CN119652704B - Channel estimation method for multi-user uplink low-orbit satellite wireless communication system - Google Patents
Channel estimation method for multi-user uplink low-orbit satellite wireless communication systemInfo
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Abstract
本发明提供了一种多用户上行低轨卫星无线通信系统的信道估计方法，本方法针对低轨卫星快速移动场景，采用了OTFS调制技术进行信号发送，并提出了一种低复杂度的联合路径数、时延、多普勒以及信道衰落的上行信道估计方法。该方法的步骤如下：首先，设计多用户在时延‑多普勒域中不同的导频符号网格位置；接着，在低轨卫星接收信号的所有时延域上进行能量阈值检测，用以估计路径总数及每条路径的时延值；然后，利用最大似然估计方法给出信道衰落的闭式表达式，并采用一维搜索方法估计多普勒频移。通过仿真验证，所提出的上行联合信道估计方法能够有效实现信道检测，并可进一步应用于遍历容量的推导工作中，具有较好的实用性与性能表现。
The present invention provides a channel estimation method for a multi-user uplink low-orbit satellite wireless communication system. Aiming at the scenario of rapid movement of low-orbit satellites, the method adopts the OTFS modulation technology for signal transmission, and proposes a low-complexity uplink channel estimation method for joint path number, delay, Doppler and channel fading. The steps of the method are as follows: first, design different pilot symbol grid positions of multiple users in the delay-Doppler domain; then, perform energy threshold detection on all delay domains of the low-orbit satellite receiving signal 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 of channel fading, and use a one-dimensional search method to estimate the Doppler frequency shift. Through simulation verification, the proposed uplink joint channel estimation method can effectively realize channel detection, and can be further applied to the derivation of ergodic capacity, with good practicality and performance.
Description
Technical Field
The invention belongs to the field of mobile communication, and particularly relates to a channel estimation method of a multi-user uplink low-orbit satellite wireless communication system.
Background
Low orbit satellite systems offer important support for the development of future communication networks by virtue of their unique advantages, but also require intensive research into the effects caused by the doppler effect. For the communication scenario of high-speed motion, conventional OFDM modulation cannot be used, because it cannot overcome the problem of inter-carrier interference caused by doppler effect. In order to use the OFDM modulation technique in the low-orbit satellite communication system, one way is to consider compensating the doppler shift of the main path and neglecting the doppler effect of different paths, and the other way is to use the method of repeated transmission of OFDM symbols to improve the time-frequency domain resolution, thereby improving the performance of uplink channel estimation. Unlike OFDM, OTFS is a new proposed waveform modulation technique suitable for use in high-speed mobile scenarios, which additionally introduces a delay-doppler (DD) domain in the traditional time-frequency domain dimension, where the multipath time-frequency bi-dispersive channel is converted into a time-invariant delay-doppler channel. The data in DD domain has strong sparsity, and dynamic channel information and data information can be obtained through proper sparse channel estimation or data reconstruction algorithm.
However, in the study on low orbit satellite OTFS modulation, one way is to consider ideal bi-orthogonal pulses and analyze a series of indicators such as outage probability, safe outage probability, etc. However, in a practical environment, the filter is affected by hardware, and perfect orthogonality is easily broken, so that the biorthogonal pulse is difficult to realize. Another way is to study multi-satellite scenarios, where the satellites are all single antennas, consider embedded OTFS pilot symbols for channel estimation, and use LMMSE for channel equalization. However, the scenario is only for single-user communication, and the scenario of multi-user communication is not studied.
In summary, in the existing research, the information acquisition of the low orbit satellite OTFS modulation channel on the basis of a multi-user scene and a non-biorthogonal waveform is not researched, so no analysis method is given in the existing research.
Disclosure of Invention
The invention aims to solve the technical problems of providing a channel estimation method of a multi-user uplink low-orbit satellite wireless communication system aiming at the defects of the prior art, transmitting signals by using OTFS modulation aiming at a scene of fast movement of a low-orbit satellite, and providing an uplink channel estimation method of low-complexity joint path number, time delay, doppler and channel fading. Firstly, designing pilot frequency symbol grid positions with multiple users located in different time delay-Doppler domains, then, carrying out energy threshold detection on received signals of low-orbit satellites in all time delay domains to estimate total number of all paths and time delay values of each path, and then, using a maximum likelihood estimation method to give a closed expression of channel fading and using a one-dimensional search method to estimate Doppler. Through simulation verification, the uplink joint estimation method provided by the invention can effectively realize channel detection and can be applied to deduction work of traversal capacity.
