A low pilot overhead channel estimation method for OTFS system

Abstract

The present invention belongs to the field of wireless communication technology, and specifically relates to a low pilot overhead channel estimation method for an OTFS system. In orthogonal time-frequency air modulation technology, channel estimation is a key link to give full play to system performance, and improving estimation accuracy and reducing pilot overhead are two important contents of channel estimation. The present invention provides a general construction method of an autoregressive model and a state space model of a delay Doppler domain channel to make full use of channel correlation. In addition, the present invention proposes a new frame structure, a configurable frame group and a frame transmission mode, which greatly reduces the pilot overhead. Finally, a channel estimation technology based on an extended Kalman filter is proposed. Simulation results show that the proposed channel estimation based on an extended Kalman filter improves the estimation performance through channel correlation and the ability to suppress noise. In combination with the designed frame transmission mode, the relevant parameters are reasonably selected, and the pilot overhead can be greatly reduced while ensuring performance.

Description

Technical Field

[0001] The invention belongs to the technical field of wireless communications, and in particular relates to a low pilot overhead channel estimation method for an OTFS system. Background Art

[0002] Orthogonal Time Frequency Space (OTFS) modulation technology has attracted wide attention for its excellent performance in high-speed scenarios. OTFS maps symbols in the delay-Doppler domain and spreads each symbol to the entire time-frequency space through a two-dimensional orthogonal function. Each symbol experiences the same time-frequency fading; the receiver's equalization algorithm obtains the same time-frequency diversity gain, thereby improving the reliability of wireless communication systems in high-speed scenarios.

[0003] Accurate channel estimation is a prerequisite for stable reception at the receiver of the OTFS system. In the literature "Murali KR, Chockalingam A. On OTFS modulation for high-doppler fading channels [C] / / 2018 Information Theory and Applications Workshop (ITA), San Diego, CA, USA. IEEE, 2018: 1-10" and "Fish A, Gurevich S, Hadani R, et al. Delay-doppler channel estimation in almost linear complexity [J]. IEEE Transactions on Information Theory, 2013, 59 (11): 7632-7644", a separate frame is used to carry a training pilot consisting of a pseudo-random noise sequence. This scheme has a high implementation complexity and seriously reduces the spectrum efficiency. The paper "Raviteja P, Phan KT, HongY. Embedded pilot-aided channel estimation for OTFS in delay–doppler channels[J]. IEEE Transactions on Vehicular Technology, 2019, 68(5): 4906-4917" proposed a threshold-based embedded pilot channel estimation method in a single-input single-output (SISO) system. The sender sets a pilot symbol in the delay-Doppler domain grid and equips it with sufficient guard symbols to prevent interference from data symbols. The delay-Doppler domain channel parameters are estimated at the receiving end through a threshold-based method. This scheme requires non-zero pilot symbols to have higher power, which increases the peak-to-average power ratio of the system; and requires a large number of guard symbols, which reduces the spectrum efficiency of the system.The compressed sensing algorithm is applied to OTFS channel estimation in the literature "Rasheed OK, Surabhi GD, Chockalingam A. Sparse delay-doppler channel estimation in rapidly time-varying channels for multiuserOTFS on the uplink[C] / / 2020IEEE 91st Vehicular Technology Conference(VTC2020-Spring), Antwerp, Belgium. IEEE, 2020: 1-5" and the literature "Zhang M, Wang F, Yuan X, et al. 2Dstructured turbo compressed sensing for channel estimation in OTFS systems[C] / / 2018IEEE International Conference on Communication Systems(ICCS), Chengdu, China. IEEE, 2018: 45-49", but it is assumed to be under the conditions of biorthogonal and ideal waveforms. The paper "Shen W, Dai L, An J, et al. Channel estimation for orthogonal time frequency space (OTFS) massive MIMO [J]. IEEE Transactions on Signal Processing, 2019, 67(16): 4204-4217" analyzes the sparsity of the three-dimensional structure of the OTFS massive multiple-input multiple-output (MIMO) system and proposes an orthogonal matching pursuit (3D-SOMP) algorithm to obtain channel state information, but the pilot overhead is large.

