阅读说明：本技术 一种基于稀疏面阵的三维参数估计方法 (Three-dimensional parameter estimation method based on sparse area array ) 是由 杨小龙 佘媛 周牧 田增山 谢良波 王嘉诚 于 2020-06-18 设计创作，主要内容包括：本发明提出了一种基于稀疏面阵的三维参数估计方法。首先,将面阵所在平面按照信号入射角的范围分为8个区域。在每一个区域内,通过分析稀疏面阵,将稀疏面阵按照信号的入射方向映射为非均匀虚拟线阵,构造稀疏面阵的方向矢量并计算稀疏面阵和非均匀虚拟线阵之间的相位差。其次,将面阵方向矢量分别乘上面阵与虚拟线阵之间的相位差,得到虚拟线阵的方向矢量。在此基础上,构造入射信号并利用三维参数估计算法进行AoA(Arrival of Angle)、ToF(Time of Flight)和DFS(Doppler Frequency Shift)的联合参数估计,并利用谱函数搜索得到一系列的峰值。最后,通过分析稀疏面阵映射为非均匀虚拟线阵的几何关系,利用角度搜索得到正确的入射角对应的峰值。本发明克服了业务天线稀疏面阵排列规则不满足空间采样定理而导致的无法进行参数估计的问题,为实际应用中基于业务天线的室内跟踪定位等应用奠定了理论基础。(The invention provides a three-dimensional parameter estimation method based on a sparse area array. First, the plane on which the area array is located is divided into 8 regions according to the range of the signal incident angle. In each region, the sparse area array is mapped into the non-uniform virtual linear array according to the incident direction of the signal by analyzing the sparse area array, the direction vector of the sparse area array is constructed, and the phase difference between the sparse area array and the non-uniform virtual linear array is calculated. And secondly, multiplying the planar array direction vectors by the phase difference between the planar array and the virtual linear array respectively to obtain the direction vectors of the virtual linear arrays. On the basis, an incident signal is constructed, the three-dimensional parameter estimation algorithm is used for carrying out AoA (arrival of angle), ToF (time of flight) and DFS (Doppler Frequency Shift) joint parameter estimation, and a series of peak values are obtained by searching through a spectrum function. And finally, obtaining a correct peak value corresponding to the incident angle by analyzing the geometric relation of the non-uniform virtual linear array mapped by the sparse planar array and utilizing angle search. The method solves the problem that parameter estimation cannot be carried out due to the fact that the sparse area array arrangement rule of the service antenna does not meet the space sampling theorem, and lays a theoretical foundation for indoor tracking positioning and other applications based on the service antenna in practical application.)

1. A three-dimensional parameter estimation method based on a sparse area array comprises the following steps:

supposing that D signal sources and N subcarriers exist in a Wi-Fi system, because the number of indoor Wi-Fi single AP service antennas is usually 4, a receiving end is a square area array 2 × 2 consisting of 4 antennas, receives CSI information in P data packets from the signal sources, the distance between the antennas is lambda, the space sampling theorem is not satisfied, the 4 antennas are numbered as antennas 1,2, 3 and 4 from left to right in sequence, and theta is formed by sequentially numbering the 4 antennas from top to bottom_iRepresenting the incident angles of signal source i ∈ {1,2, L, D }, the different signal source incident angle vectors can be expressed as Θ ═ { θ ═ θ₁,θ₂,L,θ_D}。

Step two: the plane of the area array is partitioned according to the signal incidence direction, the signal incidence angle theta is divided into 8 areas of 0-45 degrees, 45-90 degrees, 90-135 degrees, 135-180 degrees, 180-225 degrees, 225-270 degrees, 270-315 degrees and 315-360 degrees, and each area is mapped respectively.

Step three: and mapping each area along the signal incidence direction, and calculating the distance d between the projected non-uniform virtual array antennas. Then calculating the direction vector of the non-uniform linear arrayθ_iThe phase difference delta phi (theta) corresponding to a sparse planar array and a non-uniform virtual linear array is obtained after changing from-90 degrees to 90 degrees by the step length of 1 degree_i),Multiplying the planar array direction vector by the phase difference between the planar array and the linear array to obtain the direction vector of the virtual linear array

Step four: constructing the direction vector of the obtained virtual linear array into an incident signal

Step five: and removing the pseudo peak value obtained by three-dimensional parameter estimation through the geometrical relationship between the sparse area array and the non-uniform linear array to obtain correct signal parameters AoA, ToF and DFS.

2. The sparse area array-based three-dimensional parameter estimation method according to claim 1, wherein the third step of calculating the direction vector of the virtual line array comprises the following steps:

when a signal is incident to the array from the first area, the antenna 2 and the antenna 3 are projected to a connecting line of the antenna 1 and the antenna 4 along the incident direction of the signal, and the projected virtual antenna, the antenna 1 and the antenna 4 form a non-uniform virtual linear array.

