A short-time fractional fourier transform-based super-large array near-field space non-stationary channel estimation method and system

Abstract

The application discloses a short-time fractional Fourier transform-based super-large array near-field space non-stationary channel estimation method and system, belongs to the technical field of signal and information transmission, and solves the problem that existing technologies cannot accurately estimate channel parameters and have large pilot overhead when estimating a near-field space non-stationary channel. The application comprises pilot signal receiving and processing; according to a preset near-field coverage distance and an angle range, a range of a frequency modulation slope of an angular frequency is calculated, the range is uniformly sampled to obtain a frequency modulation slope set, and a fractional order rotation angle set is obtained through mapping; a short-time fractional inverse Fourier transform sub-codebook is constructed and integrated and arranged to obtain a total codebook; a sparse set and sparse coefficients of the near-field space non-stationary channel in a short-time fractional Fourier transform domain are iteratively estimated; and a near-field space non-stationary channel vector is reconstructed in combination with the total codebook. The application is suitable for a super-large array near-field space non-stationary channel estimation scene.

Description

Technical Field

[0001] This invention belongs to the field of signal and information transmission technology, specifically relating to a method for estimating near-field spatial non-stationary channels of ultra-large-scale arrays based on short-time fractional Fourier transform. Background Technology

[0002] As a core cornerstone of 5G mobile communication, Massive MIMO technology significantly enhances system capacity and coverage performance by deploying large-scale arrays at base stations and utilizing beamforming techniques. Moving towards the 6G era, to meet the stringent requirements of ultra-high data rate and spectral efficiency, Ultra-Large-Scale MIMO (XL-MIMO) has become a key evolutionary direction. Its antenna size is more than an order of magnitude larger than that of 5G, and combined with the physical characteristics of extremely short wavelengths in the millimeter-wave and terahertz bands, it makes it possible to integrate ultra-high-density array elements within a limited physical aperture.

[0003] However, the engineering implementation of XL-MIMO faces severe challenges. First, the extremely high hardware power consumption and cost of the high-frequency radio frequency chain (including power amplifiers, mixers, etc.) make large-scale deployment of all-digital precoding architectures difficult. Therefore, high-frequency XL-MIMO generally adopts a hybrid precoding architecture, aiming to drive a large antenna array with fewer radio frequency links. However, under this asymmetric observation condition, the base station cannot directly sense the signals of all array elements, resulting in extremely high pilot resource consumption for obtaining channel state information (CSI).

[0004] Secondly, the physical propagation environment has undergone a fundamental evolution. In 5G far-field communication, electromagnetic waves behave as plane waves, and the channel response is only related to the spatial angle. Therefore, efficient estimation can be achieved by utilizing the sparsity of the angle domain combined with compressed sensing algorithms. However, in XL-MIMO scenarios, the Rayleigh distance between the near and far-field boundaries in the electromagnetic radiation field increases dramatically with the square of the aperture, reaching the order of hundreds of meters. Users are highly likely to be in the near-field region. At this time, the wavefront exhibits obvious spherical wave characteristics, and the channel parameters exhibit a two-dimensional coupling of "angle-distance". This coupling causes the sparsity of the channel in the traditional angle domain to disappear, rendering traditional algorithms based on the far-field assumption ineffective.

[0005] Furthermore, XL-MIMO introduces new challenges related to spatial nonstationarity. Due to the enormous physical size of the array, the electromagnetic environment and scatterer sets observed by different array elements differ significantly, meaning that scatterers are only visible to specific local regions of the array. This combination of near-field effects and spatial nonstationarity severely degrades the performance of traditional channel estimation models.

[0006] To address the non-stationary characteristics of near-field channels, existing technologies have developed several near-field spatial non-stationary channel estimation schemes, including: designing the structure of the GTBC precoding matrix, estimating the near-field channel for each subarray using polar domain codebooks, and finally synthesizing the total near-field spatial non-stationary channel.

[0007] Channel stabilization is achieved by proposing subarray-level and scatterer-level channel estimation methods from the perspectives of subarrays and scatterers, respectively. The subarray-based method can obtain accurate channel estimation results with lower complexity, while the scatterer-based method can accurately locate the scatterer and identify almost all mapping relationships between subarrays and scatterers. By formulating channel estimation as a structured compressed sensing problem, a two-level polar domain orthogonal matching pursuit (OMP) algorithm is proposed to determine the channel quantization index and visible region (VR) to obtain the channel estimation result. By studying random access scenarios, joint activity detection and channel estimation are implemented through a bilinear Bayesian inference algorithm to capture sparse user activity and subarray activity.

[0008] Due to the non-stationarity of space and the characteristics of the near field, previous algorithms for far-field channel estimation and spatially stationary near-field channel estimation inevitably suffered from significant performance degradation. At the same time, the aforementioned schemes have drawbacks such as high computational complexity, poor interpretability, and room for improvement in channel estimation performance. Summary of the Invention

[0009] This invention provides a method and system for estimating near-field spatial non-stationary channels of ultra-large-scale arrays based on short-time fractional Fourier transform. The purpose is to solve the problems of existing technologies being unable to accurately estimate channel parameters and having large pilot overhead when estimating near-field spatial non-stationary channels.

[0010] Firstly, the purpose of this invention is to provide a method for estimating near-field spatial non-stationary channels of ultra-large-scale arrays based on short-time fractional Fourier transform, comprising the following steps:

[0011] S1. Receive pilot signals transmitted through a near-field spatial non-stationary channel, process the pilot signals, and obtain the baseband received signal;

[0012] S2. Based on the preset near-field coverage distance range and angle range, calculate the range of angular frequency modulation slope values ​​for the spatial non-stationary linear frequency modulation signal in the region, uniformly sample the range to obtain the set of modulation slopes, and map the corresponding set of fractional-order rotation angles.

