A Channel Estimation Method for Multiple-Input Multiple-Output Orthogonal Time-Frequency Spatial Modulation System Based on Fractional Doppler Shift

Abstract

The invention belongs to the field of wireless communications, and particularly relates to a channel estimation method for a multi-input multi-output orthogonal time-frequency space modulation system based on fractional Doppler frequency shift, comprising: transmitting a transmission signal through a delay Doppler equivalent channel containing inter-Doppler interference, and performing fractional Doppler channel estimation at a receiving end using an LDAMP algorithm to obtain an estimated value of the channel; the scheme proposed by the invention still has superior estimation performance even in the presence of inter-Doppler interference, and has a good compensation effect on the performance loss caused by fractional Doppler.

Description

Technical Field

[0001] The invention belongs to the field of wireless communications, and in particular relates to a channel estimation method for a multiple-input multiple-output orthogonal time-frequency space modulation system based on fractional Doppler frequency shift. Background Art

[0002] Multiple Input Multiple Output (MIMO) technology can configure multiple antennas at both ends of the transceiver to generate diversity gain to achieve spatial multiplexing. In theory, performance indicators such as channel capacity, degree of freedom, transmission rate, and link reliability will gradually increase with the increase in the number of antennas at the transceiver end. However, in the current 5G communication scenario, the modulation technology used is still Orthogonal Frequency Division Multiplexing (OFDM) technology. In a high-mobility environment, the Doppler shift generated by movement will seriously destroy the orthogonality between OFDM subcarriers, generate inter-carrier interference (ICI), reduce the performance of the OFDM system, and cannot meet the user's usage needs. Therefore, a new type of orthogonal time-frequency space (Orthogonal Time Frequency Space, OTFS) modulation technology is used to model the wireless channel in the two-dimensional delay-Doppler domain, which can directly reflect the channel delay and Doppler shift geometric characteristics. Since the running distance and speed remain roughly the same at least in the millisecond order, the delay and Doppler shift parameters can be approximately considered to be unchanged over time in the millisecond observation time, so the fast time-varying channel under high mobility can be converted into an approximately time-invariant channel in the delay-Doppler domain. In addition, since the surrounding scatterers in real communication scenarios are usually limited, there are only a few groups of reflectors with different delay and Doppler shift values, the estimated parameters are relatively few, and the channel is easier to estimate in a sparse state. Therefore, combining MIMO technology with OTFS modulation technology can not only enhance channel capacity and improve signal transmission effectiveness through spatial multiplexing, but also increase the reliability of signal transmission under high-speed mobility through an approximately time-invariant sparse delay-Doppler channel.

[0003] At present, MIMO-OTFS channel estimation technology can be divided into two categories. The first is to estimate the OTFS channel using embedded pilot patterns and threshold-based algorithms. However, this solution requires a high pilot signal-to-noise ratio, which will increase the peak-to-average ratio of the OTFS system. In addition, too many protection symbols and pilot symbols will reduce the spectral efficiency of the system. To overcome this defect, many scholars have proposed another estimation scheme based on the sparsity of the delay-Doppler channel in the OTFS system, which describes the channel estimation problem as a sparse signal recovery problem and solves it using compressed sensing algorithms such as structured orthogonal matching pursuit. However, this scheme only estimates under integer Doppler and does not consider fractional Doppler conditions that are more in line with the actual communication environment, so it is not applicable. Summary of the invention

[0004] In order to avoid the modeling error caused by the integer Doppler shift model in the MIMO-OTFS system and make it more suitable for the actual high-speed mobile communication scenario, the present invention proposes a channel estimation method for a multiple-input multiple-output orthogonal time-frequency space modulation system based on fractional Doppler shift, including using a delay Doppler equivalent channel containing inter-Doppler interference (IDI) to transmit a transmit signal, and using the LDAMP algorithm at the receiving end to perform fractional Doppler channel estimation to obtain an estimated value of the channel.