The method comprises the following steps:
step 1, modeling a multi-user uplink low-orbit satellite communication system;
step2, establishing a pilot frequency transmission model;
Step 3, estimating time delay and multipath number;
and 4, carrying out small-scale fading and Doppler estimation.
The multi-user uplink low orbit satellite communication system comprises a low orbit LEO satellite and Q ground users, wherein the LEO satellite is provided with M L uniform linear antenna arrays ULA;
At the ground end, each user is a single antenna;
all Q ground users to LEO satellite uplink communication links adopt a wideband multi-carrier orthogonal time-frequency air conditioning (OTFS) modulation technology;
the delay-doppler (DD) domain radio channel of an upstream user to a satellite is modeled as:
Where h q (τ, v) represents a DD domain wireless channel of the Q-th user, q=1,..q, τ, v is an intermediate parameter, L q represents the number of multipaths of the Q-th user, g q,i expresses a small-scale fading channel of the i-th multipath of the Q-th user, obeying a rice distribution with a mean value of β q,i and a variance of Ω q,i, i=1,..l q; A steering vector representing the ith multipath of the qth user, Wherein the method comprises the steps ofThe method is characterized in that the method comprises the steps of expressing the uplink arrival angle (AoA) of the ith multipath of the qth user, M L represents the number of uniform linear antenna arrays of LEO satellites, j represents imaginary units, e is a natural constant, delta (·) represents a Dirac delta function, and v q,i,τq,i represents Doppler and time delay values of the ith multipath of the qth user respectively.
Step 2 includes that in the multi-user uplink low orbit satellite communication system, pilot symbols of different users are embedded into DD domain, and index Γ of 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,..n-1, l=0,..m-1, Δf and T represent the subcarrier spacing and the symbol spacing, respectively, and satisfy
Setting k max,lmax to respectively represent the maximum guard intervals of pilot frequency in a discrete Doppler grid and a discrete time delay grid;
Each user transmits a single known pilot symbol in the pilot frame, and 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,lq, respectively.
Step 2 further includes that due to the characteristics of OTFS, time dispersion occurs in pilot symbols from l q to l q+lmax in the discrete time delay grid index, setting pilot position l 1 of the first user, where the pilot position of the second user only needs to satisfy the guard interval of l max, the grid index of the pilot position of the second user is l 2＝l1+lmax +1, and the position l Q＝l1+(Q-1)lmax + (Q-1) of the pilot signal of the Q-th user on the DD domain grid, in order to ensure that the pilot signals of all Q users can be deployed in the DD domain grid, the following needs to be satisfied:
lQ+lmax≤M-1 (3),
recording the DD domain pilot symbols s q＝υec(Sq sent by different users to the satellite), wherein In S q, the position of the non-zero element is (k q,lq), the value of the non-zero element is S q, the values of the rest positions are 0, and uec (S) represents matrix vectorization operation,S q representing the complex domain and DD domain is converted into a time-frequency domain through Heisenberg conversion and DD domain window function calculation in OTFS modulation, and is sent out through an antenna radio frequency link of a user, and a received signal y u of a u-th antenna of the LEO satellite is represented as:
Where u=1,..m L,yu＝υec(Yu), A DD domain received signal matrix representing the u-th antenna of the LEO satellite, η q represents the transmission power of the q-th user,Equivalent channel of DD domain, expressed asWhere T q,i is a sparse matrix, F N is N point DFT matrix, pi and delta respectively represent permutation matrix and diagonal matrix in OTFS modulation, Representing the Cronecker product operation, 0 1,MN-1 representing the all-zero row vector of 1× (MN-1), 0 MN-1,1 representing the all-zero column vector of (MN-1) ×1, I MN-1 representing the identity matrix of (MN-1) × (MN-1), and the delay and Doppler of user q at the ith multipath are represented by l q,i and k q,i, respectively, l q,i＝τq,iMΔf,kq,i＝υq,i NT; R q represents the index of non-zero element after pilot symbol vectorization of user q, r q＝kqM+lq;wu is the additive white Gaussian noise AWGN of the u-th receiving antenna, the obeying mean is 0, and the variance is 0 Wherein I MN represents the identity matrix of MN x MN.
