A terahertz cell-free receiver extrapolation method based on multi-edge trace schrodinger bridge

Abstract

The application discloses a terahertz cell-free receiver extrapolation method based on a multi-edge trace Schrodinger bridge. Each terahertz AP measures the transmission delay of a served user and returns the transmission delay to a CPU. Each terahertz AP estimates the user angle and estimates the digital domain channel on a sampling frequency band and returns the digital domain channel to the CPU. The CPU constructs a full-band digital domain channel by using the transmission delay and the sampling frequency band digital domain channel returned by all terahertz APs, calculates an equalization matrix to form a training set, and trains the forward and reverse drift on each Schrodinger bridge. The CPU constructs a multi-edge trace Schrodinger bridge by using a stochastic differential equation, and fits the forward and reverse drift on the training set by using two neural networks. The CPU inferences the equalization matrix by frequency band in the forward and reverse directions by using the trained forward and reverse drift model. The CPU weights the forward and reverse results and equalizes the received signal by frequency band by using all the frequency band digital equalization matrices. The application greatly saves the computing resources of the terahertz cell-free wireless access network.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to an extrapolation method for terahertz non-cellular receivers based on a multi-track Schrödinger bridge. Background Technology

[0002] Terahertz communication offers a promising solution to alleviate increasingly strained spectrum resources, but terahertz wireless signals also face significant path fading and weak resistance to obstruction. To offset these drawbacks, massive MIMO (Multiple-Input Multiple-Output) antenna technology is required. A common approach is to integrate very large-scale arrays using the extremely short wavelengths of terahertz to provide extremely high gain to compensate for the significant fading. However, in complex environments, especially in heavily obstructed urban areas, even very large-scale arrays struggle to provide high-quality terahertz communication services. Cellular wireless access networks, as a distributed version of massive MIMO, reduce path loss and provide more line-of-sight paths by distributing radio access points across the coverage area. Terahertz cellular wireless access networks utilize a large-scale deployment of small arrays of terahertz radio access points to provide high-performance, easily implemented terahertz wireless communication services. Due to the small size and wide beamwidth of the cellular terahertz radio access point arrays, beam splitting issues are negligible under the large bandwidth of terahertz, resulting in a low local computational burden on the terahertz radio access points.

[0003] However, the central processing unit (CPU) still faces several bottlenecks that need to be addressed. In the considered uplink scenario, the total digital channel dimension, formed by stitching together the full-band digital channels of all terahertz RF access points, still far exceeds the CPU's processing capacity, making it impractical to calculate the equalization matrix for each frequency band. In centralized terahertz massive MIMO systems, because the distances from different subarrays of a VMI to a user are almost identical, the user's digital channels across different frequency bands exhibit a uniform phase shift, allowing for simple deduction of the equalization matrix for different frequency bands. This is not the case in terahertz non-cellular systems, where the distances from different RF access points to a user often vary significantly. The digital subchannels of the same user experience different phase shifts across the frequency band, and this heterogeneity prevents the equalization matrix from being obtained through simple phase transformation. Summary of the Invention

[0004] Purpose of the invention: This invention provides an extrapolation method for terahertz non-cellular receivers based on a multi-trace Schrödinger bridge, which avoids frequent large-scale matrix inversion operations and greatly saves computing resources for terahertz non-cellular wireless access networks.

[0005] Technical solution: The present invention provides an extrapolation method for terahertz non-cellular receivers based on a multi-track Schrödinger bridge, comprising the following steps:

[0006] Step 1: The terahertz radio access point (AP) measures the transmission delay of the users it serves and sends the data back to the CPU via the fronthaul link.

[0007] Step 2: Each terahertz AP estimates the user angle and aligns the beam with the user direction, estimating the digital domain channel backhaul to the CPU in the sampling frequency band.

[0008] Step 3: The CPU constructs a full-band digital domain channel using the transmission delay and sampling frequency band digital domain channel returned by all terahertz APs, and calculates the equalization matrix to form a training set;

[0009] Step 4: The CPU trains forward and backward drift on each segment of the Schrödinger bridge. The CPU constructs a multi-trace Schrödinger bridge through stochastic differential equations and uses two neural networks to fit the forward and backward drift on the training set.

