A three-dimensional millimeter wave time-varying channel estimation method and device

Abstract

A three-dimensional millimeter wave time-varying channel estimation method and device belong to the field of wireless communication, comprising: establishing a millimeter wave communication system containing array motion; establishing a three-dimensional time-varying channel model considering Doppler effect, analyzing the synthesized signal in the three-dimensional time-varying channel caused by array motion, each column of the synthesized direction matrix being consistent with the array manifold of the planar array, indicating that the linear array in motion can form a virtual planar array; realizing sparse representation of the three-dimensional time-varying channel through linear array motion; recovering the three-dimensional time-varying channel based on the iterative meshless weighted algorithm of array motion; comprising AoAs estimation and path gain estimation. The application overcomes the negative influence of Doppler frequency shift in the time-varying channel on channel estimation, constructs virtual array elements, realizes channel estimation on the three-dimensional millimeter wave time-varying channel through linear array motion, improves channel estimation accuracy, and greatly reduces pilot overhead and algorithm complexity.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of wireless communication, and particularly relates to a three-dimensional millimeter wave time-varying channel estimation method and device. BACKGROUND

[0002] Qibo Qin, Lin Gui et al. in 2018 published Time-Varying Channel Estimation for Millimeter Wave Multiuser MIMO Systems in IEEE Transactions on Vehicular Technology focuses on the channel estimation problem of time-varying millimeter wave channel in a mobile scenario. Unlike the channel estimation problem of traditional static channel, this document considers the Doppler effect caused by user movement. By taking advantage of the fact that the angles of arrival (AoAs) and angles of departure (AoDs) on the time-varying channel usually change slower than the path gain, a new transmission frame structure is proposed, in which the channel estimation is divided into two independent stages. First, AoAs / AoDs estimation is performed in the first stage, and then path gain estimation is performed in the second stage. Specifically, in the AoAs / AoDs estimation stage, the AoAs / AoDs estimation is converted into a block sparse recovery problem by using a discrete prolate spheroidal basis expansion model (DPS-BEM), and then an adaptive angle estimation (AAE) algorithm is proposed to estimate the AoAs / AoDs. In the path gain estimation stage, the AoAs / AoDs estimated in the previous stage are used to further estimate the path gain. The method proposed in this document considers the influence of Doppler shift in time-varying channels, and the proposed scheme is suitable for channel estimation in non-static scenarios, providing a possibility for high-speed data transmission in future high-speed mobile scenarios. However, due to the limitation of antenna aperture dimension, the method proposed in this document can only realize channel estimation of two-dimensional channels with linear arrays, and if channel estimation in three-dimensional channels closer to reality is also required, more complex planar arrays need to be used, which undoubtedly increases the cost and computational complexity. In addition, although the DPS-BEM method can be used to capture the change of the channel over time, there is still a certain error compared with the real situation, and the relative channel estimation result still has room for further improvement. SUMMARY

[0003] The application aims to provide a three-dimensional millimeter wave time-varying channel estimation method and device. Compared with the prior art, the application realizes the channel estimation of a linear array on a three-dimensional channel by utilizing the array aperture dimension improvement caused by the linear array movement, thereby reducing the calculation cost and complexity. The application also overcomes the negative influence of Doppler shift on channel estimation, and significantly improves the accuracy of channel estimation and reduces the pilot overhead.

[0004] The technical scheme adopted by the application to solve the technical problems is as follows:

[0005] The application provides a three-dimensional millimeter wave time-varying channel estimation method, which comprises the following steps:

[0006] Step 1: establishing a millimeter wave communication system containing array movement;

[0007] Step 2: establishing a three-dimensional time-varying channel model considering Doppler effect, analyzing the synthesized signal in the three-dimensional time-varying channel caused by array movement, and indicating that the moving linear array can form a virtual planar array, since each column of the synthesized direction matrix is consistent with the array manifold of the planar array;

[0008] Step 3: realizing the sparse representation of the three-dimensional time-varying channel through the linear array movement;

[0009] The quantized AoAs set is defined as:

[0010]