The constructed area array direction vector is as follows:

wherein

Φ_subcarrier(t)＝[1 e^-j2πftL e^-j2π(N-1)ft]^T

Φ_array1(θ_i) Representing the signal at an angle theta_iPhase difference, phi, incident on the sparse area array caused by the spacing between the antennas_subcarrier(t) represents the phase difference of the signal caused by the transmission of different subcarriers, phi_packet(v) Indicating the phase difference between different data packets.

Taking the antenna 1 as a reference antenna, and calculating the distance between the projected non-uniform linear virtual array antennas:

the array flow pattern of the non-uniform linear array obtained by sparse area array mapping is as follows:

wherein

Representing the signal at an angle theta_iPhase difference caused by the spacing between the antennas and incident angle theta_iAnd then, the phase difference between the sparse area array and the non-uniform linear array obtained by mapping is as follows:

wherein

Representing an angle of incidence of theta_iThe signal of (2) is incident to the phase difference between the sparse area array and the non-uniform virtual line array caused by the space position.

Since the angle of incidence is unknown theta_iAnd the phase difference between the planar array and the linear array is delta phi₁(θ_i) Is related to the angle of incidence, therefore, let us let the angle of incidence θ_iFrom 0 DEG to 45 DEG by a step size of 1 DEG theta_iEach time the phase difference is changed, a corresponding phase difference delta phi is obtained₁(θ_i). Multiplying the direction vector of the sparse area array by the phase difference between the sparse area array and the non-uniform virtual linear array to obtain the direction vector of the virtual non-uniform linear array:

when a signal is incident to the array from the second area, the antenna 2 and the antenna 3 are projected to a connecting line of the antenna 1 and the antenna 4 along the incident direction of the signal, and the projected virtual antenna, the antenna 1 and the antenna 4 form a non-uniform virtual linear array.

The constructed area array direction vector is as follows:

wherein

Φ_array2(θ_i) Representing the signal at an angle theta_iPhase differences incident on the sparse area array caused by the spacing between the antennas.

Taking the antenna 1 as a reference antenna, and calculating the distance between the projected non-uniform linear virtual array antennas:

the array flow pattern of the non-uniform linear array obtained by sparse area array mapping is as follows:

wherein

Representing the signal at an angle theta_iPhase difference caused by the spacing between the antennas and incident angle theta_iAnd then, the phase difference between the sparse area array and the non-uniform linear array obtained by mapping is as follows:

wherein

Representing an angle of incidence of theta_iThe signal of (2) is incident to the phase difference between the sparse area array and the non-uniform virtual line array caused by the space position.

Let the angle of incidence theta_iFrom 45 DEG to 90 DEG by a step size of 1 DEG theta_iEach time the phase difference is changed, a corresponding phase difference delta phi is obtained₂(θ_i). Multiplying the direction vector of the sparse area array by the phase difference between the sparse area array and the non-uniform virtual linear array to obtain the direction vector of the virtual non-uniform linear array:

when a signal is incident to the array from the area three, the antenna 1 and the antenna 4 are projected to a connecting line of the antenna 2 and the antenna 3 along the incident direction of the signal, and the projected virtual antenna, the antenna 2 and the antenna 3 form a non-uniform virtual linear array.

The constructed area array direction vector is as follows:

wherein

Φ_array3(θ_i) Representing the signal at an angle theta_iPhase differences incident on the sparse area array caused by the spacing between the antennas.

Taking the antenna 3 as a reference antenna, and calculating the distance between the projected non-uniform linear virtual array antennas:

the array flow pattern of the non-uniform linear array obtained by sparse area array mapping is as follows:

wherein

wherein

Representing an angle of incidence of theta_iThe signal of (2) is incident to the phase difference between the sparse area array and the non-uniform virtual line array caused by the space position.

Let the angle of incidence theta_iFrom 90 DEG to 135 DEG by a step size of 1 DEG theta_iEach time the phase difference is changed, a corresponding phase difference delta phi is obtained₃(θ_i). Multiplying the direction vector of the sparse area array by the phase difference between the sparse area array and the non-uniform virtual linear array to obtain the direction vector of the virtual non-uniform linear array:

when a signal is incident to the array from the area four, the antenna 1 and the antenna 4 are projected to a connecting line of the antenna 2 and the antenna 3 along the incident direction of the signal, and the projected virtual antenna, the antenna 2 and the antenna 3 form a non-uniform virtual linear array.

The constructed area array direction vector is as follows:

wherein

Φ_array4(θ_i) Representing the signal at an angle theta_iPhase differences incident on the sparse area array caused by the spacing between the antennas.

Taking the antenna 3 as a reference antenna, and calculating the distance between the projected non-uniform linear virtual array antennas:

the array flow pattern of the non-uniform linear array obtained by sparse area array mapping is as follows:

wherein

wherein

Representing an angle of incidence of theta_iThe signal of (2) is incident to the phase difference between the sparse area array and the non-uniform virtual line array caused by the space position.

