensing network, the complex calculation process will lead to processing delay, affecting the real-time performance and accuracy of the system.

[0003] Currently, the research on multi-AP signal-level fusion is continuously deepening, but existing methods often need to balance between computational complexity and sensing accuracy. Some methods use complex algorithms to improve sensing accuracy, resulting in a huge amount of computation and high requirements for hardware devices; while some low-complexity methods are difficult to ensure sufficient sensing accuracy and cannot meet the actual application requirements. Therefore, it is of great practical significance to develop a multi-AP signal-level fusion method that can reduce computational complexity without sacrificing sensing accuracy. Summary of the Invention

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

[0005] An embodiment of the present invention provides a low-complexity spectral peak search method based on multi-AP cooperation, including the following steps:

[0006] Step 1, convert the received signal in the time-frequency domain to the time-delay Doppler domain through 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 the coordinate velocity space domain;

[0007] Step 2, establish an optimization objective function according to the multi-variable optimization problem obtained through matched filtering and the back-projection method, and decouple the objective function into two sub-optimization problems regarding 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 through grid traversal to obtain a rough estimate value;

[0009] Step 4: Take the rough estimate value as the initial value of the gradient method, and perform iterative optimization along the gradient direction within the local coordinate range to obtain the estimated results of the target position and target speed under signal-level fusion.

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

[0011] Construct a sensing signal model. The echo signal received by the r-th access node at the k-th subcarrier and the l-th symbol from the t-th access node is denoted 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 delay-Doppler domain, and this process is expressed as:

[0012]

[0013] where τ and ω are the indices in the delay-Doppler domain;

[0014] Map the received signal from the delay-Doppler domain to the spatial coordinate domain, and the back-projection process is expressed as:

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

[0016]

[0017] where, for the AP transceiver pair labeled r and t, τ r,t (x, y, z) is the target delay variable, ω r,t (v x , v y , v z ) is the target Doppler velocity variable, respectively represent the distances from the target to the receiving base station and the transmitting base station, Δf and c represent the subcarrier spacing and the speed of light, (x r , y r , z r ) is the three-dimensional coordinate position of the receiving AP, (x t , y t , z t ) is the three-dimensional coordinate position of the transmitting AP, (v x , v y , v z ) are the three-dimensional component velocities of the target respectively, T p and λ represent the symbol period and the wavelength.

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

[0019] The received signal in the spatial coordinate domain obtained by combining all transceiver pairs is used to obtain an optimization objective function expressed as:

[0020]

[0021] The variables include position coordinates and velocity coordinates

[0022] By solving the following problem, the position and velocity information of the target are determined:

[0023]

[0024] where, is the target position estimation result, is the target velocity estimation result, is the target position variable, is the target velocity variable;

[0025] Let the phase information of the received signal be ψ r,t , and the phase related to the sub - carrier and the phase related to the symbol are respectively expressed as:

[0026]

[0027] where, is the signal phase information of a single symbol, is the signal phase information of a single carrier, d r,t ( p ) is the target bistatic distance, is the target bistatic velocity;

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

[0029]

[0030] where, and are the optimization objective functions for position and velocity estimation respectively; represents the single - symbol signal, represents the single - carrier signal.

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

[0032] For the coordinate space, a subset of the original search space composed of equally - spaced points {p0,..., p n ,..., p N} is set where a certain grid point p n is expressed as:

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

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

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

[0036]

[0037] where, is the result of coarse search position estimation, is the result of coarse search speed estimation, f1(p n ) is the objective function of coarse search position estimation, is the objective function of coarse search speed estimation, is the speed variable in the coarse search process, is the set of coarse grid points of position, is the set of coarse grid points of speed.

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

[0039] Determine the initial value of gradient update as by the coarse estimation value obtained through coarse grid search, and calculate the numerical solution of the partial derivative of the objective function using the finite - difference method, which is approximately expressed as:

[0040]

[0041] where, Δ is an infinitesimal quantity, and the accumulated squared gradient variable in the x - axis direction is defined as:

[0042]

[0043] where, the accumulated squared gradient variable Sy y in the y - axis direction, the accumulated squared gradient variable Sz z in the z - axis direction, the accumulated squared velocity gradient variable in the x - axis direction, and the accumulated squared velocity gradient variable The variable of the cumulative velocity squared gradient in the z-axis direction The definition is similar, and the gradient update process is expressed as:

[0044]

[0045] where δ is a constant set to avoid a zero denominator; η represents the learning rate; represents the position estimation result obtained after the iteration ends; I represents the number of iterations. Substitute the estimation result into the objective function and repeat the coarse grid search process to obtain the initial value of the velocity gradient update iteration as The objective function of velocity estimation The calculation process of the partial derivative is expressed as:

[0046]