[0010] Step 5: The CPU uses the trained forward and reverse drift models to infer the equalization matrix in both forward and reverse frequency bands.

[0011] Step 6: The CPU weights the forward and reverse results and uses the digital equalization matrix of all frequency bands to equalize the received signal band by band.

[0012] Furthermore, in step 1, each terahertz AP measures the transmission delay of the user it serves, and any... Each terahertz AP selects several user services with minimal-scale fading and a line-of-sight path, and measures the transmission delay using pilot signals. The estimated transmission delay is then transmitted to the CPU via the fronthaul link. The terahertz non-cellular radio access network serves... If there are multiple users, and each terahertz AP serves all users, then the transmission delay... , Represents the complex field.

[0013] Furthermore, in step 2, each terahertz AP estimates the user angle and aligns the beam with the user's direction. After beam alignment, each terahertz AP performs digital domain channel estimation at equal intervals on different frequency bands. It is assumed that the terahertz non-cellular radio access network has a total of... For the following frequency bands, the terahertz AP performs digital domain channel estimation:

[0014]

[0015] in Indicates the estimated channel. It is the frequency band number. It is the terahertz AP serial number. It is the number of terahertz APs. and yes Integer multiples of, For the number of frequency bands, For the number of users.

[0016] Furthermore, in step 3, the CPU constructs a full-band digital domain channel using the transmission delays and sampling frequency band digital domain channels returned by all terahertz APs. The CPU concatenates the transmission delays to obtain a delay matrix and concatenates the digital domain channels to obtain a global digital domain channel. Due to the distributed deployment of terahertz APs in the terahertz non-cellular wireless access network, the digital domain channels of different frequency bands have heterogeneous phase shifts, that is, each element of the channel experiences a different phase shift in the frequency band. Using the phase shifts of the digital domain channels in the above frequency bands, the CPU calculates the digital domain channels of all frequency bands and calculates the equalization matrix band by band. The minimum equalization error equalization is adopted. The CPU integrates all the full-band equalization matrices corresponding to the channel correlation times collected for training to form a training dataset.

[0017] Furthermore, for each pair of adjacent integers The multiple sampling frequency band number will include the frequency band interval containing these two sampling frequency bands. The equalization matrix on each frequency band is used as a trajectory of probability distribution transition. Pairing it with the corresponding delay matrix yields a training data point, which is added to the training set. This process is repeated for each pair of sampling frequency band numbers in each channel coherent block to form a dataset for training.

[0018] Furthermore, in step 4, the evolution of the equalization matrix over a frequency band is considered as a continuous distribution transition within a time interval. Therefore, the equalization matrix of a training dataset is considered as a transition over the time interval. The results corresponding to each keyframe can be described by two forward and backward stochastic differential equations, respectively, for the continuous evolution from the first keyframe to the last keyframe and from the last keyframe to the first keyframe. In the forward stochastic differential equation, the differential of the keyframe is equal to the product of the forward drift velocity and the time differential plus a Brownian motion differential. In the backward stochastic differential equation, the differential of the keyframe is equal to the product of the backward drift velocity and the time differential plus a Brownian motion differential. The forward and backward drift velocities are functions of the current keyframe, the delay matrix, and the current time.

[0019] Furthermore, to estimate the forward and reverse drift velocities, two diffusion neural network models are constructed. The two models have the same structure but use different independent weights. Then, Euler-Maruyama discretization is used to rewrite the two stochastic differential equations into discrete forms with optimizable parameters. The time interval length is set to be equal to the frequency band sampling interval to simplify the equations. In the forward equation, the increment of adjacent keyframes is equal to the drift velocity plus a Gaussian noise, and in the reverse equation, the increment of adjacent keyframes is equal to the negative drift velocity plus a Gaussian noise.