[0004] At present, there is little research on using the channel correlation between adjacent OTFS frames to assist channel estimation. However, making full use of channel-related information to assist channel estimation is expected to further improve the accuracy of estimation, reduce pilot overhead, and improve the overall spectrum efficiency of the system. Summary of the invention

[0005] To solve the above problems, the present invention provides a general method for constructing a time delay Doppler domain channel autoregressive model and a state space model. At the same time, a new OTFS frame structure, a configurable frame group and a frame transmission mode that can fully utilize channel correlation are proposed, which greatly reduces the pilot overhead of the OTFS system and improves the spectrum efficiency. Finally, a channel estimation technology based on extended Kalman filtering is designed.

[0006] The technical solution of the present invention is:

[0007] A low pilot overhead channel estimation method for an OTFS system, comprising:

[0008] The frames of the OTFS system are divided into two types. The first type of frame is a frame containing pilot symbols, which is defined as type 1; the second type of frame is a frame without pilot symbols, which is defined as type 2. The type 2 frame only contains data symbols; the number of grid points of the system Doppler and delay axes are N and M respectively, and the Doppler and delay resolutions are 1 / (NT) and 1 / (M△f) respectively; based on the type 1 and type 2 frames, the frame transmission mode is set as follows: the leading part is transmitted first, followed by the data part. The leading part is composed of 0 to N type 1 frames, and the data part is composed of repeated frame groups. The leading part can also be regarded as a special frame group. The definition of the frame group is: K OTFS frames are divided into a group, wherein the first K1 OTFS frames are type 1 frames, and the remaining K-K1 OTFS frames are type 2 frames;

[0009] Channel estimation: When the current OTFS frame type is type1, a channel estimation method based on pilot symbols is used to obtain a channel estimation value;

[0010] When the current OTFS frame type is type2, the specific channel estimation method is:

[0011] For the OTFS system, the input-output relationship in the delay-Doppler domain is:

[0012]

[0013] Wherein, the subscript n∈[0,+∞) represents the frame subscript of OTFS, l∈[0,M-1], v∈[0,N-1] represent the delay and Doppler subscripts of the delay-Doppler domain grid, M and N represent the number of grid points of the delay and Doppler axes, respectively; l′∈[0,L-1], v′∈[-k v ,k v ] represent the sampling values ​​of channel delay and Doppler frequency shift respectively; L = τ max M△f represents the sampling value of the maximum delay of the channel, τ maxis the maximum channel delay, 1 / (M△f) represents the delay resolution, △f is the system subcarrier spacing; k v Represents the maximum Doppler sampling value. Since the fractional Doppler tap will cause diffusion along the Doppler axis, k is usually v ≥v max , where v max =f dmax NMT s represents the sampling value of the actual maximum Doppler frequency shift in the delay-Doppler domain, f dmax is the maximum Doppler shift, 1 / (NMT s )=1 / (NT) is the Doppler resolution, T s is the sampling interval of the system; M cp represents the length of the system cyclic prefix, and M cp ≥L; Indicates the delay-Doppler domain received data block the [l,v]th element of ; Indicates the data block sent in the delay-Doppler domain The first [(ll′) M ,(vv′) N ] elements; represents the additive white Gaussian noise matrix the [l,v]th element of ; represents the delay-Doppler domain channel response matrix the [l′,v′]th element of ;

[0014] right Build a first-order autoregressive model:

[0015] h n+1 =R n h n +v n

[0016] in represents the vector of non-zero taps of the delay-Doppler domain channel within the nth OTFS frame; is the time correlation coefficient matrix, which is a diagonal matrix, and each element on the diagonal corresponds to h n The time correlation coefficient of a delay-Doppler channel tap in ; is the transfer process noise of the channel tap, which has a mean of 0 and a covariance matrix of Gaussian white noise, Represents dimension L(2k v +1) identity matrix;

[0017] R nVectorize and establish a random walk model, combine the OTFS input-output relationship in matrix form, and get the state space model as follows:

[0018]

[0019] in, is the received symbol vector; Indicated by The observation matrix formed; They represent the process Gaussian white noise of the time correlation coefficient and the channel Gaussian white noise respectively, their mean is 0, and the covariance matrix is

[0020] For ease of expression, the state space model is simplified as:

[0021]

[0022] in, represents the state vector; Represents the nonlinear state transfer equation; is the overall process noise, with a mean of 0 and a covariance matrix

[0023] The nonlinear state transition process in the state space model is linearized using Taylor expansion:

[0024]

[0025] in,

[0026] So the state prediction equation is established as:

[0027]

