A passive near field positioning method based on array division

Abstract

The present application belongs to the field of information and communication technology, and relates to a passive near-field positioning method based on array division. For the passive near-field positioning problem of a super large antenna array in the THz band, the present application proposes an extensible near-field positioning algorithm, divides the receiving array into multiple sub-arrays so that the target is approximately located in the far-field region of each sub-array, establishes a probability model of the received signal based on the geometric constraint between the target position and the angle of arrival, and designs a target position estimation algorithm based on a message passing mechanism. On the one hand, the difference in the angle of arrival between the sub-arrays can obtain more accurate target position estimation, and on the other hand, the introduction of array division and the message passing mechanism can reduce the complexity of the algorithm.

Description

Technical Field

[0001] This invention belongs to the field of information and communication technology, and relates to a passive near-field localization method based on array partitioning. Background Technology

[0002] With the standardization of 5G NR technology in the microwave and millimeter-wave (mmWave) bands completed, the research community has shifted its focus to optimizing the performance of these systems for future cellular deployments. Meanwhile, in pursuit of greater capacity for the air interface, researchers have begun to consider the challenges of utilizing the terahertz (THz) band for cellular communications. The use of millimeter-wave and terahertz bands promises not only enormous capacity for the air interface, enabling novel rate-greedy applications such as virtual reality (VR), augmented reality (AR), and holographic telepresence, but also the potential to truly enable multi-service access networks, providing latency and throughput guarantees for applications sensitive to various parameters.

[0003] The THz band, ranging from 0.1 THz to 10 THz, offers communication bandwidth resources in the tens of gigahertz (GHz) range. The first Asia-Pacific THz frequency standard was proposed in IEEE 802.15.3d, increasing the signal frequency / bandwidth from 73 GHz / 2 GHz (5G NR) to 300 GHz / 69 GHz. However, a major drawback of operating in the THz band is that propagation loss increases quadratically with increasing carrier frequency. To overcome the severe propagation loss in the THz band, very large-scale antenna arrays (ELAAs) consisting of hundreds or even thousands of antenna elements are typically used to generate pencil-shaped beams to improve array gain. Furthermore, due to the THz band's high sensing resolution similar to optics and its good penetration through opaque materials, combined with the excellent spatial resolution of ELAAs, the combination of the THz band and ELAAs also contributes to achieving high-precision sensing and positioning capabilities.

[0004] Before fully realizing the positioning potential of the THz band and ELAA, wireless positioning faces numerous challenging problems. First, compared to traditional bands, ELAA in the THz band introduces significant near-field effects. In the near-field region (also known as the Fresnel region), accurate target positioning requires simultaneous estimation of both the target's orientation and range parameters. Traditional positioning algorithms based on far-field assumptions, which only involve estimating the target's orientation (i.e., angle of arrival (AoA) estimation), are no longer applicable. Therefore, when designing near-field positioning algorithms, it is necessary to consider the estimation of both the target's orientation and range. For example, the paper "LOS / NLOS near-field localization with a large reconfigurable intelligent surface" utilizes a reconfigurable intelligent surface (RIS) to assist near-field positioning, designing a two-step positioning method that first estimates the time of arrival (ToA) and then estimates the target's position for near-field positioning. The paper “Convex Relaxation Methods for Unified Near-Field and Far-Field TDOA-Based Localization” proposes two convex relaxation methods based on modified polar coordinate representation (MPR) and fractional programming (FP) for unified localization of near-field and far-field based on TDOA measurements.

[0005] Furthermore, existing near-field positioning algorithms face scalability issues when applied to ELAA scenarios. The core of this problem lies in the fact that ELAA employs a large number of antennas, significantly expanding the dimensionality of the received signal and leading to a substantial increase in the computational complexity of existing positioning algorithms. Taking algorithms based on Multiple Signal Classification (MUSIC) as an example, their computational complexity primarily stems from the eigenvalue decomposition of the autocorrelation matrix of the received signal. As the number of antennas increases, the execution time of this algorithm exhibits a cubic polynomial growth. In ELAA applications, the number of antennas can reach thousands or even tens of thousands. This cubic complexity places an excessive computational burden on the receiver, making real-time positioning services impossible. It is worth noting that other high-precision near-field positioning algorithms, such as those based on rotationally invariant technology (ESPRIT) and compressed sensing, also exhibit similar cubic or even higher-order complexities as the number of antennas on the base station side increases. Therefore, developing high-precision and scalable near-field positioning algorithms for ELAA systems operating in the THz band is crucial. Summary of the Invention

