A Channel Estimation Method for OTFS

Abstract

The present invention discloses a channel estimation method for OTFS. For communication in a high-speed mobile environment, the transmission system is a single-input single-output system. A basis expansion model BEM applicable to high-speed mobile scenarios is established according to the sparsity of the channel impulse response. OGCE-BEM is used to fit the OTFS channel. The channel is fitted into the form of basis function coefficients and basis functions. Given the known basis functions, the channel matrix estimation problem is transformed into the estimation problem of basis function coefficients. Then, in the traditional RLS filter algorithm, based on the relationship between the forgetting factor and the estimation error, an iterative update rule based on the forgetting function is designed, improving the real-time tracking ability of the system. The present invention can effectively ensure the effectiveness and reliability of communication, greatly improving the channel estimation accuracy.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and in particular, to a channel estimation method for Orthogonal Time Frequency Space (OTFS). Background Art

[0002] With the emergence of autonomous driving technologies, the widespread use of sensors, the Internet of Things, and immersive media, the requirements for service quality in network transmission have been further improved, and the needs of people in aspects such as interpersonal communication and information transmission in different scenarios have increased. In traditional modulation schemes, such as OFDM, signals are modeled in the time-frequency domain and perform poorly in time-frequency doubly selective channels, unable to meet the requirements of high-speed mobile communication. The 6G system requires the emergence of new modulation technologies. A key feature that differentiates OTFS modulation from other traditional modulation schemes is that OTFS transmits in the dimension of the delay-Doppler domain. If the transmitting-end signal is modulated by OTFS, the design of the equalizer can be greatly simplified, and the channel estimation overhead in a fast time-varying channel can be reduced. Therefore, OTFS is particularly suitable for communication in high-speed mobile environments. Channel estimation technology is the main method for obtaining channel state information at the receiving end. The accuracy of channel estimation technology is related to the accuracy of signal recovery at the receiving end and is an important indicator for measuring the performance of a wireless communication system. Therefore, channel estimation technology is crucial for OTFS.

[0003] Chinese Patent CN 1 113507426A discloses a joint channel estimation and signal detection based on OTFS modulation, which improves the estimation accuracy and resource utilization rate and avoids the problem of excessive pilot overhead. However, this invention is based on an MIMO system, and the number of estimated parameters increases with the increase in the number of antennas. When the number of antennas is too large, the computational complexity is high. "Channel Estimation for Orthogonal Time Frequency Space (OTFS) Massive MIMO" in the 16th issue of the 67th volume of "IEEE Transactions on Signal Processing" shows that the channels of the large-scale MIMO OTFS downlink have 3D structural sparsity and achieve accurate channel estimation with a low pilot overhead. However, OTFS is often applied to high-speed mobile environments without considering the characteristics of high-speed mobile environments. Summary of the Invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and provide an OTFS-oriented channel estimation method. For communications in a high-speed mobile environment, the transmission system is a single-input single-output system. The OGCE-BEM is used to model the channel, and the channel matrix estimation problem is transformed into a basis function coefficient estimation problem. In order to obtain the estimated values of the basis function coefficients, an RLS filter based on a variable forgetting function is designed. According to the relationship between the forgetting function and the estimation error, the forgetting function is iteratively updated in real time, thereby effectively ensuring the effectiveness and reliability of communication and greatly improving the accuracy of channel estimation.

[0005] The purpose of the present invention is achieved through the following technical solutions.

[0006] A channel estimation method for OTFS, wherein the communication system includes a transmitter and a receiver, and adopts OTFS for data transmission; in the OTFS system, the number of subcarriers is M, the number of OTFS symbols is N, the number of paths is L, and the carrier frequency is f c , the relative speed between the transmitter and the receiver is v, and the speed of light is c. In the frequency domain, the time axis is sampled at a time interval T, and the frequency axis is sampled at a frequency interval Δf. At the transmitter, the two-dimensional data sequence x[k,l] is first mapped to the delay-Doppler domain, and the data symbols are mapped to the time-frequency domain through the ISFFT transform to obtain the data sequence X[n,m]. After that, the time-frequency signal s(t) is obtained through the Heisenberg transform and then sent out through the channel. At the receiver, the receiver performs the exact opposite operation to the transmitter. The received time-domain signal r(t) is transformed through the Wigner transform to obtain the time-frequency domain signal Y[n,m]. Y[n,m] is then transformed through the SFFT to obtain the delay-Doppler domain signal y[k,l].

