A Channel Estimation Method for a Multi-User Uplink Low Earth Orbit Satellite Wireless Communication System

Abstract

The present invention provides a channel estimation method for a multi-user uplink low-earth orbit satellite wireless communication system. This method is aimed at the fast-moving scenario of low-earth orbit satellites, adopts the OTFS modulation technology for signal transmission, and proposes a low-complexity uplink channel estimation method that jointly estimates the number of paths, delay, Doppler, and channel fading. The steps of this method are as follows: First, design different pilot symbol grid positions for multiple users in the delay-Doppler domain; then, perform energy threshold detection on all delay domains of the received signal by the low-earth orbit satellite to estimate the total number of paths and the delay value of each path; then, use the maximum likelihood estimation method to give a closed-form expression for channel fading, and adopt a one-dimensional search method to estimate the Doppler frequency shift. Through simulation verification, the proposed uplink joint channel estimation method can effectively achieve channel detection and can be further applied to the derivation of the ergodic capacity, with good practicability and performance.

Description

Technical Field

[0001] The present invention belongs to the field of mobile communications, and particularly relates to a channel estimation method for a multi-user uplink low-earth orbit satellite wireless communication system. Background Art

[0002] The low-earth orbit satellite system provides important support for the development of future communication networks with its unique advantages, but it is also necessary to conduct in-depth research on the impact caused by the Doppler effect. For high-speed mobile communication scenarios, traditional OFDM modulation cannot be used because it cannot overcome the inter-carrier interference problem caused by the Doppler effect. In order to use OFDM modulation technology in a low-earth orbit satellite communication system, one way is to consider compensating for the Doppler frequency shift of the main path while ignoring the Doppler effects of different multipaths. Another way is to adopt the method of repeating OFDM symbols to improve the time-frequency domain resolution, thereby enhancing the performance of uplink channel estimation. Different from OFDM, OTFS is a newly proposed waveform modulation technology suitable for high-speed mobile scenarios. It additionally introduces a delay-Doppler (DD) domain on the traditional time-frequency domain. In the DD domain, the time-frequency two-dispersion channel of multipaths is converted into a time-invariant delay-Doppler channel. The data in the DD domain has strong sparsity. Through appropriate sparse channel estimation or data reconstruction algorithms, dynamic channel information and data information can be obtained.

[0003] However, in the research related to low-earth orbit satellite OTFS modulation, one way is to consider ideal biorthogonal pulses and analyze a series of indicators such as outage probability and secure outage probability. However, in the actual environment, due to the influence of hardware on the filter, perfect orthogonality is easily destroyed, so it is difficult to implement biorthogonal pulses. Another way is to study the multi-satellite scenario where the satellites are all single-antenna, consider embedded OTFS pilot symbols for channel estimation, and use LMMSE for channel equalization. However, its scenario only targets single-user communication and does not study the multi-user communication scenario.

[0004] In summary, in the existing research, there is no study on obtaining channel information of low-earth orbit satellite OTFS modulation based on multi-user scenarios and non-biorthogonal waveforms, so the existing research does not give an analysis method. Summary of the Invention

[0005] Purpose of the invention: The technical problem to be solved by the present invention is to provide a channel estimation method for a multi-user uplink low-orbit satellite wireless communication system in view of the shortcomings of the prior art. In view of the scenario where the low-orbit satellite moves rapidly, OTFS modulation is used to send signals, and a low-complexity uplink channel estimation method for the joint number of paths, delay, Doppler, and channel fading is proposed. First, multiple users are designed to be located at different pilot symbol grid positions in the delay-Doppler domain; then, the energy threshold detection is performed on the received signal of the low-orbit satellite in all delay domains to estimate the total number of all paths and the delay value of each path; then, the maximum likelihood estimation method is used to give a closed-form expression for channel fading and the Doppler is estimated using a one-dimensional search method. After simulation verification, the uplink joint estimation method provided by the present invention can effectively realize channel detection and can be applied in the derivation of traversal capacity.