[0013] S3. Divide the uniform linear array of the base station into multiple non-overlapping antenna subarrays. Use the size of the subarray as the window size and the position of the subarray as the window position. For each fractional rotation angle and each window position, construct a short-time fractional Fourier inverse transform subcodebook and integrate and arrange it to obtain the short-time fractional Fourier inverse transform total codebook.

[0014] S4. Using the short-time fractional Fourier inverse transform codebook as the sensing matrix, the block orthogonal matching pursuit algorithm is used to iteratively estimate the sparse set and sparse coefficients of the near-field spatial non-stationary channel in the short-time fractional Fourier transform domain.

[0015] S5. Based on the sparse set and sparse coefficients, and combined with the short-time fractional Fourier inverse transform codebook, the near-field spatial non-stationary channel vector is reconstructed, and the channel parameters are estimated simultaneously.

[0016] Furthermore, a preferred embodiment is provided: In S1, the baseband received signal is represented as:

[0017] ,

[0018] in, Represents a hybrid precoding matrix. For spatially non-stationary near-field channels, This is the noise vector.

[0019] Furthermore, a preferred embodiment is provided: In S2, the near-field coverage area is defined by the radial distance and azimuth angle between the user terminal and the base station array, wherein the range of the radial distance is denoted as... azimuth The range of values ​​is ,in, This represents the minimum distance that can be covered in the near-field region. This represents the maximum distance that the near-field region can cover. The smallest angle that can be covered by the near-field region. This represents the maximum angle that the near-field region can cover.

[0020] Furthermore, a preferred embodiment is provided: in step S2, the number of samples for uniformly sampling the range of angular frequency modulation slope values ​​is: The sampling interval is The resulting set of angular frequency modulation slopes is:

[0021] .

[0022] Furthermore, a preferred solution is provided: in S3,

[0023] The antenna array is divided into There are several antenna subarrays, and the size of each antenna subarray is... ,in This represents the number of antenna array elements.

[0024] Furthermore, a preferred embodiment is provided: S3 includes:

[0025] S3.1: Divide the ultra-large-scale uniform linear array of the base station into multiple non-overlapping antenna subarrays to obtain the number of antenna subarrays and the number of array elements in each antenna subarray;

[0026] S3.2: For a single fractional rotation angle and a single window position, construct a short-time fractional Fourier inverse transform subcodebook corresponding to the window position and the corresponding fractional rotation angle; wherein, the window size is consistent with the number of elements of the antenna subarray, and the window position corresponds one-to-one with the position of the antenna subarray;

[0027] S3.3: Combine the subcodebooks corresponding to all window positions under the same fractional rotation angle to obtain the single-angle codebook corresponding to that fractional rotation angle;

[0028] S3.4: Concatenate the single-angle codebooks corresponding to all fractional-order rotation angles to obtain the total short-time fractional-order inverse Fourier transform codebook.

[0029] Furthermore, a preferred embodiment is provided: S3.2 includes:

[0030] S3.2.1: Construct the first intermediate matrix based on the antenna array element spacing, window size, and window position;

[0031] S3.2.2: Construct the second intermediate matrix based on the fractional rotation angle, oversampling factor, and number of array elements;

[0032] S3.2.3: Construct a mask matrix based on the value interval corresponding to the window position;

[0033] S3.2.4: Based on the first intermediate matrix, the second intermediate matrix and the mask matrix, calculate the short-time fractional Fourier inverse transform subcodebook at the corresponding window position and the corresponding fractional rotation angle.

[0034] Secondly, the purpose of this invention is to propose a near-field spatial non-stationary channel estimation system for ultra-large-scale arrays based on short-time fractional Fourier transform. This system is implemented based on the near-field spatial non-stationary channel estimation method for ultra-large-scale arrays based on short-time fractional Fourier transform as described in any one of claims 1-7. The system comprises:

[0035] Signal receiving module: used to receive pilot signals transmitted through near-field non-stationary channels, process the pilot signals, and obtain baseband received signals;

[0036] Angle Calculation Module: Based on the preset near-field coverage distance range and angle range, it calculates the range of angular frequency modulation slope values ​​for spatial non-stationary linear frequency modulation signals within the area, performs uniform sampling on this range to obtain a set of modulation slope values, and maps them to obtain the corresponding set of fractional-order rotation angles.

[0037] Codebook integration module: It is used to divide the uniform linear array of the base station into multiple non-overlapping antenna subarrays. The size of the subarray is used as the window size and the position of the subarray is used as the window position. For each fractional rotation angle and each window position, a short-time fractional Fourier inverse transform subcodebook is constructed and integrated to obtain the short-time fractional Fourier inverse transform total codebook.

[0038] Coefficient estimation module: Used to iteratively estimate the sparse set and sparse coefficients of the near-field spatial non-stationary channel in the short-time fractional Fourier transform domain using the short-time fractional Fourier transform total codebook as the sensing matrix and the block orthogonal matching pursuit algorithm.

[0039] Channel reconstruction module: used to reconstruct the near-field spatial non-stationary channel vector based on the sparse set and sparse coefficients, combined with the short-time fractional Fourier inverse codebook, and simultaneously estimate the channel parameters.

[0040] Thirdly, the present invention aims to provide a computer device, the computer device including a memory and a processor, the memory storing a computer program, and when the processor runs the computer program stored in the memory, the processor executes a method for estimating near-field spatial non-stationary channels of a very large-scale array based on short-time fractional Fourier transform according to any one or more of the above-described schemes.