[0028] Where the subscript n-1|n-1 represents the optimal estimate of the state vector in the n-1th OTFS frame; n|n-1 represents the predicted value of the state vector in the nth OTFS frame, and P is the covariance matrix of the state vector χ, which represents the uncertainty of the estimate; we get χ n|n-1 After that, the channel tap h is extracted n , and recover the delay-Doppler domain channel Obtain the initial estimate of the transmitted delay-Doppler domain symbol through equalization and detection algorithms Then construct the observation matrix;

[0029] The state update equation is established as:

[0030]

[0031] in, Represents the Kalman filter gain at time n; obtains the posterior estimate of the state vector through the state update equation, further extracts and constructs the delay Doppler channel matrix, and obtains the final estimate of the transmitted symbol through the equalization and detection algorithm

[0032] The beneficial effects of the present invention are as follows: the present invention provides a general construction method of the autoregressive model and state space model of the delay Doppler domain channel to make full use of the channel correlation; designs a new frame structure, configurable frame group and frame transmission mode, which greatly reduces the pilot overhead; and proposes a channel estimation technology based on extended Kalman filtering. Simulation results show that the proposed channel estimation based on extended Kalman filtering improves the estimation performance through channel correlation and noise suppression capabilities, and cooperates with the designed frame transmission mode and reasonably selects relevant parameters, which can greatly reduce the pilot overhead while ensuring performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a type 2 frame structure.

[0034] Figure 2 It is a configurable OTFS frame group.

[0035] Figure 3 It is the frame structure of the Full Guard mode.

[0036] Figure 4 is the pilot load curve.

[0037] Figure 5 It is a structural diagram of the frame transmission mode.

[0038] Figure 6 It is the system BER performance under different PDs (120km / h).

[0039] Figure 7 It is the system BER performance (500km / h) under different PDs.

[0040] Figure 8 It is the system BER performance under different SNR (120km / h).

[0041] Fig. 9 It is the system BER performance (500km / h) under different SNR.

[0042] Fig.10 is the estimated pilot load percentage for different channels. DETAILED DESCRIPTION

[0043] The technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings and simulation examples so that those skilled in the art can better understand the present invention.

[0044] In order to solve the problem of large pilot overhead of channel estimation in the existing OTFS system, the present invention designs a new frame structure, a configurable frame group and a frame transmission mode.

[0045] The present invention divides the frames in the OTFS system into two different structural types: the frames containing pilot symbols are called type 1, and the frames without pilot symbols are called type 2. Type 1 frames can be configured accordingly according to any pilot-based channel estimation algorithm; for type 2 frames without pilot symbols, the structure is as follows Figure 1 As shown in the figure, 1 / (NT) and 1 / (M△f) represent the Doppler and time delay resolutions, respectively. N and M represent the number of grid points corresponding to the Doppler and time delay axes, respectively.

[0046] For type 1 OTFS frames, the channel estimation is obtained through the configured pilot symbols. Figure 1 The type 2 frame structure shown contains only data symbols, so it needs to obtain the channel estimation value of the current frame based on the channel estimated in the previous OTFS frame through prediction and tracking algorithms. Type 2 frames can improve spectral efficiency and use all transmitter power for data symbols, thereby improving energy efficiency.

[0047] The present invention designs a configurable OTFS frame group that can fully utilize the performance of the prediction and tracking algorithms, such as Figure 2 As shown in the figure, K OTFS frames are grouped together. First, K1 type 1 OTFS frames are sent to obtain the estimated value of the channel using the pilot. This is followed by K-K1 type 2 OTFS frames. The channel estimation value of the current frame is obtained based on the channel estimated in the previous OTFS frame using the prediction and tracking algorithm. Compared with the OTFS system that only uses type 1, assuming that its pilot load is λ1, the pilot load proposed in this scheme is:

[0048]

[0049] Therefore, by properly selecting K1 and K, the spectrum efficiency can be significantly improved. In addition, more transmitter power will be used for data symbols, thereby also improving energy efficiency.

[0050] Consider the frame structure design of the Full Guard mode in the fractional Doppler scenario. The frame structure is as follows: Figure 3 As shown:

[0051] exist Figure 3 In [k p ,l p] is the location of the pilot. In order to prevent the inter-Doppler interference introduced by the fractional Doppler tap, the frame structure of the Full Guard mode sets the symbols around the pilot along the entire Doppler axis as protection symbols; the pilot load of this scheme is

[0052] Will Figure 3 The frame structure shown is used as type 1 frame. Set the parameters K = 15, L = 26, M = 128, N = 32, and draw the pilot load curve as shown in Figure 4 As shown, from Figure 4 It can be observed that compared with the OTFS system that only uses the type 1 structure, the proposed configurable frame group scheme can greatly reduce the pilot load and obtain higher spectrum efficiency; more transmit power is used for data symbols, which also improves energy efficiency.