[0007] The channel estimation method comprises the following steps:

[0008] Step 1: At the receiving end, the received signal is vectorized into an N·M-dimensional matrix. The input and output relationship of the OTFS system can be summarized as follows:

[0009] Define x = {x[0,0],x[0,1]…,x[N-1,0],x[N-1,1],…x[N-1,M-1]} T

[0010] y={y[0,0],y[0,1]…,y[N-1,0],y[N-1,1],…y[N-1,M-1]} T As the respective transmitted and received signals; after passing through the double-selective fading channel with Doppler propagation, the vector y of the received OTFS signal in the delay-Doppler domain can be expressed as:

[0011]

[0012] Among them, F N is an N-point discrete Fourier transform matrix, w is an additive white Gaussian noise vector with zero mean and variance σ 2 , I M is an M-dimensional identity matrix, (·) H denotes the conjugate transpose, denotes the Kronecker product;

[0013] Step 2: According to BEM, the channel matrix can be represented by basis functions. H t can be expressed as:

[0014]

[0015] Among them, b q with a length of M·N represents the q-th basis function, c q =[c q [0], c q [1], …, c q [L]] T is the q-th unknown basis function coefficient with a length of (L + 1), and Q represents the number of basis functions;

[0016] Step 3: According to formula (2), it can be known that the channel matrix H t is represented by the basis function b q and the basis function coefficient c q ; The OGCE-BEM is used to represent the basis function b q , and the n-th element of its q-th basis function can be expressed as:

[0017]

[0018] Among them, n = 0, …, N - 1, the correction coefficient is the maximum Doppler frequency, is the normalized maximum Doppler frequency, Δf is the subcarrier spacing, and Z is the dense sampling coefficient;

[0019] Step 4: Update and iterate the RLS filter, including: estimating the basis function coefficient c t of the channel matrix H q , updating the estimation error e(n), updating the coefficient k(n) of the RLS filter, updating the correlation matrix R(n) of the RLS filter, iteratively updating the forgetting function according to the relationship between the forgetting function and the error, tracking the change of the channel in real time, obtaining the updated basis function expression, and obtaining the final channel matrix;

[0020] Here, the RLS filter using a variable forgetting function is cyclically iterated to estimate the basis function coefficient cq ;

[0021] When q = 1 and n = 0, initialize the RLS filter parameters, and initialize c q (0)=0, R -1 (0)=δ -2 I, λ(0)=0.99, x(0)=0, where R(n) represents the correlation matrix of the filter, λ(n) represents the forgetting function, and δ is a positive number.

[0022] Specifically, update the estimated error e(n):

[0023] e(n)=d(n)-c q T (n - 1)x(n) (4)

[0024] where d(n) represents the desired received signal.

[0025] Update the coefficient k(n) of the RLS filter:

[0026]

[0027] Update the correlation matrix R(n) of the RLS filter:

[0028] R(n)=λ -1 (n - 1)R -1 (n - 1)[1 - k(n)x T (n)] (6).

[0029] Furthermore, iteratively update the forgetting function, and track the change of the channel in real time according to the relationship between the forgetting function and the error:

[0030]

[0031] where, indicates the variance of the estimated error, indicates the variance of the θ function.

[0032]

[0032] Furthermore, from formulas (4) and (5), the updated basis function expression can be obtained:

[0033] c q (n)=c q (n - 1)+k(n)e(n) (8).

[0034] Furthermore, the process of obtaining the final channel matrix is: when q = Q and n = N - 1, stop the iteration and output c q ; Substitute c q into formula (2) to obtain the channel matrix.

[0035] Update process of the variable forgetting function:

[0036] Step1. From the formula of the estimation error \(e(n) = d(n)-c q T (n - 1)x(n)\), its variance is expressed as:

[0037]

[0038] Step2. Define a function about \(\theta\):

[0039] \(\theta(n)=x T (n)R -1 (n - 1)x(n)(10)

[0040] Calculate the variance of the \(\theta\) function from formula (10)

[0041] Step3. Since the forgetting function is related to the estimation error, the forgetting function is expressed as a formula:

[0042]

[0043] Compared with the prior art, the advantages and beneficial effects of the present invention are:

[0044] 1. The present invention represents the channel matrix with basis functions and basis function coefficients, reducing the unknown channel coefficients to be estimated and the computational complexity; on the other hand, reducing the inter-carrier interference and improving the channel estimation accuracy.