Let the angle of incidence theta_iFrom 135 to 180 DEG by a step size of 1 DEG theta_iEach time the phase difference is changed, a corresponding phase difference delta phi is obtained₄(θ_i). Multiplying the direction vector of the sparse area array by the phase difference between the sparse area array and the non-uniform virtual linear array to obtain the direction vector of the virtual non-uniform linear array:

the incidence of signals from regions 5, 6, 7, 8 on the array and the incidence of signals from regions 1,2, 3, 4 on the array are in opposite directions, and the mapping is exactly the same.

3. The sparse-area-array-based three-dimensional parameter estimation method according to claim 1, wherein in the fifth step, a pseudo peak value obtained by three-dimensional parameter estimation is removed through a geometric relationship between the sparse area array and the non-uniform linear array to obtain correct signal parameters AoA, ToF and DFS, and the method comprises the following steps:

because the spatial arrangement of the antennas of the sparse area array does not satisfy the spatial sampling theorem, many pseudo peaks exist in the peaks obtained by the search of step four. Only when the angle theta is searched_iWhen the angle of the linear array is equal to the angle of the planar array, the obtained phase difference delta phi (theta)_i) The relationship between the sparse area array and the virtual non-uniform line array can be correctly expressed. At this time, the result obtained by the parametric solution is correct and equal to θ_i. Therefore, in the obtained peak values, each peak value is inversely solved through the mapping geometrical relation, and then the incidence angle theta can be obtained_i. Firstly, a series of peak values SP (i, j, k) are obtained through peak value search, wherein i, jAnd k represents values corresponding to doppler velocity, angle of arrival, and time of flight in the peak, respectively. According to the geometrical relationship between the sparse area array and the virtual non-uniform linear array obtained by mapping, the relationship between the angle of the signal incident on the sparse area array and the angle of the signal incident on the virtual non-uniform linear array can be calculated. When signals are incident from the first area and the second area, the relation between the angle of the signals incident on the sparse area array and the angle of the signals incident on the virtual nonuniform linear array is as follows:

when signals are incident from the third area and the fourth area, the relationship between the angle of the signals incident on the sparse area array and the angle of the signals incident on the virtual nonuniform linear array is as follows:

whereinAnd theta represents the angle of the signal incident on the sparse planar array for the angle of the signal incident on the mapped non-uniform virtual linear array. Angle of signal incident on non-uniform virtual linear array

Technical Field

The invention belongs to a parameter estimation method, and particularly relates to a parameter estimation method for a system consisting of an indoor target and a transceiver by utilizing a sparse area array in a Wi-Fi system.

Background

In recent years, passive tracking and positioning technologies that target no devices are attracting much attention, and aim to perform positioning and tracking on people indoors, and specific applications include the elderly, patient safety monitoring, smart home, and many other internet of things (IoT) -based applications. Most of the existing indoor target tracking methods require a target to carry special equipment or wearable equipment, but equipment is inconvenient to carry in some cases.

Currently, the research of a tracking and positioning system based on Wi-Fi is always a focus of attention, and the system only needs a Wi-Fi Access Point (AP) and one or more receiving devices supporting the Wi-Fi protocol (such as 802.11n/ac) and is respectively arranged in different environments without additional infrastructure. Human bodies existing in the detection environment can affect the transmission environment of the Wi-Fi signals to a certain degree, and CSI (channel State information) can record the change condition of the Wi-Fi signals in a fine-grained manner, and basic motion and position information is extracted through signal reflection on a target. Passive tracking is more challenging than the location of active wireless transmitters because the reflected signal reflected by the human body is typically several orders of magnitude weaker than the direct path signal and is typically superimposed with a strong direct path signal and signals reflected from walls, furniture, and other nearby clutter. It is difficult to extract useful, accurate positioning information from the reflected signals. Moreover, the existing method for estimating parameters by utilizing WiFi is based on a uniform array meeting the space sampling theorem. However, in an actual application scenario, most antenna arrays are service antenna arrays with irregular antenna distribution and do not satisfy the spatial sampling theorem, and when an antenna array does not satisfy the spatial sampling theorem, a larger pseudo peak exists in an estimated parameter, which causes misjudgment of a peak value with correct parameter estimation, thereby affecting a parameter estimation result. Aiming at the problems, the invention designs a method for carrying out parameter estimation by mapping a sparse area array into a non-uniform linear array under a WiFi system. The sparse area array is used for parameter estimation on the basis of the existing parameter estimation of the uniform array, and the method has practicability and universality. Meanwhile, pseudo peaks caused by the sparse array are removed by utilizing the angle of the area array mapping as the linear array, so that the precision of parameter estimation is improved.