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

[0048]

[0049] The low-complexity spectral peak search method based on multi-AP cooperation in the embodiment of the present invention decomposes the high-complexity matched filtering problem into two sub-problems of position estimation and velocity estimation. First, for the matched filtering result, a coarse search is performed by setting a grid to determine the initial iteration point of the gradient method; then, the gradient ascent method is used to update the spatial coordinates, and an adaptive step size is set to obtain the peak result of the spatial spectrum. By proving the approximate convexity of the received signal after matched filtering, the objective function can adapt to the gradient-based algorithm near the peak. The method of the present invention can significantly reduce the computational complexity of the coordinate space spectral peak search for signal-level fusion without sacrificing the sensing accuracy, and is comparable to the fine grid traversal search in terms of estimation accuracy and faster than the existing peak search algorithms in terms of computational speed.

[0050] Additional aspects and advantages of the present invention will be given in part in the following description, become apparent in part from the following description, or be understood through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0053] Figure 2 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 The curve diagram of the position mean square error of the algorithm of the embodiment of the present invention and other algorithms varying with the signal-to-noise ratio;

[0055] Figure 4 The curve diagram of the speed mean square error of the algorithm of the embodiment of the present invention and other algorithms varying with the signal-to-noise ratio;

[0056] Figure 5 The curve diagram of the position mean square error of the algorithm of the embodiment of the present invention and the fine grid traversal varying with the off-grid distance;

[0057] Figure 6 The curve diagram of the speed mean square error of the algorithm of the embodiment of the present invention and the fine grid traversal varying with the off-grid distance;

[0058] Figure 7 The comparison of the number of target function calculations and calculation time between the algorithm of the embodiment of the present invention and other algorithms. Specific implementation manner

[0059] The embodiments of the present invention will be described in detail below. The examples of the embodiments are shown in the drawings, where 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 drawings are exemplary and are intended to explain the present invention, and should not be construed as limiting the present invention.

[0060] Figure 1 The flowchart of a low-complexity spectral peak search method based on multi-AP cooperation provided according to an embodiment of the present invention.

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

[0062] Step 1, convert the received signal in the time-frequency domain to the delay-Doppler domain through matched filtering, and apply the back-projection method to map the received signal in the delay-Doppler domain from the delay-Doppler domain to the coordinate position space and the coordinate rate space domain.

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

[0064] Construct a sensing signal model. The echo signal received by the rth access node at the kth subcarrier and the lth symbol from the tth access node is denoted 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 delay-Doppler domain, and this process is expressed as:

[0065]

[0066] where τ and ω are the indices in the time-delay Doppler domain;

[0067] Map the received signal from the time-delay Doppler domain to the spatial coordinate domain, and the back-projection process is expressed as:

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

[0069]

[0070] where, for the AP transceiver pair labeled r and t, τ r,t (x, y, z) is the target time-delay variable, ω r,t (v x , v y , v z ) is the target Doppler velocity variable, respectively represent the distances from the target to the receiving base station and the transmitting base station, Δf and c represent the subcarrier spacing and the speed of light, (x r , y r , z r ) is the three-dimensional coordinate position of the receiving AP, (x t , y t , z t ) is the three-dimensional coordinate position of the transmitting AP, (v x , v y , v z ) are the three-dimensional component velocities of the target respectively, T p and λ represent the symbol period and the wavelength.

[0071] Step 2: Establish an optimization objective function according to the multi-variable optimization problem obtained by the matched filtering and back-projection methods, and decouple the objective function into two sub-optimization problems regarding the target position and the target velocity.

[0072] Optionally, in an embodiment of the present invention, Step 2 specifically includes:

[0073] Combine the received signals in the spatial coordinate domain obtained by all transceiver pairs to obtain the optimization objective function expressed as:

[0074]

[0075] The variables include the position coordinates and the velocity coordinates

[0076] Determine the position and velocity information of the target by solving the following problem:

[0077]

[0078] Among them, is the target position estimation result, is the target speed estimation result, is the target position variable, is the target speed variable;

[0079] Let the phase information of the received signal be ψ r,t , and the phase related to the subcarrier and the phase related to the symbol are respectively expressed as:

[0080]

[0081] Among them, is the signal phase information of a single symbol, is the signal phase information of a single carrier, d r,t (p) is the target bistatic distance, is the target bistatic speed;

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

[0083]

[0084] Among them, and are respectively the optimization objective functions for position and speed estimation; represents a single-symbol signal, represents a single-carrier signal.

[0085] Step 3, for the two sub-optimization problems, set grid points for the target function, and perform a rough peak search through grid traversal to obtain rough estimated values.

