OTFS system channel estimation algorithm based on adaptive structure coupling sparse Bayesian learning

Abstract

The invention discloses an OTFS system channel estimation algorithm based on adaptive structure coupling sparse Bayesian learning. The OTFS system channel estimation algorithm comprises the following steps: mapping pilot frequency and data symbols at a sending end; converting a received signal into a vector matrix form at a receiving end, and extracting a pilot frequency Yp in the vector matrix form; constructing a measurement matrix phi based on the compressed sensing mathematical model and the pilot signals; the method comprises the following steps of: solving a compressed sensing signal reconstruction problem by utilizing adaptive Pattern-Coupled Sparse Bayesian Learning (APCSBL), and estimating an OTFS sparse channel, so that the compressed sensing signal reconstruction problem is solved by utilizing the adaptive Pattern-Coupled Sparse Bayesian Learning (APCSBL); according to the method, the block sparse characteristic of the OTFS system fractional Doppler channel is effectively utilized, and the estimation precision and robustness of the algorithm are greatly improved.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology and proposes a channel estimation algorithm for OTFS systems based on adaptive structurally coupled sparse Bayesian learning. Background Technology

[0002] With the rapid development of wireless communication technology, future wireless communication systems are expected to support a series of new high-mobility applications such as vehicle-to-everything (V2X) communication, drones, and low-Earth orbit (LEO) satellites. These fast-time-varying scenarios exhibit significant Doppler frequency shift. However, the widely used Orthogonal Frequency Division Multiplexing (OFDM) technology is highly sensitive to Doppler frequency shift, which will lead to a severe deterioration in the communication performance of OFDM systems.

[0003] To address the performance limitations of OFDM in high-speed mobile scenarios, R. Hadani et al. proposed a novel two-dimensional modulation scheme—Orthogonal Time-Frequency Space (OTFS) modulation. The introduction of the Delay-Doppler (DD) domain transforms the fast time-varying channel in the time-frequency (TF) domain into a two-dimensional quasi-time-invariant channel in the DD domain. This allows the OTFS system to resist the doppler shift effects caused by high user mobility or high carrier frequencies, thus exhibiting significant advantages. In OTFS systems, obtaining accurate Channel Status Information (CSI) in the DD domain is a necessary condition for the receiver to correctly demodulate the received signal; therefore, channel estimation in OTFS systems has become a current research hotspot.

[0004] Traditional OTFS channel estimation primarily employs a threshold-based embedded pilot method. However, this method only demonstrates good estimation performance under integer delay and integer Doppler conditions. Its performance is limited under fractional delay and fractional Doppler conditions, and it wastes significant network resources, reducing spectral efficiency. While sequence correlation methods have been used for channel estimation, these methods are highly complex. Therefore, it is necessary to design a channel estimation method for fractional delay and Doppler conditions to address these issues. Summary of the Invention

[0005] This invention aims to solve the problems of the prior art mentioned above, and proposes a channel estimation algorithm for OTFS systems based on adaptive structurally coupled sparse Bayesian learning, comprising the following steps:

[0006] (1) Map pilot and data symbols at the transmitting end;

[0007] (2) At the receiving end, the received signal is converted into a vector matrix form and the pilot Y is extracted. p ;

[0008] (3) Construct the measurement matrix Φ based on the compressed sensing mathematical model and pilot signal;

[0009] (4) The compressed sensing signal reconstruction problem is solved by using Adaptive Pattern-Coupled SparseBayesian Learning (APCSBL) to estimate the OTFS sparse channel.

[0010] Furthermore, the mapping between the transmitting pilot and data symbols in step (1) of this invention is as follows:

[0011]

[0012] Where k and l represent the indices along the Doppler axis and the time delay axis in the time delay-Doppler grid, respectively, M and N are the number of subcarriers and the number of symbols in a frame, respectively, and x p To transmit pilot symbols, k p =N / 2, l p =M / 2,k v The maximum Doppler frequency shift of the system is given by Q, which is an integer (with a value of 5). τ For the maximum system delay, l s The data symbol x is placed at the remaining positions of the time delay Doppler grid, where x is an integer less than the maximum time delay. d .

[0013] Furthermore, in step (2) of the present invention, the signal received by the receiving end is converted into a vector matrix form and the pilot Y is extracted from it. p Includes the following steps:

[0014] Step 2-1: Establish the channel model in the time-delay-Doppler domain:

[0015]

[0016] Where δ(·) is the Dirichlet function, P is the number of transmission paths, and h i , τ i v i These represent the channel gain, delay, and Doppler shift corresponding to the i-th transmission path, respectively.