[0053] Based on the above-mentioned concept of configurable OTFS frame group, the present invention designs the following Figure 5 The frame transmission mode shown in Figure 5 In the frame transmission mode shown, the entire transmission process is divided into a preamble part that is transmitted first, followed by a data part. The OTFS frames in the preamble part all carry pilots (type 1), the number of which is 0 to N, while the data part consists of repeated frame groups. The number of type 2 OTFS frames in the configurable frame group of the data part is defined as the pilot distance (PD), which also indicates the number of type 2 OTFS frames between two type 1 frames. At the beginning of the transmission process, the purpose of designing the preamble part is that the prediction and tracking algorithms used by the system may require some type 1 frames containing pilots in the initial stage for training related parameters.

[0054] Based on the above frame transmission mode, the present invention uses an extended Kalman filter (Extended Kalman Filter, EKF) to complete the tracking of the channel, and proposes a channel estimation method based on EKF. First, when the current OTFS frame type is type1, the channel estimation method based on pilot symbols is used to obtain the initial value of the channel estimation; otherwise, when the current OTFS frame type is type2, the initial estimate of the channel is obtained through the prediction equation of EKF. After channel equalization and symbol detection, the observation matrix is ​​constructed using the initial estimate of the transmitter symbol, and the optimal estimate of the channel and the final estimate of the transmitter symbol are obtained through the state update equation of EKF. The state prediction and state update equations of EKF are introduced below.

[0055] In order to make full use of channel correlation to assist channel estimation, the present invention proposes an autoregressive model of delay Doppler channel taps and a method for constructing a state space model.

[0056] For the Reduce-CP OTFS system, the input-output relationship in the delay-Doppler domain can be expressed as follows:

[0057]

[0058] Wherein, the subscript n∈[0,+∞) represents the frame subscript of OTFS, l∈[0,M-1], v∈[0,N-1] represent the delay and Doppler subscripts of the delay-Doppler domain grid, M and N represent the number of grid points of the delay and Doppler axes, respectively; l′∈[0,L-1], v′∈[-k v ,k v ] represent the sampling values ​​of channel delay and Doppler frequency shift respectively; L = τ max M△f represents the sampling value of the maximum delay of the channel, τ max is the maximum channel delay, 1 / (M△f) represents the delay resolution, △f is the system subcarrier spacing; k v Represents the maximum Doppler sampling value. Since the fractional Doppler tap will cause diffusion along the Doppler axis, k is usually v ≥v max , where v max =f dmax NMT s represents the sampling value of the actual maximum Doppler frequency shift in the delay-Doppler domain, f dmax is the maximum Doppler shift, 1 / (NMT s )=1 / (NT) is the Doppler resolution, T s is the sampling interval of the system; M cp represents the length of the system cyclic prefix, and M cp ≥L; Indicates the delay-Doppler domain received data block the [l,v]th element of ; Indicates the data block sent in the delay-Doppler domain The first [(ll′) M ,(vv′) N ] elements; represents the additive white Gaussian noise matrix the [l,v]th element of ; represents the delay-Doppler domain channel response matrix The [l′,v′]th element of .

[0059] against Establish a first-order autoregressive model, which can be expressed as:

[0060] h n+1 =R n h n +v n(2)

[0061] in represents the vector of non-zero taps of the delay-Doppler domain channel within the nth OTFS frame; is the time correlation coefficient matrix, which is a diagonal matrix, and each element on the diagonal corresponds to h n The time correlation coefficient of a delay-Doppler channel tap in ; is the transfer process noise of the channel tap, which has a mean of 0 and a covariance matrix of Gaussian white noise, Represents dimension L(2k v +1). For any channel model, since the time correlation coefficient of each channel tap is unknown, a model is also established and tracked. Specifically, R n Vectorize and establish a random walk model; combined with the OTFS input-output relationship in matrix form, the state space model can be expressed as:

[0062]