[0006] The method of the present invention comprises the following steps:

[0007] Step 1, modeling a multi-user uplink low-orbit satellite communication system;

[0008] Step 2, establishing a pilot transmission model;

[0009] Step 3, estimate the time delay and multipath number;

[0010] Step 4: perform small-scale fading and Doppler estimation.

[0011] Step 1 includes: the multi-user uplink low-orbit satellite communication system includes a low-orbit LEO satellite and Q ground users, and the LEO satellite is equipped with M L Uniform linear antenna array ULA;

[0012] On the ground side, each user has a single antenna;

[0013] All Q ground users to LEO satellite uplink communication links use broadband multi-carrier orthogonal time-frequency modulation (OTFS) modulation technology;

[0014] The delay-Doppler (DD) domain wireless channel from the uplink user to the satellite is modeled as:

[0015]

[0016] where h q (τ,υ) represents the DD domain wireless channel of the qth user, q=1,…,Q, τ,υ are intermediate parameters, L q represents the multipath number of the qth user, g q,i Expressing the small-scale fading channel of the qth user's i-th multipath, the mean is β q,i , with a variance of Ω q,iRice distribution, i=1,…,L q ; represents the steering vector of the ith multipath of the qth user, in represents the uplink angle of arrival (AoA) of the ith multipath of the qth user, M L represents the number of uniform linear antenna arrays of LEO satellites, j represents an imaginary unit, e is a natural constant, δ(·) represents the Dirac delta function, υ q,i ,τ q,i They represent the Doppler and delay values of the i-th multipath of the q-th user respectively.

[0017] Step 2 includes: in a multi-user uplink low-orbit satellite communication system, pilot symbols of different users are embedded into the DD domain, and the index Γ of the DD domain grid is expressed as:

[0018]

[0019] Where k and l represent the discrete Doppler grid index and discrete delay grid index respectively, k=0,…,N-1, l=0,…,M-1, Δf and T represent the subcarrier spacing and symbol spacing respectively, and satisfy

[0020] Step 2 also includes: let k max , l max They represent the maximum guard interval of the pilot in the discrete Doppler grid and the discrete delay grid respectively;

[0021] Each user sends a single known pilot symbol in the pilot frame. The position of the pilot symbol of the qth user in the discrete Doppler grid index and the discrete delay grid index is denoted as k q ,l q .

[0022] Step 2 also includes: due to the characteristics of OTFS, in the discrete delay grid index, the pilot symbol is from l q To l q +l max Time dispersion will occur at the position where the first user’s pilot signal is set to l1, and the second user’s pilot signal position only needs to satisfy l max The grid index of the second user pilot position is l2=l1+l max +1, the position l of the pilot signal of the Qth user on the DD domain grid Q =l1+(Q-1)l max +(Q-1); In order to ensure that the pilot signals of all Q users can be deployed in the grid of the DD domain, the following conditions must be met:

[0023] l Q +lmax ≤M - 1 (3),

[0024] Denote the DD - domain pilot symbols \(s\) sent by different users to the satellite as q \(=\mathrm{vec}(S q ), where represents the pilot symbol of the \(q\) - th user. In \(S q , the non - zero element positions are \((k q ,l q ), and the non - zero element value is denoted as \(s q , and the values at the remaining positions are 0; \(\mathrm{vec}(\cdot)\) represents the matrix vectorization operation, represents the complex number field. The \(S\) in the DD domain in OTFS modulation is transformed into the time - frequency domain through the Heisenberg transform and the DD - domain window function calculation and then sent out through the user's antenna RF link. The received signal \(y\) of the \(u\) - th antenna of the LEO satellite is q expressed as: u

[0025]