Disclosure of Invention

The invention aims to provide a parameter estimation method for a system consisting of an indoor target and a transceiver by utilizing a sparse area array in a Wi-Fi system, which can carry out accurate parameter estimation on a service antenna array which does not meet the space sampling theorem and track and position the indoor target.

The invention relates to a three-dimensional joint parameter estimation method based on a sparse area array, which specifically comprises the following steps:

supposing that D signal sources and N subcarriers exist in a Wi-Fi system, because the number of indoor Wi-Fi single AP service antennas is usually 4, a receiving end is a square area array 2 × 2 consisting of 4 antennas, receives CSI information in P data packets from the signal sources, the distance between the antennas is lambda, the space sampling theorem is not satisfied, the 4 antennas are numbered as antennas 1,2, 3 and 4 from left to right in sequence, and theta is formed by sequentially numbering the 4 antennas from top to bottom_iRepresenting the incident angles of the signal sources i ∈ {1,2, …, D }, the different signal source incident angle vectors can be expressed as Θ ═ θ₁,θ₂,…,θ_D}。

Step two: the plane of the area array is partitioned according to the signal incidence direction, the signal incidence angle theta is divided into 8 areas of 0-45 degrees, 45-90 degrees, 90-135 degrees, 135-180 degrees, 180-225 degrees, 225-270 degrees, 270-315 degrees and 315-360 degrees, and each area is mapped respectively.

Step three: and mapping the sparse area array into an inhomogeneous linear array along the signal incidence direction.

When a signal is incident to the array from an area I, the antenna 2 and the antenna 3 are projected to a connecting line of the antenna 1 and the antenna 4 along the incident direction of the signal, and the projected virtual antenna, the antenna 1 and the antenna 4 form a non-uniform virtual linear array.

The constructed area array direction vector is as follows:

wherein

Φ_subcarrier(t)＝[1 e^-j2πft… e^-j2π(N-1)ft]^T

Φ_array1(θ_i) Representing the signal at an angle theta_iPhase difference, phi, incident on the sparse area array caused by the spacing between the antennas_subcarrier(t) represents the phase difference of the signal caused by the transmission of different subcarriers, phi_packet(v) Indicating the phase difference between different data packets.

Taking the antenna 1 as a reference antenna, and calculating the distance between the projected non-uniform linear virtual array antennas:

the array flow pattern of the non-uniform linear array obtained by sparse area array mapping is as follows:

wherein

Representing the signal at an angle theta_iPhase difference caused by the spacing between the antennas and incident angle theta_iAnd then, the phase difference between the sparse area array and the non-uniform linear array obtained by mapping is as follows:

wherein

Representing an angle of incidence of theta_iThe signal of (2) is incident to the phase difference between the sparse area array and the non-uniform virtual line array caused by the space position.

Since the angle of incidence is unknown theta_iAnd the phase difference between the planar array and the linear array is delta phi₁(θ_i) Is related to the angle of incidence, therefore, let us let the angle of incidence θ_iFrom 0 DEG to 45 DEG by a step size of 1 DEG theta_iEach time the phase difference is changed, a corresponding phase difference delta phi is obtained₁(θ_i). Multiplying the direction vector of the sparse area array by the phase difference between the sparse area array and the non-uniform virtual linear array to obtain the direction vector of the virtual non-uniform linear array:

when a signal is incident to the array from the second area, the antenna 2 and the antenna 3 are projected to a connecting line of the antenna 1 and the antenna 4 along the incident direction of the signal, and the projected virtual antenna, the antenna 1 and the antenna 4 form a non-uniform virtual linear array.

The constructed area array direction vector is as follows:

wherein

Φ_array2(θ_i) Representing the signal at an angle theta_iPhase differences incident on the sparse area array caused by the spacing between the antennas.

Taking the antenna 1 as a reference antenna, and calculating the distance between the projected non-uniform linear virtual array antennas:

the array flow pattern of the non-uniform linear array obtained by sparse area array mapping is as follows:

wherein

Representing the signal at an angle theta_iPhase difference caused by the spacing between the antennas and incident angle theta_iAnd then, the phase difference between the sparse area array and the non-uniform linear array obtained by mapping is as follows:

wherein

Representing an angle of incidence of theta_iThe signal of (2) is incident to the phase difference between the sparse area array and the non-uniform virtual line array caused by the space position.

Let the angle of incidence theta_iFrom 45 DEG to 90 DEG by a step size of 1 DEG theta_iEach time the change is carried out once,a corresponding phase difference delta phi is obtained₂(θ_i). Multiplying the direction vector of the sparse area array by the phase difference between the sparse area array and the non-uniform virtual linear array to obtain the direction vector of the virtual non-uniform linear array:

when a signal is incident to the array from the area three, the antenna 1 and the antenna 4 are projected to a connecting line of the antenna 2 and the antenna 3 along the incident direction of the signal, and the projected virtual antenna, the antenna 2 and the antenna 3 form a non-uniform virtual linear array.