[0011] Wherein, and represent the quantized μ and γ, G μ and G γ represent the grid point numbers of μ and γ, respectively, μ = [μ1,..., μ L ] and γ = [γ1,..., γ L ] represent the sets of all the transformation parameters μ l and γ l , μ max and μ min represent the maximum and minimum values in μ, respectively, γ max and γ min represent the maximum and minimum values in γ, respectively, and the deviations and are introduced to reduce the gap between the quantized AoAs set and the real angle;

[0012] The received signal after the synthesis of the continuous M pilot signals is represented as:

[0013]

[0014] where D(t) denotes the combined channel matrix, denotes the measurement matrix, M A denotes the number of pilot signals in the AoAs estimation stage, N RF denotes the number of array receiver RF chains, denotes the direction matrix composed of the quantized AoAs set, denotes the path gain corresponding to the quantized AoAs set;

[0015] Step four, recover the three-dimensional time-varying channel based on the array motion iterative meshless weighted algorithm;

[0016] S4.1: AoAs estimation;

[0017] First, assume that the offset is 0, i.e. Δμ = 0, Δγ = 0; use the orthogonal matching pursuit algorithm to solve AoAs, after each iteration of the OMP algorithm, the selected index will be added to the support set S, and the selected AoAs are S l denotes the lth element in the support set S; then use the maximum likelihood method to estimate and the offset of the true angle, i.e. Δμ S and Δγ S ; set the learning rate of iteration, calculate the likelihood function of each iteration, and get the bias and the final estimate of AoAs and denotes:

[0018]

[0019] S4.2: path gain estimation;

[0020] Use the least squares method to estimate the path gain:

[0021]

[0022] The final estimate of the channel combination matrix is denoted as:

[0023]

[0024] where, denotes the estimate of the combined direction matrix, y syn (t) denotes the received signal after combining the consecutive M pilot signals, N denotes the number of array receiver antenna elements, L denotes the number of multipath components, and m denotes the sampling time.

[0025] Further, in the millimeter wave communication system, the linear array is loaded on a moving object, the moving speed of the object is v, the included angle between the array and the moving direction of the object is α, and the downlink signal from the roadside unit single antenna base station is received.

[0026] Further, in the millimeter wave communication system, it is assumed that the array receiver contains N antenna elements and N RF radio frequency links; the signal received at t time is represented as:

[0027] y(t) = W H (t)h(t)x(t) + W H (t)n(t)

[0028] Wherein, the superscript H represents the conjugate transpose of the matrix; h(t) represents the channel combination matrix, and the modulus of each element in the matrix is a constant h(t) represents the channel combination matrix; x(t) represents the pilot signal sent at t time; W 2 (t) represents an additive white Gaussian noise vector with a mean of zero and a variance of σ 2 .

[0029] Further, in step two, it is assumed that there are L multipath components in total, and the channel combination matrix h(t) is represented as:

[0030]

[0031] Wherein, g l represents the channel gain of the lth path, v l represents the Doppler shift caused by relative motion, a(θ l ,φ l ) represents the steering vector of the receiving antenna, θ l and φ l respectively represent the azimuth angle and the elevation angle of the lth path incident signal; for a three-dimensional channel, the steering vector of the receiving antenna is represented as:

[0032]

[0033] Wherein, f l represents the signal frequency of the lth path containing the Doppler shift, c represents the speed of light, d i (i = 1, 2,..., N-1) represents the distance between the i+1th antenna element and the 1st antenna element.

[0034] Further, in step S4.1, the maximum likelihood method is used to estimate and the offset of the true angle, that is, Δμ S and Δγ S , are represented as:

[0035]

[0036] wherein, represents the estimated path gain, represents the estimated value of the synthesized direction matrix.

[0037] Further, in step S4.1, the likelihood function is represented as:

[0038]

[0039] wherein, g represents the estimated value of the synthesized direction matrix, and Tr represents the trace of the matrix, represents the synthesized received signal, and the upper subscript represents the pseudo-inverse of the matrix.