Step 3 includes providing a low-complexity time delay index estimation algorithm for satellite received signals shown in formula (4), performing energy detection on received signals of Q users in different pilot frequency areas, firstly, converting formula (4) into a matrix form of N×M, and converting the expression of the received signals into:
Where Y u [ k, l ] represents the received signal of the u-th antenna at the grid index [ k, l ], Y u＝mat(yu), mat (·) is the vector-to-matrix operation, the intermediate parameter Intermediate parametersK' is an intermediate parameter, W u [ k, l ] represents the AWGN of the u-th antenna at the [ k, l ] grid index, W u＝mat(wu).
Step3 also includes designing multipath and time delay index estimation algorithm, defining detection area of the qth user asThen the LEO satellite is in the areaThe energy detection in is expressed as:
Wherein E q,l represents the energy detected by the qth user at the discrete delay grid index l, and by setting the detection threshold E th, when E q,l≥Eth, it is determined that multipath exists on the discrete delay grid index l, so that Representing the estimated time delayBy accumulating all of the multipath when E q,l<Eth is absentAnd estimating the total multipath number of the user q.
Step 4 includes analyzing sparsity of equation (4), adopting a received signal preprocessing method to bring s q into y u, and column vectors because pilot symbols of Q users do not interfere with each otherSimplified intoWherein (-) M represents a modulo operation;
the closed expression of t q,i is:
Wherein the intermediate parameter N' =1, & gt, N, intermediate parameter n=0, & gt, N-1, Representing a remainder fetching operation;
The expression of equation (4) at this time is converted into:
Where y q,i,u represents a simplified received signal, W q,i,u denotes a simplified additive white gaussian noise AWGN,
For Doppler estimationAnd small scale fading estimationObtaining small-scale fading estimation by using a Maximum Likelihood Estimation (MLE) methodThe method comprises the following steps:
Finally, the method obtained by the formula (9) Bringing into equation (8), doppler estimationThe maximum likelihood estimate MLE of (2) is expressed as:
one-dimensional search of k q,i over Doppler domain [ -k max,kmax ] for Finding the minimum to determine Doppler estimates
The invention also provides an electronic device comprising a processor and a memory, the memory storing program code which, when executed by the processor, causes the processor to perform the steps of the method.
The invention also provides a storage medium storing a computer program or instructions which, when run on a computer, perform the steps of the method.
The invention has the following beneficial effects that the invention carries out intensive research on multi-user uplink communication in a broadband LEO satellite system. Firstly, establishing a multi-user to star channel model, considering the actual scene of satellite and user movement, the invention uses OTFS modulation, designs pilot symbol frames by combining fractional Doppler and rectangular pulse, analyzes the sparsity of uplink pilot received signals, and provides a low-complexity joint multipath, time delay, doppler and channel estimation algorithm. In addition, the invention also provides a closed expression of the transmission rate based on the statistical CSI condition in consideration of small-scale information estimation errors in the data transmission frame, and the reliability of a theoretical result is verified through simulation. Research shows that the method can realize efficient channel estimation and communication performance analysis in the multi-user uplink broadband LEO satellite communication system, and provides important reference for subsequent research and practical application.
Drawings
The foregoing and/or other advantages of the invention will become more apparent from the following detailed description of the invention when taken in conjunction with the accompanying drawings and detailed description.
Fig. 1 is a schematic diagram of a multi-user uplink LEO satellite channel estimation analysis method according to an embodiment of the present invention.
Fig. 2 is a model diagram of a multi-user uplink LEO satellite communication system according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of a multi-user uplink OTFS pilot frame in an embodiment of the present invention.
Fig. 4 is a graph of a channel estimation method versus different estimation algorithms used in an embodiment of the present invention.