[0020] To train the forward and backward diffusion neural networks, time is sampled uniformly for each pair of adjacent keyframe moments. The weights of the two diffusion neural networks are trained and optimized using the square of the difference between the estimated drift velocity and the estimated intermediate time as the loss function, where the estimated drift velocity is determined by the estimated intermediate time. The slope between the drift result of the keyframes and the forward or reverse endpoint keyframes is obtained, and the intermediate time is estimated. The drift results of keyframes are obtained by sampling from a Gaussian distribution determined by adjacent keyframes.

[0021] Furthermore, the forward and backward diffusion neural networks adopt the U-Net architecture, which includes: input convolution module, first time-embedded residual block, first downsampling module, second time-embedded residual block, second downsampling module, third time-embedded residual block, third downsampling module, fourth time-embedded residual block, attention module, fifth time-embedded residual block, first upsampling module, sixth time-embedded residual block, second upsampling module, seventh time-embedded residual block, third upsampling module, eighth time-embedded residual block, and output convolution module in sequence;

[0022] The input convolutional module needs to encode the delay matrix and use it together with the equalization matrix as input features to predict the drift. Embedding encoding is performed using a conventional encoder module, and then combined with an equalization matrix passed through a convolutional layer. The features are summed, and then a convolution is performed again to output the result.

[0023] Time-embedded residual blocks require for each pair of time... Random sampling is performed, and forward and backward models are trained segment by segment.

[0024] Furthermore, in step 5, the CPU calculates the equalization matrix of the sampling frequency band using the digital domain channel of the sampling frequency band. For the equalization matrix of every two adjacent sampling frequency bands... Using the trained forward and backward diffusion models, the equalization matrix of the unsampled frequency bands is inferred band by band according to the following formula:

[0025]

[0026]

[0027] in For group number, , Let be the delay matrix. For frequency band number, For the number of users, The positive drift velocity is simulated using a neural network. The reverse drift velocity is simulated using a neural network. For the variance of the Wiener process, As the increment of the sequence number, we obtain Forward and inverse estimations of all intermediate frequency bands, Let them be Gaussian variables. The first predicted by the positive drift model Digital domain equalization matrix in each frequency band The first predicted by the positive drift model Digital domain equalization matrix in each frequency band The first predicted by the positive drift model Digital domain equalization matrix in each frequency band The first predicted by the reverse drift model Digital domain equalization matrix in each frequency band The first predicted by the reverse drift model Digital domain equalization matrix in each frequency band For the first Digital domain equalization matrix across each frequency band.

[0028] Furthermore, in step 6, the CPU performs a weighted merging of the equalization matrices from the forward and backward inference to obtain the final predicted equalization matrix. Using the mean of the forward and backward inference as the prediction result, the equalization matrix for all frequency bands is then obtained.

[0029]

[0030] in, This is the digital domain equalization matrix for the nth frequency band. For frequency band number, For the number of users, This is the digital domain equalization matrix predicted by the positive drift model for the nth frequency band. This is the digital domain equalization matrix predicted by the reverse drift model for the nth frequency band. Number of frequency bands;

[0031] use The CPU performs global equalization on the received signals transmitted across all frequency bands according to the following formula.

[0032]

[0033] in For the first The first frequency band Preliminary symbol estimation after simulation equalization on a terahertz AP This is the final symbol estimation after digital equalization on the CPU side. It is the number of terahertz APs. For frequency band number, Given the number of frequency bands, the CPU now obtains user symbol estimates for all frequency bands. This is the digital domain equalization matrix for the final predicted nth frequency band.

[0034] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: Terahertz AP only needs to transmit a small number of digital domain channels back. The CPU predicts the equalization matrix band by band through the multi-trace Schrödinger bridge, avoiding frequent large-scale matrix inversion operations, which greatly saves the computing resources of the terahertz non-cellular wireless access network. The implemented multi-trace Schrödinger bridge model has superior performance, simple process and easy engineering implementation compared with similar general diffusion models. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of the method flow of the present invention.

[0036] Figure 2 This diagram illustrates the scenario presented in this invention and the reasons for the core problems.