[0005] Furthermore, the delay-Doppler equivalent channel including IDI is expressed as:

[0006]

[0007] in, represents the delay-Doppler equivalent channel matrix including IDI between the t-th transmitting antenna and the r-th receiving antenna; L p N represents the number of channel paths between the tth transmitting antenna and the rth receiving antenna; p,r,t represents the fractional Doppler shift k on the pth path between the tth transmitting antenna and the rth receiving antenna p,r,t,F The generated virtual path; I N (-[qk p,r,t,I ] N ) is the N-order unit matrix I N -[qk p,r,t,I ] N The matrix obtained after circular shift, q represents the index of the virtual path, k p,r,t,I The Doppler tap index k of the pth path from the tth transmitting antenna to the rth receiving antenna is p,r,t Integer index in [·] N Represents modulo N operation; Expressed as a Kronecker product operation, is a diagonal matrix; I M (l p,r,t ) is the M-order unit matrix I M With l p,r,t The matrix obtained after cyclic shift, l p,r,t represents the delay tap index of the pth path from the tth transmitting antenna to the rth receiving antenna; h p,r,t represents the channel fading coefficient of the pth path between the tth transmitting antenna and the rth receiving antenna; k p,r,t,F The Doppler tap index k of the pth path from the tth transmitting antenna to the rth receiving antenna is p,r,t The fractional index in ; For a block matrix Δ, -[qk p,r,t,I ] N The matrix obtained by cyclic shifting; M is the dimension in the delay domain, and N is the dimension in the Doppler domain.

[0008] Furthermore, the diagonal elements of the lth row and lth column of the diagonal matrix Λ are:

[0009]

[0010] Where l represents the delay variable of the delay-Doppler channel in the fractional Doppler case.

[0011] Furthermore, the block matrix Δ is a diagonal matrix, and the diagonal elements of the nth row and nth column are represented by Δ n =ΨI M (l p,r,t ), Ψ is a diagonal matrix, and the diagonal elements of the mth row and mth column are expressed as:

[0012]

[0013] Among them, I M (l p,r,t ) is the M-order unit matrix I M With l p,r,t The matrix obtained after circular shift.

[0014] Furthermore, the iterative process of fractional Doppler channel estimation using the LDAMP algorithm is expressed as:

[0015]

[0016]

[0017] in, It represents the delay-Doppler channel estimation value under fractional Doppler condition output by the lth layer neural network of the LDAMP algorithm; Indicates the noise level range is Denoiser; It is represented as the transmission signal matrix of the MIMO-OTFS system including inter-Doppler interference; (z IDI ) l+1 It is represented as the residual vector of the fractional Doppler output of the l-th layer neural network of the LDAMP algorithm; It is represented as the received signal vector of the MIMO-OTFS system including inter-Doppler interference; It is expressed as the Onsager correction term in the case of fractional Doppler; Indicates the divergence operation of the denoiser; (·) T Represents a transpose operation.

[0018] Furthermore, for the trained denoiser, we use an independent and identically distributed random vector Get the divergence Approximate value, expressed as:

[0019]

[0020] in, represents the fractional Doppler channel vector after adding noise, expressed as It is expressed as the true value of the fractional Doppler channel in the actual communication scenario, It is expressed as the equivalent noise superimposed during the transmission process; E b {·} represents the expected operation; ∈ is a minimum value; represents the parameter b that conforms to the standard normal distribution, and I represents the identity matrix.

[0021] Furthermore, the denoiser acquisition process includes:

[0022] Set the noise level range affected by noise, and divide the noise level range into multiple small ranges;

[0023] For each noise level range, a received signal under a fractional Doppler condition and a delay Doppler channel under a fractional Doppler condition corresponding to the noise range are generated as a training data set;

[0024] A DnCNN network is constructed and trained using the training data to obtain a denoiser corresponding to each noise level range.

[0025] Furthermore, during the iteration of the first layer of the LDAMP algorithm network, a denoiser is randomly selected from denoisers in various noise level ranges, and during the iteration of subsequent layers, a corresponding denoiser is selected based on the noise level range corresponding to the noise standard deviation estimate of the input and output of the previous layer.

[0026] According to the simulation results, when inter-Doppler interference exists, the NMSE performance of the method of the present invention can still be better than other algorithms (such as OMP algorithm, LS algorithm, LMMSE algorithm and D-AMP series algorithms, D-AMP series algorithms include NLM-AMP algorithm, Bilateral-AMP algorithm, Gauss-AMP algorithm, etc.) at any SNR. The simulation proves that the LDAMP algorithm can be well applied to the channel estimation problem under fractional Doppler by relying on the model basis of the iterative algorithm and the powerful generalization ability of deep learning; and the comparison curves of NMSE changing with SNR under integer Doppler and fractional Doppler of the method of the present invention and the LS algorithm are compared, which proves that the algorithm of the present invention has a good compensation effect on the performance loss caused by fractional Doppler compared with the traditional algorithm LS. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 This is a block diagram of the MIMO-OTFS system model used in the present invention;