[0026] where \(u = 1,\cdots,M L , and \(y u =\mathrm{vec}(Y u ), represents the DD - domain received signal matrix of the \(u\) - th antenna of the LEO satellite; \(\eta q represents the transmission power of the \(q\) - th user, is the equivalent channel in the DD domain, expressed as where \(T q,i is a sparse matrix, F N is an \(N\) - point DFT matrix, \(\Pi\) and \(\Delta\) respectively represent the permutation matrix and the diagonal matrix in OTFS modulation, represents the Kronecker product operation, 0 1,MN-1 represents a \(1\times(MN - 1)\) all - zero row vector, 0 MN-1,1 represents an \((MN - 1)\times1\) all - zero column vector, \(I MN-1 represents an \((MN - 1)\times(MN - 1)\) identity matrix; the delay and Doppler of the \(q\) - th user on the \(i\) - th multipath are respectively denoted by \(l q,i and \(k q,i , \(l q,i =\tau q,i M\Delta f,k q,i =\upsilon q,i NT; represents the expectation operation; \(r q ​Denote the indices of non-zero elements after vector quantization of the pilot symbols of user q, r q = k q M + l q ; w u is the additive white Gaussian noise (AWGN) of the u-th receiving antenna, which follows a complex Gaussian distribution with a mean of 0 and a variance of where I MN represents the MN×MN identity matrix.

[0027] Step 3 includes: For the satellite received signal shown in formula (4), a low-complexity time-delay index estimation algorithm is proposed to perform energy detection on the received signals of Q users in different pilot regions. First, transform formula (4) into an N×M matrix form, then the expression of the received signal is transformed into:

[0028]

[0029] where Y u [k, l] represents the received signal of the u-th antenna at the grid index [k, l], and Y u = mat(y u ), mat(·) is an operation from vector to matrix, and the intermediate parameter intermediate parameter k′ is an intermediate parameter, and W u [k, l] represents the AWGN of the u-th antenna at the [k, l] grid index, and W u = mat(w u ).

[0030] Step 3 also includes: Design a multipath and time-delay index estimation algorithm. Define the detection region of the q-th user as Then the energy detection of the LEO satellite in the region is expressed as:

[0031]

[0032] where E q,l represents the energy detected by the q-th user at the discrete time-delay grid index l. By setting the detection threshold E th , when E q,l ≥ E th , it is determined that there is multipath on the discrete time-delay grid index l. Let represent the estimated time delay, then When E q,l < E th , there is no multipath; by accumulating the number of all , the total number of multipaths of user q is estimated.

[0033] Step 4 includes: analyzing the sparsity of formula (4), and adopting a received signal preprocessing method to substitute s q into y u . Since the pilot symbols of Q users do not interfere with each other, the column vector is simplified to where (·) M represents the modulo operation;

[0034] t q,i has a closed-form expression as:

[0035]

[0036] where the intermediate parameter n′ = 1, …, N, the intermediate parameter n = 0, …, N - 1, represents the remainder operation;

[0037] At this time, the expression of formula (4) is transformed into:

[0038]

[0039] where y q,i,u represents the simplified received signal, w q,i,u represents the simplified additive white Gaussian noise AWGN,

[0040] For Doppler estimation and small-scale fading estimation , the maximum likelihood estimation MLE method is used to obtain the small-scale fading estimation as:

[0041]

[0042] Finally, substituting obtained from formula (9) into formula (8), the maximum likelihood estimation MLE of Doppler estimation is expressed as:

[0043]

[0044] Perform a one-dimensional search for k max in the Doppler domain [-k max , k q,i , and find the minimum value to determine the Doppler estimation

[0045] The present invention also provides an electronic device, including a processor and a memory. The memory stores program code. When the program code is executed by the processor, the processor is caused to execute the steps of the above method.​

[0046] The present invention also provides a storage medium storing a computer program or instruction, which, when running on a computer, executes the steps of the above method.