[0037] Figure 3 This is a schematic diagram of the polyhedral trace Schrödinger bridge of the present invention.

[0038] Figure 4 This is a schematic diagram illustrating one implementation of the forward and backward diffusion model based on the U-Net architecture provided by the present invention.

[0039] Figure 5 This is a schematic diagram of the input convolution module of the forward and backward diffusion models under the U-Net architecture of this invention.

[0040] Figure 6 This is a schematic diagram of the temporal embedding residual block of the forward and backward diffusion models under the U-Net architecture of this invention.

[0041] Figure 7 The figure shows the simulation results of the normalized mean square error (NMSE) for the prediction of the frequency band equalization matrix in this invention. Detailed Implementation

[0042] like Figure 1 and Figure 2 As shown, the configuration of a distributed terahertz AP is equivalent to making the distances from different terahertz subarrays to the same user different, resulting in different transmission delays. Originally, in a centralized array, the channel for the same user had a uniform phase drift across different frequency bands, so the equalization matrix across different frequency bands could be directly inferred.

[0043]

[0044] because ,in It is a diagonal matrix representing the phase transition caused by the propagation distance. It is the frequency band number. For the digital domain equivalent receiver noise correlation matrix, For the digital domain channel in the 0th frequency band, This is the conjugate transpose of the digital domain channel in the nth frequency band. This is a digital domain equalization matrix covering 0 frequency bands. However, in terahertz non-cellular wireless access networks, each subarray experiences different phase drift. , For frequency band number, The delay matrix prevents direct inference of the equalization matrix. In this case, the CPU needs to calculate the equalization matrix band-by-band, which involves a large number of bands in the wide bandwidth of terahertz, resulting in unacceptable computational complexity. This invention provides an extrapolation method for terahertz non-cellular receivers based on a multi-trace Schrödinger bridge, comprising the following steps:

[0045] Step 1: Terahertz access points (APs) calculate transmission delay and send it back to the central processing unit (CPU): Each terahertz AP measures the transmission delay of the user it serves and sends it back to the CPU via the fronthaul link.

[0046] In this process, terahertz APs independently perform user selection and delay measurement. Each terahertz AP operates in a fully distributed manner during this stage to prevent dimensionality explosion. User selection algorithms include, but are not limited to, any known analytical or heuristic algorithms based on large-scale fading, and delay measurement algorithms include, but are not limited to, any known analytical or heuristic algorithms such as the time-of-flight method. (The last sentence appears to be incomplete and possibly refers to a different context.) Each terahertz AP selects several user services with minimal-scale fading and a direct-line path, and measures the transmission delay using pilot signals, estimating the transmission delay. Transmitted to the CPU via a fronthaul connection. Terahertz non-cellular wireless access network services... If there are 10 users, and each terahertz AP serves all users, then , Represents the complex field.

[0047] Step 2: Terahertz APs calculate the digital domain channel of the sampling band and transmit it back to the CPU: Each terahertz AP estimates the user angle and aligns the beam with the user direction, estimating the digital domain channel in the sampling band and transmitting it back to the CPU.

[0048] Each terahertz AP estimates the user's angle and aligns the beam in the user's direction. After beam alignment, each terahertz AP performs digital domain channel estimation at equal intervals on different frequency bands. The channel estimation algorithms include, but are not limited to, analytical or heuristic algorithms such as least squares and least mean square error. Assume the terahertz non-cellular radio access network has... For the following frequency bands, the terahertz AP performs digital domain channel estimation:

[0049]

[0050] in It is the frequency band number. It is the terahertz AP serial number. It is the number of terahertz APs. and yes Integer multiples of, For the number of frequency bands, For the number of users.

[0051] extreme situations The equalization matrices of the first and last frequency bands are used to predict the equalization matrices of all frequency bands. Here, the terahertz AP is still a fully distributed process, but the sampling frequency band numbers must be consistent.

[0052] Step 3, CPU constructs training dataset: The CPU constructs full-band digital domain channel using the transmission delay and sampling frequency band digital domain channel of all terahertz APs and calculates the equalization matrix to form training set.