[0041] Fourthly, the present invention aims to provide a computer-readable storage medium for storing a computer program that executes a method for estimating near-field spatial non-stationary channels of a very large-scale array based on short-time fractional Fourier transform, as described in any one or more of the above-described schemes.

[0042] Compared with the prior art, the advantages of the present invention are:

[0043] Traditional channel estimation methods based on the plane wave assumption exhibit significant angle-range coupling and spatial non-stationarity in near-field scenarios with ultra-large-scale arrays due to the spherical wavefront effect, making it impossible for traditional methods to achieve sparse channel representation. This invention constructs a codebook adapted to the characteristics of linear frequency modulated (LFM) signals using short-time fractional Fourier transform (STFRFT), achieving a block-like sparse representation of the near-field channel in the STFRFT domain. This overcomes the limitations of traditional methods in modeling near-field spatially non-stationary channels and significantly improves the accuracy of channel estimation.

[0044] The method proposed in this invention combines a block-based orthogonal matching pursuit algorithm, significantly reducing algorithm complexity and improving estimation efficiency. Addressing the block-based sparsity of the STFRFT codebook, this invention employs a block-based orthogonal matching pursuit algorithm, performing iterative solutions on a subarray basis. This avoids the high complexity of the traditional OMP algorithm's atom-by-atom search. Simultaneously, by utilizing the block structure of the STFRFT codebook, the number of iterations and computational load are significantly reduced. While maintaining estimation accuracy, this significantly reduces the computational overhead on the base station side, adapting to the real-time processing requirements of large-scale arrays.

[0045] This invention is applicable to near-field spatial non-stationary channel estimation scenarios for ultra-large-scale arrays. Attached Figure Description

[0046] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0047] Figure 1 This is a schematic diagram of a channel estimation model under a hybrid precoding architecture.

[0048] Figure 2 A schematic diagram of a near-field spatial non-stationary channel model with two multipath paths;

[0049] Figure 3 A schematic diagram of a spatially non-stationary linear frequency modulated signal and its short-time fractional Fourier transform;

[0050] Figure 4 The graph shows the optimal angle results of the short-time fractional Fourier transform of a spatially non-stationary linear frequency modulated signal under different windows.

[0051] Figure 5 The graph shows the non-optimal angle results of the short-time fractional Fourier transform of a spatially non-stationary linear frequency modulated signal under different windows.

[0052] Figure 6 The flowchart shows the near-field spatial non-stationary channel estimation algorithm based on the short-time fractional Fourier transform domain.

[0053] Figure 7 A performance comparison chart of different channel estimation algorithms at different distances;

[0054] Figure 8 A performance comparison chart of different channel estimation algorithms under different signal-to-noise ratios;

[0055] Figure 9A performance comparison chart of different channel estimation algorithms under different pilot overheads;

[0056] Figure 10 This figure illustrates the impact of different lower pilot overheads on the channel estimation performance of different algorithms. Detailed Implementation

[0057] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application can also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of this application with unnecessary detail.

[0058] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0059] Many specific details are set forth in the following description in order to provide a full understanding of this application. However, this application may also be implemented in other ways different from those described herein. Those skilled in the art can make similar extensions without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0060] Implementation Method 1

[0061] System model and principle derivation:

[0062] This invention applies to a very large-scale array antenna system based on uplink time-division duplexing. The system's base station (BS) employs a hybrid precoding architecture and is equipped with... One radio frequency chain and A uniform linear array composed of antennas, wherein Antenna element spacing ,in For carrier wavelength. BS service Single-antenna users, of which For uplink channel estimation, it is assumed that... Each user sends mutually orthogonal pilot sequences to the BS, meaning that the channel estimation for each user is independent. Therefore, channel estimation for any user can be considered.

[0063] Assume the user exists in the BS. The first transmission path, recorded as the first path to the first The distance between the antennas is ,in The index is the antenna index, and the index corresponding to the center of the antenna array is... .like Figure 1 As shown, a Cartesian coordinate system is established with the center of the antenna array as the origin, the antenna index direction as the y-axis, and the x-axis perpendicular to the antenna index direction through the origin. Let be the coordinate system. and The included angle of the axis is .make For the user baseband transmit signal, its corresponding passband transmit signal is: ,in For signal carrier frequency, This indicates taking the real part of the signal. It is the speed of light.

[0064] Due to the linear time-invariant channel and normalization, its users reach the BS level. The channel time-domain impulse response of the root antenna is:

[0065] , (1)

[0066] In the formula, For the first Path gain, For the first The path signal reaches BS number The propagation delay of the root antenna, i.e.

[0067] (2)

[0068] According to antenna theory, under near-field conditions, there is... Combined with Taylor expansion , for example Performing a Taylor expansion and retaining the second-order terms, we have:

[0069] , (3)

[0070] Therefore, on the BS end... The root antenna receives data from the first... The noiseless passband signal of the path is:

[0071] , (4)

[0072] If the passband signal is converted to baseband for processing, then:

[0073] , (5)

[0074] Consider a narrowband array antenna, which satisfies:

[0075] , (6)

[0076] in, For signal bandwidth, The maximum aperture transit time is defined as:

[0077] , (7)

[0078] in, Let be the array length. Under this assumption, it is known that the envelope of the signal received across the entire array is almost identical. Therefore, we have: .