[0017] Step 2-2: In the time-delay-Doppler domain, the relationship between the received signal y[k,l] and the transmitted signal x[k,l] of the OTFS system can be expressed as:

[0018]

[0019] Among them, <·> N and <·> M These represent modulo N and modulo M operations, respectively. w[k, l] represents the channel gain when the Doppler tap of the transmission path is k′ and the delay tap is l′, and w[k, l] represents the variance in the delay-Doppler domain with σ. 2 The complex Gaussian white noise, where α[q, κ′] is the attenuation coefficient caused by fractional Doppler, can be expressed as:

[0020]

[0021] In real-world systems, ideal pulses do not exist. Therefore, rectangular pulses are usually used as substitutes for ideal pulses. Rectangular pulses introduce a certain phase shift β[k, l], which can be expressed as...

[0022]

[0023] Furthermore, the vector form Y of the received signal described in this invention can be obtained by vectorizing the time-delay-Doppler domain two-dimensional signal y[k, l] at the receiving end, as shown in the following expression:

[0024] Y = [y0, y1, ..., y2] M-1 ] T

[0025] Y m =[y[0,m],y[1,m],…,y[N-1,m]] T

[0026] Step 2-3: Select the received symbol matrix Y dd The l in p List to l p +l s Column, kth p -k v Go to k p +k v Line, expand to obtain the pilot signal vector y p The expression is:

[0027]

[0028] Y m =[y[k p -k v ,m],y[k p -k v +1, m],…,y[k p +k v ,m]] T

[0029] Furthermore, the OTFS channel estimation mathematical model constructed based on compressed sensing in step (3) can be expressed as:

[0030] Y P =Φh+W=(X p ⊙B)h+W

[0031] Among them, Y P Let X be the measurement vector, Φ be the measurement matrix, and X be the sensing matrix of the transmitted signal. p The Hadamard inner product of the phase offset matrix B is obtained, where W is the additive white Gaussian noise vector.

[0032] Furthermore, the signal sensing matrix X is sent. p For a double-block cyclic matrix, the expression is as follows:

[0033]

[0034] Among them, A m It is a block cyclic matrix with a size of (2k v +1)×(2k v +2Q+1) is obtained by cyclically shifting the time-delay-Doppler domain two-dimensional signal x[k,l] at the transmitting end, and its expression is:

[0035]

[0036] Furthermore, in step (4), when using adaptive structurally coupled sparse Bayesian learning to solve the compressed sensing signal reconstruction problem, the following steps are included:

[0037] Step 4-1: Initialization: Hyperparameter α (0) =|Φ H Y p Noise power The number of iterations t=1, the maximum number of iterations t max and convergence threshold ε min ;

[0038] Step 4-2: Calculate the expected posterior probability μ = σ - σ using the Gaussian distribution formula. 2 ∑Φ T y and covariance matrix ∑=(σ -2 Φ T Φ+D) -1 ;

[0039] Where D is the diagonal variance matrix, it can be represented as:

[0040] Step 4-3: Calculate parameters based on the EM algorithm And update hyperparameters

[0041] Step 4-4: Determine the stopping condition for iteration: <ε min or t>t max If yes, proceed to step 4-6; otherwise, proceed to step 4-5.

[0042] Step 4-5: Let the iteration number t = t + 1, and go back to step 4-2;

[0043] Steps 4-6: Output channel impulse response approximation: which is the estimated time-delay-Doppler domain sparse channel of the OTFS system.

[0044] Compared with the prior art, the present invention has the following advantages:

[0045] (1) The channel estimation algorithm for the OTFS system based on adaptive structural coupling sparse Bayesian learning proposed in this invention uses the same signal-to-noise ratio for the pilot and the data, which effectively reduces the power of the pilot signal.

[0046] (2) The OTFS system channel estimation algorithm proposed in this invention utilizes the structurally coupled Gaussian prior model and the adaptive hyperparameter strategy to fully exploit the block sparsity characteristics of the time delay-Doppler domain channel under fractional Doppler frequency shift, which greatly improves the estimation accuracy of the algorithm. Attached Figure Description

[0047] Figure 1 This is a flowchart illustrating the implementation process of the present invention.

[0048] Figure 2 The pilot distribution diagram used in this invention

[0049] Figure 3 This chart compares the normalized mean square error (NMSE) performance of the proposed algorithm with other channel estimation algorithms.

[0050] Figure 4 This chart compares the bit error rate (BER) performance of the algorithm proposed in this invention with other channel estimation algorithms. Detailed Implementation

[0051] The method described in this invention will be explained in detail with reference to the accompanying drawings and specific embodiments.