[0053] The CPU constructs a full-band digital domain channel using the transmission delays and sampling frequency bands returned by all terahertz APs. The CPU then concatenates the transmission delays to obtain the delay matrix.

[0054]

[0055] By concatenating digital domain channels, a global digital domain channel is obtained.

[0056]

[0057] Due to the distributed terahertz AP deployment in terahertz non-cellular wireless access networks, the digital domain channels of different frequency bands have the following properties:

[0058]

[0059] For the first Channels in one frequency band, For the first Channels in one frequency band, Incrementing the sequence number This is for the Hadamard product operation.

[0060] That is, it has phase shift properties; for the sake of convenience, we may use... This also represents the adjacent band phase shift matrix corresponding to the delay. Utilizing the phase shift properties of the digital domain channel in the aforementioned frequency bands, the CPU calculates the digital domain channel for all frequency bands.

[0061]

[0062] The equalization matrix is ​​calculated band-by-band, and the minimum equalization error equalization method is adopted.

[0063]

[0064] in For the first Equalization matrix for each frequency band To obtain the equivalent received noise correlation matrix in the digital domain, the CPU integrates all the full-band equalization matrices corresponding to the channel correlation times collected for training, forming the training dataset. .

[0065] Furthermore, for each pair of sampling frequency band numbers , For group number, of The equalization matrix in each frequency band is used as a trajectory for a probability distribution transition, and then paired with the corresponding delay matrix. That is, a training data point is obtained and added to This process is repeated for each pair of sampling frequency band numbers in each channel coherent block to form a dataset for training.

[0066] Step 4: The CPU trains forward and backward drift on each Schrödinger bridge segment: The CPU constructs a polygonal trace Schrödinger bridge using stochastic differential equations and fits the forward and backward drifts on the training set using two neural networks. For example... Figure 3 As shown, the evolution of the equalization matrix is ​​regarded as a continuous process, while the equalization matrix in the frequency band is regarded as a series of key frames of this continuous process.

[0067] The evolution of the equalization matrix in the frequency band is regarded as a time-varying process. Above the time interval A continuous distribution transition within a training dataset results in an equilibrium matrix.

[0068]

[0069] It can be considered as a time interval On The results corresponding to each keyframe are here. , Assuming a continuously varying duration, then from arrive Continuous evolution and from arrive The continuous evolution can be described by the following two forward and backward stochastic differential equations, respectively.

[0070]

[0071]

[0072] in For the equilibrium matrix, and These are the forward and reverse drift velocities, respectively. Time and delay matrix Down The direction of change, For the variance of the Wiener process, This is Brownian motion. The above stochastic differential equations can also model motion with its own drift. It can also be time-varying.

[0073] To estimate drift speed and Construct two diffusion neural network models and The two models have the same structure but use different independent weights. Then, using Euler-Maruyama discretization, the two stochastic differential equations are rewritten in the following discrete form with optimizable parameters.

[0074]

[0075]

[0076] in Indicates the change over time. It follows an independent standard normal distribution. The positive drift velocity is simulated using a neural network. The reverse drift velocity is simulated using a neural network. and These represent the weights of the two neural networks, For the first indivual Integers, Set as ,but It is exactly an integer and Additionally, to distinguish between the equilibrium matrices obtained from forward and reverse drift, superscripts are added. and Then the forward and backward stochastic differential equations can be rewritten as follows:

[0077]

[0078]

[0079] The first predicted by the positive drift model Digital domain equalization matrix in each frequency band The first predicted by the reverse drift model Digital domain equalization matrix across each frequency band.

[0080] For training and For each pair of keyframe times In which uniform sampling time The weights of the two diffusion neural networks are trained and optimized according to the following loss function.

[0081]

[0082]

[0083] Let be the mathematical expectation, where The sample obtained by the following formula Results of time drift

[0084]

[0085] It follows a complex Gaussian distribution.

[0086] Optionally, the Adam optimizer is used based on the total loss function.