[0028] Figure 2 Schematic diagram of the network structure of the first layer of the LDAMP algorithm framework in the case of fractional Doppler in the present invention;

[0029] Figure 3 This is a schematic diagram of the DnCNN denoiser network architecture used in the present invention;

[0030] Figure 4 It is a comparison curve of NMSE of different algorithms in the MIMO-OTFS system of the present invention as a function of SNR;

[0031] Figure 5 It is a comparison curve of the NMSE changing with SNR in the case of integer Doppler and fractional Doppler of the present invention. DETAILED DESCRIPTION

[0032] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0033] The present invention provides a channel estimation method for a multiple-input multiple-output orthogonal time-frequency space modulation system based on fractional Doppler shift, comprising: transmitting a transmission signal through a delay Doppler equivalent channel including inter-Doppler interference, and performing fractional Doppler channel estimation at a receiving end using an LDAMP algorithm to obtain an estimated value of the channel.

[0034] The present invention models the fractional Doppler situation for a MIMO-OTFS modulation system, analyzes the inter-Doppler interference caused by the fractional Doppler in detail, and provides a channel estimation scheme based on a learnable denoising approximate message passing algorithm.

[0035] In this embodiment, the MIMO-OTFS system model and the delay Doppler channel model under fractional Doppler are first given, and then the inter-Doppler interference is analyzed in detail, and the OTFS channel is estimated using the Learned Denoising based Approximate Message Passing (LDAMP) algorithm; finally, in order to verify the performance of the proposed scheme under fractional Doppler in the MIMO-OTFS system, a performance comparison study is conducted between the proposed scheme and the traditional algorithm. Specifically, the following steps are included:

[0036] 1. MIMO-OTFS system model

[0037] Figure 1 This is a block diagram of the MIMO-OTFS system model, showing the N t There are N transmitting antennas and N receivers. r MIMO-OTFS system with 100 receive antennas, where the number of transmit and receive antennas is the same (N t =N r ). Each transmitting antenna at the transmitter independently transmits OTFS modulated data symbols to all receiving antennas, and each receiving antenna at the receiver receives data symbols that are N at the transmitter. t At the transmitting end, the delay Doppler domain symbol x transmitted by the tth transmitting antenna t [l,k] can be mapped to the time-frequency domain transmission symbol X through the InverseSymplectic Finite Fourier Transform (ISFFT) t [m,n], where l = 0, 1, ..., M-1, k = 0, 1, ..., N-1, m = 0, 1, ..., M-1, n = 0, 1, ..., N-1. Similarly, at the receiving end, the time-frequency domain symbol Y transmitted by the rth receiving antenna r [m,n] can be mapped to the delay-Doppler domain received symbol y through the symplectic Finite Fourier Transform (SFFT) r [l,k].

[0038] In this embodiment, for the MIMO-OTFS modulation system, the information symbols are placed in an M×N two-dimensional delay-Doppler domain grid, where M is the delay domain dimension and N is the Doppler domain dimension. First, the transmission model of the OTFS system between the tth transmitting antenna and the rth receiving antenna is established as follows:

[0039]

[0040] in, is the delay-Doppler domain received signal vector at the rth receiving antenna, is the delay-Doppler domain equivalent channel matrix between the tth transmitting antenna and the rth receiving antenna, is the delay-Doppler domain transmitted signal vector at the tth transmitting antenna, is the superimposed Gaussian white noise vector; N r The number of antennas that receive signals at the receiving end.

[0041] To expand the above single-antenna system to a multi-antenna MIMO system, N r The signals received by the receiving antennas are stacked as the observation vector Where T is the transposed symbol, the signal model of the MIMO-OTFS system is:

[0042] y DD =H DD x DD +v DD

[0043] in, N r The delay-Doppler domain transmit signal vector of the stacked transmit antennas is: N is the receiver r The noise vector received by the receiving antennas is is the stacked delay-Doppler domain equivalent channel matrix in the MIMO-OTFS system, and its expression is as follows:

[0044]

[0045] Where t=1,2,...,N t ,r=1,2,...,N r .