[0006] To effectively improve positioning accuracy while reducing algorithm complexity, this invention proposes dividing the receiving array into multiple subarrays, such that the target is approximately located in the far-field region of each subarray. Based on the geometric constraints between the target position and the angle of arrival, a probabilistic model of the received signal is established, and a target position estimation algorithm based on a message passing mechanism is designed. By utilizing the differences in the angles of arrival between subarrays, a more accurate target position estimate can be obtained, while the introduction of array partitioning and the message passing mechanism can reduce the algorithm's complexity.

[0007] First, the ELAA (Earth Area Allocation Array) on the base station side is divided into multiple non-overlapping subarrays, so the target can be approximated as being located within the far-field region of each subarray. Since the relative positions of each subarray and the target are different, different angles of arrival (AoA) will occur when the target's transmitted signal reaches different subarrays, i.e., AoA drift. This means that an AoA-based far-field localization algorithm can be used to estimate the AoA on each subarray, and the AoA drift effect can be used to achieve near-field localization of the target. Through this division, the target position can be directly estimated from the observed subarray AoA, thus significantly reducing the dimensionality of the data to be processed.

[0008] After partitioning the ELAA, a probabilistic model of the received signal was established using the geometric constraints between the target position and the subarray AoA. Based on the factor graph representation of this probabilistic model, a message passing algorithm, namely the Array Partition-Based Position Estimation (APLE) algorithm, was designed. In this algorithm, the process of calculating extrinsic information is introduced in multiple signal processing steps, which can significantly improve the accuracy and stability of near-field localization.

[0009] The APLE algorithm mainly consists of two modules: an AoA estimation module and an AoA fusion module. The AoA estimation module uses an AoA-based far-field localization algorithm to obtain the AoA estimate of each subarray from the received signals. The AoA estimates of all subarrays are input into the AoA fusion module for target position estimation. The position estimation results are then input into the AoA estimation module to correct the AoA estimates of each subarray. The corrected AoA estimates of all subarrays are returned to the AoA fusion module to update the localization results. The AoA estimation module and the AoA fusion module iterate against each other until the algorithm converges.

[0010] The technical solution adopted in this invention includes the following steps:

[0011] S1. The pilot signal x transmitted by the target arrives at the base station via the physical channel. The channel coefficient between the target and the (i, j)th antenna element at the base station is...

[0012]

[0013] Where β is the common antenna gain, For the path loss between the target and the (i, j)th antenna element, r (i，j) Let be the propagation distance of the path between the target and the (i, j)th antenna element. The single-shot signal received at the base station can be represented as...

[0014] y = hx + n

[0015] in This represents the channel between the target and the base station. It is additive white Gaussian noise.

[0016] S2. Divide the ELAA on the base station side into M non-overlapping subarrays. Taking the m-th subarray as an example, the m-th subarray contains N... m =N m，x ×N m，y There are N antenna elements, of which N m，x and N m，y Let be the number of antennas in the m-th subarray along the x-axis and y-axis, respectively. After dividing the ELAA, the target can be approximated as being located in the far-field region of each subarray. Taking the center of the m-th subarray as the reference point, under the far-field assumption, the received signal model at the m-th subarray can be simplified as follows:

[0017] y m =α m a m (θ m,x θ m，y )+n m

[0018] Where α m =h m x is the complex channel gain, θ m，x and θ m，y Let AoA and a be the x and y directions respectively at the m-th subarray. m (θ m，x θ m，y () represents the two-dimensional steering vector at the m-th subarray. It is the additive white Gaussian noise at the m-th subarray.

