A Channel Estimation Method for Massive MIMO-OTFS System Based on 2D-ROMP

Abstract

The present invention discloses a channel estimation method for a Massive MIMO-OTFS system based on 2D-ROMP, belonging to the field of communication technologies, and solving the technical problems of the limitations of existing methods. The present invention utilizes the sparse characteristics of the Massive MIMO-OTFS channel, characterizes it as a two-dimensional sparse model of time delay-Doppler-angle, and transforms the channel estimation into a two-dimensional sparse signal reconstruction problem; first, regularize the time delay-Doppler dimension, select the most relevant number of atoms, and after fixing the positions of the most relevant atoms, start to select the relevant indices of the angle dimension; then, after performing an up-dimension operation on the antenna dimension, select the most relevant index of the antenna angle dimension, where by traversing each index of the selected time delay-Doppler dimension, explore all possibilities of the antenna angle dimension, so as to find the most relevant atomic index of the angle dimension; finally, update the two-dimensional index set to obtain the most relevant index sets of the two dimensions, and obtain the channel estimation through sparse reconstruction.

Description

Technical Field

[0001] The present invention relates to the field of communication technologies, and specifically to a channel estimation method for a Massive MIMO-OTFS system based on 2D-ROMP. Background Art

[0002] At present, in future 6G communications, high-mobility communication scenarios, such as high-speed vehicle-to-everything (V2X), unmanned aerial vehicles (UAVs), and low-earth orbit (LEO) satellites, play an important role and are also one of the main challenges faced by 6G systems. In high-mobility communication scenarios, the channel has the characteristics of time and frequency selectivity. The orthogonal frequency division multiplexing (OFDM) modulation technology widely adopted in 4G and 5G faces severe Doppler frequency shift in time-frequency selective channels, and the orthogonality between subcarriers is damaged, unable to meet the requirements of high-performance transmission. Therefore, to break through the limitations of the OFDM modulation method in 6G systems, researching new modulation technologies to improve high-performance transmission in time-frequency selective channels has become an urgent need. The orthogonal time frequency space (OTFS) modulation technology modulates data in the delay-Doppler (DD) domain and spreads it over the entire time-frequency domain, achieving high-reliability and high-rate transmission in time-frequency selective channels. The OTFS technology has received extensive attention from the industry due to its unique performance advantages and has become a research hotspot in the field of 6G high-mobility communications.

[0003] However, the performance of a mobile communication system is affected by the wireless channel. Whether the channel parameters can be accurately estimated is the key to realizing the communication system. In a Massive MIMO-OTFS system, with the increase in the number of antennas and bandwidth on both the transmitter and receiver sides, the number of channel parameters increases significantly; at the same time, the Doppler effect of high-mobility communication channels is more obvious than that of traditional channels. Obtaining channel state information has become a bottleneck problem in the Massive MIMO-OTFS communication system. How to accurately obtain channel state information is the core and key of Massive MIMO-OTFS communication. Therefore, to meet the development needs of 6G high-mobility communications, research on channel estimation methods for Massive MIMO-OTFS systems has important theoretical significance and engineering application value.

[0004] At present, domestic and foreign scholars' research on channel estimation for OTFS systems mainly focuses on researching corresponding channel estimation methods by combining Massive MIMO technology on the basis of pilot assistance. Traditional pilot channel estimation in Massive MIMO-OTFS systems has problems such as large pilot overhead and high computational complexity, resulting in poor channel estimation performance.

[0005] For high-mobility communication scenarios, introducing Massive Multiple-Input Multiple-Output (Massive MIMO) technology into the OTFS system not only increases the robustness of the doubly selective channel but also improves the spectral efficiency. The DD-domain signal processing adopted by OTFS can effectively combat the time-varying MIMO channel, and the multi-antenna technology enables the OTFS system to achieve higher spectral efficiency and better robustness. The combination of Massive MIMO technology and OTFS technology can meet the requirements of the new generation of mobile communication in terms of improving system capacity, spectral efficiency, and data rate.

