A space-time-frequency beam-based statistical channel modeling method for very large-scale MIMO

Abstract

The present invention discloses a very large-scale MIMO space-time-frequency beam-based statistical channel modeling method. The present invention represents the space-time-frequency channel between the user terminal and the base station as the product of a multiple beam matrix and a beam domain channel by sampling the angle, relative position, delay and Doppler, wherein the multiple beam matrix is ​​related to the relative geographical location of the user and the subcarrier number of the broadband system, and the beam domain channel is fully characterized by the beam domain channel energy vector. The statistical channel modeling method proposed in the present invention can be applied to actual very large-scale MIMO systems, providing channel model support for the design of very large-scale MIMO systems, and the established model can more accurately characterize the actual very large-scale MIMO channels than traditional statistical channel models.

Description

Technical Field

[0001] The invention belongs to the technical field of communication and relates to a super-large-scale MIMO space-time-frequency beam-based statistical channel model. Background Art

[0002] With the emergence of new applications, the spectrum efficiency of the sixth generation mobile communication system (6G) is expected to be 10 times higher than that of the fifth generation mobile communication system (5G). Very large-scale multiple-input multiple-output (MIMO) technology is one of the technologies that is expected to achieve this goal. Compared with large-scale MIMO, very large-scale MIMO further increases the number of antennas on the base station side, thereby achieving higher spectrum efficiency, energy efficiency and spatial resolution. In order to achieve the above system performance gains, it is first necessary to establish an accurate channel model.

[0003] For massive MIMO systems, the beam-based statistical channel model (BSCM) was first used in the literature for robust linear precoder design. The BSCM model is extended from the joint correlation channel model, where the characteristic matrix is ​​replaced by the oversampled discrete Fourier transform (DFT) matrix. Since the number of antennas per column or row is usually limited in massive MIMO equipped with uniform planar arrays (UPA), the BSCM model is more accurate than the DFT-based beam domain channel model. In addition, a posteriori BSCM model can be established to characterize the inaccurate channel state information (CSI) part caused by channel aging and other factors, and it brings obvious performance gain in robust linear precoders. Furthermore, by extending the model to the angular delay domain, a two-dimensional BSCM model is formed, and in massive MIMO channel estimation, the channel estimation algorithm based on this model can achieve significant performance gain.

[0004] With the increase in the order of magnitude of the antenna array dimensions on the base station side, a very large-scale MIMO system has been formed, which brings a series of challenges to the establishment of channel models. First, when the antenna scale is further increased significantly, different parts of the array have different propagation environments, such as different channel propagation paths or the same propagation path but different power. This phenomenon is called spatial non-stationarity. Spatial non-stationarity makes the modeling of very large-scale MIMO channels more complicated. In current cellular systems, large-scale MIMO prefers to use compact uniform arrays. Even in very large-scale MIMO systems, compact design can effectively alleviate the impact of spatial non-stationarity. Secondly, when equipped with very large-scale antenna arrays or reflection clusters close to the base station, the traditional plane wavefront model is no longer applicable. The phase difference from the same path to different base station antennas is not only related to the angle of arrival, but also to the distance. That is, the influence of spherical wavefront needs to be considered at this time. In addition, in the case of large transmission bandwidth, as the array scale increases, the physical propagation delay of the electromagnetic waves propagating in the entire array will become very large, resulting in different angles of arrival on different subcarriers of orthogonal frequency division multiplexing (OFDM) for the same path. This phenomenon is called spatial broadband effect. For ultra-large-scale MIMO scenarios with large transmission bandwidth, the spatial broadband effect is also a factor that cannot be ignored in channel modeling. Summary of the invention

[0005] Purpose of the invention: In view of the shortcomings of the prior art, the present invention discloses a very large-scale MIMO space-time-frequency beam-based statistical channel modeling method, which can more accurately characterize the characteristics of very large-scale MIMO channels.

[0006] Technical solution: In order to achieve the above-mentioned purpose, the present invention provides a very large-scale MIMO space-time-frequency beam-based statistical channel modeling method, which represents the space-time-frequency channel between the user terminal and the base station as the product of a multiple beam matrix and a beam domain channel by sampling the angle, relative position, delay, and Doppler; the multiple beam matrix is ​​related to the relative geographical location of the user and the subcarrier number of the broadband system; the beam domain channel is fully characterized by its statistical characteristics by the beam domain channel energy vector, wherein the beam domain channel energy vector is the expectation of the square of the amplitude of the beam domain channel.