[0019] S3. Based on the array partitioning and the far-field received signal model at the subarray, establish a probabilistic model for the localization problem. Taking the m-th subarray as an example, the likelihood function p(y m |θ m,x ,θ m,y ,α m and the conditional probability density function p(θ) m,l |P U ) are respectively

[0020]

[0021]

[0022] in e represents the geometric constraint between AoA at the m-th subarray and the target position. l Let be the unit vector of the array along the l-axis, and δ(·) be the Dirac function. The complex channel gain α m The prior distribution of the target location is modeled using a complex Gaussian distribution and an information-free Gaussian distribution, respectively. Among them, variance It is a relatively large value. The joint probability density function p(p U (y, θ, α) can be represented as

[0023]

[0024] S4. For the joint probability density function p(p U Factor graph representation of m, p, y, θ, α) is performed. U ,y m ,θ m，x and θ m，y Each of these is a variable node in the factor graph, and each probability factor is a validation node. For simplicity, we use... Represents the verification node p(θ) m，l |P U ), using Δ a→b (·) represents a message from node a to node b, denoted by m. a→b and C a→b Indicates message Δ a→b The mean vector and covariance matrix of (·) are obtained. An iterative message passing algorithm is designed based on the factor graph, with the left half of the factor graph being the AoA fusion module and the right half being the AoA estimation module.

[0025] S5. Set frequency f and noise power σ 2 Number of antennas N x With N y Antenna spacing d x With d y And the number of blocks M; the location P of the base station is known. BS Given the received signal y; define 1≤m≤M, l∈{x,y}; preset the maximum number of iterations required n1.

[0026] S6. For any m and l, based on the received signal y m Based on the MVALSE algorithm proposed in the literature "Multidimensional variationalline spectra estimation", AoA estimation is performed to obtain the estimate of the complex channel gain. and θ m，1 posterior estimation

[0027]

[0028] S7. For any m and l, calculate the variable node θ. m，l To factor node News Assumption For the von Mises distribution And Consider it as θ m，l The prior distribution is calculated using the following formula.

[0029]

[0030] Where ∝ denotes proportionality, due to the closure of the von Mises distribution with respect to multiplication. and satisfy

[0031]

[0032] S8. For any M and l, the factor nodes are calculated using the following formula. To variable node p U News

[0033]

[0034] S9. According to the sum-product rule, variable node p U To factor node News for

[0035]

[0036] in Let the set {(u,υ)|1≤u≤M,υ∈{x,y}} be represented. For any m and l, let h be the value of the set. m，l (·)express The exponential function h is obtained by solving the gradient ascent method. m,l Local maximum of (·)

[0037]

[0038] S10. For any m and l, calculate the variable node p using the following formula. U To factor node News

[0039]

[0040] in This is the local maximum point obtained in the previous step.

[0041] S11, Order use Indicates in and e l Zhang Cheng's plane is perpendicular to The unit vector, where × denotes the cross product. According to the sum-product rule, the factor nodes... To variable node θ m，l News for

[0042]

[0043] The above integral does not have a closed-form expression. To simplify the calculation, we only focus on the target position error within v. m，l The effect of projection on the integral. Using This represents the projection of the position error onto the vector, where Under the subarray far-field assumption, since Large enough, θ m,l and x m,l Geometric constraints between them can be used It is expressed as follows. For any m and l, it is calculated using the following formula.

[0044]

[0045] in and Satisfy the following formula

[0046]

[0047]

[0048] S12. Repeat steps S6-S7 and S8-S11 until the maximum number of iterations of the AoA estimation module and the AoA fusion module is reached. After completing the iterations, the posterior distribution of the target location is obtained, and the mean of this posterior distribution is used as the final estimate of the target location.

[0049] The beneficial effects of this invention are improved positioning accuracy and reduced algorithm complexity. The receiving array is divided into multiple subarrays, making the target approximately located in the far-field region of each subarray. Based on the geometric constraints between the target position and the angle of arrival, a probabilistic model of the received signal is established, and a target position estimation algorithm based on a message passing mechanism, namely the APLE algorithm, is designed. By fully utilizing the differences in the angle of arrival between subarrays, more accurate target position estimation is achieved, while the introduction of array partitioning and message passing mechanisms reduces the algorithm's complexity. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of a passive near-field positioning system based on array partitioning;

[0051] Figure 2 It is a factor graph of a probability model;

[0052] Figure 3 These are NMSE simulation curves for near-field localization using different algorithms;

[0053] Figure 4 These are NMSE simulation curves for near-field localization considering different numbers of blocks and distances. Detailed Implementation

[0054] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples.