The constructed area array direction vector is as follows:

wherein

Φ_array3(θ_i) Representing the signal at an angle theta_iPhase differences incident on the sparse area array caused by the spacing between the antennas.

Taking the antenna 3 as a reference antenna, and calculating the distance between the projected non-uniform linear virtual array antennas:

the array flow pattern of the non-uniform linear array obtained by sparse area array mapping is as follows:

wherein

Representing the signal at an angle theta_iPhase difference caused by the spacing between the antennas and incident angle theta_iAnd then, the phase difference between the sparse area array and the non-uniform linear array obtained by mapping is as follows:

wherein

Representing an angle of incidence of theta_iThe signal of (2) is incident to the phase difference between the sparse area array and the non-uniform virtual line array caused by the space position.

Let the angle of incidence theta_iFrom 90 DEG to 135 DEG by a step size of 1 DEG theta_iEach time the phase difference is changed, a corresponding phase difference delta phi is obtained₃(θ_i). Multiplying the direction vector of the sparse area array by the phase difference between the sparse area array and the non-uniform virtual linear array to obtain the direction vector of the virtual non-uniform linear array:

when a signal is incident to the array from the area four, the antenna 1 and the antenna 4 are projected to a connecting line of the antenna 2 and the antenna 3 along the incident direction of the signal, and the projected virtual antenna, the antenna 2 and the antenna 3 form a non-uniform virtual linear array.

The constructed area array direction vector is as follows:

wherein

Φ_array4(θ_i) Representing the signal at an angle theta_iPhase differences incident on the sparse area array caused by the spacing between the antennas.

Taking the antenna 3 as a reference antenna, and calculating the distance between the projected non-uniform linear virtual array antennas:

the array flow pattern of the non-uniform linear array obtained by sparse area array mapping is as follows:

wherein

Representing the signal at an angle theta_iPhase difference caused by the spacing between the antennas and incident angle theta_iAnd then, the phase difference between the sparse area array and the non-uniform linear array obtained by mapping is as follows:

wherein

Representing an angle of incidence of theta_iThe signal of (2) is incident to the phase difference between the sparse area array and the non-uniform virtual line array caused by the space position.

Let the angle of incidence theta_iFrom 135 to 180 degrees by 1 degree step changeChange of theta_iEach time the phase difference is changed, a corresponding phase difference delta phi is obtained₄(θ_i). Multiplying the direction vector of the sparse area array by the phase difference between the sparse area array and the non-uniform virtual linear array to obtain the direction vector of the virtual non-uniform linear array:

the incidence of signals from regions 5, 6, 7, 8 on the array and the incidence of signals from regions 1,2, 3, 4 on the array are in opposite directions, and the mapping is exactly the same.

Step four: when a signal enters the array from the area i (i is more than or equal to 1 and less than or equal to 8), a direction vector of the virtual linear array is obtained

Constructing the direction vector of the obtained virtual linear array into an incident signal

Calculating the covariance matrix of the incident signal:

where H denotes conjugate transpose, S is the incident signal,is an array flow pattern matrix with dimension M × D, wherein M and D are the numbers of the antenna and the incident signal respectively, W is white Gaussian noise, the probability density of the white Gaussian noise follows normal distribution,mean μ ═ 0 and variance σ²。

Performing characteristic decomposition on the matrix S to obtain NMP characteristic values, wherein NMP-D smaller characteristic values are equal to the variance sigma of the noise²NMP-D smaller eigenvalues are only related to noise, assuming λ_minIs the minimum eigenvalue, S₀Is the eigenvector of the matrix S, then there is λ_minS₀＝σ²I. NMP-the eigenvectors corresponding to the smaller eigenvalues constitute the noise subspace.

When the number D of incident signals is less than the product NMP of the number of subcarriers and the number of antenna arrays and data packets,

is less than NMP, so:

at S ═ λ S₀Multiplying both sides by e simultaneously_i，e_iObtaining the following characteristic vector corresponding to the minimum characteristic value:

Se_i＝λ_iS₀e_i,i＝D+1,...,NMP

because:

then:

namely:

due to the fact thatS_FNot equal to 0, so:

all the minimum eigenvectors e of the matrix S can be obtained from the above formula_iAnd matrixThe noise subspace is constructed into a noise eigenvector matrix E with NMP × (NMP-D) dimension_NAnd a (theta, tau, v) is a direction vector which is the same as the array flow pattern of the linear array obtained by mapping, and theta, tau and v are parameters to be estimated, namely the arrival angle, the flight time and the speed of an incident signal. Calculation of E_NSpectral function with vector a (θ, τ, v):

where H is the conjugate transposed symbol. The spectral function f (θ, τ, v) is searched to obtain a series of peaks.