[0007] Preferably, the angle sampling method is to uniformly sample the vertical direction cosine and the horizontal direction cosine in the range of -1 to 1, and the number of sampling points is greater than or equal to the number of vertical direction antennas and the number of horizontal direction antennas.

[0008] Preferably, the relative position sampling method is to perform inverse uniform sampling of the distance between the reflection cluster or the user terminal and the base station antenna in the range from 0 to the Rayleigh distance of the array antenna, and the number of sampling points is greater than or equal to 1.

[0009] Preferably, the delay sampling method is to uniformly sample the delay within the OFDM cyclic prefix length range, and the number of sampling points is greater than or equal to the ratio of the cyclic prefix length to the OFDM symbol length multiplied by the number of transmission subcarriers used.

[0010] Preferably, the Doppler sampling method is to uniformly sample the Doppler frequency shift within the range of positive and negative maximum Doppler frequency shifts, and the number of sampling points is greater than or equal to twice the ratio of the maximum Doppler frequency shift to the subcarrier spacing multiplied by the number of OFDM symbols in the considered signal period.

[0011] Preferably, the beam domain channel is modeled as the Hadamard product of a beam domain channel amplitude vector and a standard complex Gaussian random vector, wherein the standard complex Gaussian random vector is a random vector whose elements are independently and identically distributed in a standard complex Gaussian distribution, and each element of the beam domain channel amplitude vector is the square root of the corresponding element of the beam domain channel energy vector; the beam domain channel energy vector is a sparse vector.

[0012] Preferably, when the base station is equipped with a super-large-scale MIMO antenna and the transmission bandwidth multiplied by the base station antenna array size is far less than the speed of light, the multi-beam matrix is ​​expressed as the direct product of the time beam matrix and the space-frequency beam matrix, where the space-frequency beam matrix is ​​the direct product of the multi-carrier space beam matrix and the frequency beam matrix. The product of the n-dimensional unit matrices, is the number of sampling points in the angle range domain; the time beam matrix is ​​a matrix composed of time rudder vectors under Doppler sampling; the frequency beam matrix is ​​a matrix composed of frequency rudder vectors under delay sampling; the multi-carrier space beam matrix is ​​N p The block diagonal matrix is ​​composed of spatial beam matrices, where the i-th spatial beam matrix is ​​the n-th spatial beam matrix under angle and relative position sampling. i The matrix composed of the spatial steering vectors on the subcarriers, N p is the number of transmitted subcarriers, n i is the index of the i-th transmission subcarrier.

[0013] Preferably, when the base station is equipped with ultra-large-scale MIMO antennas and the transmission bandwidth multiplied by the base station antenna array size is much smaller than the speed of light, the multiple beam matrix is ​​expressed as the direct product of the time beam matrix, the frequency beam matrix and the space beam matrix; the time beam matrix is ​​a matrix composed of time steering vectors under Doppler sampling; the frequency beam matrix is ​​a matrix composed of frequency steering vectors under delay sampling; the space beam matrix is ​​a matrix composed of space steering vectors under angle sampling and relative position sampling.

[0014] Preferably, when the base station is equipped with a massive MIMO antenna and the transmission bandwidth multiplied by the base station antenna array size is far less than the speed of light, the multi-beam matrix is ​​expressed as the direct product of the time beam matrix and the space-frequency beam matrix, where the space-frequency beam matrix is ​​the direct product of the multi-carrier space beam matrix and the frequency beam matrix M r The multi-carrier spatial beam matrix is ​​the direct product of the multi-carrier vertical spatial beam matrix and the multi-carrier horizontal spatial beam matrix. r is the number of sampling points in the angle domain; the time beam matrix is ​​a matrix composed of time steering vectors under Doppler sampling; the frequency beam matrix is ​​a matrix composed of frequency steering vectors under delay sampling; the multi-carrier vertical space beam matrix is ​​N p The block diagonal matrix is ​​composed of vertical spatial beam matrices, where the i-th vertical spatial beam matrix is ​​the n-th vertical spatial beam matrix under angle sampling. i The matrix composed of the vertical space steering vectors on the subcarriers, N p is the number of transmitted subcarriers, n i is the index of the i-th transmission subcarrier; the multi-carrier horizontal spatial beam matrix is ​​N p The block diagonal matrix is ​​composed of horizontal spatial beam matrices, where the i-th horizontal spatial beam matrix is ​​the n-th horizontal spatial beam matrix under angle sampling. i A matrix composed of horizontal space steering vectors on subcarriers.