[0079] So, the formula Substituting into equation (4), we get:

[0080] , (8)

[0081] Pilot design can enable Then there is

[0082] , (9)

[0083] In non-stationary spatial scenarios, since not all array elements on an antenna can necessarily observe a certain path component, for ease of analysis, let's denote the total number of antennas receiving data from the first antenna along the antenna index direction. The signal vector formed by the signals from the paths is:

[0084] , (10)

[0085] The second part on the right-hand side of the above equation is written as Represents the mask vector, where is The element represents the corresponding array element that can observe the first... The path is 0, and the element with a value of 0 indicates that the corresponding array element cannot observe the path. There are several paths. Among them, Represents a visibility mask, used to select the first... Which antennas are visible for this path? It is the first The index value of the visible antenna along the path.

[0086] In particular, The Each element is defined as:

[0087] , (11)

[0088] Furthermore, considering the noise, the total received signal can be obtained as:

[0089] , (12)

[0090] In the formula, Let the noise vector be denoted as:

[0091] (13)

[0092] in, This indicates that the equivalent baseband value has a mean of 0 and a variance of . Gaussian white noise.

[0093] Furthermore, let:

[0094] , (14)

[0095] And record The array near-field steering vector can be written as:

[0096] (15)

[0097] remember The continuous variable corresponding to the array spatial domain can be seen from equation (15) as the near-field steering vector. It can be viewed as a continuous linear frequency modulated signal in the spatial domain, and can be written as:

[0098] , (16)

[0099] Furthermore, equation (12) can be written as:

[0100] , (17)

[0101] Furthermore, It can be seen as The linear combination of a linear frequency modulated signal with several windows and the superposition of the noise signal, and the first term on the right side of the equal sign in equation (17) is the near-field spatial non-stationary channel vector that needs to be estimated. ,Right now:

[0102] , (18)

[0103] Therefore, we can conclude that:

[0104] , (19)

[0105] Although a certain path is visible to some array elements, in practical applications, the system cannot know in advance the specific index of the visible array elements corresponding to a certain path. In addition, due to the characteristics of scattering, the visible array elements of a certain path are often continuous, that is, the visible array elements are distributed in a regional manner.

[0106] Figure 2 shows that when there are obstructions, both paths are partially visible, and these visible areas are continuous and exist as regions.

[0107] Existing spatial non-stationary channel estimation methods often use the method of dividing the visible subarray to model the spatial non-stationary channel. .

[0108] Consider dividing the very large-scale array into A small subarray, assuming It is an integer. (Set) Used to collect information for the first A path-visible subarray, namely:

[0109] , (20)

[0110] in, Represents the index of the subarray, and .

[0111] Furthermore, equation (11) can be written as:

[0112] , (twenty one)

[0113] Therefore, at any moment At this point, the received signal after hybrid precoding is:

[0114] , (twenty two)

[0115] in, Indicates in A hybrid precoding matrix that satisfies the constant-modulus constraint at all times, where each element... Independent and randomly selected with equal probability from Select from the options. Set the pilot length to... ,and .go through After a certain time, the total received signal is recorded as follows: Then we have:

[0116] , (twenty three)

[0117] in, The vector is Gaussian white noise. express The overall hybrid precoding matrix at each time step, and its elements are mutually independent.

[0118] Due to the number of BS antennas Very large, receives signals dimension Typically much lower This makes it possible to... estimate It is challenging.

[0119] Since a non-stationary channel in the near field can be viewed as a superposition of multiple linear frequency modulated signals with several windows, it exhibits block sparse characteristics in the short-time fractional Fourier transform domain. Therefore, the short-time fractional Fourier transform is an advantageous tool for studying non-stationary scenarios in the near field.

[0120] From equations (16) and (18), it can be seen that the near-field spatial non-stationary channel vector It can be regarded as The result is a linearly superimposed linearly modulated (LFM) signal with several windows applied consecutively in the spatial domain, sampled in a uniform spatial domain. Considering that the windowed LFM signal is a basis function of the short-time fractional Fourier transform (SFT), the SFT is a natural tool for analyzing windowed LFM signals. This paper aims to realize a spatially non-stationary channel from the SFT domain. Accurate estimation requires further analysis of the characteristics of spatially continuous windowed linear frequency modulated signals in the short-time fractional Fourier transform domain. Therefore, it is necessary to introduce the definition of the short-time fractional Fourier transform.

[0121] Any signal with finite energy For a given window function Its short-time fractional Fourier transform can be defined as:

[0122] , (twenty four)

[0123] in, For signal The short-time fractional Fourier transform, This is the shift bias for the window function. fractional rotation angle The fractional angular frequency. Two continuous signals and Fractional convolution is defined as:

[0124] , (25)

[0125] The fractional convolution in equation (25) can be written as a conventional convolution:

[0126] , (26)

[0127] Substituting equation (25) into equation (24) yields:

[0128] , (27)

[0129] in for:

[0130] , (28)

[0131] Figure 3 illustrates the short-time fractional Fourier transform (SFT) of a spatially non-stationary linear frequency modulated (LFM) signal at its optimal angle and at non-optimal angles. It can be observed that the SFT clearly identifies the fractional frequencies of each component of the LFM signal. Figures 4 and 5 show the results of the SFT at different window positions for this LFM signal at the optimal angle. It can be seen that if the LFM signal is a superposition of multiple LFM signals within a certain window, then multiple [signals] will be obtained within that window. The peak value of the function. At non-optimal angles, multiple Fresnel integrals of the spatially non-stationary linear frequency modulated signal are obtained. Therefore, it can be verified that the near-field spatially non-stationary channel exhibits block sparse characteristics in the short-time fractional Fourier transform domain.