[0055] Figure 1 A passive near-field positioning system was demonstrated, with an N-type localization unit deployed on the base station side. x =9, N y The array is M=9, and the array is divided into M=9 subarrays, so that the target is located in the near field region of the array and approximately in the far field region of the subarray.

[0056] Figure 2 The diagram shows the factor plot corresponding to the probability model. The left half of the factor plot is the AoA fusion module, and the right half of the factor plot is the AoA estimation module.

[0057] The following is a specific implementation method of the present invention based on the above algorithm, and the parameter settings of the specific method are as follows:

[0058] The simulation environment was set as follows: the frequency of the pilot signal transmitted by the target was f = 28 GHz, the corresponding wavelength was λ = 0.0107 m, and the antenna spacing was... The number of antennas on the base station side is N x =N y =30, divide the array into M=9 subarrays. The Fraunhofer distance of the array is R. F = 2.4107m, and the Fraunhofer distance of each subarray is R. m，F=0.1507m. The distance between the target and the array center is set to r = R. F =2.4107m and r=R m，F =0.1507m, discuss the performance of the algorithm at the near and far field boundaries of the array and the near and far field boundaries of the subarray.

[0059] Based on the above parameter settings, the specific steps of this simulation are as follows:

[0060] S1. The pilot signal x transmitted by the target arrives at the base station via the physical channel. The channel coefficient between the target and the (i,j)th antenna element at the base station is...

[0061]

[0062] Where β is the common antenna gain, Let r be the path loss between the target and the (i,j)th antenna element. (i,j) Let be the propagation distance of the path between the target and the (i, j)th antenna element. The single-shot signal received at the base station can be represented as...

[0063] y = hx + n

[0064] in This represents the channel between the target and the base station. It is additive white Gaussian noise.

[0065] S2. Divide the ELAA on the base station side into M = 9 non-overlapping subarrays. Taking the m-th subarray as an example, the m-th subarray contains N... m =100 antenna elements. After dividing the ELAA, the target can be approximated as being located in the far-field region of each subarray. Taking the center of the m-th subarray as the reference point, under the far-field assumption, the received signal model at the m-th subarray can be simplified to...

[0066] y m =α m a m (θ m,x ,θ m,y )+n m

[0067] Where α m =h m x is the complex channel gain, θ m,x and θ m,y Let AoA and a be the x and y directions respectively at the m-th subarray. m (θ m，x θ m，y () represents the two-dimensional steering vector at the m-th subarray. It is the additive white Gaussian noise at the m-th subarray.

[0068] S3. Based on the array partitioning and the far-field received signal model at the subarray, establish a probabilistic model for the localization problem. Taking the m-th subarray as an example, the likelihood function p(y m |θ m，x θ m，y α m and the conditional probability density function p(θ) m,l |P U ) are respectively

[0069]

[0070]

[0071] in e represents the geometric constraint between AoA at the m-th subarray and the target position. l Let be the unit vector of the array along the l-axis, and δ(·) be the Dirac function. The complex channel gain α m The prior distribution of the target location is modeled using a complex Gaussian distribution and an information-free Gaussian distribution, respectively. Among them, variance It is a relatively large value. The joint probability density function p(p U (y, θ, α) can be represented as

[0072]

[0073] S4. For the joint probability density function p(p U Factor graph representation of m, p, y, θ, α) is performed. U y m θ m，x and θ m，y Each of these is a variable node in the factor graph, and each probability factor is a validation node. For simplicity, we use... Represents the verification node p(θ) m，l |p U ), using Δ a→b (·) represents a message from node a to node b, denoted by m. a→b and C a→b Indicates message Δ a→b The mean vector and covariance matrix of (·) are obtained. An iterative message passing algorithm is designed based on the factor graph, with the left half of the factor graph being the AoA fusion module and the right half being the AoA estimation module.

[0074] S5. Set the frequency f = 28GHz and the number of antennas N. x =30 and N y =30, Antenna Spacing And the number of blocks M = 9; the location p of the base station is known.BS Given the received signal y; define 1≤m≤9, l∈{x,y}; preset the maximum number of iterations required n1=50.