[0063] in, is the received symbol vector; Indicated by The observation matrix formed; They represent the process Gaussian white noise of the time correlation coefficient and the channel Gaussian white noise respectively, their mean is 0, and the covariance matrix is For easier expression, formula (3) can be simplified as:

[0064]

[0065] in, represents the state vector; Represents the nonlinear state transfer equation; is the overall process noise, with a mean of 0 and a covariance matrix

[0066] The nonlinear state transfer process in equation (4) is linearized using Taylor expansion, and we can obtain:

[0067]

[0068] in, The specific state prediction and update equations are introduced below:

[0069] A. State Prediction Process

[0070] According to the state space equation shown in equation (6), the state prediction equation can be expressed as:

[0071]

[0072] The subscript n-1|n-1 represents the optimal estimate (a posteriori estimate) of the state vector in the n-1th OTFS frame; n|n-1 represents the predicted value (a priori estimate) of the state vector in the nth OTFS frame. P is the covariance matrix of the state vector χ, which represents the uncertainty of the estimate. n|n-1 After that, we can extract the channel tap h n , and recover the delay-Doppler domain channel Obtain the initial estimate of the transmitted delay-Doppler domain symbol through equalization and detection algorithms Then construct the observation matrix.

[0073] B. Status Update Process

[0074] According to the state space equation shown in equation (8), the state update equation can be expressed as:

[0075]

[0076] in, Represents the Kalman filter gain at time n. The a posteriori estimate of the state vector is obtained through equation (7), and the delay-Doppler channel matrix is ​​further extracted and constructed, and the final estimate of the transmitted symbol is obtained through the equalization and detection algorithm.

[0077] Simulation example:

[0078] Under the conditions of M=128, N=32, △f=15kHz, K1=1, and the leading part contains 3 type1 frames for training EKF parameters, the sparse Doppler frequency shift channel is generated using the Vehicular A channel model for simulation, and the channel delay is set to [0,3,7,10,17,25]*T s , where T sis the system sampling interval; taking the reference “Raviteja P, Phan KT, Hong Y.Embedded pilot-aided channel estimation for OTFS in delay–doppler channels[J].IEEE Transactions on Vehicular Technology, 2019, 68(5):4906-4917” as an example (hereinafter referred to as the reference), the channel estimation method proposed in the reference is used as the pilot-based channel estimation, and other pilot-based channel estimation methods can be directly replaced; and according to the generation method of the sparse Doppler frequency shift channel in the reference: a Doppler tap is generated for each delay path, and satisfies v i =v max cosθ i , where v max represents the sampling value of the maximum Doppler frequency shift, θ i Uniformly distributed in [-π,π]. The simulation results are compared and analyzed with the references:

[0079] At different speeds, the relationship between system BER performance and pilot distance (PD) is as follows: Figure 6 and Figure 7 As shown in the figure, as the pilot distance increases, the BER performance decreases, because the larger the pilot distance, the more errors are accumulated. Comparing the situations at the two speeds, at a high signal-to-noise ratio, the algorithm proposed by the present invention can not only obtain the advantage of greatly reducing the pilot load, but also has certain performance advantages. The reason is that the Kalman filter is based on the minimum mean square error criterion and has a certain inhibitory effect on noise. However, at a low signal-to-noise ratio, especially at a high speed, the performance degradation is more obvious due to the large accumulated error value generated by the type 2 frame.

[0080] At different speeds, the relationship between system BER performance and SNR is as follows: Figure 8 and Fig. 9 As shown in the figure, the system performance improves with the increase of SNR, because the noise interference becomes smaller and the demodulation becomes more accurate. At a speed of 120km / h, due to the small amount of error accumulation, even if the pilot distance is 6, the BER performance of the system is more advantageous than the comparative literature that only uses pilots for channel estimation; and the pilot load is reduced by about 1 / 6, which greatly improves the spectrum efficiency of the system. At 500km / h, due to the large amount of error accumulation, the performance is slightly worse than the comparative literature that only uses pilots for channel estimation under low signal-to-noise ratio and PD>2, but it can be observed from the local enlarged figure that the BER performance is only 1dB different when PD=6 and SNR=10dB, and only 0.5dB different when PD=2.

[0081] The pilot load curve compared with the reference is as follows Fig.10 As shown in the figure: when the pilot distance is 0, the BER has a significant gain, because the extended Kalman filter is based on the minimum mean square error criterion and can suppress noise. However, the threshold-based embedded pilot channel estimation does not process the noise. The BER performance gradually decreases with the increase of PD, which is due to the cumulative effect of errors; the decrease in pilot load is significant compared with the comparative literature, which greatly improves the spectrum efficiency and energy efficiency of the OTFS system.