[0047] The present invention has the following beneficial effects: The present invention conducts in-depth research on multi-user uplink communication in a broadband LEO satellite system. First, a channel model for multi-user satellite communication is established; considering the actual scenario of satellite and user movement, the present invention uses OTFS modulation, designs a pilot symbol frame in combination with fractional Doppler and rectangular pulses, analyzes the sparsity of the uplink pilot received signal, and proposes a low-complexity joint multi-path, delay, Doppler, and channel estimation algorithm; the present invention verifies the effectiveness of channel estimation by comparing with other channel estimation algorithms using the normalized mean square error (NMSE) metric. In addition, in the data transmission frame, considering the small-scale information estimation error, the present invention gives a closed-form expression of the transmission rate based on the statistical CSI condition and verifies the reliability of the theoretical results through simulation. Research shows that this method can achieve efficient channel estimation and communication performance analysis in a multi-user uplink broadband LEO satellite communication system, providing an important reference for subsequent research and practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The following further describes the present invention in detail with reference to the drawings and specific embodiments, and the above and / or other advantages of the present invention will become clearer.

[0049] Figure 1 Schematic diagram of the multi-user uplink LEO satellite channel estimation and analysis method in the embodiment of the present invention.

[0050] Figure 2 Model diagram of the multi-user uplink LEO satellite communication system in the embodiment of the present invention.

[0051] Figure 3 Schematic diagram of the multi-user uplink OTFS pilot frame in the embodiment of the present invention.

[0052] Figure 4 Curve diagram comparing different estimation algorithms of the channel estimation method used in the embodiment of the present invention.

[0053] Figure 5 Curve diagram of simulation and theory of the transmission rate of signal detection using the channel estimation method in the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0054] As Figure 1 shown, the embodiment of the present invention provides a channel estimation method for a multi-user uplink low-earth orbit satellite wireless communication system, specifically including:

[0055] Step 1: Model the multi-user uplink large-scale MIMO low-earth orbit satellite network;

[0056] The multi-user uplink large-scale MIMO low-earth orbit satellite network is as follows Figure 2 shown. The system includes a low-earth orbit satellite and Q ground users. Let denote the user set. The LEO satellite has an orbital altitude of H and is equipped with a large-scale linear planar antenna array (ULA) of M; in addition, at the ground end, each user has a single antenna. All multi-user to LEO satellite uplink communication links adopt broadband multi-carrier OTFS modulation technology. Considering the actual dynamic scenario of the high-speed movement of the LEO satellite and the movement of ground users, the uplink user-to-satellite DD-domain wireless channel is modeled as:

[0057]

[0058] where (τ, υ) represents the delay-Doppler domain, and g q,i represents the small-scale fading channel, which follows a Rice distribution with parameters (β q,i , Ω q,i ). Under the ULA model where represents the angle of arrival (AoA) of the q-th user's i-th path to the satellite. In addition, u = [0, …, M - 1] T .

[0059] Step 2: Establish a pilot transmission model;

[0060] In a satellite system such as Figure 3 , the pilot symbols of different users are embedded in the DD domain. The index of the DD domain grid is expressed as:

[0061]

[0062] where k = 0, …, N - 1 and l = 0, …, M - 1 represent the discrete Doppler grid index and the discrete delay index respectively. The multi-path delay and Doppler of the q-th user are represented by l q,i and k q,i respectively, where the sub-carrier spacing and symbol interval are Δf and T respectively, and satisfy In addition, let k max , l max represent the maximum guard intervals of the pilot symbols in the discrete Doppler grid and the discrete delay grid respectively.