Step five: because the spatial arrangement of the antennas of the sparse area array does not satisfy the spatial sampling theorem, many pseudo peaks exist in the peaks obtained by the search of step four. Only when the angle theta is searched_iWhen the angle of the linear array is equal to the angle of the planar array, the obtained phase difference delta phi (theta)_i) The relationship between the sparse area array and the virtual non-uniform line array can be correctly expressed. At this time, the result obtained by the parametric solution is correct and equal to θ_i. Therefore, in the obtained peak values, each peak value is inversely solved through the mapping geometrical relation, and then the incidence angle theta can be obtained_i. Firstly, a series of peak values SP (i, j, k) are obtained through peak value searching, wherein i, j, k respectively represent values corresponding to Doppler velocity, arrival angle and flight time in the peak values. According to the geometrical relationship between the sparse area array and the virtual non-uniform linear array obtained by mapping, the relationship between the angle of the signal incident on the sparse area array and the angle of the signal incident on the virtual non-uniform linear array can be calculated. When signals are incident from the first area and the second area, the relation between the angle of the signals incident on the sparse area array and the angle of the signals incident on the virtual nonuniform linear array is as follows:

when signals are incident from the third area and the fourth area, the relationship between the angle of the signals incident on the sparse area array and the angle of the signals incident on the virtual nonuniform linear array is as follows:

whereinAnd theta represents the angle of the signal incident on the sparse planar array for the angle of the signal incident on the mapped non-uniform virtual linear array. Angle of signal incident on non-uniform virtual linear arrayIncluded in a series of peaks SP (i, j, k) obtained by peak search, an angle corresponding to each peak is associated with an angleThe comparison results in accurate estimates of three parameters, AoA (arrival of Angle), ToF (time of flight), and DFS (Doppler Frequency Shift).

Advantageous effects

Firstly, in order to overcome the problem of low accuracy of parameter estimation caused by the fact that the antenna arrangement rule of the sparse area array does not meet the space sampling theorem, the space arrangement rule of the sparse area array, the geometric relation for mapping the area array into a linear array and the conventional parameter estimation method are analyzed, and the method is proved to be effective in improving the accuracy of parameter estimation by using the sparse area array. The method comprises the steps of firstly, mapping a sparse area array into a non-uniform virtual linear array according to the incident direction of a signal by analyzing the sparse area array, constructing the direction vector of the sparse area array and calculating the phase difference between the sparse area array and the non-uniform virtual linear array. And secondly, multiplying the planar array direction vectors by the phase difference between the planar array and the virtual linear array respectively to obtain the direction vectors of the virtual linear arrays. On the basis, an incident signal is constructed, the three-dimensional parameter estimation algorithm is utilized to carry out the combined parameter estimation of AoA, ToF and DFS, and a series of peak values are obtained by utilizing the spectral function search. And finally, obtaining a correct peak value corresponding to the incident angle by analyzing the geometric relation of the non-uniform virtual linear array mapped by the sparse planar array and utilizing angle search. The method solves the problem that parameter estimation cannot be carried out due to the fact that the sparse area array arrangement rule of the service antenna does not meet the space sampling theorem, and lays a theoretical foundation for indoor tracking positioning and other applications based on the service antenna in practical application.

Drawings

Fig. 1 is a specific implementation flow of three-dimensional joint estimation based on a sparse area array.

Fig. 2 is a schematic diagram of signal incidence on a sparse area array.

Fig. 3 is a diagram of a parameter estimation result.

Detailed description of the preferred embodiments

Supposing that D signal sources and N subcarriers exist in a Wi-Fi system, because the number of indoor Wi-Fi single AP service antennas is usually 4, a receiving end is a square area array 2 × 2 consisting of 4 antennas, receives CSI information in P data packets from the signal sources, the distance between the antennas is lambda, the space sampling theorem is not satisfied, the 4 antennas are numbered as antennas 1,2, 3 and 4 from left to right in sequence, and theta is formed by sequentially numbering the 4 antennas from top to bottom_iRepresenting the incident angles of the signal sources i ∈ {1,2, …, D }, the different signal source incident angle vectors can be expressed as Θ ═ θ₁,θ₂,…,θ_D}。

Step two: the plane of the area array is partitioned according to the signal incidence direction, the signal incidence angle theta is divided into 8 areas of 0-45 degrees, 45-90 degrees, 90-135 degrees, 135-180 degrees, 180-225 degrees, 225-270 degrees, 270-315 degrees and 315-360 degrees, and each area is mapped respectively.

Step three: and mapping the sparse area array into an inhomogeneous linear array along the signal incidence direction.

When a signal is incident to the array from an area I, the antenna 2 and the antenna 3 are projected to a connecting line of the antenna 1 and the antenna 4 along the incident direction of the signal, and the projected virtual antenna, the antenna 1 and the antenna 4 form a non-uniform virtual linear array.