[0040] Further, in step S4.1, in each iteration process, it is assumed that the learning rate of the nth iteration is and then the bias obtained in the nth iteration is and respectively:

[0041]

[0042] wherein, and respectively represent the gradients of the likelihood function with respect to S and S

[0043] The application further provides a three-dimensional millimeter wave time-varying channel estimation device, comprising a memory and a processor; the memory stores executable instructions, and the processor is configured to execute the executable instructions in the memory to realize the steps of the three-dimensional millimeter wave time-varying channel estimation method.

[0044] The application has the following beneficial effects:

[0045] ​The application provides a three-dimensional millimeter wave time-varying channel estimation method and device, which can realize sparse representation and sparse recovery of a three-dimensional time-varying millimeter wave channel by using a linear array. Specifically, through in-depth analysis of a synthetic signal in a time-varying channel caused by array movement, it is found that a virtual planar array can be formed by the moving linear array. Based on this, the application provides a sparse representation method of a three-dimensional channel realized by linear array movement. In order to fully utilize this sparsity, the application further provides an efficient sparse channel recovery algorithm, which is divided into two stages: first, a grid point and non-grid point-based parameter estimation method is used to estimate the angles of arrival (AoAs), and then a least square method is used to estimate the path gain based on the estimated AoAs. The application realizes channel estimation of a three-dimensional channel by a linear array by utilizing the array aperture dimension improvement brought by linear array movement to construct a virtual element. The application also greatly improves the channel estimation accuracy by overcoming the negative effects of Doppler shift in the time-varying channel on channel estimation; the simple array structure and the phased channel estimation scheme greatly reduce the pilot overhead and also reduce the algorithm complexity. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 It is a linear array movement schematic diagram (three-dimensional diagram).

[0047] Figure 2 It is a linear array movement schematic diagram (top view).

[0048] Figure 3 It is a schematic diagram of a millimeter wave communication system containing array movement (taking a vehicle movement scene as an example).

[0049] Figure 4 It is an array motion-based iterative gridless weighted (AM-IGW) algorithm flowchart. DETAILED DESCRIPTION

[0050] The technical problem to be solved by the application is how to realize high-precision, low-complexity and low-pilot-overhead three-dimensional channel estimation by using a linear array under a time-varying channel caused by rapid channel change of array movement. The application first provides a sparse representation method of a three-dimensional time-varying millimeter wave channel realized by linear array movement, and further provides an efficient sparse channel recovery algorithm for channel estimation, which mainly includes the following steps:

[0051] Step one, establish a millimeter wave communication system containing array movement;

[0052] Step two, a three-dimensional time-varying channel model considering Doppler effect is established, and the synthesized signal in the three-dimensional time-varying channel caused by array movement is analyzed, each column of the synthesized direction matrix is consistent with the array manifold of the planar array, which indicates that the linear array movement can form a virtual planar array.

[0053] Step three, sparse representation of the three-dimensional time-varying channel is realized through linear array movement.

[0054] Step four, three-dimensional time-varying channel is recovered based on the iterative meshless weighted algorithm of array movement.

[0055] The application also provides a three-dimensional millimeter wave time-varying channel estimation device realized through linear array movement, mainly comprising a memory and a processor; wherein the memory stores executable instructions, and the processor is configured to execute the executable instructions in the memory to realize the steps of the three-dimensional millimeter wave time-varying channel estimation method of the application. DETAILED DESCRIPTION

[0057] In the embodiment, the movement mode of the array is linear motion, so the scenario of linear array linear motion is taken as a preferred embodiment of the application.

[0058] The three-dimensional millimeter wave time-varying channel estimation method provided in the embodiment has the implementation process as follows:

[0059] (1) a millimeter wave communication system containing array movement is established;

[0060] As shown in Figure 1 , Figure 2 and Figure 3 , a millimeter wave communication system containing array movement is considered. The linear array is loaded on an object moving along a straight line, and the movement speed of the object is v. The angle between the linear array and the movement direction of the object is α, and the downlink signal from the roadside unit single antenna base station is received.