[0046] 2. Delay-Doppler channel model

[0047] Assume that the channel path between the tth transmitting antenna and the rth receiving antenna has L p The corresponding delay-Doppler domain impulse response channel h r,t (τ,ν) is:

[0048]

[0049] Among them, τ is the time delay variable, v is the Doppler frequency shift variable, L p is the number of paths from the tth transmitting antenna to the rth receiving antenna; δ(·) is the Dirac function, h p,r,t is the channel fading coefficient of the pth path from the tth transmitting antenna to the rth receiving antenna, τ p,r,t is the delay parameter corresponding to the pth path from the tth transmitting antenna to the rth receiving antenna, v p,r,t is the Doppler frequency shift parameter corresponding to the pth path from the tth transmitting antenna to the rth receiving antenna, and its expression is as follows:

[0050]

[0051]

[0052] Where Δf is the subcarrier spacing, l p,r,t is the delay tap index corresponding to the pth path from the tth transmitting antenna to the rth receiving antenna, which is generally an integer value, because in actual broadband communication systems, the resolution of the delay axis is Δτ Very high, enough to approximate the delay value corresponding to the channel path to the nearest sampling point, so there is no need to consider the fractional delay; T is the duration of the symbol, k p,r,t is the Doppler tap index, Doppler tap index k p,r,t Contains integer index k p,r,t,I and fractional index Two parts, denoted as k p,r,t =k p,r,t,I +k p,r,t,F .

[0053] Because the resolution of the Doppler axis in the OTFS system It depends on the duration NT of the OTFS block. In the future, high-speed mobile communications require that the time used for information transmission is as short as possible, which means that NT will be relatively small, which will cause Δv to be very low, and the Doppler frequency shift corresponding to the channel path cannot be accurately approximated to the nearest sampling point on the two-dimensional delay Doppler plane. Therefore, the fractional Doppler frequency shift k must be considered when estimating the OTFS channel. p,r,t,F , to reduce the integer Doppler frequency shift k p,r,t,I The model brings about large modeling errors.

[0054] 3. Doppler Interference Analysis

[0055] Assume that the transmitted pulse waveform is g tx (t) and the received pulse waveform g rx(t) are all ideal waveforms, at the receiving end, the time-frequency domain symbol Y transmitted by the rth receiving antenna r [m,n] can be mapped to the delay-Doppler domain received symbol y through the symplectic Finite Fourier Transform (SFFT) r [l,k], the formula is as follows:

[0056]

[0057] Among them, x t [m,n] represents the QAM symbol transmitted by the tth transmitting antenna, v r [k,l] represents additive Gaussian white noise, Represented as h w,r,t (τ,v) The sampling value at , define h w,r,t (τ,v) is the delay Doppler channel impulse response h between the tth transmitting antenna and the rth receiving antenna r,t (τ,ν) and the window function w r,t The circular convolution between (τ,ν) is expressed as:

[0058]

[0059] Among them, h p,r,t represents the channel fading coefficient corresponding to the pth path between the tth transmitting antenna and the rth receiving antenna; τ p,r,t represents the delay parameter corresponding to the pth path from the tth transmitting antenna to the rth receiving antenna; ν p,r,t The Doppler frequency shift parameter corresponding to the pth path between the tth transmitting antenna and the rth receiving antenna; w r,t (τ,v) represents the window function added between the tth transmitting antenna and the rth receiving antenna; the channel gain term is defined as The delay term is The Doppler shift term is when When the delay term F(τ,τ p,r,t )for:

[0060]

[0061] From the above formula, we can get that when m=[ll p,r,t ] M hour, in[·] M It is expressed as a modulo M operation. Similarly, when When the Doppler frequency shift term G(v,ν p,r,t )for:

[0062]

[0063] Considering the fractional Doppler k p,r,t,F , so for any k, no matter what value n takes, the Doppler frequency shift term And define is the Doppler frequency shift dispersion produced by fractional Doppler, and its modulus is simplified as follows:

[0064]

[0065] Among them, the definition The following conclusion can be drawn: when n = kk p,r,t,I When θ becomes very small, the above formula has a tight upper bound, which means that at very small θ values, can reach a peak value, and when |θ| continues to increase (that is, n gradually moves away from kk p,r,t,I ), the upper bound will follow the slope The direction of decreases continuously when n is far away from kk p,r,t,I The distance exceeds N p,r,t hour, Therefore, in order to simplify the analysis, only 2N needs to be considered in the OTFS system. p,r,t +1 virtual path with greater contribution can be used, so x t [l,k] and y r The input-output relationship between [l,k] is:

[0066]