[0132] Depend on Figure 4 and Figure 5 It can be seen that for any linear frequency modulated signal with a window in the spatial domain, there exists a codebook for the short-time fractional Fourier inverse transform at various angles and at various window positions. ,in, This is the window's position index. (When the codebook...) When the codebook is at the optimal angle and corresponding window position, there will be optimal energy concentration. Equation (27) shows that the optimal fractional-order rotation angle for a windowed linear frequency modulated signal is... ,in Let be the angular frequency modulation slope of the linear frequency modulated (LFM) signal. However, regardless of whether it's at the optimal or non-optimal angle in the short-time fractional domain, the spatially windowed LFM signal exhibits a blocky characteristic, meaning its main energy is distributed within a finite interval of the short-time fractional domain. Therefore, any spatially windowed LFM signal exhibits block sparsity in the short-time fractional Fourier inverse transform domain. Furthermore, according to the fractional energy uncertainty principle, the bandwidth of the signal in any two fractional Fourier transform domains with different fractional rotation angles cannot be simultaneously sufficiently small. There exists a fractional rotation angle, the optimal fractional rotation angle, where the signal energy is optimally concentrated in a minimal interval within the fractional Fourier transform domain at this rotation angle.

[0133] Therefore, for any windowed linear frequency modulated signal corresponding to a path, the block sparsity characteristic it exhibits in the short-time fractional Fourier transform domain can be utilized to construct the corresponding short-time fractional Fourier inverse transform codebook. Then, based on the coefficient energy of the codewords in a block of a certain size, the minimum interval can be extracted, thereby extracting the basis vectors of the path channel under the short-time fractional Fourier transform. Finally, the near-field spatial non-stationary channel vector can be reconstructed through these basis vectors.

[0134] Based on the above analysis, a short-time fractional-order inverse Fourier transform codebook containing multiple fractional-order rotation angles and multiple window positions needs to be constructed. First, the range of the near-field region needs to be calculated, denoted as […]. , ,in, This represents the minimum distance that can be covered in the near-field region. This represents the maximum distance that the near-field region can cover. The smallest angle that can be covered by the near-field region. This represents the maximum angle that the near-field region can cover.

[0135] Subsequently, the range of angular frequency modulation slopes that can be obtained in this near-field region is calculated, i.e. And the angular frequency modulation slope range should be uniformly sampled, where , .

[0136] The set is obtained by uniformly sampling the angular frequency modulation slope:

[0137] , (29)

[0138] In the formula, The number of samples for the angular frequency modulation slope, and the sampling interval. for .

[0139] The set of angular frequency modulation slopes in equation (29) can be used to obtain the set of fractional rotation angles. :

[0140] , (30)

[0141] Subsequently, a codebook for the inverse short-time fractional Fourier transform at any angle is constructed. The construction process can be referenced from the following discrete short-time fractional Fourier transform:

[0142] (31)

[0143] In the formula, For discrete time (in near-field spatial non-stationary channel estimation), Also serves as an index for antenna array elements. For discrete fractional angular frequencies, For discrete window size, The number of sampling points at the fractional-order angular frequency. For oversampling factor, For window position index, The sampling time is [time]. The synthesis window function is [function name]. If and only if:

[0144] (32)

[0145] Equation (31) holds true.

[0146] In near-field spatial non-stationary channel estimation, the near-field channel model is used. Channel parameters are estimated by exhibiting block sparse characteristics in the short-time fractional Fourier transform domain.

[0147] The window is set to a rectangular window, and the window function... The window size is The window's movement step size is set to This means there is no overlapping area between windows. The size of the window is the same as the size of the subarray, and the number of windows is the same as the number of subarrays. .

[0148] Therefore, the window function is defined as:

[0149] , (33)

[0150] Furthermore, the time-domain sampling interval in equation (31) , The distance between array elements.

[0151] Since the number of windows is the same as the number of subarrays, equation (31) can be further written as:

[0152] (34)

[0153] The synthesis window function can be obtained from equation (32). :

[0154] , (35)

[0155] When constructing the codebook for the short-time fractional Fourier inverse transform, the position of the synthesis window is first fixed. Without loss of generality, let the window position index be . At this time, the range of values ​​in the window is , recorded as Obviously, the window corresponds to The range of values ​​is also .

[0156] make Defined as:

[0157] , (36)

[0158] in, This indicates that the vector is diagonalized. Defined as:

[0159] , (37)

[0160] make Defined as:

[0161] , (38)

[0162] in Defined as:

[0163] , (39)

[0164] By the The mask matrix can be determined from the value range of each window. :

[0165] , (40)

[0166] in, Let be a mask vector, and its index range is... Its index is The element is defined as:

[0167] , (41)

[0168] Therefore, we can obtain the first... The codebook for a window function is:

[0169] , (42)

[0170] Since there are a total of [number] under each fractional rotation angle Each window (subarray) can then be used to obtain the single fractional rotation angle. The short-time fractional Fourier inverse codebook for:

[0171] , (43)

[0172] The short-time fractional Fourier inverse codebooks under multiple fractional rotation angles are integrated and arranged into a total short-time fractional Fourier inverse codebook, thus obtaining the final codebook. for:

[0173] , (44)

[0174] Because of the hybrid precoding matrix It follows a Bernoulli distribution, therefore As discussed earlier, near-field spatially non-stationary channels exhibit block sparsity in the short-time fractional Fourier transform domain, namely:

[0175] , (45)

[0176] in, Given a block sparse vector, equation (23) can be written as:

[0177] , (46)

[0178] In the formula, .

[0179] because It is sparse, so the block orthogonal matching pursuit algorithm can be used to estimate... To obtain the estimated value This leads to an estimate of the spatially non-stationary channel:

[0180] (47)

[0181] Implementation Method 2

[0182] Reference Figure 6 This implementation method is described below.