[0063] Each user sends a single known pilot symbol in the pilot frame. Without loss of generality, assume that the position of the pilot symbol of the q-th user is (k q , l q)。In the time delay domain, the pilot signal only expands by l max grid indices. Based on this phenomenon, set the pilot position of the first user to then the pilot position of the second user only needs to satisfy l max guard intervals, and its grid index is And so on, the position of the pilot signal of the Qth user on the DD domain grid is To ensure that the pilot signals of all Q users can be deployed within the DD domain grid, the following needs to be satisfied:

[0064] l Q +l max ≤M - 1 (3)

[0065] Denote the DD domain pilot symbol s q sent by different users to the satellite as υec(S q ), where represents the pilot symbol of the qth user, and S q in the DD domain is transformed into the time-frequency domain through the Heisenberg transform and the DD domain window function in OTFS modulation and sent out through the user's antenna radio frequency link. Here, the received signal of the u-th antenna of the LEO satellite can be expressed as:

[0066]

[0067] where y u =υec(Y u ), represents the DD domain received signal matrix of the u-th antenna of the LEO satellite. η q represents the transmit power of the user, represents the equivalent channel in the DD domain, which can be expressed as where u ∈ [0, …, M t -1] T . In addition, according to the modulation method of OTFS, is a sparse matrix, and its dimension can be expressed as

[0068] For the pilot signal matrix S q with size M×N, define the index position:

[0069] r q =k q M + l q (5)

[0070] where (k q , l q ) is the grid position of the pilot symbol in Figure 3 , satisfying is the AWGN of the u-th receiving antenna. Since the transmitted signal s in the DD domain q is given, and the small-scale fading, delay, Doppler, and number of multipaths in the channel information are unknown. The purpose of channel estimation is to design corresponding estimation algorithms for the channel parameters {g q,i , τ q,i , υ q,i , L q} of the channels from users q = 1, …, Q to the satellite.

[0071] Step 3, perform delay and number of multipaths estimation;

[0072] For the satellite received signal shown in formula (4), a low-complexity delay index estimation algorithm is proposed. The main method is to perform energy detection on the received signals of Q users in different pilot regions. First, transform formula (4) into an N×M matrix form, then the expression of the received signal is transformed into:

[0073]

[0074] where and Due to the property of the modulo operation in the delay domain, the detection region is (l q,i , l q,i + l max ). Based on the above principle, design a multipath and delay index estimation algorithm. Define the detection region of the q-th user as Then the energy detection of the LEO satellite in the region is expressed as:

[0075]

[0076] By setting the detection threshold Γ, when E q,l ≥ Γ, it is considered that there are multipaths on this delay grid, denoted as In contrast, when E q,l < Γ, there are no multipaths, where the value of Γ is described in the simulation part. Finally, by accumulating the number of all , the total number of paths of user q can be estimated.

[0077] Step 4, perform small-scale fading and Doppler estimation;

[0078] First, analyze the sparsity of formula (4) and propose a received signal preprocessing method. According to Figure 3 it can be known that s q only has values at (k q , l q ) and is 0 elsewhere. Therefore, s qSubstitute into y u Among them, since the pilot symbols of Q users do not interfere with each other, the column vector The expression of is:

[0079]

[0080] Since And I M Represents the identity matrix. Combining the properties of the Kronecker product, the column vector in formula (8) is obtained. It only has non-zero elements at the abscissa x ∈ [(r q ) M ,…,(r q ) M +(N - 1)M], and its value is In addition, for the matrix Analyze the numerical values of the elements in the r-th row. First, When in the r-th row It has non-zero elements at y ∈ [(r) M ,…,(r) M +(N - 1)M]l q,i And its value is Multiply with According to the properties of the permutation matrix Right multiplication is equivalent to shifting the elements of to the left by l q,i . Therefore, the position of the non-zero elements in the r-th row of the matrix can be recorded as y ∈ [(r - l q,i ) M ,…,(r - l q,i ) M +(N - 1)M]. Combining It can be deduced that the numerical value of the elements in the r-th row is

[0081] Finally, substitute and into formula (8), then the closed-form expression of t q,i can be obtained by using the sparse property as:

[0082]

[0083] where n′ = 1,…,N. At this time, the expression of formula (4) is transformed into:

[0084]