Fig. 5 is a graph showing simulation and theory of a transmission rate of signal detection using a channel estimation method in an embodiment of the present invention.
Detailed Description
As shown in fig. 1, an embodiment of the present invention provides a channel estimation method for a multi-user uplink low-orbit satellite wireless communication system, which specifically includes:
step 1, modeling a multi-user uplink large-scale MIMO low-orbit satellite network;
multi-user uplink large-scale MIMO low-orbit satellite network as shown in figure 2, the system comprises one low-orbit satellite and Q ground users, and the system comprises the following steps of Representing a set of users. LEO satellite orbit height is H, equipped with large-scale linear area array antenna array (ULA) of M, and furthermore, at ground end. Each user is a single antenna. All multi-user to LEO satellite uplink communication links employ wideband multi-carrier OTFS modulation techniques. Considering the dynamic scenario of actual LEO satellite high-speed motion and ground user movement, the DD domain wireless channel from the uplink user to the satellite is modeled as:
Where (τ, v) represents the delay-doppler domain, g q,i expresses a small scale fading channel, subject to the rice distribution with parameter (β q,i,Ωq,i). In the model of ULA Wherein the method comprises the steps ofThe uplink angle of arrival (AoA) of the ith path of user q to the satellite is represented, and furthermore u= [0,..m-1 ] T.
Step2, establishing a pilot frequency transmission model;
In a satellite system as in fig. 3, pilot symbols of different users are embedded in the DD domain, and the index of the DD domain grid is expressed as:
Where k=0,..n-1, l=0,..m-1 represents the discrete doppler grid index and the discrete delay index, respectively. The multipath delay and Doppler for user q are denoted by l q,i and k q,i, respectively, where The subcarrier spacing and the symbol spacing are Δf and T, respectively, and satisfyFurther, let k max,lmax denote the maximum guard interval of the pilot symbols in the discrete doppler grid and the discrete delay grid, respectively.
Each user transmits a single known pilot symbol in the pilot frame, assuming the position of the pilot symbol for the qth user is (k q,lq). In the delay domain, the pilot signal would only extend by one max grid indices. Based on this phenomenon, the pilot position of the first user is set toThe pilot position of the second user only needs to meet the guard interval of l max with grid index ofBy analogy, the position of the pilot signal of the Q-th user on the DD domain grid isIn order to ensure that all the pilot signals of Q users can be deployed in the grid of the DD domain, it is necessary to satisfy:
lQ+lmax≤M-1 (3)
recording the DD domain pilot symbols s q＝υec(Sq sent by different users to the satellite), wherein The pilot symbol representing the q-th user, the S q of the DD domain is converted into the time-frequency domain by Heisenberg conversion and DD domain window function in OTFS modulation, and sent out through the antenna radio frequency link of the user, where the received signal of the u-th antenna of the LEO satellite can be obtained and expressed as:
Wherein y u＝υec(Yu), The DD domain receive signal matrix for the u-th antenna of the LEO satellite is represented. η q represents the transmission power of the user,Equivalent channels representing DD domains may be expressed asU e [0 ], M t-1]T. In addition, according to the modulation scheme of the OTFS,As a sparse matrix, its dimensions can be expressed as
For a pilot signal matrix S q of size mxn, an index position is defined:
rq＝kqM+lq (5)
wherein (k q,lq) is the pilot symbol at the grid position as in FIG. 3, satisfy AWGN for the u-th receive antenna. Since the transmitted signal s q in the DD domain is given and the small-scale fading, delay, doppler, and multipath numbers in the channel information are unknown, the purpose of the channel estimation is to design a corresponding estimation algorithm to estimate the channel parameters { g q,i,τq,i,υq,i,Lq } in the user q=1.