[0006] In recent research, some researchers have proposed using compressive sensing methods for channel estimation in the OTFS system. Existing research has proposed a channel estimation method for the Massive MIMO-OTFS system based on the classical Orthogonal Matching Pursuit (OMP); compared with the least squares (LS) estimation method of the traditional pilot structure, the use of compressive sensing methods significantly improves the channel estimation performance. The performance of OMP is better than that of the pilot method, and as the signal-to-noise ratio increases, the NMSE decreases. However, compared with more advanced sparse recovery techniques, its performance is still poor, especially at higher signal-to-noise ratios, because OMP does not fully utilize the multi-dimensional sparsity of the channel. Summary of the Invention

[0007] Aiming at the disadvantages and deficiencies in the prior art, the present invention provides an algorithm that systematically combines the most relevant indices in the time-delay Doppler and antenna angle dimensions, reduces the computational complexity, while maintaining high-precision channel estimation. Its robust performance is significantly improved, and a channel estimation method for the Massive MIMO-OTFS system based on 2D-ROMP with significantly improved performance in terms of reconstruction accuracy and computational efficiency.

[0008] To achieve the above objectives, the present invention is realized through the following technical solutions: The channel estimation method for the Massive MIMO-OTFS system based on 2D-ROMP provided by the present invention utilizes the sparse characteristics of the Massive MIMO-OTFS channel, characterizes it as a two-dimensional sparse model - a time-delay Doppler-angle sparse model, treats the channel time-delay Doppler dimension as a sparse dimension for processing, and the angle dimension as another special sparse dimension for processing. A two-dimensional (2D) compressive sensing sparse reconstruction method is used to achieve sparse channel estimation for the Massive MIMO-OTFS system, and the channel estimation is transformed into a two-dimensional sparse signal reconstruction to obtain the channel estimation, including the following steps:

[0009] First, perform two-dimensional regularization on the time delay-Doppler dimension, select the most relevant number of atoms, and after fixing the positions of the most relevant atoms, start selecting the relevant indices in the angle dimension;

[0010] Then, after performing a dimension-increasing operation on the antenna dimension, select the index with the highest correlation in the antenna angle dimension, where by traversing the indices of each selected time delay-Doppler dimension, all possibilities in the antenna angle dimension are explored to find the atom index with the highest correlation in the angle dimension;

[0011] Finally, update the two-dimensional index set to obtain the index sets with the highest correlation in both dimensions, and obtain the channel estimation through sparse reconstruction.

[0012] Preferably, the algorithm first focuses on the time delay-Doppler dimension, sums the correlation values along one dimension in this dimension to obtain a more concise representation; regularize this sum vector to identify the indices with the highest correlation, and these indices are regarded as the most promising candidate indices in the time delay-Doppler dimension; for each selected index in the time delay-Doppler dimension, continue to explore the antenna dimension, extract the correlation matrix slice corresponding to the selected time delay-Doppler index, and perform a lifting transformation on this slice, which helps to identify the most important indices in the antenna angle dimension;

[0013] By summing and reshaping the transformed slice, the algorithm selects the index with the highest correlation in the antenna angle dimension;

[0014] Combine the selected indices in these two dimensions to form a two-dimensional support set, and then use it to update the overall support set; use this updated support set to calculate a new estimate of the channel vector;

[0015] At the same time, update the residual by subtracting the projection of the new estimate from the measured values.

[0016] Preferably, in each iteration, calculate the correlation vector between the current residual and the columns of the sensing matrix; then, reshape this correlation vector into a two-dimensional matrix to facilitate the selection process;

[0017] The iterative process will continue until a predefined number of iterations is reached, thereby gradually optimizing the channel estimation; the final output is the recovered channel vector, which represents the estimated channel after all iterations.

[0018] Preferably, it includes the following specific steps:

[0019] S1: Collect Massive MIMO-OTFS signals to obtain a signal reception matrix;

[0020] S2: Use the compressive sensing reconstruction algorithm to transform the channel estimation problem of the Massive MIMO-OTFS system into solving the signal h;

[0021] S3: Use the two-dimensional regularized orthogonal matching pursuit 2D-ROMP algorithm for specific operations, and finally obtain the signal h to complete the channel estimation in the time delay-Doppler-angle domain.

[0022] Preferably, in S1, the obtained signal reception matrix is divided into different domains. First, the two-dimensional regularization is used to select the most relevant atoms to process the time delay-Doppler domain, and then for the angle domain, the dimension is increased, and the compressive sensing method is continued to be used for processing. Finally, the best atom set in the three dimensions is selected for channel estimation.