[0087]

[0088]

[0089] To optimize the weights. Among them, For time interval ( , The loss function.

[0090] The implemented forward and backward diffusion neural networks are as follows Figure 4The U-Net architecture shown consists of an input convolutional module, a first temporal embedding residual block, a first downsampling module, a second temporal embedding residual block, a second downsampling module, a third temporal embedding residual block, a third downsampling module, a fourth temporal embedding residual block, an attention module, a fifth temporal embedding residual block, a first upsampling module, a sixth temporal embedding residual block, a second upsampling module, a seventh temporal embedding residual block, a third upsampling module, an eighth temporal embedding residual block, and an output convolutional module, all in sequence. There are also feature concatenations between the first and eighth temporal embedding residual blocks, the second and seventh temporal embedding residual blocks, the third and sixth temporal embedding residual blocks, and the fourth and fifth temporal embedding residual blocks. Figure 5 As shown, for Embedding encoding is performed using a standard encoder module, and then combined with an equalization matrix passed through a convolutional layer. The features are summed, and then a convolution is performed again for output. The difference between the implementation of temporally embedded residual blocks and the general diffusion model lies in temporal sampling, such as... Figure 6 As shown, for each pair of times Random sampling is performed, and forward and backward models are trained segment by segment.

[0091] Step 5, CPU generates digital domain equalization matrix in forward and backward directions: CPU uses the trained forward and backward drift model to infer equalization matrix in forward and backward frequency bands.

[0092] The CPU calculates the equalization matrix of the sampling frequency band using the digital domain channel of the sampling frequency band. For each pair of adjacent sampling frequency bands, the equalization matrix... Using the trained forward and backward diffusion models, the equalization matrix of the unsampled frequency bands is inferred band by band according to the following formula.

[0093]

[0094]

[0095] in , Let be the delay matrix. For frequency band number, For the number of users, The positive drift velocity is simulated using a neural network. The reverse drift velocity is simulated using a neural network. For the variance of the Wiener process, As the increment of the sequence number, we obtain Forward and inverse estimations of all intermediate frequency bands, Let them be Gaussian variables. The first predicted by the positive drift model Digital domain equalization matrix in each frequency band The first predicted by the positive drift model Digital domain equalization matrix in each frequency band The first predicted by the positive drift model Digital domain equalization matrix in each frequency band The first predicted by the reverse drift model Digital domain equalization matrix in each frequency band The first predicted by the reverse drift model Digital domain equalization matrix in each frequency band For the first Digital domain equalization matrix across each frequency band.

[0096] Step 6: The CPU weights the forward and reverse results and uses the digital equalization matrix of all frequency bands to equalize the received signal band by band.

[0097] The CPU performs a weighted merging of the equalization matrices from forward and backward inference to obtain the final predicted equalization matrix. Optionally, the mean of forward and backward inference can be used as the prediction result, then the equalization matrix for all frequency bands is...

[0098]

[0099] in, This is the digital domain equalization matrix for the nth frequency band. For frequency band number, For the number of users, This is the digital domain equalization matrix predicted by the positive drift model for the nth frequency band. This is the digital domain equalization matrix predicted by the reverse drift model for the nth frequency band. Number of frequency bands;

[0100] use The CPU performs global equalization on the received signals transmitted across all frequency bands according to the following formula.

[0101]

[0102] in For the first The first frequency band Preliminary symbol estimation after simulation equalization on a terahertz AP This is the final symbol estimation after digital equalization on the CPU side. It is the number of terahertz APs. For frequency band number, Given the number of frequency bands, the CPU now obtains user symbol estimates for all frequency bands. This is the digital domain equalization matrix for the final predicted nth frequency band.

[0103] Through the above six steps, a method for extrapolating terahertz non-cellular receivers based on a multi-track Schrödinger bridge is completed. Figure 7 As shown, the results indicate that the present invention effectively predicts the equalization matrix in the frequency band and has little dependence on the training data, and can approximate the ordinary diffusion model with small data samples.