[0015] Preferably, when the base station is equipped with a massive MIMO antenna and the transmission bandwidth multiplied by the base station antenna array size is much smaller than the speed of light, the multiple beam matrix is ​​expressed as the direct product of the time beam matrix, the frequency beam matrix, the vertical space beam matrix and the horizontal space beam matrix; the time beam matrix is ​​a matrix composed of time steering vectors under Doppler sampling; the frequency beam matrix is ​​a matrix composed of frequency steering vectors under delay sampling; the vertical space beam matrix is ​​a matrix composed of vertical space steering vectors under angle sampling; the horizontal space beam matrix is ​​a matrix composed of horizontal space steering vectors under angle sampling.

[0016] Beneficial effects: The ultra-large-scale MIMO space-time-frequency beam-based statistical channel modeling method proposed in the present invention can be applied to actual ultra-large-scale MIMO systems to provide support for channel estimation and precoding transmission methods. In addition, the method of the present invention refines the sampling of angle, delay and Doppler, and the established model can more accurately characterize the channel than the traditional statistical channel model. At the same time, the spherical wavefront and spatial broadband effects are taken into account, which can further bring accuracy performance gains when equipped with ultra-large-scale arrays and large transmission bandwidths. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a three-dimensional coordinate diagram of ultra-large-scale MIMO;

[0018] Figure 2 The model approximation error performance of BSCM model and SW-BSCM model with the number of antennas;

[0019] Figure 3 The model approximation error performance of BSCM model, SW-BSCM model and SW-SWE-BSCM model with transmission bandwidth. DETAILED DESCRIPTION

[0020] The technical solution provided by the present invention will be described in detail below in conjunction with specific embodiments. It should be understood that the following specific implementation methods are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0021] The method of the present invention is mainly applicable to a very large-scale MIMO system equipped with a very large number of antenna arrays on the base station side. The very large-scale MIMO space-time-frequency beam-based statistical channel modeling method involved in the present invention is described in detail below in conjunction with a specific communication system example. It should be noted that the model of the present invention is not only applicable to the specific system model given in the following example, but also to system models with other configurations.

[0022] 1. System Configuration

[0023] Consider a terrestrial single-cell ultra-large-scale MIMO system, where a base station equipped with UPA simultaneously serves K users equipped with a single antenna, and OFDM modulation is used to combat frequency selective fading. The number of antennas on the base station side is N r =N r,v ×N r,h , where N r,v and N r,h are the number of vertical antennas and the number of horizontal antennas respectively. The vertical and horizontal antenna spacings of the base station UPA are d v and d h , and d v ,d h All are set to half wavelength. The number of OFDM symbols is N o In OFDM modulation, the number of subcarriers is recorded as N c , where N p subcarriers are used for data or pilot transmission, and the transmission subcarrier index set is The OFDM cyclic prefix length is denoted as N g , the subcarrier spacing is denoted as Δf, and the sampling interval is Transmission bandwidth B = N p Δf.

[0024] 2. Space-time-frequency beam-based statistical channel modeling method for ultra-large-scale MIMO

[0025] 1. Space-time-frequency domain channel model

[0026] Remember c k,m (t,τ) is the time domain equivalent channel impulse response (CIR) from the kth user to the mth antenna of the base station, where t and τ represent the large-scale time and small-scale delay respectively. CIR can be expressed as P k The set of discernible paths is

[0027]

[0028] where exp{·} represents the exponential function, f c represents the carrier frequency, α k,p represents the complex channel gain of the pth path of the kth user, υ k,p and τ k,p,m They represent the Doppler shift of the p-th path from the k-th user to the base station and the delay of the p-th path from the k-th user to the m-th antenna of the base station. Assume that the delay and Doppler shift where υ max is the maximum Doppler frequency shift. By taking Fourier transform of the delay domain of equation (1), we can get the frequency response from the kth user to the mth antenna of the base station:

[0029]

[0030] The time and frequency are sampled as f = lΔf, the frequency gain on the lth subcarrier of the nth OFDM symbol can be obtained for

[0031]

[0032] where h k,p =α k,p exp{-j2πf c τ k,p}, τ k,p =τ k,p,1 , Δτ k,p,m =τ k,p,m -τ k,p Next, consider the delay difference Δτ k,p,m Modeling. Figure 1 As shown, with the first antenna of the array as the origin O, the horizontal direction as the x-axis, and the vertical direction as the z-axis, a rectangular coordinate system is established. The coordinates of the mth antenna can be written as Q m =(m h d h ,0,m v d v ),in Symbol <·> N , denote N-modulo and round down respectively. Assume that the position of the reflection cluster of the pth path of user k (the user terminal position for the LoS path) is P = r k,p (cosθ k,p sinφ k,p ,cosθ k,p cosφ k,p ,sinθ k,p ), where θ k,p ,φ k,p are the vertical arrival angle and horizontal arrival angle of the p-th path of user k to the first antenna on the base station side, r k,p is the distance from point P to the origin. So the delay difference Δτ k,p,m It can be expressed as

[0033]

[0034] Where c is the speed of light, is the wavelength of electromagnetic wave, v k,p = cosθ k,p sinφ k,p ,u k,p = sinθ k,p are the horizontal cosine and vertical cosine respectively. When the wavelength and antenna spacing are determined, Δτ k,p,m The parameter m and the spatial domain parameter set E k,p =(u k,p ,v k,p ,r k,p ) is determined, so let Δτ k,p,m Denoted as Δτ m (E k,p ). Define the spatial domain channel vector The superscript T represents the transpose of a matrix or vector. And define the spatial steering vector v on subcarrier l l (E k,p )for

[0035]

[0036] Then the spatial channel vector g k,l,n It can be written as

[0037]

[0038] Further define the space-frequency domain channel vector and the frequency rudder vector u(τ k,p )for

[0039]

[0040] Since the path p can be obtained by the gain h k,pAnd the parameter set {u k,p ,v k,p ,r k,p ,τ k,p ,υ k,p} is determined, so h k,p Written in function form h k (u k,p ,v k,p ,r k,p ,τ k,p ,υ k,p ). So the space-frequency domain channel vector g k,n It can be expressed as

[0041]

[0042] where ⊙ represents the Hadamard product, represents the direct product, 1 N×M represents an N×M-dimensional all-one matrix or vector. Further definition of the space-time-frequency domain channel vector and the time rudder vector is

[0043]

[0044] So the space-time-frequency domain channel matrix g k It can be expressed as

[0045]

[0046] 2. Space-time-frequency beam-based statistical channel modeling method

[0047] Based on formula (10), consider angle, relative position, delay, and Doppler sampling. The angle sampling method is to uniformly sample the vertical direction cosine and the horizontal direction cosine in the range of -1 to 1, and the number of sampling points is greater than or equal to the number of vertical direction antennas and the number of horizontal direction antennas. The specific sampling of vertical direction cosine and horizontal direction cosine is:

[0048]

[0049]

[0050] in Represents a set of positive integers less than or equal to N, M v =F v N r,v ,M h =F h N r,h is the number of sampling points in the angle domain, F v ,F h is the angle domain refinement factor and is greater than or equal to 1.

[0051] The relative position sampling method is to uniformly sample the distance between the reflection cluster or the user terminal and the base station antenna inversely within the Rayleigh distance range of the array antenna, the number of sampling points is greater than or equal to 1, and the inverse of the sampling distance is specifically

[0052]

[0053] in is the antenna array Rayleigh distance, D is the antenna array size, M q is the number of relative position sampling points.

[0054] The delay sampling method is to uniformly sample the delay within the OFDM cyclic prefix length range, and the number of sampling points is greater than or equal to the ratio of the cyclic prefix length to the OFDM symbol length multiplied by the number of transmission subcarriers used. The sampling delay is specifically

[0055]

[0056] Among them, M p =F p N p , F p is the delay domain refinement factor and is greater than or equal to 1. is the number of sampling points in the delay domain, is the ceiling function.