[0023] Preferably, in S2, the input-output vector formula of the Massive MIMO-OTFS system is y = Z c,W h + v, where Z c,W represents a two-dimensional matrix, v represents a noise matrix, and Z c,W is set as the sensing matrix Ψ = Z c,W . The above vector formula then represents a sparse reconstruction problem y = Ψh + v, and the compressive sensing sparse reconstruction algorithm is used to recover the Massive MIMO-OTFS channel vector h.

[0024] Preferably, in S3, the 2D-ROMP algorithm is specifically as follows:

[0025] Input: measurement signal y, sensing matrix Ψ;

[0026] Output: sparse reconstructed channel

[0027] Initialization: Initialize the iteration number i = 0; initialize the channel h (i) = 0; initialize the residual r = y - Ψh (i) ; initialize the index set Ω = φ; sparse path number N p ;

[0028] Start the loop: i ≤ N p ,

[0029] S31. Calculate the correlation vector e = Ψ H r;

[0030] S32. Transform the correlation vector into a two-dimensional matrix ε = reshape(e, M g ×N g , N t ), and the two dimensions are reflected as: time delay Doppler - angle dimension, and the matrix size is (M g N g , Nt ); M g N g represents the product of the time delay and Doppler dimensions, and N t is the number of antennas;

[0031] S33. Select the support set of the time delay-Doppler dimension. The specific algorithm steps are as follows:

[0032] For the time delay-Doppler dimension, calculate its total energy and find the maximum position through regularization;

[0033] e taov = sum(ε, 2);

[0034] [~, pos taov = regularize(e taov , 2);

[0035] Regularize is a regularization operation. Different from the selection in traditional regularization, in 2D-ROMP regularization, the maximum number of elements selected from the inner product value set no longer considers the sparsity, but only selects the two most relevant groups of elements, which reduces the probability of having non-most relevant elements in the optimal subset;

[0036] S34. Traverse all the best time delay-Doppler indices to select the maximum correlation support set in the antenna angle dimension. The specific algorithm steps are as follows:

[0037] Extract the corresponding antenna size: e Nt = ε(pos taov );

[0038] Dimension elevation operation: d Nt = L H × transpose(e Nt );

[0039] Data conversion: g Nt = ∑(reshape(d Nt ));

[0040] Select the maximum correlation index: [~, pos Nt = max(g Nt );

[0041] Update the two-dimensional support index set: Ω = Ω ∪ pos, where pos = {pos taov , pos Nt};

[0042] End the traversal;

[0043] S35. Calculate the new estimated channel:

[0044] S36. Update the residual: r = y - Ψh (i) ;

[0045] End the loop.

[0046] Preferably, in S1, in the MassiveMIMO-OTFS system, the delay-Doppler-angle channel has finite lengths in the Doppler dimension and the delay dimension, which are [-N max / 2:N max / 2 - 1] and [0:M max - 1]; the guard interval along the Doppler axis should be at least N g / 2 ≥ (N max / 2 - 1), and the guard interval along the delay axis should be M g ≥ (M max - 1).

[0047] Preferably, to minimize the overall pilot overhead in the system, a non-orthogonal pilot method is adopted. Although the pilots transmitted from different antennas completely overlap in the delay-Doppler space, the complex Gaussian random sequences used as pilots for each antenna are still independent. Therefore, in the delay-Doppler domain, the training pilot of the (p + 1)-th antenna is represented by y x l,k,p where l = 0, 1,..., M τ - 1, k = -N ν / 2,..., 0,..., N ν / 2 - 1, p = 0, 1,..., N t - 1, and the pilot signal y l，k received at the user side in the DD domain is as follows:

[0048]

[0049] where x l-l′，k-k′，p represents the transmitted signal, represents the phase compensation, k = -N ν / 2,..., 0, / , N ν / 2 - 1, and l = 0, 1,..., M τ - 1, v l，k represents the noise. Express the channel in the DFT form as The formula is as follows:

[0050]

[0051] Substitute formula (2) into formula (1) and rearrange the expression to obtain

[0052]

[0053] where y l，k is the signal received in the time delay-Doppler-angle domain;

[0054] For ease of analysis, equation (3) is expressed in vector matrix form, with y l，k arranged as a column vector, arranged as a column vector where h r The element (l′N g +k′+N g / 2 + 1)-th in it is equal to Therefore, equation (3) is re-expressed in vector matrix form as

[0055]

[0056] In the formula is a two-dimensional periodic convolution matrix, is a matrix, and the elements are Denote and The above formula is expressed as

[0057] y = Z c,W h + v (5)

[0058] v represents the noise matrix; the channel h can be inversely vectorized to obtain the truncated time delay-Doppler-angle channel, denoted as It consists of the non-zero part of, where and r = -N t / 2,..., 0,..., N t / 2 - 1.