The constructed area array direction vector is as follows:

wherein

Φ_subcarrier(t)＝[1 e^-j2πft… e^-j2π(N-1)ft]^T

Φ_array1(θ_i) Representing the signal at an angle theta_iPhase difference, phi, incident on the sparse area array caused by the spacing between the antennas_subcarrier(t) represents the phase difference of the signal caused by the transmission of different subcarriers, phi_packet(v) Indicating the phase difference between different data packets.

Taking the antenna 1 as a reference antenna, and calculating the distance between the projected non-uniform linear virtual array antennas:

the array flow pattern of the non-uniform linear array obtained by sparse area array mapping is as follows:

wherein

Representing the signal at an angle theta_iPhase difference caused by the spacing between the antennas and incident angle theta_iAnd then, the phase difference between the sparse area array and the non-uniform linear array obtained by mapping is as follows:

wherein

Representing an angle of incidence of theta_iThe signal of (2) is incident to the phase difference between the sparse area array and the non-uniform virtual line array caused by the space position.

Since the angle of incidence is unknown theta_iAnd the phase difference between the planar array and the linear array is delta phi₁(θ_i) Is related to the angle of incidence, therefore, let us let the angle of incidence θ_iFrom 0 DEG to 45 DEG by a step size of 1 DEG theta_iEach time the phase difference is changed, a corresponding phase difference delta phi is obtained₁(θ_i). Multiplying the direction vector of the sparse area array by the phase difference between the sparse area array and the non-uniform virtual linear array to obtain the direction vector of the virtual non-uniform linear array:

when a signal is incident to the array from the second area, the antenna 2 and the antenna 3 are projected to a connecting line of the antenna 1 and the antenna 4 along the incident direction of the signal, and the projected virtual antenna, the antenna 1 and the antenna 4 form a non-uniform virtual linear array.

The constructed area array direction vector is as follows:

wherein

Φ_array2(θ_i) Representing the signal at an angle theta_iPhase differences incident on the sparse area array caused by the spacing between the antennas.

Taking the antenna 1 as a reference antenna, and calculating the distance between the projected non-uniform linear virtual array antennas:

the array flow pattern of the non-uniform linear array obtained by sparse area array mapping is as follows:

wherein

Representing the signal at an angle theta_iPhase difference caused by the spacing between the antennas and incident angle theta_iAnd then, the phase difference between the sparse area array and the non-uniform linear array obtained by mapping is as follows:

wherein

Representing an angle of incidence of theta_iThe signal of (2) is incident to the phase difference between the sparse area array and the non-uniform virtual line array caused by the space position.

Let the angle of incidence theta_iFrom 45 DEG to 90 DEG by a step size of 1 DEG theta_iEach time the change is carried out once,a corresponding phase difference delta phi is obtained₂(θ_i). Multiplying the direction vector of the sparse area array by the phase difference between the sparse area array and the non-uniform virtual linear array to obtain the direction vector of the virtual non-uniform linear array:

when a signal is incident to the array from the area three, the antenna 1 and the antenna 4 are projected to a connecting line of the antenna 2 and the antenna 3 along the incident direction of the signal, and the projected virtual antenna, the antenna 2 and the antenna 3 form a non-uniform virtual linear array.

The constructed area array direction vector is as follows:

wherein

Φ_array3(θ_i) Representing the signal at an angle theta_iPhase differences incident on the sparse area array caused by the spacing between the antennas.

Taking the antenna 3 as a reference antenna, and calculating the distance between the projected non-uniform linear virtual array antennas:

the array flow pattern of the non-uniform linear array obtained by sparse area array mapping is as follows:

wherein

Representing the signal at an angle theta_iPhase difference caused by the spacing between the antennas and incident angle theta_iAnd then, the phase difference between the sparse area array and the non-uniform linear array obtained by mapping is as follows:

wherein

Representing an angle of incidence of theta_iThe signal of (2) is incident to the phase difference between the sparse area array and the non-uniform virtual line array caused by the space position.

Let the angle of incidence theta_iFrom 90 DEG to 135 DEG by a step size of 1 DEG theta_iEach time the phase difference is changed, a corresponding phase difference delta phi is obtained₃(θ_i). Multiplying the direction vector of the sparse area array by the phase difference between the sparse area array and the non-uniform virtual linear array to obtain the direction vector of the virtual non-uniform linear array:

when a signal is incident to the array from the area four, the antenna 1 and the antenna 4 are projected to a connecting line of the antenna 2 and the antenna 3 along the incident direction of the signal, and the projected virtual antenna, the antenna 2 and the antenna 3 form a non-uniform virtual linear array.

The constructed area array direction vector is as follows:

wherein

Φ_array4(θ_i) Representing the signal at an angle theta_iPhase differences incident on the sparse area array caused by the spacing between the antennas.