[0057] The Doppler sampling method is to uniformly sample the Doppler frequency shift within the range of positive and negative maximum Doppler frequency shifts, and the number of sampling points is greater than or equal to twice the ratio of the maximum Doppler frequency shift to the subcarrier spacing multiplied by the number of OFDM symbols in the considered period. The sampling Doppler frequency shift is specifically

[0058]

[0059] Among them, M d =F d N d , F d is the Doppler domain refinement factor and is greater than or equal to 1.

[0060] Further define the collection

[0061]

[0062]

[0063] make The sampling delay difference is further obtained as Δτ m (E i,j,q ). In particular, it is stipulated Then when the number of sampling points Mv ,M h ,M f ,M d ,M q When it is large enough, the space-time-frequency domain channel vector of ultra-large-scale MIMO can be approximately written as

[0064]

[0065] in for

[0066]

[0067] The space-time-frequency channel (18) can be expressed as the product of the multi-beam matrix and the beam domain channel, specifically:

[0068] g k =Ph k (20)

[0069] Where P is the multi-beam matrix, h k is the beam domain channel vector, and the above model is a space-time-frequency beam-based statistical channel model. Assuming that the elements of the beam domain channel vector are independent of each other and obey the complex Gaussian distribution, the beam domain channel is composed of the beam domain channel energy vector ω k The beam channel energy vector is the expectation of the square of the amplitude of the beam domain channel. Specifically, the beam domain channel vector is modeled as the beam domain channel amplitude vector m k and a standard complex Gaussian random vector w k The Hadamard product is

[0070] h k =m k ⊙w k (twenty one)

[0071] where the standard complex Gaussian random vector w k is a random vector whose elements are independently and identically distributed in a standard complex Gaussian distribution, and the beam domain channel amplitude vector m k Each element is the beam domain channel energy vector ω k The square root of the corresponding element. And the beam domain channel energy vector is a sparse vector.

[0072] The multi-beam matrix has different expressions in different situations, and can be divided into four situations according to the number of antennas equipped in the base station and the size of the transmission bandwidth.

[0073] 1) When the base station is equipped with ultra-large-scale MIMO antennas and BD<<c is not satisfied, where B, D, and c are the transmission bandwidth, base station antenna array size, and the speed of light, respectively, the influence of spherical wavefront and spatial broadband effects needs to be considered. At this time, the multi-beam matrix P is expressed as the direct product of the time beam matrix D and the space-frequency beam matrix, where the space-frequency beam matrix is ​​the multi-carrier spatial beam matrix Direct product with the frequency beam matrix U The product of the n-dimensional unit matrices, is the number of sampling points in the angle distance domain, and P is specifically expressed as

[0074]

[0075] Among them N is an N-dimensional unit matrix, D and U are the matrices composed of the time rudder vector under Doppler sampling and the frequency rudder vector under delay sampling respectively.

[0076]

[0077]

[0078] as well as N p The block diagonal matrix composed of spatial beam matrices is

[0079]

[0080] Where 0 is a vector or matrix of all zeros, and the i-th spatial beam matrix The nth sampling angle and relative position i The matrix composed of the spatial steering vectors on the subcarriers is specifically:

[0081]

[0082] I i,j,q =(i-1)M h M q +(j-1)M q +q (27)

[0083] 2) When the base station is equipped with ultra-large-scale MIMO antennas and satisfies BD<<c, the influence of spherical wavefront needs to be considered. However, due to the Therefore, the influence of spatial broadband effect can be ignored, so the spatial beam matrices on all subcarriers are approximately equal, and the spatial beam matrix V = V l At this time, the multi-beam matrix is ​​expressed as the direct product of the time beam matrix, the frequency beam matrix, and the space beam matrix, specifically:

[0084]

[0085] The definitions of the time beam matrix D and the frequency beam matrix U are the same as those in equations (23) and (24). The space beam matrix V is a matrix composed of the space rudder vectors under angle and relative position sampling, specifically:

[0086]

[0087] I i,j,q =(i-1)M h M q +(j-1)M q +q (30)

[0088] The space rudder vector v(E k,p )for

[0089]

[0090] 3) When the base station is equipped with massive MIMO antennas and BD < < c is not satisfied, the influence of spatial broadband effect needs to be considered. However, since the distance between the reflection cluster or the user terminal and the base station is much greater than D, the wavefront is approximately a plane wavefront. The delay difference in equation (4) can be approximately expressed as