[0085] where represents the r-th q,i of the matrix Tq column, and r q = Mk q + l q ,

[0086] After dimensionality reduction, for the i-th path of different users q, it is not difficult to see from formula (9) that it is independent of i. Using the maximum likelihood estimation method for formula (10), where y q,i,u and s q are known in the pilot transmission frame. Given the Doppler and small-scale fading ξ q,i =(k q,i , g q,i ) to be estimated, it can be found that y q,i,u is a Gaussian vector with a mean of and a variance of Combining the received signals of the ULA antenna, the purpose is to better detect the estimated parameter ξ q,i =(k q,i , g q,i ). The likelihood function of the received signal is expressed as:

[0087]

[0088] Therefore, maximizing f(y q,i,u ; ξ) to estimate ξ q,i =(k q,i , g q,i ) is expressed as:

[0089]

[0090] Expanding it gives:

[0091]

[0092] For the minimization problem shown in formula (13), setting it to 0 to obtain the minimum solution, then 's closed-form expression is:

[0093]

[0094] Finally, substituting the of the above formula into formula (12), the maximum likelihood estimation of the Doppler estimation can be expressed as:

[0095]

[0096] By observation, formula (15) is a one-dimensional optimization problem with a single variable. In the Doppler domain [-k max , k maxPerforming a one-dimensional search for its peak value, the Doppler estimation of the $i$-th path from the $q$-th user to the satellite can be obtained as

[0097] Step 5, analyze the transmission rate;

[0098] During the satellite uplink communication process, information such as the number of paths, delay index, and Doppler index $L$ q,i , $l$ q,i , $k$ q,i and so on changes slowly. In addition, by increasing the transmission power of the pilot frame, the estimation accuracy of $L$ q,i , $l$ q,i , $k$ q,i can also be improved. Therefore, in the signal transmission frame, it is assumed that $L$ q,i , $l$ q,i , $k$ q,i information is completely known. Substituting the received signal $y$ q,i,u into formula (14), the estimation of the small-scale fading is obtained as:

[0099]

[0100] where represents the equivalent Gaussian white noise channel. In the signal transmission frame, according to the form of formula (4), the transmission rate of the $q$-th user in the uplink is:

[0101]

[0102] where $I_0(r)$, $I$ q1 $(r)$, $I$ q2 $(r)$, $w$ ul,q $(r)$ represent the desired signal, the inter-symbol interference signal, the inter-user interference signal, and the noise respectively;

[0103] Simulation parameter settings: Currently, consider the carrier frequency of communication to be 10 GHz, the subcarrier spacing $\Delta f$ to be 300 KHz, $(M, N)$ in OTFS modulation to be (64, 8) respectively, the symbol to use QPSK, the number of satellite antennas to be $M = 16$, the satellite altitude to be 800 km, its running speed to be approximately 7.58 km / s, and the delay and Doppler ranges after delay compensation and Doppler compensation to be 0 - 0.52 $\mu$s and 0 - 230 KHz. The results of channel estimation are as Figure 4 shown. The low-complexity optimization algorithm adopted is compared with the simulation curve in the case of perfect delay-Doppler to reflect the effectiveness of the algorithm. In addition, the curve of the system transmission rate can be reflected from Figure 5 it. It can be seen from the figure that in the case of different numbers of antennas, the theoretical value and the simulation value can coincide to verify the transmission performance in the data transmission frame.

[0104] The present invention provides a channel estimation method for a multi-user uplink low-earth orbit satellite wireless communication system. There are many methods and ways to specifically implement this technical solution. The above is only the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art of this technology, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention. Each component not clearly defined in this embodiment can be implemented by using existing technologies.