Step 3, estimating time delay and multipath number;
For satellite received signals shown in formula (4), a low-complexity time delay index estimation algorithm is provided, and the main method is to perform energy detection on the received signals of Q users in different pilot frequency areas. First, the expression of the received signal is converted into n×m matrix form by converting the expression (4):
Wherein the method comprises the steps of AndThe detection area is (l q,i,lq,i+lmax) due to the characteristic of modulo operation in the time delay domain. Based on the principle, a multipath and time delay index estimation algorithm is designed, and the detection area of the q-th user is defined asThen the LEO satellite is in the areaThe energy detection in is expressed as:
By setting the detection threshold Γ, when E q,l is greater than or equal to Γ, multipath is considered to exist on the delay grid, and the result is recorded In contrast, there is no multipath when E q,l < Γ, where the value of Γ is illustrated in the simulation part. Finally, by accumulating allThe total number of paths of the user q can be estimated.
Step 4, carrying out small-scale fading and Doppler estimation;
Firstly, the sparsity of the formula (4) is analyzed, and a received signal preprocessing method is provided. As can be seen from FIG. 3, s q has a value only at (k q,lq) and 0at the rest, thus bringing s q into y u, since the pilot symbols of the Q users do not interfere with each other, column vectors The expression of (2) is:
Due to And I M represents an identity matrix, and combines the properties of the Kronecker product to obtain a column vector in formula (8)Only at x.epsilon [ (r q)M,…,(rq)M + (N-1) M ] on the abscissa are non-zero elements with values ofIn addition, for matrixThe values of the r-th line elements are analyzed. First of all,At the r th lineIt has a non-zero element at y E [ (r) M,…,(r)M+(N-1)M]lq,i with a value of And (3) withMatrix multiplication according to permutation matricesIs equal toIs shifted left by l q,i so that the matrix of non-zero elements is inThe position of the r-th line in (2) can be marked as y E [ (r-l q,i)M,…,(r-lq,i)M + (N-1) M ], combined withThe value of the element in row r can be deduced as
Finally, willAndSubstituting into formula (8), the sparse characteristic can be utilized to obtain the closed expression of t q,i as follows:
where N' =1,..n. The expression of equation (4) at this time is converted into:
Wherein the method comprises the steps of Represents the r q column of matrix T q,i, and r q＝Mkq+lq,
With the reduction in dimension, it is apparent from equation (9) that for the ith path of different users q, it is independent about i. Using the maximum likelihood estimation method for equation (10), where y q,i,u and s q are known in the pilot transmission frame, given the doppler and small scale fading ζ q,i＝(kq,i,gq,i that need to be estimated), y q,i,u can be found to be a gaussian vector whose mean isVariance isThe received signals of ULA antennas are combined for better detection of the estimation parameters ζ q,i＝(kq,i,gq,i). The likelihood function of the received signal is expressed as:
Maximizing f (y q,i,u; ζ) to estimate ζ q,i＝(kq,i,gq,i) is therefore expressed as:
And (3) unfolding to obtain:
For the minimization problem shown in equation (13), let it be 0 to obtain the minimum solution, then The closed expression of (2) is:
Finally, the above formula With respect to Doppler estimation, brought into equation (12)The maximum likelihood estimate of (2) can be expressed as:
From observation, equation (15) is a single variable one-dimensional optimization problem. One-dimensional search of its peak over the Doppler domain [ -k max,kmax ] can obtain the ith path Doppler estimate from the qth user to satellite as
Step 5, analyzing the transmission rate;
In the satellite uplink communication process, the information such as the path number, the time delay index, the Doppler index L q,i,lq,i,kq,i and the like slowly change. In addition, by increasing the transmission power of the pilot frame, the estimation accuracy of L q,i,lq,i,kq,i can be improved. Therefore, in the signal transmission frame, it is completely known to set L q,i,lq,i,kq,i information, and the received signal y q,i,u is substituted into equation (14), so as to obtain an estimate of the small-scale fading as follows:
Wherein the method comprises the steps of Representing an equivalent gaussian white noise channel. In the signal transmission frame, according to the form of formula (4), the transmission rate of the q-th uplink user is:
Wherein I 0(r),Iq1(r),Iq2(r),wul,q (r) represents a desired signal, an intersymbol interference signal, and noise, respectively;
the simulation parameter setting is that the carrier frequency of the communication is 10GHz, the subcarrier spacing is delta f to 300KHz, the (M, N) in OTFS modulation are (64, 8) respectively, the symbol adopts QPSK, the antenna number of the satellite is M=16, the satellite height is 800km, the running speed is about 7.58km/s, and the time delay and Doppler range after time delay compensation and Doppler compensation are 0-0.52 mu s and 0-230 KHz. The result of channel estimation is shown in fig. 4, and the adopted low-complexity optimization algorithm is compared with a simulation curve under the condition of perfect time delay Doppler, so that the effectiveness of the algorithm is reflected. In addition, the curve of the transmission rate of the system can be represented in fig. 5, and it can be seen from the graph that, under the condition of different antenna numbers, the theoretical value and the simulation value can be coincident, so as to verify the transmission performance in the data transmission frame.