[0091]

[0092] The time delay difference is independent of the distance and the vertical cosine and horizontal cosine are separable, so the space rudder vector v l (E k,p ) can be decomposed into the vertical space rudder vector v v,l (u k,p ) and the horizontal space rudder vector v h,l (u k,p ), specifically

[0093]

[0094] where v v,l (u),v h,l (u) are

[0095]

[0096]

[0097] At this time, the multi-beam matrix is ​​expressed as the direct product of the time beam matrix D and the space-frequency beam matrix, where the space-frequency beam matrix is ​​the direct product of the multi-carrier space beam matrix and the frequency beam matrix U The product of the dimensional unit matrix, the multi-carrier spatial beam matrix is ​​the multi-carrier vertical spatial beam matrix and multi-carrier horizontal beam matrix The direct product of P is specifically expressed as

[0098]

[0099] The definitions of the time beam matrix D and the frequency beam matrix U are the same as (23) and (24). and N p The block diagonal matrix composed of vertical spatial beam matrices and N p The block diagonal matrix composed of horizontal spatial beam matrices is:

[0100]

[0101]

[0102] The i-th vertical spatial beam matrix and the i-th horizontal spatial beam matrix are the n-th i The matrix composed of the vertical space steering vectors on the subcarriers and the nth i The matrix composed of the horizontal space steering vectors on the subcarriers is specifically:

[0103]

[0104]

[0105] 4) When the base station is equipped with massive MIMO antennas and satisfies BD<<c, there is no need to consider the influence of spatial broadband effect, and the wavefront can be approximated as a plane wavefront. At this time, the spatial beam matrices on all subcarriers are equal, and the spatial beam matrix can be expressed as the direct product of the vertical spatial beam matrix and the horizontal spatial beam matrix. Therefore, the multi-beam matrix is ​​expressed as the time beam matrix D, the frequency beam matrix U, and the vertical spatial beam matrix V v and the horizontal spatial beam matrix V h The direct product of

[0106]

[0107] The definitions of the time beam matrix D and frequency beam matrix U are the same as those in (23) and (24), and the vertical space beam matrix V v and the horizontal spatial beam matrix V h are respectively the matrix composed of the vertical space rudder vector under angle sampling and the matrix composed of the horizontal space rudder vector under angle sampling, specifically:

[0108]

[0109]

[0110] The vertical space rudder vector v v (u) and the horizontal space rudder vector v h (u) are

[0111] v v (u)=[1,exp{jπu},…,exp{jπ(N r,v -1)u}] T (44)

[0112] v h (v)=[1,exp{jπv},…,exp{jπ(N r,h -1)v}] T (45)

[0113] 3. Implementation Effect

[0114] In order to enable those skilled in the art to better understand the scheme of the present invention, the accuracy simulation of the ultra-large-scale MIMO space-frequency beam-based statistical channel modeling method in this embodiment under a specific system configuration is given below, in which the Doppler domain is omitted for simplicity. In the simulation, the influence of the spherical wavefront and spatial broadband effects on the accuracy of the channel model will be verified. The beam-based statistical channel model that considers the spherical wavefront and spatial broadband effects in case 1) is referred to as SW-SWE-BSCM, the beam-based statistical channel model that only considers the spherical wavefront in case 2) is referred to as SW-BSCM, and the beam-based statistical channel model that does not consider the spherical wavefront and spatial broadband effects in case 3) is referred to as BSCM. Since the spherical wavefront effect and the spatial broadband effect are mainly related to the antenna size and have nothing to do with whether the antenna is a linear array or a planar array, in order to reduce the complexity of the simulation, a uniform linear array (ULA) is configured on the base station side in the simulation.

[0115] First, the specific system configuration of this embodiment is introduced. Consider a large-scale MIMO system equipped with ULA, with N horizontal antennas on the base station side. r,h The range is 16 to 256, the number of users is K = 50, and the number of transmission subcarriers is N p =120, the cyclic prefix and total subcarrier numbers are N g =144,N c =2048, and the subcarrier spacing Δf is set to 30~1920KHz. In order to evaluate the accuracy of the model, the model approximation error (MAE) is defined as

[0116]

[0117] where ||·|| F represents the Frobenius norm of the matrix, G k represents the actual spatial frequency domain channel of the kth user, proj M (G k) represents the set of channels that satisfy model M and G k The channel with the shortest distance.