[0183] Based on the principle described in Implementation Method 1, this implementation method proposes a near-field spatial non-stationary channel estimation method for ultra-large-scale arrays based on short-time fractional Fourier transform, including the following steps:

[0184] S1. Receive pilot signals transmitted through a near-field spatial non-stationary channel, process the pilot signals, and obtain the baseband received signal;

[0185] The baseband received signal is represented as follows:

[0186] , (48)

[0187] in, Represents a hybrid precoding matrix. For spatially non-stationary near-field channels, This is the noise vector.

[0188] S2. Based on the preset near-field coverage distance range and angle range, calculate the range of angular frequency modulation slope values ​​for the spatial non-stationary linear frequency modulation signal in the region, uniformly sample the range to obtain the set of modulation slopes, and map the corresponding set of fractional-order rotation angles.

[0189] The near-field coverage area is defined by the radial distance and azimuth angle between the user terminal and the base station array, wherein the range of the radial distance is denoted as... azimuth The range of values ​​is ,in, This represents the minimum distance that can be covered in the near-field region. This represents the maximum distance that the near-field region can cover. The smallest angle that can be covered by the near-field region. This represents the maximum angle that the near-field region can cover.

[0190] The range of angular frequency modulation slopes of spatially non-stationary linear frequency modulated signals that can be obtained in this region is denoted as... Specifically:

[0191] (49)

[0192] The set of frequency modulation slopes obtained by uniform sampling is represented as:

[0193] , (50)

[0194] in, The number of samples for the angular frequency modulation slope, and the sampling interval. for .

[0195] S3. Divide the uniform linear array of the base station into multiple non-overlapping antenna subarrays. Use the size of the subarray as the window size and the position of the subarray as the window position. For each fractional rotation angle and each window position, construct a short-time fractional Fourier inverse transform subcodebook and integrate and arrange it to obtain the short-time fractional Fourier inverse transform total codebook.

[0196] Furthermore, based on the set of angular frequency modulation slopes obtained in S2, this step calculates the corresponding set of fractional rotation angles, expressed as:

[0197] (51)

[0198] The construction steps of the short-time fractional Fourier inverse codebook include:

[0199] S3.1: Divide the antenna array into multiple antenna subarrays, the number of which is... The size of the antenna subarray is ,in The number of antenna array elements;

[0200] S3.2: Construct a fractional rotation angle Next window position Short-time fractional-order inverse Fourier transform codebook ;

[0201] S3.3: Combination fractional rotation angle The fractional-order rotation angle is obtained by using the short-time fractional-order inverse Fourier transform subcodebook for all window positions. Short-time fractional Fourier inverse transform codebook ;

[0202] S3.4: Integrate and arrange the short-time fractional-order inverse Fourier transform codebooks for all fractional-order rotation angles into a total short-time fractional-order inverse Fourier transform codebook. .

[0203] Furthermore, S3.2 includes:

[0204] S3.2.1: Constructing the intermediate matrix Defined as:

[0205] , (52)

[0206] in, This indicates that the vector is diagonalized. Defined as:

[0207] , (53)

[0208] In the formula, The spacing between antenna elements. The window size is equal to the size of the antenna subarray, i.e. , For the window position index of the short-time fractional Fourier transform, the first... Each window position has a value range of... , recorded as ;

[0209] S3.2.2: Constructing the intermediate matrix Defined as:

[0210] , (54)

[0211] in, For oversampling factor, Defined as:

[0212] , (55)

[0213] S3.2.3: Constructing the intermediate matrix Defined as:

[0214] , (56)

[0215] in, The mask vector has an index range of 1. Its index is The element is defined as:

[0216] , (57)

[0217] S3.2.4: Calculate a fractional rotation angle Next window position Short-time fractional-order inverse Fourier transform codebook Specifically:

[0218] (58)

[0219] Furthermore, the fractional rotation angle obtained in S3.3 Short-time fractional Fourier inverse transform codebook Represented as:

[0220] (59)

[0221] Furthermore, S3.4 integrates and arranges the short-time fractional-order inverse Fourier transform codebooks under all fractional-order rotation angles to obtain the total short-time fractional-order inverse Fourier transform codebook. Recorded as:

[0222] (60)

[0223] S4. Using the short-time fractional Fourier transform total codebook as the sensing matrix, the block orthogonal matching pursuit algorithm is employed to iteratively estimate the sparse set of the near-field spatial non-stationary channel in the short-time fractional Fourier transform domain. With sparsity coefficient;

[0224] S5. Based on the sparse set and sparse coefficients, and combined with the short-time fractional Fourier inverse transform codebook, the near-field spatial non-stationary channel vector is reconstructed, and the channel parameters are estimated simultaneously, as follows:

[0225] (61)

[0226] Specifically, the method flow described in this embodiment is as follows:

[0227] Input: Received signal Overall hybrid precoding matrix Block size , the number of multipaths Short-time fractional-order inverse Fourier transform codebook Number of subarrays Number of sub-array elements .

[0228] Output: Near-field channel estimate .

[0229] Initialization: Calculate the perception matrix For the perception matrix Normalize each column; sparse support set residual ;

[0230] Divided by column The size of the block is That is, each block contains of Adjacent columns. Furthermore, the matrix... Classified as Each block, that is The support sets corresponding to these blocks are ;

[0231] when Execute the following loop:

[0232] Step 1: Calculate the correlation vector and detect the new support set. ;

[0233] Step 2: Update the support set ;

[0234] Step 3: Compute on the support set by minimizing the optimization problem. coefficients on ;

[0235] Step 4: Update residuals ;

[0236] End the loop.

[0237] Calculate the estimation results of the near-field channel. ,

[0238] return .