[0052] (1) Map pilot and data symbols at the transmitting end;

[0053] like Figure 2 As shown, the transmitting pilot of the entire system adopts an embedded structure. The shaded area represents the pilot, which is placed on the time-delay Doppler grid [k]. p , l pWithin a certain range around the transmitter, the remaining grid cells are used to place data symbols. The mapping between the transmitter pilot and the data symbols is as follows:

[0054]

[0055] Where k and l represent the indices along the Doppler axis and the time delay axis in the time delay-Doppler grid, respectively, M and N are the number of subcarriers and the number of symbols in a frame, respectively, and x p To transmit pilot symbols, k p =N / 2, l p =M / 2,k v The maximum Doppler frequency shift of the system is given by Q, which is an integer (with a value of 5). τ For the maximum system delay, l s x is an integer less than the maximum delay. d The data symbols to be transmitted. In this invention, the signal-to-noise ratio at the pilot signal does not need to be set too high; it can be the same as the signal-to-noise ratio at the data symbol signal, which effectively reduces the transmission power of the pilot signal.

[0056] (2) At the receiving end, the received signal is converted into a vector matrix form and the pilot Y is extracted. p ;

[0057] Step 2-1: Establish the channel model in the time-delay-Doppler domain:

[0058]

[0059] Where δ(·) is the Dirichlet function, P is the number of transmission paths, and h i , τ i v i These represent the channel gain, delay, and Doppler shift corresponding to the i-th transmission path, respectively.

[0060] Step 2-2: In the time-delay-Doppler domain, the relationship between the received signal y[k,l] and the transmitted signal x[k,l] of the OTFS system can be expressed as:

[0061]

[0062] Among them, <·> N and <·> M These represent modulo N and modulo M operations, respectively. w[k, l] represents the channel gain when the Doppler tap of the transmission path is k′ and the delay tap is l′, and w[k, l] represents the variance in the delay-Doppler domain with σ. 2 The complex Gaussian white noise, where α[q, κ′] is the attenuation coefficient caused by fractional Doppler, can be expressed as:

[0063]

[0064] In real-world systems, ideal pulses do not exist. Therefore, rectangular pulses are usually used as substitutes for ideal pulses. Rectangular pulses introduce a certain phase shift β[k, l], which can be expressed as...

[0065]

[0066] Furthermore, the vector form Y of the received signal described in this invention can be obtained by vectorizing the time-delay-Doppler domain two-dimensional signal y[k, l] at the receiving end, as shown in the following expression:

[0067] Y = [y0, y1, ..., y2] M-1 ] T

[0068] Y m =[y[0,m],y[1,m],…,y[N-1,m]] T

[0069] Steps 2-3: (e.g.) Figure 2 As shown, the symbols marked with five stars are pilot signals used for channel estimation. The l-th symbol in the received symbol matrix Y is selected. p List to l p +l s Column, kth p -k v Go to k p +k v Line, that is, the pilot signal vector at the receiving end is

[0070]

[0071] Y m =[y[k p -k v ,m],y[k p -k v +1, m],…,y[k p +k v ,m]] T

[0072] (3) Construct the measurement matrix Φ based on the compressed sensing mathematical model and pilot signal;

[0073] Y P =Φh+W=(X p ⊙B)h+W

[0074] Among them, Y P Let X be the measurement vector, Φ be the measurement matrix, and X be the sensing matrix of the transmitted signal. p The Hadamard inner product of the phase offset matrix B is used to obtain W, which is an additive white Gaussian noise vector. In the observation vector Y... PGiven that the measurement matrix Φ is known, the sparse channel vector h can be estimated using the model. est .

[0075] Furthermore, the signal sensing matrix X is sent. p For a double-block cyclic matrix, the expression is as follows:

[0076]

[0077] Among them, A m It is a block cyclic matrix with a size of (2k v +1)×(2k v +2Q+1), can be obtained by cyclically shifting the time-delay-Doppler domain two-dimensional signal x[k,l] at the transmitting end, and the expression is:

[0078]

[0079] (4) The problem of compressed sensing signal reconstruction is solved by using Adaptive Structure Coupled Sparse Bayes Learning (APCSBL) to estimate the OTFS sparse channel;

[0080] Step 4-1: Initialization: Hyperparameter α (0) =|Φ H Y p Noise power The number of iterations t=1, the maximum number of iterations t max and convergence threshold ε min ;

[0081] Step 4-2: Calculate the expected posterior probability μ = σ according to the Gaussian distribution formula. -2 ΦA T y and covariance matrix Φ = (σ -2 A T A+D) -1 ;

[0082] Specifically, a hierarchical Gaussian model is established, assuming that each component of the vector h follows a Gaussian distribution. Unlike the traditional sparse Bayesian learning framework, in the structurally coupled Bayesian hierarchical model, the variance of each parameter is determined not only by its corresponding hyperparameter but also by its neighboring hyperparameters.