[0059] The present invention provides a channel estimation method for a Massive MIMO-OTFS system based on 2D-ROMP. It has the following beneficial effects:

[0060] The algorithm of the present invention utilizes the unique sparse pattern in the Massive MIMO-OTFS channel, characterizes it as a two-dimensional sparse model - the time delay-Doppler-angle sparse model, and transforms the channel estimation into a two-dimensional sparse signal reconstruction problem, solving the limitations of existing methods.

[0061] Compared with the existing three-dimensional processing method, one of the innovations lies in the dimension reduction strategy, where the time delay and Doppler dimensions are combined into one dimension, and the antenna angle is regarded as a separate dimension. This method simplifies the problem into a more manageable two-dimensional sparse recovery task.

[0062] Another innovation lies in using regularization techniques to select the most relevant indices in the delay-Doppler (DD) dimension. This initial selection captures the main sparse components of the channel; subsequently, a dimension elevation operation is performed to optimize the selection within the antenna dimension by leveraging the bursty sparsity characteristics. The combined indices in these two dimensions form a comprehensive two-dimensional index set for accurate channel reconstruction. By reducing the dimension of the problem and using a regularization strategy, the 2D-ROMP algorithm reduces the computational complexity to a certain extent compared with the 3D-SOMP method while maintaining high-precision channel estimation. Simulation results show that the 2D-ROMP algorithm outperforms the traditional OMP and 3D-SOMP methods in terms of reconstruction accuracy and computational efficiency. Description of the Drawings

[0063] Figure 1 is the block diagram of the Massive MIMO-OTFS system.

[0064] Figure 2 is the comparison diagram of the mean square error and signal-to-noise ratio performance of different algorithms.

[0065] Figure 3 is the comparison diagram of the performance of different algorithms under different numbers of antennas.

[0066] Figure 4 is the comparison diagram of the bit error rate performance of different algorithms. Detailed Implementation Manner

[0067] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments.

[0068] Embodiment 1

[0069] The channel estimation method for the Massive MIMO-OTFS system based on 2D-ROMP provided by the present invention, as Figure 1 shown in the block diagram of the Massive MIMO-OTFS system, utilizes the sparse characteristics of the Massive MIMO-OTFS channel, characterizes it as a two-dimensional sparse model - the delay-Doppler-angle sparse model, treats the channel delay-Doppler dimension as a sparse dimension, and the angle dimension as another special sparse dimension, and uses a two-dimensional (2D) compressive sensing sparse reconstruction method to implement the sparse channel estimation of the Massive MIMO-OTFS system, and converts the channel estimation into a two-dimensional sparse signal reconstruction to obtain the channel estimation, including the following steps:

[0070] First, perform two-dimensional regularization on the delay-Doppler dimension. Along one dimension in this dimension, sum the correlation values to obtain a more concise representation. Regularize this sum vector to identify the indices with the highest correlation, which are regarded as the most promising candidate indices in the delay-Doppler dimension. After selecting the number of most relevant atoms and fixing the positions of the most relevant atoms, for each selected index in the delay-Doppler dimension, the algorithm will continue to explore the antenna dimension and start selecting the relevant indices in the angle dimension.

[0071] Then, after performing the up-dimension operation on the antenna dimension, select the index with the highest correlation in the antenna angle dimension. By traversing each selected index in the delay-Doppler dimension, explore all possibilities in the antenna angle dimension to find the atom index with the highest correlation in the angle dimension.

[0072] When exploring the antenna dimension, extract the correlation matrix slice corresponding to the selected delay-Doppler index and perform a lifting transformation on this slice. This transformation helps to identify the most important indices in the antenna angle dimension. By summing and reshaping the transformed slice, the algorithm selects the index with the highest correlation in the antenna angle dimension.

[0073] Finally, combine the selected indices in these two dimensions to form a two-dimensional support set, which is then used to update the overall support set. Update the two-dimensional index set to obtain the set of indices with the highest correlation in the two dimensions, and obtain the channel estimation through sparse reconstruction.