[0045] 2. The present invention uses OGCE - BEM to model the OTFS channel, which can effectively reduce the problem of spectral leakage for more dense sampling of Doppler, reduce the error brought by high-frequency basis functions to the model, and is beneficial to improving the performance of the system in a high-speed mobile environment.

[0046] 3. The present invention uses the RLS filter with a variable forgetting function to estimate the basis function coefficients, and by iteratively updating the forgetting function, it can track the system changes, making the system more traceable and having a small estimation error when the system converges. Description of the Drawings

[0047] Figure 1 is a schematic diagram of the channel estimation system model of an embodiment of the present invention.

[0048] Figure 2 is a schematic diagram of the simplified process of an embodiment of the present invention.

[0049] Figure 3 is a flowchart of the method of an embodiment of the present invention. Detailed implementation mode

[0050] A channel estimation method for an orthogonal time-frequency space (OTFS) modulation system according to the present invention establishes a basis expansion model (BEM) applicable to high-speed mobile scenarios based on the sparsity of the channel impulse response, and uses OGCE-BEM to fit the OTFS channel. The channel is fitted into the form of basis function coefficients and basis functions. When the basis functions are known, the channel matrix estimation problem is transformed into the problem of estimating the basis function coefficients. On the one hand, the number of unknown channel coefficients to be estimated is reduced, and the computational complexity is reduced; on the other hand, the inter-carrier interference is reduced, and the channel estimation accuracy is improved. Then, in the traditional RLS filter algorithm, based on the relationship between the forgetting function and the estimation error, an iterative update rule based on the forgetting function is designed to improve the real-time tracking ability of the system. The present invention has certain superiority in terms of accuracy and complexity compared with the existing methods.

[0051] The following further describes the present invention in detail with reference to the accompanying drawings.

[0052] As Figure 1 shown, it is a channel estimation system model diagram of an embodiment of the present invention. At the transmitting end, the two-dimensional data sequence x[k, l] is first mapped to the delay-Doppler domain, and the data symbols are mapped to the time-frequency domain through the ISFFT transform to obtain the data sequence X[n, m]. These two steps are called OTFS modulation. Then, the time-frequency signal s(t) is obtained through the Heisenberg transform and sent through the channel. At the receiving end, the receiver performs exactly the opposite operations to those at the transmitting end. The received time-domain signal r(t) is transformed through the Wigner transform to obtain the time-frequency domain signal Y[n, m], and Y[n, m] is then transformed through the SFFT transform to obtain the signal y[k, l] in the delay-Doppler domain.

[0053] A channel estimation method for OTFS based on the BEM model according to the present invention, the communication system includes a transmitting end and a receiving end, and data transmission is carried out in the OTFS manner. In the OTFS system, the number of subcarriers is M, the number of OTFS symbols is N, the number of paths is L, and the carrier frequency is f c , and the relative speed between the transmitting end and the receiving end is v, and the speed of light is c. In the frequency domain, the time axis is sampled at time intervals T, and the frequency axis is sampled at frequency intervals Δf; the channel estimation method includes the following steps:

[0054] Step 1: At the receiving end, the received signal is vectorized into a matrix of N·M dimensions. The input-output relationship of the OTFS system can be summarized into the following vectorized form.

[0055] Define \(x = \{x[0,0],x[0,1],\cdots,x[N - 1,0],x[N - 1,1],\cdots,x[N - 1,M - 1]\}\) T

[0056] \(y=\{y[0,0],y[0,1],\cdots,y[N - 1,0],y[N - 1,1],\cdots,y[N - 1,M - 1]\}\) T As the respective transmit and receive signals. After passing through a doubly selective fading channel with Doppler propagation, the received OTFS signal in the time-delay - Doppler domain vector \(y\) can be expressed as:

[0057]

[0058] where \(F\) N is an \(N\)-point discrete Fourier transform matrix, \(w\) is an additive white Gaussian noise vector with zero mean and variance \(\sigma\) 2 \(I\) M is an \(M\)-dimensional identity matrix, \((\cdot)^{H}\) H denotes the conjugate transpose, denotes the Kronecker product.