[0083] p(h i |α i α i+1 α i-1 )=N(0,|(α i +βα i+1 +βα i-1 ) -1 )

[0084] Furthermore, due to the symmetry and attenuation of the time-delay-Doppler domain channel, we introduce three different coupling factors β1, β2, and β3 to adaptively characterize the strength of the correlation between channel coefficients, thereby more fully exploiting the sparsity characteristics within the channel. Therefore, the above equation can be rewritten as:

[0085]

[0086] Where j = 1, 2, 3, β1, β2, β3 are 0.8, 0.7, 0.6 respectively;

[0087] Further assume that the hyperparameter α follows a Gamma distribution, i.e.

[0088]

[0089] Where a and b are parameters in the gamma distribution;

[0090] The prior distribution of h can be calculated by the following formula.

[0091] p(h|α,y)∝p(h|α)p(y|h)

[0092] in p(h|α) and p(y|h) are defined as follows:

[0093]

[0094] Based on the aforementioned adaptive structurally coupled Bayesian hierarchical model, the MAP estimation result of vector h can usually be obtained iteratively using the Expectation-Maximization (EM) algorithm. For the E-step of the Expectation-Maximization (EM) algorithm, given the hyperparameter α, the posterior probability p(h|α, y) of vector h follows a Gaussian distribution with mean and variance as follows:

[0095] μ = σ -2 ΦA T y

[0096] Φ=(σ -2 A T A+D) -1

[0097] Where D is a diagonal matrix, and the i-th element on its diagonal is... Right now

[0098]

[0099] When the iteration process stops, the MAP estimate of vector h is the mean μ of its Gaussian distribution;

[0100] Step 4-3: Calculate parameters based on the EM algorithm And update hyperparameters

[0101] Where κ is a constant, κ∈[0,1];

[0102] Step 4-4: Determine the stopping condition for iteration: <ε min Or t > t max If yes, proceed to step 4-6; otherwise, proceed to step 4-5.

[0103] Step 4-5: Let the iteration number t = t + 1, and go back to step 4-2;

[0104] Steps 4-6: Output channel impulse response approximation: which is the estimated time-delay-Doppler domain sparse channel of the OTFS system.

[0105] The effects of this invention can be further illustrated by the following simulations:

[0106] 1. The simulation conditions are shown in Table 1 below.

[0107] Table 1 OTFS Modulation System Parameters

[0108] System parameters Parameter value OTFS Delay-Doppler Plane Parameters (N, M) (64，256) Subcarrier spacing Δf 15kHz carrier frequency f 4GHz <![CDATA[CP duration t CP > 4.38μs Modulation method 4-QAM User movement speed V 500kmph <![CDATA[Maximum Doppler shift v max > 1852Hz <![CDATA[Maximum Doppler delay index l max > 17 <![CDATA[Maximum Doppler index k max > 8

[0109] 2. Simulation Content

[0110] Figure 3 and Figure 4 The following table compares the performance of the channel estimation algorithm of this invention with other channel estimation algorithms under different signal-to-noise ratios in terms of normalized mean square error (NMSE) and bit error rate (BER). EP represents the channel estimation algorithm based on the threshold method, OMP represents the channel estimation algorithm based on orthogonal matching pursuit, SBL represents the channel estimation algorithm based on sparse Bayesian learning, and APCSBL represents the channel estimation algorithm proposed in this invention based on adaptive structurally coupled sparse Bayesian learning. It can be seen that the algorithm proposed in this invention significantly outperforms other algorithms.

[0111] The above is merely a further description of the present invention and is not intended to limit the implementation and application of this patent. All equivalent implementations of the present invention should be included within the scope of the claims of this patent.

Claims

1. A channel estimation algorithm for an OTFS system based on adaptive structurally coupled sparse Bayesian learning, characterized in that, Includes the following steps: (1) Map pilot and data symbols at the transmitting end; (2) At the receiving end, the received signal is converted into a vector matrix form and the pilot Y is extracted. p ; (3) Construct the measurement matrix Φ based on the compressed sensing mathematical model and pilot signal; (4) The compressed sensing signal reconstruction problem is solved by using Adaptive Pattern-Coupled SparseBayesian Learning (APCSBL) to estimate the 0TFS sparse channel.