[0239] Implementation Method 3

[0240] This embodiment simulates a near-field spatial non-stationary channel estimation method for ultra-large-scale arrays based on short-time fractional Fourier transform as described in Embodiment 2. The simulation parameters are shown in Table 1.

[0241] Table 1 Simulation parameter settings

[0242] carrier frequency Number of radio frequency chains Oversampling factor Number of antennas Number of user multipaths parameter parameter block size Number of visible area divisions

[0243] Figure 7 shows the performance comparison of the proposed near-field spatial non-stationary channel estimation method based on short-time fractional Fourier transform (STFRFT-BOMP) with the least squares channel estimation method (LS), the far-field network channel estimation algorithm (SWOMP), the polar domain-based channel estimation method (P-SOMP), the polar domain-based block time coding channel estimation algorithm (GP-SOMP), the fractional Fourier transform-based sparse domain channel estimation method (FRFT-BOMP), and the fractional Fourier transform-based block time coding channel estimation algorithm (GFRFT-BOMP) at different distances using normalized mean square error (NMSE).

[0244] Wherein, the pilot overhead ratio is set to Signal-to-noise ratio set to For polar-domain methods, existing technologies have proposed a near-field spatial non-stationary channel estimation method based on polar domain. The idea is to construct a specific hybrid precoding matrix, then use received pilots in different time slots to separate the channel for each subarray, and then apply the polar-domain-based near-field channel estimation method to each subarray channel. Finally, the estimated channels of multiple subarrays are synthesized to obtain the spatial non-stationary channel estimation result. This method is called GP-SOMP. Applying this idea to the fractional Fourier transform domain yields GFRFT-BOMP. As shown in Figure 7, it is easy to see that the proposed spatial non-stationary channel estimation performance of the ultra-large-scale array near-field spatial non-stationary channel estimation method based on short-time fractional Fourier transform is significantly improved compared to GP-SOMP and GFRFT-BOMP. Furthermore, since STFRFT does not require complex GTBC encoding and decoding and has no special requirements for the hybrid precoding matrix, it effectively improves the applicability of the algorithm and reduces the pilot overhead of channel estimation.

[0245] Figure 8 shows a comparison of the normalized mean square error performance of the proposed near-field spatial non-stationary channel estimation method for ultra-large-scale arrays based on short-time fractional Fourier transform (STFRFT-BOMP) with the least squares channel estimation method (LS), the far-field network channel estimation algorithm (SWOMP), the polar domain-based channel estimation method (P-SOMP), the polar domain-based block-time coding channel estimation algorithm (GP-SOMP), the fractional Fourier transform-based sparse domain-block channel estimation method (FRFT-BOMP), and the fractional Fourier transform-based block-time coding channel estimation algorithm (GFRFT-BOMP) under different signal-to-noise ratios (SNR).

[0246] Wherein, the pilot overhead ratio is set to ,distance exist Random selection is performed within the range. It is not difficult to observe that, under near-field spatial non-stationary channel conditions, the channel estimation performance of the proposed method for near-field spatial non-stationary channel estimation of ultra-large-scale arrays based on short-time fractional Fourier transform is superior to several other near-field channel estimation methods.

[0247] Figure 9 shows the performance comparison of the proposed near-field spatial non-stationary channel estimation method based on short-time fractional Fourier transform (STFRFT-BOMP) with the least squares channel estimation method (LS), the far-field network channel estimation algorithm (SWOMP), the polar domain-based channel estimation method (P-SOMP), the polar domain-based block time coding channel estimation algorithm (GP-SOMP), the fractional Fourier transform-based sparse domain channel estimation method (FRFT-BOMP), and the fractional Fourier transform-based block time coding channel estimation algorithm (GFRFT-BOMP) under different pilot overhead ratios.

[0248] Where parameters exist Random selection within, signal-to-noise ratio set to The proposed method for spatial near-field non-stationary channel estimation of ultra-large-scale arrays based on short-time fractional Fourier transform has superior channel estimation performance compared to other near-field channel estimation methods.

[0249] Figure 10 shows the proposed methods for estimating near-field spatial non-stationary channels for very large-scale arrays based on short-time fractional Fourier transform (STFRFT-BOMP), channel estimation algorithm based on polar domain block time-block coding (GP-SOMP), and block time-block coding channel estimation algorithm based on fractional Fourier transform (GFRFT-BOMP) with different numbers of partitions in different visible regions. Comparison of Normalized Mean Square Error (NMSE) performance under different pilot overhead ratios in the channel.

[0250] Where parameters exist Random selection within, pilot overhead ratio set to Signal-to-noise ratio set to The channel estimation performance of the proposed method for spatial near-field non-stationary channel estimation of ultra-large-scale arrays based on short-time fractional Fourier transform is satisfactory under different conditions. The performance of the above methods is superior to several other near-field channel estimation methods. Furthermore, it was found that the performance of the same algorithm improves with increasing performance. It decreases as it increases.

[0251] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A method for estimating near-field spatial non-stationary channel based on short-time fractional Fourier transform for ultra-massive array, characterized in that, Includes the following steps: S1. Receive pilot signals transmitted through a near-field spatial non-stationary channel, process the pilot signals, and obtain the baseband received signal; S2. Based on the preset near-field coverage distance range and angle range, calculate the range of angular frequency modulation slope values ​​for the spatial non-stationary linear frequency modulation signal in the region, uniformly sample the range to obtain the set of modulation slopes, and map the corresponding set of fractional-order rotation angles. S3. Divide the uniform linear array of the base station into multiple non-overlapping antenna subarrays. Use the size of the subarray as the window size and the position of the subarray as the window position. For each fractional rotation angle and each window position, construct a short-time fractional Fourier inverse transform subcodebook and integrate and arrange it to obtain the short-time fractional Fourier inverse transform total codebook. S4. Using the short-time fractional Fourier inverse transform codebook as the sensing matrix, the block orthogonal matching pursuit algorithm is used to iteratively estimate the sparse set and sparse coefficients of the near-field spatial non-stationary channel in the short-time fractional Fourier transform domain. S5. Based on the sparse set and sparse coefficients, and combined with the short-time fractional Fourier inverse transform codebook, the near-field spatial non-stationary channel vector is reconstructed, and the channel parameters are estimated simultaneously.