[0074] Using this updated support set, calculate the new estimated value of the channel vector. At the same time, update the residual by subtracting the projection of the new estimated value from the measured value.

[0075] In each iteration, calculate the correlation vector between the current residual and the columns of the sensing matrix. Then, reshape this correlation vector into a two-dimensional matrix to facilitate the selection process.

[0076] The iterative process will continue until the predefined number of iterations is reached, thereby gradually optimizing the channel estimation. The final output is the recovered channel vector, which represents the estimated channel after all iterations.

[0077] Embodiment 2

[0078] A channel estimation method for a Massive MIMO-OTFS system based on 2D-ROMP includes the following steps:

[0079] S1: Collect Massive MIMO-OTFS signals to obtain a signal reception matrix;

[0080] The obtained signal reception matrix is divided into different domains. First, the two-dimensional regularization is used to select the most relevant atoms to process the time delay-Doppler domain, and then for the angle domain, the dimension is increased for processing, and the compressed sensing method is continued to be used for processing. Finally, the best atom set in the three dimensions is selected for channel estimation.

[0081] In the massive MIMO-OTFS system, the time delay-Doppler-angle channel has finite lengths in the Doppler dimension and the time delay dimension, which are [-N max / 2:N max / 2-1] and [0:M max -1] respectively; the guard interval along the Doppler axis should be at least N g / 2≥(N max / 2-1), and the guard interval along the time delay axis should be M g ≥(M max -1).

[0082] To minimize the overall pilot overhead in the system, the non-orthogonal pilot method is adopted. Although the pilots transmitted from different antennas completely overlap in the time delay-Doppler space, the complex Gaussian random sequences used as pilots for each antenna are still independent. Therefore, in the time delay-Doppler domain, the training pilot of the (p+1)-th antenna is represented by , where l = 0, 1,..., M τ -1, k = -N ν / 2,..., 0,..., N ν / 2-1, p = 0, 1,..., N t -1, and the pilot signal y l，k received by the user side in the DD domain is as follows:

[0083]

[0084] In the formula, x l-l′，k-k′，p represents the transmitted signal, represents the phase compensation, k = -N ν / 2,..., 0, / , N ν / 2-1, and l = 0, 1,..., M τ -1, v l，k represents the noise. The channel is expressed in the DFT form as The formula is as follows:

[0085]

[0086] Substitute formula (2) into formula (1) and rearrange the expression to obtain

[0087]

[0088] where y l，k is the signal received in the time-delay-Doppler-angle domain;

[0089] For ease of analysis, equation (3) is expressed in vector matrix form, with y l，k arranged into a column vector, arranged into a column vector where h r the element (l′N g + k′ + N g / 2 + 1)-th in it is equal to Therefore, equation (3) is re-expressed in vector matrix form as

[0090]

[0091] In the formula is a two-dimensional periodic convolution matrix, is a matrix with elements Denote and The above formula is expressed as

[0092] y = Z c,W h + v (5)

[0093] v represents the noise matrix; the channel h can be reversely vectorized to obtain the truncated time-delay-Doppler-angle channel, denoted as It consists of the non-zero part of, where and r = -N t / 2,..., 0,..., N t / 2 - 1.

[0094] Example 3

[0095] S2: Use the compressive sensing reconstruction algorithm to transform the channel estimation problem of the Massive MIMO-OTFS system into solving for the signal h;

[0096] The input-output vector formula of the Massive MIMO-OTFS system is y = Z c,W h + v, where Z c,W represents a two-dimensional matrix, v represents the noise matrix, and set Z c,W as the sensing matrix Ψ = Z c,W , then the above vector formula represents a sparse reconstruction problem y = Ψh + v, and use the compressive sensing sparse reconstruction algorithm to recover the Massive MIMO-OTFS channel vector h.

[0097] S3: Perform specific operations using the two-dimensional Regularized Orthogonal Matching Pursuit (2D-ROMP) algorithm, and finally obtain the signal h, completing the channel estimation in the time-delay - Doppler - angle domain.