[0061] It is assumed that the linear array receiver contains N antenna elements and N RF RF links. The signal received at t time can be represented as:

[0062] y(t)=W H (t)h(t)x(t)+W H (t)n(t)

[0063] Wherein, the superscript H represents the conjugate transpose of the matrix, h(t) represents the channel combination matrix, and the modulus of each element in the matrix is a constant h(t) represents the channel combination matrix; x(t) represents the pilot signal sent at t time, and for the convenience of subsequent discussion, it is assumed that x(t)=1; represents a zero-mean and σ 2 -variance additive white Gaussian noise vector.

[0064] (2) a three-dimensional time-varying channel model considering Doppler effect is established, and a synthesized signal in the three-dimensional time-varying channel caused by array movement is analyzed in depth;

[0065] In order to better reflect the actual situation, the application adopts a three-dimensional time-varying channel model considering Doppler effect. Assuming that there are L multipath components in total, at this time, the channel combination matrix h(t) can be expressed as:

[0066]

[0067] wherein g l represents a channel gain of the lth path, v l represents a Doppler shift caused by relative movement, a(θ l , φ l ) represents a steering vector of a receiving antenna, θ l and φ l respectively represent an azimuth angle and an elevation angle of the lth path incident signal. For a three-dimensional channel, the steering vector of the receiving antenna can be expressed as:

[0068]

[0069] wherein f l represents a signal frequency of the lth path containing Doppler shift, c represents light speed, d i (i = 1, 2,..., N-1) represents a spacing between the i+1th antenna element and the 1st antenna element.

[0070] In order to simplify the expression, a transformation parameter μ l = cos(θ l ) sin(φ l ), γ l = sin(θ l ) sin(φ l ), p l = μ l cos(α) + γ l sin(α) is defined. Under this definition, the signal frequency containing Doppler shift f wherein f represents a carrier frequency, and λ represents a carrier wavelength. The n th element in the receiving antenna steering vector can be expressed as:

[0071]

[0072] Because v << c, |p l | ≤ 2, |μl ≤ 1, m' represents a constant around 1, so The steering vector of the receive antenna can be further expressed as:

[0073]

[0074] Consider the m-th sampling time after time t, and combine the Doppler shift The channel matrix at this sampling time can be expressed as:

[0075]

[0076] where τ represents the sampling period, d α = vτ represents the distance moved by the object carrying the linear array in one sampling period, represents the path gain including the Doppler shift, represents the direction matrix at time m, μ = [μ1,..., μ L ] and γ = [γ1,..., γ L ] represent the sets of transformation parameters μ l and γ l for all paths, respectively.

[0077] Therefore, the signal received at time t + mτ can be expressed as:

[0078]

[0079] Consider the received signal synthesized from the continuous M pilot signals, which can be expressed as:

[0080]

[0081] where the synthesized direction matrix is expressed as The synthesized channel combination matrix is expressed as The synthesized noise vector is expressed as

[0082] At this time, any column in the synthesized direction matrix A syn (μ, γ) can be expressed as:

[0083]

[0084] where represents the steering vector of the motion direction. From the above formula, it can be seen that each column of the synthesized direction matrix is consistent with the array manifold of the planar array, and thus it can be shown that the moving linear array forms a virtual planar array.

[0085] (3) Sparse representation of three-dimensional time-varying channel by linear array motion;

[0086] To demonstrate the sparsity of the above three-dimensional time-varying channel model, the quantized AoAs set is defined as:

[0087]

[0088] wherein, and denote the quantized μ and γ, respectively, μ max and μ min denote the maximum and minimum values in μ, respectively, γ max and γ min denote the maximum and minimum values in γ, respectively, G μ and G γ denote the number of quantized grid points of μ and γ, respectively. However, in practical applications, the real AoAs are continuous and cannot completely match the quantized AoAs set. Therefore, the deviation and are introduced to narrow the gap between the quantized AoAs set and the real angle.

[0089] At this time, the synthesized received signal can be further represented as:

[0090]

[0091] wherein, denotes the measurement matrix, M A denotes the number of pilot signals in the AoAs estimation stage, denotes the direction matrix composed of the quantized AoAs set, denotes the path gain corresponding to the quantized AoAs set. At this time, ||β(t)||0=L, L<<G μ G γ , which means that the sparsity of the above formula is L. The method of sparse signal recovery can be used to estimate the parameters, thereby performing channel estimation.