[0067] Among them, N p,r,t It is expressed as the fractional Doppler shift k on the pth path from the tth transmitting antenna to the rth receiving antenna. p,r,t,F The virtual path generated, q represents the index of the virtual path. According to the above analysis, fractional Doppler will produce Doppler frequency shift dispersion phenomenon, forming a fractional Doppler frequency shift virtual propagation path that does not exist in the actual environment, causing Inter Doppler Interference (IDI), which may cause the transmitted information symbols to be contaminated. Moreover, Inter Doppler interference is a nonlinear interference and cannot be compensated by linear methods. It will not only reduce the inherent sparsity of the delay Doppler channel and the accuracy of channel estimation, but also increase the computational complexity of channel estimation.

[0068] It should be noted that the pulse waveform g tx (t) and the received pulse waveform g rx(t) The ideal waveform used under the condition of satisfying the dual orthogonality cannot be realized in the actual system, so in practical applications, a rectangular waveform is usually used instead. The matrix form of the delay-Doppler equivalent channel containing IDI is can be equivalently written as:

[0069]

[0070] Among them, definition I N (-[qk p,r,t,I ] N ) is the N-order unit matrix I N -[qk p,r,t,I ] N The matrix obtained after circular shift is, Expressed as a Kronecker product operation, define is a diagonal matrix, and its diagonal elements in the lth row and lth column are:

[0071]

[0072] definition For a block matrix Δ, -[qk p,r,t,I ] N The expression of the matrix obtained by cyclic shift is:

[0073]

[0074] In which, define Δ n =ΨI M (l p,r,t ), Ψ is a diagonal matrix, and the diagonal element Ψ in the mth row and mth column mm for:

[0075]

[0076] Accordingly, the MIMO-OTFS system signal model including the inter-Doppler interference (IDI) should be rewritten as:

[0077]

[0078] in, Denote the received signal vector of the MIMO-OTFS system including inter-Doppler interference, It is represented as the delay-Doppler domain equivalent channel matrix of the MIMO-OTFS system including inter-Doppler interference, It is represented as the transmitted signal vector of the MIMO-OTFS system including inter-Doppler interference.

[0079] 4. LDAMP algorithm

[0080] Figure 2 This is a schematic diagram of the network structure of the first layer of the LDAMP algorithm framework under fractional Doppler conditions. The entire LDAMP algorithm framework consists of L layers of the same AMP algorithm network in a cascaded manner. and divergence estimator The structure of is the same, and the difference between each denoiser is that it is trained on a different range of noise levels.

[0081] Figure 3 This is a schematic diagram of the denoiser DnCNN network architecture. The entire DnCNN network consists of 20 convolutional layers. The first convolutional layer uses 64 convolutional kernels of size 3×3×1 to generate 64 feature maps. Each of the 2nd to 19th convolutional layers uses 64 convolutional kernels of size 3×3×64. Each convolutional kernel is configured with a ReLU unit and a BN layer to speed up training and improve denoising performance. The last convolutional layer uses a convolutional kernel of size 3×3×64 to reconstruct the learned noise signal.

[0082] Using the LDAMP algorithm, the iterative expression for fractional Doppler channel estimation is as follows:

[0083]

[0084]

[0085] in, It is represented as the l-th layer neural network of the LDAMP algorithm, and the output delay Doppler channel estimation value under fractional Doppler condition, (z IDI ) l+1 Represented as the residual vector of the l-th layer neural network of the LDAMP algorithm under the output of fractional Doppler, Denoiser The learned parameter is the standard deviation of the noise in the fractional Doppler case. Expressed as the Onsager correction term for fractional Doppler, In order to more intuitively reflect the denoiser The function can be used to denoise Input It is understood as the fractional Doppler channel vector after adding noise, which can be defined as:

[0086]

[0087] in, It is expressed as the true value of the fractional Doppler channel in the actual communication scenario, It is expressed as the equivalent noise superimposed during the transmission process. So The role is to Elimination To get the real It should be noted that because the divergence It is not easy to calculate, so we use the Monte Carlo method to approximate it. Specifically, for the trained denoiser Using independent and identically distributed random vectors Get the divergence The approximate value is:

[0088]

[0089] Among them, ∈ is a very small number, which is set according to the experience of those skilled in the art. In this embodiment, its value is

[0090] In this embodiment, the LDAMP algorithm network is trained by training the denoisers one by one, and the training process specifically includes:

[0091] First, a noise level range affected by noise is set. In this embodiment, the noise level range affected by noise is set to [0-60dB];

[0092] Secondly, the noise level range is divided into multiple small ranges. For example, in this embodiment, the noise level range [0-60dB] is divided into 10 small ranges, namely [0-20dB], [20-26dB], [26-32dB], [32-35dB], [35-38dB], [38-41dB], [41-44dB], [44-50dB], [49-54dB], and [54-60dB].