[0059] Step 2: According to the BEM, the channel matrix can be represented by basis functions and basis functions. \(H\) t can then be expressed as:

[0060]

[0061] where \(b\) of length \(M\cdot N\) q represents the \(q\)-th basis function, \(c = [c[0],c[1],\cdots,c[L]]\) q q is the \(q\)-th unknown basis function coefficient of length \((L + 1)\), and \(Q\) represents the number of basis functions. q q T

[0062] Step 3: According to formula (2), it can be known that the channel matrix \(H\) t is represented by the basis function \(b\) q and the basis function coefficient \(c\) q . The present invention uses OGCE - BEM to represent the basis function \(b\) q . OGCE - BEM can effectively reduce the problem of spectral leakage for more dense sampling of Doppler, and reduce the error brought by high - frequency basis functions to the model. The \(n\)-th element of the \(q\)-th basis function of \(b\) q can be expressed as:

[0063]

[0064] where \(n = 0,\cdots,N - 1\), the correction coefficient is the maximum Doppler frequency, is the normalized maximum Doppler frequency, Δf is the subcarrier spacing, and Z is the dense sampling coefficient.

[0065] Step 4. Update and iterate the RLS filter, including: estimating the basis function coefficients c t of the channel matrix H q , updating the estimation error e(n), updating the coefficients k(n) of the RLS filter, updating the correlation matrix R(n) of the RLS filter, iteratively updating the forgetting function according to the relationship between the forgetting function and the error, tracking the change of the channel in real time, obtaining the updated basis function expression, and obtaining the final channel matrix;

[0066] Here, the RLS filter using a variable forgetting function is cyclically iterated to estimate the basis function coefficients c q ;

[0067] When q = 1 and n = 0, initialize the RLS filter parameters, initialize c q (0) = 0, R -1 (0) = δ -2 I, λ(0) = 0.99, x(0) = 0, where R(n) represents the correlation matrix of the filter, λ(n) represents the forgetting function, and δ is a positive number.

[0068] The updated estimation error e(n):

[0069] e(n) = d(n) - c q T (n - 1)x(n) (4)

[0070] where d(n) represents the expected received signal.

[0071] The updated coefficients k(n) of the RLS filter:

[0072]

[0073] The updated correlation matrix R(n) of the RLS filter:

[0074] R(n) = λ -1 (n - 1)R -1 (n - 1)[1 - k(n)x T (n)] (6).

[0075] The iterative update of the forgetting function, tracking the change of the channel in real time according to the relationship between the forgetting function and the error:

[0076]

[0077] Among them, represents the variance of the estimation error, represents the variance of the θ function.

[0078] From the above formulas (4) and (5), the updated basis function expression can be obtained:

[0079]

[0080] The process of obtaining the final channel matrix is as follows: when q = Q and n = N - 1, stop the iteration and output c q . Substitute c q into formula (2) to obtain the channel matrix.

[0081] The update process of the variable forgetting function:

[0082] Step1: From the formula of the estimation error e(n) = d(n) - c q T (n - 1)x(n), it can be seen that its variance is expressed as:

[0083]

[0084] Step2: Define a function about θ:

[0085]

[0086] From formula (10), calculate the variance of the θ function

[0087] Step3: Since the forgetting function is related to the estimation error, the forgetting function is expressed as a formula:

[0088]