[0098] The specific 2D-ROMP algorithm is as follows:

[0099] Input: Measurement signal y, sensing matrix Ψ;

[0100] Output: Sparse reconstructed channel

[0101] Initialization: Initialize the iteration count i = 0; Initialize the channel h (i) = 0; Initialize the residual r = y - Ψh (i) ; Initialize the index set Ω = φ; Number of sparse paths N p ;

[0102] Start loop: i ≤ N p ,

[0103] S31: Calculate the correlation vector e = Ψ H r;

[0104] S32: Convert the correlation vector into a two-dimensional matrix ε = reshape(e, M g ×N g , N t ), where the two dimensions are: time-delay Doppler - angle dimensions, and the matrix size is (M g N g , N t ); M g N g represents the product of the time-delay and Doppler dimensions, and N t is the number of antennas;

[0105] S33: Select the support set in the time-delay - Doppler dimension. The specific algorithm steps are as follows:

[0106] For the time-delay - Doppler dimension, calculate its total energy and find the maximum position through regularization;

[0107] e taov = sum(ε, 2);

[0108] [~, pos taov = regularize(e taov , 2);

[0109] Regularize is a regularization operation. Different from traditional regularization, in 2D-ROMP regularization, the maximum number of elements selected from the inner product value set is no longer considered based on the sparsity, but only the two most relevant groups of elements are selected, which reduces the probability of having non - most relevant elements in the optimal subset;

[0110] S34. Traverse all the optimal time delay-Doppler indices to select the maximum correlation support set in the antenna angle dimension. The specific algorithm steps are as follows:

[0111] Extract the corresponding antenna size: e Nt = ε(pos taov );

[0112] Dimension elevation operation: d Nt = L H ×transpose(e Nt );

[0113] Data conversion: g Nt = ∑(reshape(d Nt ));

[0114] Select the maximum correlation index: [~, pos Nt = max(g Nt );

[0115] Update the two-dimensional support index set: Ω = Ω ∪ pos, where pos = {pos taov , pos Nt};

[0116] End the traversal;

[0117] S35. Calculate the new estimated channel:

[0118] S36. Update the residual: r = y - Ψh (i) ;

[0119] End the loop.

[0120] Next, the performance of the channel estimation method of the 2D-ROMP-based Massive MIMO-OTFS system of the present invention is evaluated.

[0121] Test example

[0122] In this test example, the mean square error (NMSE) and bit error rate (BER) performances of different channel estimation methods of the Massive MIMO-OTFS system are simulated and compared under the 3GPP urban macrocell channel. Three algorithms, namely the pilot method, the OMP method, and the three-dimensional structured OMP (3D-SOMP method), are selected for analysis and comparison with the method of the present invention. The specific simulation parameters are shown in Table 1.

[0123] Table 1 Simulation parameters

[0124]

[0125] (1) FromFigure 2 From the performance comparison data graphs of the mean square error and signal-to-noise ratio of different algorithms, it can be seen that the channel estimation method of the present invention has the best mean square error (NMSE) performance. Among them, it can be observed that the traditional pilot-based channel estimation technique performs poorly in terms of NMSE performance at all signal-to-noise ratio levels, and the NMSE value is greater than a certain threshold. This is due to the inherent inefficiency of the pilot-based method, which fails to utilize the sparsity of the channel, resulting in poor estimation accuracy. The performance of the OMP algorithm is better than that of the pilot method, and the NMSE decreases as the signal-to-noise ratio increases. However, compared with more advanced sparse recovery techniques, its performance is still poor, especially at higher signal-to-noise ratios, because OMP does not fully utilize the multi-dimensional sparsity of the channel.

[0126] The 3D-SOMP algorithm has obvious improvements compared with OMP because it takes into account the sparsity in three dimensions: time delay, Doppler, and antenna angle, thus reducing the NMSE value at all signal-to-noise ratio levels. By effectively utilizing the two-dimensional sparsity in the time delay-Doppler and antenna angle domains, the channel estimation method of the present invention achieves the lowest NMSE value across the entire signal-to-noise ratio range.

[0127] (2) From Figure 3 From the performance data comparison graphs of different algorithms under different numbers of antennas, it can be seen that the channel estimation method of the present invention has optimal performance. The traditional pilot method performs the worst, and as the number of antennas increases, the NMSE value increases significantly, indicating its poor scalability. The OMP algorithm performs slightly better, but the NMSE value also increases as the number of antennas increases, which shows that it is difficult to fully utilize the sparsity of the channel. The 3D-SOMP algorithm has been significantly improved compared with the pilot and OMP methods. Although the NMSE value increases slightly as the number of antennas increases, it generally remains at a relatively low level. In contrast, the 2D-ROMP algorithm of the present invention is always superior to all other methods, achieving the lowest NMSE value and demonstrating excellent performance and scalability. This method effectively utilizes the two-dimensional sparsity in the time delay-Doppler and antenna angle domains and can maintain robust performance even in the case of a large number of antennas, which is an efficient solution for accurate channel estimation in Massive MIMO-OTFS systems.