[0075] S6. For any m and l, based on the received signal y m The AoA estimation is performed using the MVALSE algorithm to obtain the estimate of the complex channel gain. and θ m，l posterior estimation

[0076]

[0077] S7. For any m and l, calculate the variable node θ. m，l To factor node News Assumption For the von Mises distribution And Consider it as θ m，l The prior distribution is calculated using the following formula.

[0078]

[0079] Where ∝ denotes proportionality, due to the closure of the von Mises distribution with respect to multiplication. and satisfy

[0080]

[0081] S8. For any m and l, the factor nodes are calculated using the following formula. To variable node p U News

[0082]

[0083] S9. According to the sum-product rule, variable node p U To factor node News for

[0084]

[0085] in Let the set {(u, v) | 1 ≤ u ≤ M, v ∈ {x, y}} be represented. For any m and l, let h be the value of the set. m，l (·)express The exponential function h is obtained by solving the gradient ascent method. m，l Local maximum of (·)

[0086]

[0087] S10. For any m and l, calculate the variable node p using the following formula. U To factor node News

[0088]

[0089] in This is the local maximum point obtained in the previous step.

[0090] S11, Order use Indicates in and e l Zhang Cheng's plane is perpendicular to The unit vector, where × denotes the cross product. According to the sum-product rule, the factor nodes... To variable node θ m，l News for

[0091]

[0092] The above integral does not have a closed-form expression. To simplify the calculation, we only focus on the target position error within v. m，l The effect of projection on the integral. Using This represents the projection of the position error onto the vector, where Under the subarray far-field assumption, since Large enough, θ m，l and x m，l Geometric constraints between them can be used It is expressed as follows. For any m and l, it is calculated using the following formula.

[0093]

[0094] in and Satisfy the following formula

[0095]

[0096]

[0097] S12. Repeat steps S6-S7 and S8-S11 until the maximum number of iterations of the AoA estimation module and the AoA fusion module is reached. After completing the iterations, the posterior distribution of the target location is obtained, and the mean of this posterior distribution is used as the final estimate of the target location.

[0098] Figure 3 These are NMSE simulation curves for target location estimation using different algorithms. The algorithm named "MUSIC" corresponds to the improved MUSIC algorithm based on "O. Rinchi, A. Elzanaty, and M.-S. Alouini, 'Compressive near-field localization for multipath RIS-aided environments,' IEEE Commun. Lett., vol. 26, no. 6, pp. 1268-1272, Jun. 2022." The algorithm named "OMP" corresponds to the improved OMP algorithm based on "X. Wei and L. Dai, 'Channelestimation for extremely large-scale massive MIMO: Far-field, near-field, or hybrid-field,' IEEE Commun. Lett., vol. 26, no. 1, pp. 177-181, Jan. 2022." The algorithm named "APLE" corresponds to the algorithm proposed in this invention. Figure 3 The performance of the APLE, MUSIC, and OMP algorithms on the near-far field boundaries of the array and the near-far field boundaries of the subarray is demonstrated when r = R. m，F When r = R, APLE's performance is significantly better than the MUSIC and OMP algorithms, indicating that the algorithm proposed in this invention has higher positioning accuracy at the near-field and far-field boundaries of the subarray. F At that time, the APLE algorithm was similar to the MUSIC algorithm in performance. However, as the signal-to-noise ratio (SNR) increased, the NMSE of the APLE algorithm was significantly lower than that of the MUSIC algorithm.

[0099] Figure 4 It is an NMSE simulation curve that considers different numbers of blocks and distances for target position estimation. Figure 4 Different antenna sizes N were shown. x The impact of AoA drift effect on the NMSE performance of the APLE algorithm under the conditions of block number M and distance r. SNR is set to 20dB and antenna spacing is set to... N x Set to 60, 120, and 180. First, Figure 4Simulation results show that the APLE algorithm is scalable with respect to array size; the larger the antenna size, the higher the achievable positioning accuracy. Secondly, the performance of NMSE gradually deteriorates with increasing number of blocks M and distance r. This is because the AoA drift effect between subarrays gradually weakens as M and r increase, leading to a decrease in positioning accuracy. However, despite the performance degradation of NMSE, the APLE algorithm still approaches MCRB very closely, indicating that the APLE algorithm has significant practical value for high-precision target localization tasks.