Claims

1. A method for extrapolating terahertz non-cellular receivers based on a multi-track Schrödinger bridge, characterized in that, The steps include the following: Step 1: The terahertz AP measures the transmission delay of the users it serves and sends the data back to the CPU via the fronthaul link. Step 2: Each terahertz AP estimates the user angle and aligns the beam with the user direction, estimating the digital domain channel backhaul to the CPU in the sampling frequency band. Step 3: The CPU uses the transmission delay and sampling frequency band digital domain channel returned by all terahertz APs to construct a full-band digital domain channel and calculates the equalization matrix to form a training set. Step 4: The CPU trains forward and backward drift on each segment of the Schrödinger bridge. The CPU constructs a multi-trace Schrödinger bridge through stochastic differential equations and uses two neural networks to fit the forward and backward drift on the training set. If the evolution of the equalization matrix over a frequency band is viewed as a continuous distribution transition within a time interval, then the equalization matrix of a training dataset is considered as a transition over the time interval. The results corresponding to each keyframe are described by two forward and backward stochastic differential equations, respectively, for the continuous evolution from the first keyframe to the last keyframe and from the last keyframe to the first keyframe. In the forward stochastic differential equation, the differential of the keyframe equals the product of the forward drift velocity and the time differential plus a Brownian motion differential. Similarly, in the backward stochastic differential equation, the differential of the keyframe equals the product of the backward drift velocity and the time differential plus a Brownian motion differential. The forward and backward drift velocities are functions of the current keyframe, the delay matrix, and the current time step. For the number of users, It is the terahertz AP serial number; To estimate the forward and reverse drift velocities, two diffusion neural network models are constructed. The two models have the same structure but use different independent weights. Then, Euler-Maruyama discretization is used to rewrite the two stochastic differential equations into discrete forms with optimizable parameters. The time interval length is set to be equal to the frequency band sampling interval to simplify the equations. In the forward equation, the increment of adjacent keyframes is equal to the drift velocity plus a Gaussian noise, and in the reverse equation, the increment of adjacent keyframes is equal to the negative drift velocity plus a Gaussian noise. To train the forward and backward diffusion neural networks, time is sampled uniformly for each pair of adjacent keyframe moments. The weights of the two diffusion neural networks are trained and optimized using the square of the difference between the estimated drift velocity and the estimated intermediate time as the loss function, where the estimated drift velocity is determined by the estimated intermediate time. The slope between the drift result of the keyframes and the forward or reverse endpoint keyframes is obtained, and the intermediate time is estimated. The drift results of keyframes are obtained by sampling from a Gaussian distribution determined by adjacent keyframes; Step 5: The CPU uses the trained forward and reverse drift models to infer the equalization matrix in both forward and reverse frequency bands. Step 6: The CPU weights the forward and reverse results and uses the digital equalization matrix of all frequency bands to equalize the received signal band by band.

2. The extrapolation method for terahertz non-cellular receivers based on a multi-track Schrödinger bridge as described in claim 1, characterized in that, In step 1, each terahertz AP measures the transmission delay of the user it serves, and any... Each terahertz AP selects several user services with minimal-scale fading and a line-of-sight path, and measures the transmission delay using pilot signals. The estimated transmission delay is then transmitted to the CPU via the fronthaul link. The terahertz non-cellular radio access network serves... If there are multiple users, and each terahertz AP serves all users, then the transmission delay... , Represents the complex field.

3. The extrapolation method for terahertz non-cellular receivers based on a multi-track Schrödinger bridge as described in claim 1, characterized in that, In step 2, each terahertz AP estimates the user angle and aligns the beam with the user's direction. After beam alignment, each terahertz AP performs digital domain channel estimation at equal intervals on different frequency bands. It is assumed that the terahertz non-cellular radio access network has a total of... For the following frequency bands, the terahertz AP performs digital domain channel estimation: in Indicates the estimated channel. It is the frequency band number. It is the terahertz AP serial number. It is the number of terahertz APs. and yes Integer multiples of, For the number of frequency bands, For the number of users.