[0118] Figure 2 The curves of the model approximation error of BSCM and SW-BSCM as the number of base station antennas changes are given. The subcarrier spacing Δf = 30kHz, and the spatial broadband effect can be ignored due to the small transmission bandwidth. First, the traditional DFT-based beam domain channel model is compared, that is, the refinement factor F r,h =F p =1, it can be seen that the accuracy performance of the refined (SW-)BSCM model has been significantly improved. In addition, comparing the MAE performance of the two channel models, as the antenna size increases, the spherical wavefront effect has a greater impact on the BSCM model, and the accuracy gain of the SW-BSCM model relative to the BSCM model is greater. Therefore, for the ultra-large-scale MIMO system with ultra-large-scale antennas in the base station, the SW-BSCM model can more accurately characterize the channel than the BSCM model.

[0119] Figure 3 The curves of the approximate errors of the BSCM, SW-BSCM and SW-SWE-BSCM models varying with the transmission bandwidth are given, where the number of base station antennas is N. r =64. As can be seen from the figure, as the transmission bandwidth increases, the spatial broadband effect has a greater impact on the accuracy of the channel model. When the base station is equipped with a very large-scale antenna array and a large transmission bandwidth, the SW-SWE-BSCM model outperforms the other two models in terms of accuracy.

[0120] In the embodiments provided in this application, it should be understood that the disclosed methods can be implemented in other ways without exceeding the spirit and scope of this application. The current embodiment is only an illustrative example and should not be used as a limitation. The specific content given should not limit the purpose of this application. For example, some features can be ignored or not executed.

[0121] The technical means disclosed in the scheme of the present invention are not limited to the technical means disclosed in the above-mentioned implementation mode, but also include technical schemes composed of any combination of the above-mentioned technical features. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications are also regarded as the protection scope of the present invention.

Claims

1. A method for modeling a space-time-frequency beam-based statistical channel for ultra-large-scale MIMO, characterized in that: The beam-based statistical channel modeling method represents the space-time-frequency channel between the user terminal and the base station as the product of a multiple beam matrix and a beam domain channel by sampling the angle, relative position, delay, and Doppler; the multiple beam matrix is ​​related to the relative geographical location of the user and the subcarrier number of the broadband system; the statistical characteristics of the beam domain channel are fully characterized by the beam domain channel energy vector. The beam domain channel energy vector is the expectation of the square of the amplitude of the beam domain channel; When the base station is equipped with ultra-large-scale MIMO antennas and the transmission bandwidth multiplied by the base station antenna array size is far less than the speed of light, the multi-beam matrix is ​​expressed as the direct product of the time beam matrix and the space-frequency beam matrix, where the space-frequency beam matrix is ​​the direct product of the multi-carrier space beam matrix and the frequency beam matrix. The product of the n-dimensional unit matrices, is the number of sampling points in the angle range domain; the time beam matrix is ​​a matrix composed of time rudder vectors under Doppler sampling; the frequency beam matrix is ​​a matrix composed of frequency rudder vectors under delay sampling; the multi-carrier space beam matrix is ​​N p The block diagonal matrix is ​​composed of spatial beam matrices, where the i-th spatial beam matrix is ​​the n-th spatial beam matrix under angle and relative position sampling. i The matrix composed of the spatial steering vectors on the subcarriers, N p is the number of transmitted subcarriers, n i is the index of the i-th transmission subcarrier.

2. According to the ultra-large-scale MIMO space-time-frequency beam-based statistical channel modeling method of claim 1, the angle sampling method is to uniformly sample the vertical direction cosine and the horizontal direction cosine in the range of -1 to 1, and the number of sampling points is greater than or equal to the number of vertical direction antennas and the number of horizontal direction antennas.

3. According to the ultra-large-scale MIMO space-time-frequency beam-based statistical channel modeling method of claim 1, the relative position sampling method is to inversely uniformly sample the distance between the reflection cluster or the user terminal and the base station antenna in the range of 0 to the Rayleigh distance of the array antenna, and the number of sampling points is greater than or equal to 1.