[0092] (4) AoAs estimation and path gain estimation;

[0093] In order to obtain higher accuracy while reducing the pilot overhead and computational complexity, the present application divides the channel estimation into two stages: AoAs estimation and path gain estimation, and M A and M P pilots are used in the two stages, respectively. Based on this, the present application proposes an array motion-based iterative gridless weighted (AM-IGW) algorithm to recover the three-dimensional time-varying channel, and the specific implementation process is as follows:Figure 4 are shown.

[0094] Considering that the direct estimation of AoAs is complicated, it is assumed that the offsets are 0, i.e., Δμ = 0 and Δγ = 0. In this case, the estimation problem of AoAs can be converted into a standard grid-based sparse signal recovery problem, and a grid-based parameter estimation method is used to estimate the parameters. Specifically, an orthogonal matching pursuit (OMP) algorithm can be used to solve it. After each iteration of the OMP algorithm, the selected index is added to the support set S, and the selected AoAs are where S l denotes the l-th element in the support set S.

[0095] However, in practice, the predefined quantization set does not match the real angles. In order to further improve the accuracy of parameter estimation, a non-grid-based parameter estimation method is needed to estimate the bias. Specifically, a maximum likelihood method can be used to estimate and the offsets of the real angles, i.e., Δμ S and Δγ S , which can be specifically represented as:

[0096]

[0097] wherein, denotes the estimated path gain, denotes the estimated value of the synthesized direction matrix. After some processing, the likelihood function can be represented as:

[0098]

[0099] wherein, Tr denotes the trace of the matrix, denotes the synthesized received signal, and the superscript denotes the pseudo-inverse of the matrix.

[0100] In each iteration process, it is assumed that the learning rate of the n-th iteration is and respectively. Then the offsets obtained in the n-th iteration are and respectively:

[0101]

[0102] wherein, and denote the likelihood function with respect to Δμ S and Δγ SGradient. To ensure the stability and efficiency of the optimization process, the present application also employs a backtracking algorithm to dynamically adjust the learning rate of each iteration and

[0103] Finally, the more accurate AoA estimate and can be expressed as:

[0104]

[0105] In addition, the estimates of the direction angle and the pitch angle can be expressed as:

[0106]

[0107] In the path gain estimation stage, the least squares method is used to estimate the path gain:

[0108]

[0109] Finally, the estimate of the channel combination matrix can be expressed as:

[0110]

[0111] where, denotes the estimate of the synthesized direction matrix.

[0112] The present application fully considers the array aperture dimension improvement caused by array motion and the influence of Doppler shift in time-varying channels on channel estimation, and proposes a channel estimation method with high estimation accuracy, low pilot overhead and low complexity, which realizes the channel estimation of three-dimensional channels using linear array motion in time-varying channels.

[0113] The above only describes the preferred embodiments of the present application, and it should be noted that for those skilled in the art, without departing from the principles of the present application, a number of improvements and refinements can be made, and these improvements and refinements should also be considered as the protection scope of the present application.