[0086] Optionally, in an embodiment of the present invention, as Figure 2 shown, Step 3 specifically includes:

[0087] For the coordinate space, set the original search space subset composed of equally spaced points {p0,...,p n ,...,p N} Among them, a certain grid point p n is expressed 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 is the three-dimensional coordinate vector form of the grid point, (x0, y0, z0) is the three-dimensional coordinate of the first grid point, and (Δx, Δy, Δz) is the grid interval in three dimensions;

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

[0091]

[0092] Among them, is the coarse search position estimation result, is the coarse search velocity estimation result, f1(p n ) is the coarse search position estimation objective function, is the coarse search velocity estimation objective function, is the velocity variable during the coarse search process, is the set of coarse grid points for position, is the set of coarse grid points for velocity.

[0093] Step 4: Use the coarse estimation value as the initial value of the gradient method, and 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 an embodiment of the present invention, Step 4 specifically includes:

[0095] Determine the initial value of gradient update as using the coarse estimation value obtained through coarse grid search. Calculate the numerical solution of the partial derivative of the objective function using the finite difference method, which is approximately expressed as:

[0096]

[0097] Among them, Δ is an infinitesimal quantity. Define the accumulated squared gradient variable in the x-axis direction as:

[0098]

[0099] Among them, the accumulated squared gradient variable S y in the y-axis direction, the accumulated squared gradient variable S z in the z-axis direction, the accumulated squared velocity gradient variable in the x-axis direction, the accumulated squared velocity gradient variable in the y-axis direction, and the accumulated squared velocity gradient variable in the z-axis direction are defined similarly. Then the gradient update process is expressed as:

[0100]

[0101] Among them, δ is a constant set to avoid a zero denominator; η represents the learning rate, and the position estimation result obtained after the iteration ends I represents the number of iterations, and the estimation result is substituted into the objective function And repeat the coarse grid search process, and the initial value of the velocity gradient update iteration is The objective function of velocity estimation The calculation process of the partial derivative is expressed as:

[0102]

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

[0104]

[0105] The specific algorithm steps are as follows.

[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 device and parameters

[0109] For the pseudocode of the algorithm proposed in the present invention, the simulation experiment parameters are shown in Table 1.

[0110] Table 1 Simulation experiment parameter settings

[0111]

[0112] (2) Perception accuracy

[0113] It is assumed that the position and velocity parameters of the target are within the range set in Table 1, and the signal-to-noise ratio (SNR) is in [-20, 20] dB. Figure 3 And Figure 4 show the RMSE results of the target position and velocity coordinates under different signal-to-noise ratios. The error of the method proposed in the present invention is very close to the error of the global traversal method with a search interval of 0.2 m (m / s). At the same time, the method of the present invention can break through the fine grid limit under high signal-to-noise ratio conditions and achieve a smaller error 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 the present invention, but the root mean square error of the target velocity is significantly higher than that of the method of the present invention.

[0114] Figure 5 And Figure 6Under the condition that the signal-to-noise ratio (SNR) is 20 dB, the target is set at different off-grid distances from the coarse search grid. The maximum spacing of the coarse grid is set to We calculate the RMSE results within the range of . Figure 5 It shows that there is little difference in the RMSE of the traversal search at different off-grid positions, while the RMSE results of the method of the present invention are all smaller than those of the traversal search method. The result accuracy of the method of the present invention decays with the increase of the off-grid distance, but it is still better than the traversal grid search. This proves that the simulation experiment appropriately sets the coarse search grid interval, and the restricted coordinates basically ensure that the results converge to the target position.

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

[0116] (3) Computational complexity

[0117] Figure 7 Lists the average number of calculations and running times of all simulation experiment data. Compared with the fine grid search, the particle swarm optimization method reduces the amount of calculation by 96.85% on average, while the method of the present invention reduces the amount of calculation by 99.24% on average. In terms of running time, the particle swarm optimization method reduces the calculation time by 96.36%, and the method of the present invention reduces the time by 99.12%. The method of the present invention greatly reduces the complexity of the multi-AP signal-level fusion peak search and can better meet the timeliness requirements of the target discovery process in the sensing network.

[0118] The low-complexity spectral peak search method based on multi-AP cooperation proposed according to the embodiments of the present invention is applied to the signal-level fusion problem of multi-AP cooperation in the integrated communication and sensing scenario, significantly reducing the computational complexity of the coordinate space spectral peak search for signal-level fusion, being equivalent to the fine grid traversal search in terms of estimation accuracy, and faster in calculation speed than the existing peak search algorithms.

[0119] In the description of this specification, the description referring to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any one or N embodiments or examples in a suitable manner. In addition, without contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and 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 quantity of the indicated technical features. Thus, features defined with "first" and "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, the meaning of "N" is at least two, such as two, three, etc., unless otherwise specifically defined.