Taking the antenna 3 as a reference antenna, and calculating the distance between the projected non-uniform linear virtual array antennas:

the array flow pattern of the non-uniform linear array obtained by sparse area array mapping is as follows:

wherein

Representing the signal at an angle theta_iPhase difference caused by the spacing between the antennas and incident angle theta_iAnd then, the phase difference between the sparse area array and the non-uniform linear array obtained by mapping is as follows:

wherein

Representing an angle of incidence of theta_iThe signal of (2) is incident to the phase difference between the sparse area array and the non-uniform virtual line array caused by the space position.

Let the angle of incidence theta_iFrom 135 to 180 degrees by 1 degree step changeChange of theta_iEach time the phase difference is changed, a corresponding phase difference delta phi is obtained₄(θ_i). Multiplying the direction vector of the sparse area array by the phase difference between the sparse area array and the non-uniform virtual linear array to obtain the direction vector of the virtual non-uniform linear array:

the incidence of signals from regions 5, 6, 7, 8 on the array and the incidence of signals from regions 1,2, 3, 4 on the array are in opposite directions, and the mapping is exactly the same.

Step four: when a signal enters the array from the area i (i is more than or equal to 1 and less than or equal to 8), a direction vector of the virtual linear array is obtainedConstructing the direction vector of the obtained virtual linear array into an incident signalCalculating the covariance matrix of the incident signal:

where H denotes conjugate transpose, S is the incident signal,is an array flow pattern matrix with dimension M × D, wherein M and D are the numbers of the antenna and the incident signal respectively, W is white Gaussian noise, the probability density of the white Gaussian noise follows normal distribution,mean μ ═ 0 and variance σ²。

Performing characteristic decomposition on the matrix S to obtain NMP characteristic values, wherein NMP-D smaller characteristic values are equal to the variance sigma of the noise²NMP-D smaller eigenvalues are only related to noise, assuming λ_minIs the minimum eigenvalue, S₀Is momentThe eigenvector of the matrix S is then λ_minS₀＝σ²I. NMP-the eigenvectors corresponding to the smaller eigenvalues constitute the noise subspace.

When the number D of incident signals is less than the product NMP of the number of subcarriers and the number of antenna arrays and data packets,is less than NMP, so:

at S ═ λ S₀Multiplying both sides by e simultaneously_i，e_iObtaining the following characteristic vector corresponding to the minimum characteristic value:

Se_i＝λ_iS₀e_i,i＝D+1,...,NMP

because:

then:

namely:

due to the fact that

S_FNot equal to 0, so:

all the minimum eigenvectors e of the matrix S can be obtained from the above formula_iAnd matrix

The noise subspace is constructed into a noise eigenvector matrix E with NMP × (NMP-D) dimension_NAnd a (theta, tau, v) is a direction vector which is the same as the array flow pattern of the linear array obtained by mapping, and theta, tau and v are parameters to be estimated, namely the arrival angle, the flight time and the speed of an incident signal. Calculation of E_NSpectral function with vector a (θ, τ, v):

where H is the conjugate transposed symbol. The spectral function f (θ, τ, v) is searched to obtain a series of peaks.

Step five: because the spatial arrangement of the antennas of the sparse area array does not satisfy the spatial sampling theorem, many pseudo peaks exist in the peaks obtained by the search of step four. Only when the angle theta is searched_iWhen the angle of the linear array is equal to the angle of the planar array, the obtained phase difference delta phi (theta)_i) The relationship between the sparse area array and the virtual non-uniform line array can be correctly expressed. At this time, the result obtained by the parametric solution is correct and equal to θ_i. Therefore, in the obtained peak values, each peak value is inversely solved through the mapping geometrical relation, and then the incidence angle theta can be obtained_i. Firstly, a series of peak values SP (i, j, k) are obtained through peak value searching, wherein i, j, k respectively represent values corresponding to Doppler velocity, arrival angle and flight time in the peak values. According to the geometrical relationship between the sparse area array and the virtual non-uniform linear array obtained by mapping, the relationship between the angle of the signal incident on the sparse area array and the angle of the signal incident on the virtual non-uniform linear array can be calculated. When signals are incident from the first area and the second area, the relation between the angle of the signals incident on the sparse area array and the angle of the signals incident on the virtual nonuniform linear array is as follows:

when signals are incident from the third area and the fourth area, the relationship between the angle of the signals incident on the sparse area array and the angle of the signals incident on the virtual nonuniform linear array is as follows:

wherein

And theta represents the angle of the signal incident on the sparse planar array for the angle of the signal incident on the mapped non-uniform virtual linear array. Angle of signal incident on non-uniform virtual linear arrayIncluded in a series of peaks SP (i, j, k) obtained by peak search, an angle corresponding to each peak is associated with an angleThe comparison results in accurate estimates of three parameters, AoA (arrival of Angle), ToF (time of flight), and DFS (Doppler Frequency Shift).