Claims

1. A method for three-dimensional millimeter wave time-varying channel estimation, the method comprising: The method comprises the following steps: Step 1: establishing a millimeter wave communication system containing array movement; Step 2: establishing a three-dimensional time-varying channel model considering Doppler effect, and analyzing the synthesized signal in the three-dimensional time-varying channel caused by array movement, wherein each column of the synthesized direction matrix is consistent with the array manifold of the planar array, indicating that the linear array movement can form a virtual planar array; Step 3: realizing sparse representation of the three-dimensional time-varying channel through linear array movement; The quantized AoA set is defined as: where, and denote the quantized μ and γ, G μ and G γ denote the number of grid points for μ and γ quantization, respectively, μ = [μ1,..., μ L ] and γ = [γ1,..., γ L ] denote the set of transform parameters μ l and γ l for all ranges, μ max and μ min denote the maximum and minimum values in μ, respectively, γ max and γ min denote the maximum and minimum values in γ, respectively; and introduce bias and to reduce the gap between the quantized AoAs set and the true angles. The received signal after synthesis of the continuous M pilot signals is represented as: where D(t) represents the combined channel matrix after synthesis, denotes the measurement matrix, M A denotes the number of pilot signals in the AoAs estimation phase, N RF denotes the number of array receiver radio frequency links, denotes the direction matrix composed of the quantized AoAs set, denotes the path gain corresponding to the quantized AoAs set; ζ(t) denotes the combined noise vector; N denotes the number of antenna elements. Step 4: recovering the three-dimensional time-varying channel based on an iterative meshless weighted algorithm of array movement; S4.1: AoA estimation; First, assume the offset is 0, that is, Δμ = 0, Δγ = 0; using orthogonal matching pursuit algorithm to solve AoAs, after each iteration of the OMP algorithm, the selected index will be added to the support set S, the selected AoAs are S l The lth element in the support set S is represented; then use the maximum likelihood method to estimate and The offset of the true angle, that is, Δμ S and Δγ S ; Set the learning rate of iteration, calculate the likelihood function of each iteration, and get the bias and The final estimated value of AoAs and is represented as: S4.2: path gain estimation; The least square method is used to estimate the path gain: The final estimated value of the channel combination matrix is represented as: wherein, represents the estimated value of the synthesized direction matrix, y syn (t) represents the received signal after the synthesis of the continuous M pilot signals, N represents the number of array receiver antenna elements, L represents the number of multipath components, and m represents the sampling time.

2. The method of claim 1, wherein, In the millimeter wave communication system, the linear array is loaded on a moving object, the moving speed of the object is v, the included angle between the array and the moving direction of the object is alpha, and the downlink signal from the roadside unit single antenna base station is received.

3. The method of claim 1, wherein, In the millimeter wave communication system, it is assumed that the array receiver contains N antenna elements and N RF radio frequency links; the signal received at time t is represented as: y(t) = W H (t)h(t)x(t) + W H (t)n(t) where the upper index H denotes the conjugate transpose of a matrix; denotes a channel combination matrix, and each element in the matrix has a constant modulus denotes a channel matrix; x(t) denotes a pilot signal transmitted at time t; denotes a zero-mean Gaussian white noise vector with variance σ 2 .

4. The method of claim 1, wherein, In step 2, it is assumed that there are L multipath components in total, and the channel matrix h(t) is represented as: where g l represents the channel gain of the lth ray, v l represents the Doppler shift caused by the relative motion, a(θ l ,φ l ) represents the steering vector of the receiving antenna, θ l and φ l represent the azimuth and elevation angles of the lth ray incident signal, respectively; for a three-dimensional channel, the steering vector of the receiving antenna is represented as: where f l represents the signal frequency with Doppler shift, c represents the speed of light, d i represents the distance between the i+1th antenna element and the 1st antenna element.

5. The method of claim 1, wherein, In step S4.1, the maximum likelihood method is used to estimate and the offset from the true angle, i.e. Δμ S and Δγ S are expressed as: wherein denotes the estimated path gain, denotes the estimate of the combined steering matrix.

6. The method of claim 1, wherein, In step S4.1, the likelihood function is represented as: wherein g denotes an estimate of the direction matrix after the synthesis, Tr denotes the trace of a matrix, denotes the received signal after the synthesis, the upper index denotes the pseudo-inverse of a matrix.

7. The method of claim 1, wherein, In step S4.1, in each iteration process, assuming the learning rate of the n-th iteration is and then the bias obtained in the n-th iteration is and respectively. where, and denote the likelihood function with respect to Δμ S and Δγ S the gradients are computed.

8. A three-dimensional millimeter wave time-varying channel estimation apparatus, characterized by comprising: It comprises: A memory and a processor; The memory stores executable instructions, and the processor is configured to execute the executable instructions in the memory to realize the steps of the three-dimensional millimeter wave time-varying channel estimation method in any one of claims 1 to 7.

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