Claims

1. A channel estimation method for a multi-user uplink low-earth orbit satellite wireless communication system, characterized in that, Including the following steps: Step 1: Model the multi-user uplink low-earth orbit satellite communication system; The multi-user uplink low Earth orbit satellite communication system includes a low Earth orbit (LEO) satellite and Q ground users. The LEO satellite is equipped with M L uniform linear antenna arrays (ULA); At the ground end, each user has a single antenna; For all Q ground users' uplink communication links to the LEO satellite, broadband multi-carrier orthogonal time-frequency space modulation technology is adopted; Step 2: Establish a pilot transmission model; in the multi-user uplink low-earth orbit satellite communication system, the pilot symbols of different users are embedded in the DD domain, and the index Γ of the DD domain grid is expressed as: where \(k\) and \(l\) represent the discrete Doppler grid index and the discrete delay grid index respectively, \(k = 0,\ldots,N - 1\), \(l = 0,\ldots,M - 1\), \(\Delta f\) and \(T\) represent the subcarrier spacing and the symbol interval respectively, and satisfy Step 3: Perform energy detection on the received signals of Q users in different pilot regions, design a multi-path and delay index estimation algorithm, and estimate the total number of all paths and the delay values of each path by setting a detection threshold; Define the detection region of the q-th user, E q,l Denote the energy detected by the q-th user at the discrete delay grid index l. By setting the detection threshold E th , when E q,l ≥E th , it is determined that there is multipath on the discrete delay grid index l. Let Denote the estimated delay, then When E q,l <E th , there is no multipath; by accumulating the number of all , the total number of multipaths of user q is estimated; l1 is the pilot position of the first user; l max Is the pilot protection interval; Step 4: Use the maximum likelihood estimation method to give a closed-form expression of the channel fading and use the one-dimensional search method to estimate the Doppler; 2. The method according to claim 1, characterized in that, Step 1 includes: Modeling the wireless channel in the delay-Doppler domain from the uplink user to the satellite as: where h q (τ, v) represents the DD-domain wireless channel of the q-th user, q = 1, …, Q, τ, v are intermediate parameters, L q represents the number of multipaths of the q-th user, g q,i represents the small-scale fading channel of the i-th multipath of the q-th user, which follows a Rice distribution with a mean of β q,i and a variance of Ω q,i , i = 1, …, L q ; represents the steering vector of the i-th multipath of the q-th user, where represents the angle of arrival of the i-th multipath of the q-th user in the uplink, M L represents the number of uniformly linear antenna arrays of the LEO satellite, j represents the imaginary unit, e is the natural constant, δ(·) represents the Dirac δ function, v q,i , τ q,i respectively represent the Doppler and delay values of the i-th multipath of the q-th user.

3. The method according to claim 2, wherein Step 2 includes: setting k max which represents the maximum Doppler grid index of all users within the satellite coverage area; Each user transmits a single known pilot symbol in the pilot frame. Let the discrete Doppler grid index position and the discrete delay grid index position of the pilot symbol of the q-th user in Γ be denoted as k q ,l q .