[0128] (3) From Figure 4As can be seen from the comparison chart of the bit error rate (BER) performance of different algorithms, the traditional pilot method performs the worst, with a high BER value and only a slight decrease as the signal-to-noise ratio (SNR) increases. The 3D-SOMP algorithm performs significantly better, achieving lower BER values by leveraging three-dimensional sparsity, especially at higher SNR levels. The 2D-ROMP algorithm of the present invention exhibits the best performance among all the estimation techniques. At all SNR levels, its BER is very close to the Perfect Channel State Information (Perfect CSI) benchmark. This indicates that 2D-ROMP has excellent capabilities in accurately estimating the channel using two-dimensional sparsity, thus enabling more reliable data transmission. The results highlight that 2D-ROMP is an efficient solution for achieving low BER in Massive MIMO-OTFS systems, and its robust performance can be comparable to the ideal scenario with Perfect CSI.

[0129] In summary, the channel estimation method for the Massive MIMO-OTFS system based on 2D-ROMP of the present invention reduces the computational complexity while maintaining high-precision channel estimation, and its robust performance is significantly improved. The simulation results show that the 2D-ROMP algorithm is superior to the traditional OMP and 3D-SOMP methods in terms of reconstruction accuracy and computational efficiency.

[0130] Based on the above embodiments, the present invention further describes in detail the technical features involved and the functions and roles played by these technical features in the present invention to help those skilled in the art fully understand the technical solution of the present invention and reproduce it.

[0131] Finally, although this specification is described in terms of embodiments, not every embodiment only contains an independent technical solution. This narrative style of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment are also appropriately combined to form other embodiments understood by those skilled in the art.

[0132] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, makes equivalent substitutions or changes, and all should be covered within the protection scope of the present invention.

Claims

1. A channel estimation method for a Massive MIMO-OTFS system based on 2D-ROMP, characterized in that: The sparse characteristics of the Massive MIMO-OTFS channel are used to characterize it as a two-dimensional sparse model, namely the delay-Doppler-angle sparse model. The channel delay-Doppler dimension is treated as a sparse dimension, and the angle dimension is treated as another special sparse dimension. A two-dimensional (2D) compressed sensing sparse reconstruction method is used to realize the sparse channel estimation of the Massive MIMO-OTFS system. The channel estimation is converted into a two-dimensional sparse signal reconstruction to obtain the channel estimation, including the following steps: First, the delay-Doppler dimension is regularized in two dimensions, the most relevant number of atoms is selected, and after the most relevant atomic positions are fixed, the selection of relevant indices in the angle dimension is started; Then, after performing the dimension upscaling operation on the antenna dimension, the maximum correlation index of the antenna angle dimension is selected, wherein all possibilities of the antenna angle dimension are explored by traversing the index of each selected delay-Doppler dimension, so as to find the most relevant atomic index of the angle dimension; Finally, the two-dimensional index set is updated to obtain the most relevant index set in the two dimensions, and the channel estimate is obtained through sparse reconstruction; The specific steps are as follows: S1: Collect Massive MIMO-OTFS signals and obtain the signal receiving matrix; S2: Use the compressed sensing reconstruction algorithm to transform the channel estimation problem of the Massive MIMO-OTFS system into solving the signal h; S3: Use the two-dimensional regularized orthogonal matching pursuit 2D-ROMP algorithm to perform specific operations, and finally obtain the signal h to complete the channel estimation in the delay-Doppler-angle domain. In S3, the 2D-ROMP algorithm is specifically: Input: measurement signal y, perception matrix Ψ; Output: sparse reconstructed channel Initialization: Initialize the number of iterations i = 0; initialize the channel h (i) = 0; initial residual r = y-Ψh (i) ; Initialize index set Ω = φ; The number of sparse paths N p ; Start loop: i≤N p , S31, calculate the correlation vector e=Ψ H r; S32, convert the related vector into a two-dimensional matrix ε=reshape(e, M g ×N g , N t ), the two-dimensional representation is: delay Doppler-angle dimension, the matrix size is (M g N g , Nt), M g N g represents the product of delay and Doppler dimension, N t is the number of antennas; S33, select the support set of the delay-Doppler dimension, the specific algorithm steps are: For the delay-Doppler dimension, calculate its total energy and find the maximum position through regularization; e taov =sum(e,2); [~,pos taov ]=regularize(and taov ,2); Regularization is a regularization operation. Different from the selection in traditional regularization, in 2D-ROMP regularization, the maximum number of elements selected in the inner product value set is no longer considered based on sparsity, but only the two most relevant groups of elements are selected, which reduces the probability of non-most relevant elements existing in the optimal subset. S34, traverse all the best delay-Doppler indexes to select the maximum correlation support set in the antenna angle dimension. The specific algorithm steps are as follows: Extract the corresponding antenna size: e Nt =ε(pos taov ); Dimension up operation: d Nt =L H ×transpose(e Nt ); Data conversion: g Nt =∑(reshape(d Nt )); Select the maximum relevant index: [~,pos Nt ]=max(g Nt ); Update the two-dimensional support index set: Ω = Ω∪pos, where pos = {pos taov ,pos Nt }; End traversal; S35, calculate a new estimated channel: S36. Update residual: r = y - Ψh (i) ; End the loop.