[0093] Next, this embodiment generates corresponding received signals under fractional Doppler conditions and delay Doppler channels under fractional Doppler conditions for the 10 noise levels obtained by stratification, as input and labels of the data set, and trains the DnCNN network of the corresponding noise level; for example, when training the 0-20dB DnCNN denoiser, the generated real delay Doppler channel under fractional Doppler conditions is used as a label, and the noise in this range is added to it as the input of the neural network, and the subsequent processing of the noise range is similar;

[0094] Then, gradient descent and adaptive learning rate are used to find the gradient factor through the back propagation algorithm, and the Adam optimizer is used to obtain the adaptive learning rate with an initial learning rate of 0.001. When the verification error no longer decreases, the optimal weights and bias parameters of the DnCNN network under the noise range are stored to obtain the DnCNN denoiser under the 0-20dB noise range. The learning and training process of the DnCNN denoiser in the other 9 ranges is similar. The DnCNN denoisers corresponding to 10 noise level ranges are obtained in turn, and the unknown fractional Doppler channel can be denoised and estimated.

[0095] When in the online estimation process, when the first layer of the LDAMP algorithm network starts to iterate, a trained DnCNN denoiser is randomly selected for denoising. After the iteration, the noise standard deviation of the input signal of this layer is calculated. In the subsequent iteration process, the denoiser model trained in the corresponding noise level range is selected for estimation based on the estimated value of the noise standard deviation calculated by this layer falling within a certain interval.

[0096] Figure 4 This is a comparison curve of the NMSE of different algorithms in the MIMO-OTFS system as the SNR changes. The present invention compares the performance of the LDAMP algorithm with the OMP algorithm, the LS algorithm, the LMMSE algorithm, and the D-AMP series of algorithms (NLM-AMP, Bilateral-AMP, Gauss-AMP). The simulation results show that even when inter-Doppler interference exists, the NMSE performance of the LDAMP algorithm can still be better than other algorithms at any SNR. It is proved that the LDAMP algorithm can rely on the model foundation of the iterative algorithm and the powerful generalization ability of deep learning to be well applied to the channel estimation problem under fractional Doppler.

[0097] Figure 5It is a comparison curve of the NMSE performance of the LS algorithm and the LDAMP algorithm in the case of integer Doppler and fractional Doppler in the MIMO-OTFS system with the change of SNR. The simulation results show that under any SNR, whether it is the LS algorithm or the LDAMP algorithm, the NMSE performance in the case of integer Doppler is better than the NMSE performance in the case of fractional Doppler. Because compared with integer Doppler, the fractional Doppler case will have Doppler frequency shift dispersion, which will cause the OTFS system to add some non-existent virtual paths, increase the delay Doppler channel estimation error, and reduce the estimation performance. However, it is worth mentioning that when SNR = 20dB, the performance gap of the LDAMP algorithm in the two cases of integer Doppler and fractional Doppler remains within an order of magnitude, while the performance gap of LS is much greater than an order of magnitude. It can be well proved that the inter-Doppler interference caused by fractional Doppler is a nonlinear interference, and it is difficult to compensate for the performance using traditional linear algorithms such as LS. However, the LDAMP algorithm has the advantage of deep learning technology and has a good compensation effect on the performance loss caused by fractional Doppler.