Claims

1. A low pilot overhead channel estimation method for an OTFS system, characterized in that: include: The frames of the OTFS system are divided into two types. The first type of frame is a frame containing pilot symbols, which is defined as type 1. The second type of frame is a frame without pilot symbols, which is defined as type 2. Type 2 frames only contain data symbols. Based on type 1 and type 2 frames, the frame transmission mode is set as follows: the leading part is transmitted first, followed by the data part, the leading part is composed of 0 to N type 1 frames, the data part is composed of repeated frame groups, and the definition of the frame group is: K OTFS frames are divided into one group, wherein the first K1 OTFS frames are type 1 frames, and the remaining K-K1 OTFS frames are type 2 frames; Channel estimation: When the current OTFS frame type is type1, a channel estimation method based on pilot symbols is used to obtain a channel estimation value; When the current OTFS frame type is type2, the specific channel estimation method is: For the OTFS system, the input-output relationship in the delay-Doppler domain is: Wherein, the subscript n∈[0,+∞) represents the frame subscript of OTFS, l∈[0,M-1], v∈[0,N-1] represent the delay and Doppler subscripts of the delay-Doppler domain grid, M and N represent the number of grid points of the delay and Doppler axes, respectively; l′∈[0,L-1], v′∈[-k v ,k v ] represent the sampling values ​​of channel delay and Doppler frequency shift respectively; L = τ max M△f represents the sampling value of the maximum delay of the channel, τ max is the maximum channel delay, 1 / (M△f) represents the delay resolution, △f is the system subcarrier spacing; k v Represents the maximum Doppler sampling value. Since the fractional Doppler tap will cause diffusion along the Doppler axis, k is usually v ≥v max , where v max =f dmax NMT s represents the sampling value of the actual maximum Doppler frequency shift in the delay-Doppler domain, f dmax is the maximum Doppler shift, 1 / (NMT s )=1 / (NT) is the Doppler resolution, T s is the sampling interval of the system; M cp represents the length of the system cyclic prefix, and M cp ≥L; Y n DD [l,v] represents the delay-Doppler domain received data block the [l,v]th element of ; Indicates the data block sent in the delay-Doppler domain The first [(ll′) M ,(vv′) N ] elements; represents the additive white Gaussian noise matrix the [l,v]th element of ; represents the delay-Doppler domain channel response matrix the [l′,v′]th element of ; right Build a first-order autoregressive model: h n+1 =R n h n +v n in represents the vector of non-zero taps of the delay-Doppler domain channel within the nth OTFS frame; is the time correlation coefficient matrix, which is a diagonal matrix, and each element on the diagonal corresponds to h n The time correlation coefficient of a delay-Doppler channel tap in ; is the transfer process noise of the channel tap, which has a mean of 0 and a covariance matrix of Gaussian white noise, Represents dimension L(2k v +1) identity matrix; R n Vectorize and establish a random walk model, combine the OTFS input-output relationship in matrix form, and get the state space model as follows: in, is the received symbol vector; Indicated by The observation matrix formed; They represent the process Gaussian white noise of the time correlation coefficient and the channel Gaussian white noise respectively, their mean is 0, and the covariance matrix is For ease of expression, the state space model is simplified as: in, represents the state vector; Represents the nonlinear state transfer equation; is the overall process noise, with a mean of 0 and a covariance matrix The nonlinear state transition process in the state space model is linearized using Taylor expansion: in, So the state prediction equation is established as: Where the subscript n-1|n-1 represents the optimal estimate of the state vector in the n-1th OTFS frame; n|n-1 represents the predicted value of the state vector in the nth OTFS frame, and P is the covariance matrix of the state vector χ, which represents the uncertainty of the estimate; we get χ n|n-1 After that, the channel tap h is extracted n , and recover the delay-Doppler domain channel Obtain the initial estimate of the transmitted delay-Doppler domain symbol through equalization and detection algorithms Then construct the observation matrix; The state update equation is established as: in, Represents the Kalman filter gain at time n; obtains the posterior estimate of the state vector through the state update equation, further extracts and constructs the delay Doppler channel matrix, and obtains the final estimate of the transmitted symbol through the equalization and detection algorithm

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