2. The method for estimating near-field spatial non-stationary channels of ultra-large-scale arrays based on short-time fractional Fourier transform according to claim 1, characterized in that, In S1, the baseband received signal is represented as follows: ， in, Represents a hybrid precoding matrix. For spatially non-stationary near-field channels, This is the noise vector.

3. The method for estimating near-field spatial non-stationary channels of ultra-large-scale arrays based on short-time fractional Fourier transform according to claim 1, characterized in that, In S2, the near-field coverage area is defined by the radial distance and azimuth angle between the user terminal and the base station array, wherein the range of the radial distance is denoted as... azimuth The range of values ​​is ,in, This represents the minimum distance that can be covered in the near-field region. This represents the maximum distance that the near-field region can cover. The smallest angle that can be covered by the near-field region. This represents the maximum angle that the near-field region can cover.

4. The method for estimating near-field spatial non-stationary channels of ultra-large-scale arrays based on short-time fractional Fourier transform according to claim 1, characterized in that, In step S2, the number of samples for uniformly sampling the range of angular frequency modulation slope values ​​is: The sampling interval is The resulting set of angular frequency modulation slopes is: 。 5. The method for estimating near-field spatial non-stationary channels of a very large-scale array based on short-time fractional Fourier transform according to claim 1, characterized in that, In S3, The antenna array is divided into There are several antenna subarrays, and the size of each antenna subarray is... ,in This represents the number of antenna array elements.

6. The method for estimating near-field spatial non-stationary channels of ultra-large-scale arrays based on short-time fractional Fourier transform according to claim 1, characterized in that, S3 includes: S3.1: Divide the ultra-large-scale uniform linear array of the base station into multiple non-overlapping antenna subarrays to obtain the number of antenna subarrays and the number of array elements in each antenna subarray; S3.2: For a single fractional rotation angle and a single window position, construct a short-time fractional Fourier inverse transform subcodebook corresponding to the window position and the corresponding fractional rotation angle; wherein, the window size is consistent with the number of elements of the antenna subarray, and the window position corresponds one-to-one with the position of the antenna subarray; S3.3: Combine the subcodebooks corresponding to all window positions under the same fractional rotation angle to obtain the single-angle codebook corresponding to that fractional rotation angle; S3.4: Concatenate the single-angle codebooks corresponding to all fractional-order rotation angles to obtain the total short-time fractional-order inverse Fourier transform codebook.

7. The method for estimating near-field spatial non-stationary channels of ultra-large-scale arrays based on short-time fractional Fourier transform according to claim 6, characterized in that, S3.2 includes: S3.2.1: Construct the first intermediate matrix based on the antenna array element spacing, window size, and window position; S3.2.2: Construct the second intermediate matrix based on the fractional rotation angle, oversampling factor, and number of array elements; S3.2.3: Construct a mask matrix based on the value interval corresponding to the window position; S3.2.4: Based on the first intermediate matrix, the second intermediate matrix and the mask matrix, calculate the short-time fractional Fourier inverse transform subcodebook at the corresponding window position and the corresponding fractional rotation angle.

8. A near-field spatial non-stationary channel estimation system for ultra-large-scale arrays based on short-time fractional Fourier transform, characterized in that, The system is implemented based on a near-field spatial non-stationary channel estimation method for ultra-large-scale arrays based on short-time fractional Fourier transform as described in any one of claims 1-7. The system includes: Signal receiving module: used to receive pilot signals transmitted through near-field non-stationary channels, process the pilot signals, and obtain baseband received signals; Angle Calculation Module: Based on the preset near-field coverage distance range and angle range, it calculates the range of angular frequency modulation slope values ​​for spatial non-stationary linear frequency modulation signals within the area, performs uniform sampling on this range to obtain a set of modulation slope values, and maps them to obtain the corresponding set of fractional-order rotation angles. Codebook integration module: It is used to divide the uniform linear array of the base station into multiple non-overlapping antenna subarrays. The size of the subarray is used as the window size and the position of the subarray is used as the window position. For each fractional rotation angle and each window position, a short-time fractional Fourier inverse transform subcodebook is constructed and integrated to obtain the short-time fractional Fourier inverse transform total codebook. Coefficient estimation module: Used to iteratively estimate the sparse set and sparse coefficients of the near-field spatial non-stationary channel in the short-time fractional Fourier transform domain using the short-time fractional Fourier transform total codebook as the sensing matrix and the block orthogonal matching pursuit algorithm. Channel reconstruction module: used to reconstruct the near-field spatial non-stationary channel vector based on the sparse set and sparse coefficients, combined with the short-time fractional Fourier inverse codebook, and simultaneously estimate the channel parameters.

9. A computer device, characterized in that, The computer device includes a memory and a processor. The memory stores a computer program. When the processor runs the computer program stored in the memory, the processor executes a method for estimating near-field spatial non-stationary channels of a very large-scale array based on short-time fractional Fourier transform according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium is used to store a computer program that executes a method for estimating near-field spatial non-stationary channels of a very large-scale array based on short-time fractional Fourier transform, as described in any one of claims 1-7.

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