4. The method according to claim 3, wherein Step 2 further includes: in the discrete time-delay grid index, time dispersion occurs for pilot symbols from l q to l q + l max ; the pilot position of the second user only needs to satisfy the guard interval of l max , and the grid index of the pilot position of the second user is l2 = l1 + l max + 1. The position l Q of the pilot signal of the Qth user on the DD domain grid is l max = l1 + (Q - 1)l max + (Q - 1); to ensure that the pilot signals of all Q users can be deployed within the grid of the DD domain, it is necessary to satisfy: l Q +l max ≤M-1 (3)， Denote the DD-domain pilot symbols s sent by different users to the satellite q = vec(S q ), where represents the pilot symbol of the q-th user. In S q , the non-zero element positions are (k q , l q ), the non-zero element value is denoted as s q , and the values at the remaining positions are 0; vec(·) represents the matrix vectorization operation, represents the complex domain. The S in the DD domain q is transformed into the time-frequency domain through the Heisenberg transform and the DD-domain window function calculation in OTFS modulation and is sent out through the user's antenna RF link. The received signal y u of the u-th antenna of the LEO satellite is expressed as: where \(u = 1,\ldots,M\) L , \(y\) u =\(\text{vec}(Y\) u ), denotes the DD-domain received signal matrix of the \(u\)-th antenna of the LEO satellite; \(\eta\) q denotes the transmit power of the \(q\)-th user, is the equivalent channel in the DD domain, expressed as where \(T\) q,i is a sparse matrix, \(F\) N is an \(N\)-point DFT matrix, \(\Pi\) and \(\Delta\) respectively represent the permutation matrix and the diagonal matrix in OTFS modulation, represents the Kronecker product operation, \(0\) 1,MN-1 represents a \(1\times(MN - 1)\) all-zero row vector, \(0\) MN-1,1 represents a \((MN - 1)\times1\) all-zero column vector, \(I\) MN-1 represents an \((MN - 1)\times(MN - 1)\) identity matrix; the delay and Doppler of the \(q\)-th user on the \(i\)-th multipath are respectively denoted by \(l\) q,i and \(k\) q,i , \(l\) q,i =\(\tau\) q,i \(M\Delta f,k\) q,i =\(v\) q,i \(NT\); represents the expectation operation; \(r\) q represents the index of the non-zero elements after vector quantization of the pilot symbol of the \(q\)-th user, \(r\) q =\(k\) q \(M + l\) q ; \(w\) u is the additive white Gaussian noise (AWGN) of the \(u\)-th receiving antenna, following a complex Gaussian distribution with mean 0 and variance , where \(I\) MN represents an \(MN\times MN\) identity matrix.

5. The method according to claim 4, characterized in that Step 3 includes: For the satellite received signal shown in formula (4), a low-complexity delay index estimation algorithm is proposed, and energy detection is performed on the received signals of Q users in different pilot regions. First, convert formula (4) into an N×M matrix form, and then the expression of the received signal is converted to: where Y u [k, l] represents the received signal of the u-th antenna at the grid index [k, l], Y u = mat(y u ), mat(·) is the operation from vector to matrix, and the intermediate parameter intermediate parameter k' is the intermediate parameter, W u [k, l] represents the AWGN of the u-th antenna at the [k, l] grid index, W u = mat(w u ).

6. The method according to claim 5, wherein Step 3 further includes: designing a multipath and time delay index estimation algorithm, and defining the detection area of the q-th user as Then the energy detection of the LEO satellite in the area is expressed as:

7. The method according to claim 6, wherein Step 4 includes: analyzing the sparsity of formula (4), and adopting a received signal preprocessing method to substitute s q into y u . Since the pilot symbols of Q users do not interfere with each other, the column vector is simplified to where (·) M denotes the modulo operation; t q,i The closed-form expression for: where the intermediate parameter n′ = 1, …, N, and the intermediate parameter n = 0, …, N−1, represents the modulo operation; At this time, the expression of formula (4) is converted to: where y q,i,u represents the simplified received signal, w q,i,u represents the simplified additive white Gaussian noise AWGN, For Doppler estimation and small-scale fading estimation Using the maximum likelihood estimation (MLE) method, the small-scale fading estimation is obtained as follows: Finally, substitute what is obtained from Equation (9) into Equation (8), and the maximum likelihood estimate (MLE) of the Doppler estimation is expressed as: In the Doppler domain [-k max ,k max ] on k q,i Perform a one-dimensional search for Find the minimum to determine the Doppler estimate where k max Indicates the maximum Doppler grid index of all users within the satellite coverage area.

8. An electronic device, characterized in that, Including a processor and a memory, the memory stores program code, and when the program code is executed by the processor, the processor is caused to execute the steps of the method according to any one of claims 1 to 7.

9. A storage medium, characterized in that, Stored with a computer program or instruction, when the computer program or instruction runs on a computer, it executes the steps of the method according to any one of claims 1 to 7.

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