Claims

1. A channel estimation method for OTFS, whose communication system includes a transmitter and a receiver, and uses the OTFS method for data transmission; in the OTFS system, the number of subcarriers is M, the number of OTFS symbols is N, the number of paths is L, and the carrier frequency is f c , the relative speed between the transmitter and the receiver is v, and the speed of light is c; in the frequency domain, the time axis is sampled at time interval T, and the frequency axis is sampled at frequency interval Δf; at the transmitter, first the two-dimensional data sequence x[k, l] is mapped to the delay-Doppler domain, and the data symbols are mapped to the time-frequency domain through the ISFFT transform to obtain the data sequence X[n, m]; then, the time-frequency signal s(t) is obtained through the Heisenberg transform and sent through the channel; at the receiver, the receiver performs the exact opposite operations of the transmitter. The received time-domain signal r(t) undergoes the Wigner transform to obtain the time-frequency domain signal Y[n, m], and Y[n, m] undergoes the SFFT transform to obtain the delay-Doppler domain signal y[k, l]; The described channel estimation method includes the following steps: Step 1: At the receiving end, the received signal is vectorized into an N·M-dimensional matrix; the input-output relationship of the OTFS system is summarized in the following vectorized form: Define \(x = \{x[0,0], x[0,1], \ldots, x[N - 1,0], x[N - 1,1], \ldots, x[N - 1,M - 1]\}\) T y = {y[0,0], y[0,1]…, y[N-1,0], y[N-1,1],…y[N-1,M-1]} T As their respective transmitted and received signals; after passing through a doubly selective fading channel with Doppler propagation, the received OTFS signal in the time-delay - Doppler domain can be represented by the vector y as follows: Among them, F N is an N-point discrete Fourier transform matrix, w is an additive white Gaussian noise vector with zero mean and variance σ 2 , I M is an M-dimensional identity matrix, (·) H denotes the conjugate transpose, denotes the Kronecker product; Step 2. According to BEM, the channel matrix can be represented by basis functions, and H t can be expressed as: Among them, b with a length of M`N q represents the q-th basis function, and c q = [c q [0], c q [1], …, c q [L]] T is the q-th unknown basis function coefficient of length (L + 1), and Q represents the number of basis functions; Step 3. According to formula (2), the channel matrix H t is represented by the basis function b q and the basis function coefficient c q ; The OGCE-BEM is used to represent the basis function b q , and the nth element of its qth basis function can be expressed as: where n = 0, …, N - 1, the correction factor is the maximum Doppler frequency, is the normalized maximum Doppler frequency, Δf is the subcarrier spacing, and Z is the dense sampling factor; Step 4: Update the RLS filter iteratively, including: t The basis function coefficient c q Estimate and update the estimated error e(n), update the coefficient k(n) of the RLS filter, update the correlation matrix R(n) of the RLS filter, iteratively update the forgetting function based on the relationship between the forgetting function and the error, track the changes in the channel in real time, obtain the updated basis function expression, and obtain the final channel matrix; Here, the RLS filter with a variable forgetting function iteratively estimates the basis function coefficients c q ; When q = 1 and n = 0, initialize the RLS filter parameters, and initialize c q (0) = 0, R -1 (0) = δ -2 I, λ(0) = 0.99, x(0) = 0, where R(n) represents the correlation matrix of the filter, λ(n) represents the forgetting function, and δ is a positive number.

2. The channel estimation method for OTFS according to claim 1, wherein The described updated estimation error e(n): e(n) = d(n) - c q T (n - 1)x(n) (4) where d(n) represents the signal expected to be received.

3. The channel estimation method for OTFS according to claim 1, wherein The described update of the coefficient k(n) of the RLS filter:

4. The channel estimation method for OTFS according to claim 1, wherein The described iterative update of the forgetting function, tracking the change of the channel in real time according to the relationship between the forgetting function and the error: Among them, represents the variance of the estimation error, represents the variance of the θ function.

5. A channel estimation method for OTFS according to claim 2 or 3, characterized in that, From formulas (4) and (5), the updated basis function expression can be obtained: c q y(n) = c q y(n - 1)+k(n)e(n) (8).

6. The channel estimation method for OTFS according to claim 1, wherein The process of obtaining the final channel matrix is as follows: when q = Q and n = N - 1, stop the iteration and output c q ; Substitute c q into formula (2) to obtain the channel matrix.

7. A channel estimation method for OTFS according to claim 1 or 4, characterized in that The update process of the variable forgetting function: Step 1. From the formula for the estimation error \(e(n)=d(n)-c(n - 1)x(n)\), it can be seen that its variance is expressed as: q T (n - 1)x(n), it can be seen that its variance is expressed as: Step 2: Define a function about θ: θ(n) = x T (n)R -1 (n - 1)x(n) (10) Calculate the variance of the θ function from Equation (10). Step 3: Since the forgetting function is related to the estimation error, the forgetting function is expressed as a formula:

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