[0098] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for channel estimation of a multiple-input multiple-output orthogonal time-frequency spatial modulation system based on fractional Doppler shift, characterized in that: The transmission signal is transmitted using a delay-Doppler equivalent channel including inter-Doppler interference. At the receiving end, the LDAMP algorithm is used to perform fractional Doppler channel estimation to obtain the estimated value of the channel. The delay-Doppler equivalent channel including inter-Doppler interference is expressed as: in, represents the delay-Doppler equivalent channel matrix including inter-Doppler interference between the t-th transmitting antenna and the r-th receiving antenna; L p N represents the number of channel paths between the tth transmitting antenna and the rth receiving antenna; p,r,t represents the fractional Doppler shift k on the pth path between the tth transmitting antenna and the rth receiving antenna p,r,t,F The generated virtual path; I N (-[qk p,r,t,I ] N ) is the N-order unit matrix I N -[qk p,r,t,I ] N The matrix obtained after circular shift, q represents the index of the virtual path, k p,r,t,I The Doppler tap index k of the pth path from the tth transmitting antenna to the rth receiving antenna is p,r,t Integer index in [·] N Represents modulo N operation; Expressed as a Kronecker product operation, is a diagonal matrix; I M (l p,r,t ) is the M-order unit matrix I M With l p,r,t The matrix obtained after cyclic shift, l p,r,t represents the delay tap index of the pth path from the tth transmitting antenna to the rth receiving antenna; h p,r,t represents the channel fading coefficient of the pth path between the tth transmitting antenna and the rth receiving antenna; k p,r,t,F The Doppler tap index k of the pth path from the tth transmitting antenna to the rth receiving antenna is p,r,t The fractional index in ; For a block matrix Δ, -[qk p,r,t,I ] N The matrix obtained by cyclic shifting; M is the dimension in the delay domain, and N is the dimension in the Doppler domain.

2. The method for channel estimation of a multiple-input multiple-output orthogonal time-frequency spatial modulation system based on fractional Doppler shift according to claim 1, characterized in that: The diagonal elements of the lth row and lth column of the diagonal matrix Λ are: Where l represents the delay variable of the delay-Doppler channel in the fractional Doppler case.

3. The method for channel estimation of a multiple-input multiple-output orthogonal time-frequency spatial modulation system based on fractional Doppler shift according to claim 1, characterized in that: The block matrix Δ is a diagonal matrix, and the diagonal elements of the nth row and nth column are represented by Δ n =ΨI M (l p,r,t ), Ψ is a diagonal matrix, and the diagonal elements of the mth row and mth column are expressed as: Among them, I M (l p,r,t ) is the M-order unit matrix I M With l p,r,t The matrix obtained after circular shift.

4. The method for channel estimation of a multiple-input multiple-output orthogonal time-frequency spatial modulation system based on fractional Doppler shift according to claim 1, characterized in that: The iterative process of fractional Doppler channel estimation using the LDAMP algorithm is expressed as: in, It represents the delay-Doppler channel estimation value under the fractional Doppler condition output by the l-th layer neural network of the LDAMP algorithm; Indicates the noise level range is Denoiser; It is represented as the transmission signal matrix of the MIMO-OTFS system including inter-Doppler interference; (z IDI ) l+1 It is represented as the residual vector of the fractional Doppler output of the l-th layer neural network of the LDAMP algorithm; It is represented as the received signal vector of the MIMO-OTFS system including inter-Doppler interference; It is expressed as the Onsager correction term in the case of fractional Doppler; Indicates the divergence operation of the denoiser; (·) T Represents a transpose operation.

5. The method for channel estimation of a multiple-input multiple-output orthogonal time-frequency spatial modulation system based on fractional Doppler shift according to claim 4, characterized in that: For the trained denoiser, use an independent and identically distributed random vector Get the divergence Approximate value, expressed as: in, represents the fractional Doppler channel vector after adding noise, expressed as It is expressed as the true value of the fractional Doppler channel in the actual communication scenario, It is represented as the equivalent noise superimposed during the transmission process; Eb{·} represents the expected operation based on the random vector b; ∈ is a minimum value; It indicates that the random vector b conforms to the standard normal distribution, and I represents the identity matrix.

6. A method for channel estimation of a multiple-input multiple-output orthogonal time-frequency spatial modulation system based on fractional Doppler shift according to claim 4 or 5, characterized in that: The process of obtaining the denoiser includes: Set the noise level range affected by noise, and divide the noise level range into multiple small ranges; For each small range, a received signal under a fractional Doppler condition and a delay Doppler channel under a fractional Doppler condition corresponding to the noise range are generated as a training data set; A DnCNN network is constructed and trained using the training data to obtain a denoiser corresponding to each noise level range.

7. The method for channel estimation of a multiple-input multiple-output orthogonal time-frequency spatial modulation system based on fractional Doppler shift according to claim 5, characterized in that: During the iteration of the first layer of the LDAMP algorithm network, a denoiser is randomly selected from the denoisers in each small range. During the iteration of the subsequent layers, the corresponding denoiser is selected according to the noise level range corresponding to the noise standard deviation estimate of the input and output of the previous layer.

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