The present invention provides a channel estimation method for a multi-user uplink low-orbit satellite radio communication system, and the method and the way for realizing the technical scheme are numerous, the above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be regarded as the protection scope of the present invention. The components not explicitly described in this embodiment can be implemented by using the prior art.
Claims (9)
1. A method for channel estimation in a multi-user uplink low-orbit satellite radio communication system, comprising the steps of:
Step 1, modeling a multi-user uplink low-orbit satellite communication system, wherein the multi-user uplink low-orbit satellite communication system comprises a low-orbit LEO satellite and Q ground users, and the LEO satellite is provided with M L uniform linear antenna arrays ULA;
At the ground end, each user is a single antenna;
All Q ground users to LEO satellite uplink communication links adopt a broadband multi-carrier orthogonal time-frequency air conditioning modulation technology;
in the multi-user uplink low-orbit satellite communication system, pilot symbols of different users are embedded into DD domains, and indexes Γ of DD domain grids are expressed as follows:
Where k and l represent the discrete doppler grid index and the discrete delay grid index, respectively, k=0,..n-1, l=0,..m-1, Δf and T represent the subcarrier spacing and the symbol spacing, respectively, and satisfy
Step 3, carrying out energy detection on the received signals of Q users in different pilot frequency areas, designing a multipath and time delay index estimation algorithm, and estimating the total number of all paths and the time delay value of each path by setting a detection threshold value;
Defining the detection area of the q-th user, E q,l represents the energy detected by the q-th user at the discrete time delay grid index l, and by setting the detection threshold E th, when E q,l≥Eth, determining that the discrete time delay grid index l has multiple paths, so that Representing the estimated time delayBy accumulating all of the multipath when E q,l<Eth is absentEstimating the total multipath number of the user q, wherein l 1 is the pilot frequency position of the first user, and l max is the pilot frequency guard interval;
and 4, giving a closed expression of channel fading by using a maximum likelihood estimation method and estimating Doppler by using a one-dimensional search method.
2. The method of claim 1, wherein step 1 comprises modeling an upstream user-to-satellite delay-doppler domain wireless channel as:
Where h q (τ, v) represents a DD domain wireless channel of the Q-th user, q=1, & gt, Q, τ, v is an intermediate parameter, L q represents the number of multipaths of the Q-th user, g q,i expresses a small-scale fading channel of the i-th multipath of the Q-th user, obeying a rice distribution with a mean value of β q,i and a variance of Ω q,i, i=1, & gt, L q; A steering vector representing the ith multipath of the qth user, Wherein the method comprises the steps ofThe method is characterized in that the method comprises the steps of representing the uplink arrival angle of the ith multipath of the qth user, M L represents the number of uniform linear antenna arrays of the LEO satellite, j represents an imaginary unit, e is a natural constant, delta (·) represents a dirac delta function, and v q,i,τq,i represents Doppler and delay values of the ith multipath of the qth user respectively.
3. The method of claim 2, wherein step 2 comprises setting k max to represent a maximum Doppler index for all users within satellite coverage;
Each user transmits a single known pilot symbol in the pilot frame, and the discrete doppler grid index position and the discrete delay grid index position of the pilot symbol of the qth user in Γ are set to be k q,lq respectively.