2. The channel estimation algorithm for the OTFS system based on adaptive structurally coupled sparse Bayesian learning as described in claim 1, characterized in that, The mapping between the transmitting pilot and data symbols in step (1) is as follows: Where k and l represent the indices along the Doppler axis and the time delay axis in the time delay-Doppler grid, respectively, M and N are the number of subcarriers and the number of symbols in a frame, respectively, and x p To transmit pilot symbols, k p =N / 2, l p =M / 2,k v The maximum Doppler frequency shift of the system is given by Q, which is an integer (with a value of 5). τ For the maximum system delay, l s The data symbol x is placed at the remaining positions of the time delay Doppler grid, where x is an integer less than the maximum time delay. d .

3. The channel estimation method for the OTFS system based on adaptive structurally coupled sparse Bayesian learning as described in claim 1, characterized in that, In step (1), the signal-to-noise ratio of the pilot inserted at the transmitting end is the same as that of the data symbol, which effectively reduces the transmission power of the pilot.

4. The channel estimation method for OTFS system based on adaptive structurally coupled sparse Bayesian learning as described in claim 1, characterized in that, In step (2), the relationship between the received symbol y[k, l] and the transmitted signal x[k, l] of the OTFS system can be expressed as: Among them, <·> N and <·> M These represent modulo N and modulo M operations, respectively. w[k, l] represents the channel gain when the Doppler tap of the transmission path is k′ and the delay tap is l′, and w[k, l] represents the variance in the delay-Doppler domain with σ. 2 The complex Gaussian white noise, where α[q, κ′] is the attenuation coefficient caused by fractional Doppler, can be expressed as: In real-world systems, ideal pulses do not exist. Therefore, rectangular pulses are usually used as substitutes for ideal pulses. Rectangular pulses introduce a certain phase shift β[k, l], which can be expressed as...

5. The channel estimation method for the OTFS system based on adaptive structurally coupled sparse Bayesian learning as described in claim 1, characterized in that, In step (2), the vector form Y of the received signal can be obtained by vectorizing the time-delay-Doppler domain two-dimensional signal y[k, l] at the receiving end, as shown in the following expression: Y=[y0,y1,…,y M-1 ] T Y m =[y[0,m],y[1,m],…,y[N-1,m]] T 6. The channel estimation method for an OTFS system based on adaptive structurally coupled sparse Bayesian learning as described in claim 1, characterized in that, In step (2), the data symbols used by the receiver for channel estimation occupy Y. dd The l in p List to l p +l s Column, kth p -k v Go to k p +k v Line, that is, the pilot signal vector at the receiving end is Y m =[y[k p -k v ,m],y[k p -k v +1,m],…,y[k p +k v ,m]] T 7. The channel estimation method for OTFS system based on adaptive structurally coupled sparse Bayesian learning as described in claim 1, characterized in that, In step (3), the mathematical model for OTFS channel estimation based on compressed sensing can be expressed as: Y P =Φh+W=(X p ⊙B)h+W Among them, Y P Let X be the measurement vector, Φ be the measurement matrix, and X be the sensing matrix of the transmitted signal. p The Hadamard inner product of the phase offset matrix B is obtained, where W is the additive white Gaussian noise vector.

8. The channel estimation method for an OTFS system based on adaptive structurally coupled sparse Bayesian learning as described in claim 1, characterized in that, In step (3), the signal sensing matrix X is sent. p For a double-block cyclic matrix, the expression is as follows: Among them, A m It is a block cyclic matrix with a size of (2k v +1)×(2k v +2Q+1) is obtained by cyclically shifting the time-delay-Doppler domain two-dimensional signal x[k,l] at the transmitting end, and its expression is:

9. The channel estimation method for an OTFS system based on adaptive structurally coupled sparse Bayesian learning as described in claim 1, characterized in that, In step (4), when solving the compressed sensing signal reconstruction problem using adaptive structural coupled sparse Bayesian learning, the following steps are included: Step 4-1: Initialization: Hyperparameter α (0) =|Φ H Y p Noise power The number of iterations t=1, the maximum number of iterations t max and convergence threshold ε min ; Step 4-2: Calculate the expected posterior probability μ = σ according to the Gaussian distribution formula. -2 ∑Φ T y and covariance matrix ∑=(σ -2 Φ T Φ+D) -1 ; Where D is the diagonal variance matrix, it can be represented as: Step 4-3: Calculate parameters based on the EM algorithm And update hyperparameters Step 4-4: Determine the stopping condition for iteration: <ε min Or t > t max If yes, proceed to step 4-6; otherwise, proceed to step 4-5. Step 4-5: Let the iteration number t = t + 1, and go back to step 4-2; Steps 4-6: Output channel impulse response approximation: which is the estimated time-delay-Doppler domain sparse channel of the OTFS system.

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