Claims

1. A passive near-field localization method based on array partitioning, characterized in that, Includes the following steps: S1. Define the single-shot signal received at the base station as: y = hx + n in, This represents the channel between the target and the base station, where x is the pilot signal transmitted by the target. It is additive white Gaussian noise; S2. Divide the ultra-large-scale antenna array on the base station side into M non-overlapping subarrays, and the m-th subarray contains N... m =N m，x ×N m，y There are N antenna elements, of which N m，x and N m，y Let be the number of antennas in the m-th subarray along the x-axis and y-axis, respectively. Approximating the target as located in the far-field region of each subarray, and taking the center of the m-th subarray as the reference point, under the far-field assumption, the received signal model at the m-th subarray is simplified as follows: y m =a m a m (i m，x ,the m，y )+n m Where α m =h m x is the complex channel gain, θ m，x and θ m，y Let AoA and a be the x and y directions respectively at the m-th subarray. m (θ m，x θ m，y () represents the two-dimensional steering vector at the m-th subarray. The additive white Gaussian noise at the m-th subarray; S3. Based on the array partitioning and the far-field received signal model at the subarray, establish a probabilistic model for the localization problem, and define the likelihood function p(y) of the m-th subarray. m |θ m，x θ m，y α m and the conditional probability density function p(θ) m，l |p U They are respectively: in Let AoA at the m-th subarray be the position of the target p. U Geometric constraints between, e l Let δ(·) be the unit vector of the array along the l-axis, and let δ(·) be the Dirac function; the complex channel gain α m The prior distribution of the target location is modeled using a complex Gaussian distribution and an information-free Gaussian distribution, respectively. Among them, variance For a relatively large value; the joint probability density function p(p U (y, θ, α) is represented as: S4. For the joint probability density function p(p U Factor graph representation of (m, y, θ, α) is performed. For any m, P U y m θ m，x and θ m，y Each of these is a variable node in the factor graph, and each probability factor is a validation node; definition Represents the verification node p(θ) m，l |p U ), Δ a→b (·) represents a message from node a to node b, m a→b and C a→b Indicates message Δ a→b The mean vector and covariance matrix of (·); an iterative message passing algorithm is designed based on the factor graph, with the left half of the factor graph being the AoA fusion module and the right half being the AoA estimation module; S5. Set frequency f and noise power σ 2 Number of antennas N x With N y Antenna spacing d x With d y And the number of blocks M; the location p of the base station is known. BS With the received signal y; define 1≤m≤M, l∈{x,y}; preset the maximum number of iterations required n1; S6. For any m and l, based on the received signal y m The AoA estimation is performed using the MVALSE algorithm to obtain the estimate of the complex channel gain. and θ m，1 Posterior estimation: S7. For any m and l, calculate the variable node θ. m，l To factor node News definition For the von Mises distribution And Consider it as θ m，l The prior distribution is calculated using the following formula. Where ∝ denotes proportionality, due to the closure of the von Mises distribution with respect to multiplication. and satisfy: S8. For any m and l, the factor nodes are calculated using the following formula. To variable node P U News S9. According to the sum-product criterion, variable node p U To factor node News for: in Let the set {(u, v) | 1 ≤ u ≤ M, u ∈ {x, y}} be represented by h. m，l (·)express The exponential function h is obtained by solving the gradient ascent method. m，l Local maximum of (·) S10. For any m and l, calculate the variable node p using the following formula. U To factor node News in This is the local maximum point obtained in the previous step; S11, Order use Indicates in and e l Zhang Cheng's plane is perpendicular to The unit vector, where × denotes the cross product; according to the sum-product criterion, the factor nodes To variable node θ m，l News for: definition This represents the projection of the position error onto the vector, where Under the subarray far-field assumption, since Large enough, θ m，l and x m，l Geometric constraints between It is indicated that for any m and l, the following formula is used to calculate... in and Satisfy the following formula: S12. Repeat steps S6-S7 and S8-S11 until the maximum number of iterations of the AoA estimation module and the AoA fusion module is reached. After completing the iteration, the posterior distribution of the target location is obtained, and the mean of the posterior distribution is used as the final estimate of the target location.

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