4. The method of claim 3, wherein step 2 further comprises the step of generating a time dispersion phenomenon from a pilot symbol position l q to a pilot symbol position l q+lmax in a discrete time delay grid index, wherein the pilot position of the second user only needs to meet a guard interval of l max, the grid index of the pilot position of the second user is l 2＝l1+lmax +1, the position of the pilot signal of the Q-th user on the DD domain grid is l Q＝l1+(Q-1)lmax + (Q-1), and the step of ensuring that the pilot signals of all Q users can be deployed in the DD domain grid is required to meet the following conditions:
lQ+lmax≤M-1 (3),
Recording the DD domain pilot symbols s q＝vec(Sq sent by different users to the satellite), wherein Representing the pilot symbol of the qth user, in S q, the non-zero element position is (k q,lq), the non-zero element value is S q, the remaining position values are 0, vec (·) represents the matrix vectorization operation,S q representing the complex domain and DD domain is converted into a time-frequency domain through Heisenberg conversion and DD domain window function calculation in OTFS modulation, and is sent out through an antenna radio frequency link of a user, and a received signal y u of a u-th antenna of the LEO satellite is represented as:
Where u=1,..m L,yu＝vec(Yu), A DD domain received signal matrix representing the u-th antenna of the LEO satellite, η q represents the transmission power of the q-th user,Equivalent channel of DD domain, expressed asWhere T q,i is a sparse matrix, F N is N point DFT matrix, pi and delta respectively represent permutation matrix and diagonal matrix in OTFS modulation, Representing the Cronecker product operation, 0 1,MN-1 representing the all-zero row vector of 1× (MN-1), 0 MN-1,1 representing the all-zero column vector of (MN-1) ×1, I MN-1 representing the identity matrix of (MN-1) × (MN-1), and the delay and Doppler of user q at the ith multipath are represented by l q,i and k q,i, respectively, l q,i＝τq,iMΔf,kq,i＝vq,i NT; R q represents the index of non-zero element after pilot symbol vectorization of user q, r q＝kqM+lq;wu is the additive white Gaussian noise AWGN of the u-th receiving antenna, the obeying mean is 0, and the variance is 0 Wherein I MN represents the identity matrix of MN x MN.
5. The method of claim 4, wherein step 3 comprises providing a low-complexity time delay index estimation algorithm for the satellite received signals shown in formula (4), performing energy detection on the received signals of Q users in different pilot frequency areas, firstly, converting formula (4) into a matrix form of NxM, and converting the expression of the received signals into:
Where Y u [ k, l ] represents the received signal of the u-th antenna at the grid index [ k, l ], Y u＝mat(yu), mat (·) is the vector-to-matrix operation, the intermediate parameter Intermediate parametersK' is an intermediate parameter, W u [ k, l ] represents the AWGN of the u-th antenna at the [ k, l ] grid index, W u＝mat(wu).
6. The method of claim 5, wherein step 3 further comprises designing a multipath and delay index estimation algorithm to define the detection region of the qth user asThen the LEO satellite is in the areaThe energy detection in is expressed as:
7. The method of claim 6, wherein step 4 comprises analyzing sparsity of equation (4) by a received signal preprocessing method to bring s q into y u, and column vectors because the pilot symbols of the Q users do not interfere with each other Simplified intoWherein (-) M represents a modulo operation;
the closed expression of t q,i is:
Wherein the intermediate parameter N' =1, & gt, N, intermediate parameter n=0, & gt, N-1, Representing a remainder fetching operation;
The expression of equation (4) at this time is converted into:
Where y q,i,u represents a simplified received signal, W q,i,u denotes a simplified additive white gaussian noise AWGN,
For Doppler estimationAnd small scale fading estimationObtaining small-scale fading estimation by using a Maximum Likelihood Estimation (MLE) methodThe method comprises the following steps:
Finally, the method obtained by the formula (9) Brought to disclosure (8), doppler estimationThe maximum likelihood estimate MLE of (2) is expressed as:
one-dimensional search of k q,i over Doppler domain [ -k max,kmax ] for Finding the minimum to determine Doppler estimatesWhere k max represents the maximum doppler grid index for all users within satellite coverage.
8. An electronic device comprising a processor and a memory, the memory storing program code that, when executed by the processor, causes the processor to perform the steps of the method of any of claims 1 to 7.
9. A storage medium storing a computer program or instructions which, when run on a computer, performs the steps of the method of any one of claims 1 to 7.
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