[0121] Any process or method description, whether in a flowchart or otherwise described herein, can be understood to represent a module, segment, or portion of code including one or N executable instructions for implementing a customized logical function or process. The scope of the preferred embodiments of the present invention includes additional implementations, where the functions may be performed in an order not shown or discussed, including in a substantially simultaneous manner or in a reverse order according to the functions involved, which should be understood by those skilled in the art to which the embodiments of the present invention pertain.

Claims

1. A low-complexity spectrum peak search method based on multi-AP collaboration, characterized in that: The following steps are involved: Step 1, converting the received signal in the time-frequency domain into the delay-Doppler domain by matched filtering, and applying the back-projection method to map the received signal in the delay-Doppler domain from the delay-Doppler domain into the coordinate position space and the coordinate velocity space domain; Step 2, establishing an optimization objective function according to the multivariable optimization problem obtained by the matched filtering and back-projection method, and decoupling the objective function into two sub-optimization problems regarding the target position and the target speed; Step 3, for the two sub-optimization problems, set grid points for the objective function, perform a rough search for peak values ​​through grid traversal, and obtain a rough estimated value; Step 4: Use the rough estimate as the initial value of the gradient method, perform iterative optimization along the gradient direction within the local coordinate range, and obtain the target position and target speed estimation results under signal level fusion.

2. The method according to claim 1, characterized in that Step 1 specifically includes: Construct the perception signal model. The rth access node receives the echo signal from the tth access node at the kth subcarrier and the lth symbol, which is expressed 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 delay-Doppler domain. The process is expressed as: Where τ and ω are the indices in the delay-Doppler domain; Map the received signal from the delay-Doppler domain to the spatial coordinate domain, and the back-projection process is expressed as: τ r,t (x,y,z)=(d r (x,y,z)+d t (x,y,z))KΔf / c, Among them, for the AP transceiver pair labeled r and t, τ r,t (x,y,z) is the target delay variable, ω r,t (v x ,v y ,v z ) is the target Doppler velocity variable, Represent the distance from the target to the receiving base station and the sending base station respectively, Δf and c represent the subcarrier spacing and the speed of light, (x r ,y r , z r ) is the three-dimensional coordinate position of the receiving AP, (x t ,y t , z t ) is the 3D coordinate position of the sending AP, (v x ,v y ,v z ) are the target three-dimensional velocity, T p and λ represent the symbol period and wavelength.

3. The method according to claim 2, characterized in that Step 2 specifically includes: Combining the spatial coordinate domain received signals obtained by all the transmitting and receiving pairs, the optimization objective function is expressed as: Variables include position coordinates and velocity coordinates Determine the position and velocity information of the target by solving the following problem: in, is the target position estimation result, is the target speed estimation result, is the target position variable, is the target speed variable; Assume the phase information of the received signal is ψ r,t , the phase associated with the subcarrier and the phase associated with the symbol are expressed as: in, is the signal phase information of a single symbol, is the signal phase information of a single carrier, d r,t (p) is the target bistatic distance, is the target bistatic speed; The optimization objective function is decoupled into two sub-optimization problems, expressed as: in, and They are the optimization objective functions for position and velocity estimation respectively; represents a single symbol signal, Represents a single carrier signal.

4. The method according to claim 1, characterized in that: Step 3 specifically includes: For the coordinate space, set the equidistant points {p0,...,p n ,...,p N } is a subset of the original search space A grid point p n It is expressed 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 is the three-dimensional coordinate vector form of the grid point, (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, is the rough search position estimation result, is the rough search speed estimation result, f1(p n ) is the rough search position estimation objective function, is the rough search speed estimation objective function, is the speed variable in the rough search process, is the set of coarse grid points of the position, is the set of velocity coarse grid points.

5. The method according to claim 1, characterized in that Step 4 specifically includes: The rough estimate obtained by coarse grid search determines the initial value of the gradient update The finite difference method is used to calculate the numerical solution of the partial derivative of the objective function, which is approximately expressed as: Among them, Δ is an infinitesimal quantity, and the accumulated square gradient variable in the x-axis direction is defined as: Among them, the accumulated square gradient variable S in the y-axis direction y , the accumulated square gradient variable S in the z-axis direction z , the accumulated velocity square gradient variable in the x-axis direction Accumulated velocity square gradient variable in the y-axis direction The accumulated velocity square gradient variable in the z-axis direction The definition is similar to that of , so the gradient update process is expressed as: Among them, δ is a constant set to avoid the denominator being 0; η represents the learning rate; It represents the position estimation result after the iteration; I represents the number of iterations, and the estimation result is substituted into the objective function Repeat the coarse grid search process to obtain the initial value of the velocity gradient update iteration as Objective function of velocity estimation The partial derivative calculation process is expressed as: The gradient update process of velocity estimation is expressed as:

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