4. The extrapolation method for terahertz non-cellular receivers based on a multi-track Schrödinger bridge as described in claim 1, characterized in that, In step 3, the CPU constructs a full-band digital domain channel using the transmission delays and sampling frequency band digital domain channels returned by all terahertz APs. The CPU concatenates the transmission delays to obtain a delay matrix and concatenates the digital domain channels to obtain a global digital domain channel. Each element of the channel experiences a different phase offset in the frequency band. The CPU calculates the digital domain channels for all frequency bands and calculates the equalization matrix band by band, using minimum equalization error equalization. The CPU integrates all the full-band equalization matrices corresponding to the channel correlation times collected for training to form a training dataset.

5. The extrapolation method for terahertz non-cellular receivers based on a multi-track Schrödinger bridge as described in claim 4, characterized in that, For each pair of adjacent integers The multiple sampling frequency band number will include the frequency band interval containing these two sampling frequency bands. The equalization matrix on each frequency band is used as a trajectory for a probability distribution transition. Pairing this with the corresponding delay matrix yields a training data point, which is added to the training set. This process is repeated for each pair of sampling frequency band numbers in each channel coherence block, forming a dataset for training. For the number of users, It is the terahertz AP serial number.

6. The extrapolation method for terahertz non-cellular receivers based on a multi-track Schrödinger bridge as described in claim 1, characterized in that, The forward and backward diffusion neural networks use the U-Net architecture, which includes: an input convolutional module, a first-time embedded residual block, a first downsampling module, a second-time embedded residual block, a second downsampling module, a third-time embedded residual block, a third downsampling module, a fourth-time embedded residual block, an attention module, a fifth-time embedded residual block, a first upsampling module, a sixth-time embedded residual block, a second upsampling module, a seventh-time embedded residual block, a third upsampling module, an eighth-time embedded residual block, and an output convolutional module in sequence.

7. The extrapolation method for terahertz non-cellular receivers based on a multi-track Schrödinger bridge as described in claim 1, characterized in that, In step 5, the CPU calculates the equalization matrix of the sampling frequency band using the digital domain channel of the sampling frequency band. For each pair of adjacent sampling frequency bands, the equalization matrix... Using the trained forward and backward diffusion models, the equalization matrix of the unsampled frequency bands is inferred band by band according to the following formula: in The first predicted by the positive drift model Digital domain equalization matrix in each frequency band For the first Digital domain equalization matrix in each frequency band For group number, The first predicted by the positive drift model Digital domain equalization matrix in each frequency band For the number of users, The positive drift velocity is simulated using a neural network. The first predicted by the positive drift model Digital domain equalization matrix in each frequency band Let be the delay matrix. , For frequency band number, Incrementing the sequence number For the variance of the Wiener process, Let them be Gaussian variables. The first predicted by the reverse drift model Digital domain equalization matrix in each frequency band The reverse drift velocity is simulated using a neural network. The first predicted by the reverse drift model Digital domain equalization matrix across each frequency band.

8. The extrapolation method for terahertz non-cellular receivers based on a multi-track Schrödinger bridge as described in claim 1, characterized in that, In step 6, the CPU performs weighted merging of the equalization matrices from forward and backward inference to obtain the final predicted equalization matrix. Using the mean of forward and backward inference as the prediction result, the equalization matrix for all frequency bands is then obtained. in, This is the digital domain equalization matrix for the nth frequency band. For frequency band number, For the number of users, This is the digital domain equalization matrix predicted by the positive drift model for the nth frequency band. This is the digital domain equalization matrix predicted by the reverse drift model for the nth frequency band. Number of frequency bands; use The CPU performs global equalization on the received signals transmitted across all frequency bands according to the following formula. in This is the final symbol estimation after digital equalization on the CPU side. This is the final predicted digital domain equalization matrix for the nth frequency band. For the first The first frequency band Preliminary symbol estimation after simulation equalization on a terahertz AP It is the number of terahertz APs. For frequency band number, Given the number of frequency bands, the CPU now obtains user symbol estimates for all frequency bands.

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