4. According to the ultra-large-scale MIMO space-time-frequency beam-based statistical channel modeling method described in claim 1, the delay sampling method is to uniformly sample the delay within the OFDM cyclic prefix length range, and the number of sampling points is greater than or equal to the ratio of the cyclic prefix length to the OFDM symbol length multiplied by the number of transmission subcarriers used.

5. According to the ultra-large-scale MIMO space-time-frequency beam-based statistical channel modeling method described in claim 1, the Doppler sampling method is to uniformly sample the Doppler frequency shift within the range of positive and negative maximum Doppler frequency shifts, and the number of sampling points is greater than or equal to twice the ratio of the maximum Doppler frequency shift to the subcarrier spacing multiplied by the number of OFDM symbols in the considered signal period.

6. The method for modeling ultra-large-scale MIMO space-time-frequency beam-based statistical channels according to claim 1, characterized in that: The beam domain channel is modeled as the Hadamard product of a beam domain channel amplitude vector and a standard complex Gaussian random vector, wherein the standard complex Gaussian random vector is a random vector whose elements are independently and identically distributed in a standard complex Gaussian distribution, and each element of the beam domain channel amplitude vector is the square root of the corresponding element of the beam domain channel energy vector; the beam domain channel energy vector is a sparse vector.

7. The method for modeling ultra-large-scale MIMO space-time-frequency beam-based statistical channels according to claim 1, characterized in that: When the base station is equipped with ultra-large-scale MIMO antennas and the transmission bandwidth multiplied by the size of the base station antenna array is much smaller than the speed of light, the multiple beam matrix is ​​expressed as the direct product of the time beam matrix, the frequency beam matrix and the space beam matrix; the time beam matrix is ​​a matrix composed of time steering vectors under Doppler sampling; the frequency beam matrix is ​​a matrix composed of frequency steering vectors under delay sampling; the space beam matrix is ​​a matrix composed of space steering vectors under angle and relative position sampling.

8. The method for modeling ultra-large-scale MIMO space-time-frequency beam-based statistical channels according to claim 1, characterized in that: When the base station is equipped with a massive MIMO antenna and the transmission bandwidth multiplied by the base station antenna array size is far less than the speed of light, the multi-beam matrix is ​​expressed as the direct product of the time beam matrix and the space-frequency beam matrix, where the space-frequency beam matrix is ​​the direct product of the multi-carrier space beam matrix and the frequency beam matrix M r The multi-carrier spatial beam matrix is ​​the direct product of the multi-carrier vertical spatial beam matrix and the multi-carrier horizontal spatial beam matrix. r is the number of sampling points in the angle domain; the time beam matrix is ​​a matrix composed of time steering vectors under Doppler sampling; the frequency beam matrix is ​​a matrix composed of frequency steering vectors under delay sampling; the multi-carrier vertical space beam matrix is ​​N p The block diagonal matrix is ​​composed of vertical spatial beam matrices, where the i-th vertical spatial beam matrix is ​​the n-th vertical spatial beam matrix under angle sampling. i The matrix composed of the vertical space steering vectors on the subcarriers, N p is the number of transmitted subcarriers, n i is the index of the i-th transmission subcarrier; the multi-carrier horizontal spatial beam matrix is ​​N p The block diagonal matrix is ​​composed of horizontal spatial beam matrices, where the i-th horizontal spatial beam matrix is ​​the n-th horizontal spatial beam matrix under angle sampling. i A matrix composed of horizontal space steering vectors on subcarriers.

9. The method for modeling ultra-large-scale MIMO space-time-frequency beam-based statistical channels according to claim 1, characterized in that: When the base station is equipped with a massive MIMO antenna and the transmission bandwidth multiplied by the size of the base station antenna array is much smaller than the speed of light, the multiple beam matrix is ​​expressed as the direct product of the time beam matrix, the frequency beam matrix, the vertical space beam matrix and the horizontal space beam matrix; the time beam matrix is ​​a matrix composed of time steering vectors under Doppler sampling; the frequency beam matrix is ​​a matrix composed of frequency steering vectors under delay sampling; the vertical space beam matrix is ​​a matrix composed of vertical space steering vectors under angle sampling; the horizontal space beam matrix is ​​a matrix composed of horizontal space steering vectors under angle sampling.

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