2. According to a 2D-ROMP-based Massive MIMO-OTFS system channel estimation method according to claim 1, it is characterized in that: First, we focus on the delay-Doppler dimension, where we sum the correlation values ​​along one dimension to obtain a more compact representation; we regularize this sum vector to identify the indexes with the highest correlation, which are considered as the most promising candidate indexes in the delay-Doppler dimension; for each selected index in the delay-Doppler dimension, we continue to explore the antenna dimension, extract the correlation matrix slice corresponding to the selected delay-Doppler index, and perform a lifting transformation on this slice, which helps to identify the most important index in the antenna angle dimension; By summing and reshaping the transformed slices, the index with the maximum correlation in the antenna angle dimension is selected; The selected indices in the two dimensions are combined to form a two-dimensional support set, which is then used to update the overall support set; using this updated support set, a new estimate of the channel vector is calculated; At the same time, the residuals are updated by subtracting the projection of the new estimate from the measurement.

3. The channel estimation method for a Massive MIMO-OTFS system based on 2D-ROMP according to claim 2, characterized in that: In each iteration, the correlation vector between the current residual and the perception matrix column is calculated; then, this correlation vector is reshaped into a two-dimensional matrix to facilitate the selection process; The iterative process will continue until a predefined number of iterations is reached, thereby gradually optimizing the channel estimate; the final output is the recovered channel vector, which represents the estimated channel after all iterations.

4. The channel estimation method for a Massive MIMO-OTFS system based on 2D-ROMP according to claim 3, characterized in that: In S1, the signal receiving matrix is ​​divided into different domains. First, the most relevant atoms are selected through two-dimensional regularization to process the delay-Doppler domain. Then, for the angle domain, dimensionality upscaling is used. The compressed sensing method is continued to be used for processing, and finally the best set of atoms in three dimensions is selected for channel estimation.

5. The channel estimation method for a Massive MIMO-OTFS system based on 2D-ROMP according to claim 3, characterized in that: In S2, the input and output vector formula of the Massive MIMO-OTFS system is y=Z c,W h+v, where Z c,W represents a two-dimensional matrix, v represents the noise matrix, and Z c,W Let the perception matrix Ψ = Z c,W , the above vector formula is expressed as a sparse reconstruction problem y=Ψh+v, and the compressed sensing sparse reconstruction algorithm is used to restore the Massive MIMO-OTFS channel vector h.

6. The channel estimation method for a Massive MIMO-OTFS system based on 2D-ROMP according to claim 5, characterized in that: In S1, in the Massive MIMO-OTFS system, the delay-Doppler-angle channel has finite lengths in the Doppler dimension and the delay dimension, which are [-N max / 2:N max / 2-1] and [0:M max -1]; the guard interval along the Doppler axis should be at least N g / 2≥(N max / 2-1), the protection interval along the delay axis should be M g ≥(M max -1).

7. The channel estimation method for a Massive MIMO-OTFS system based on 2D-ROMP according to claim 6, characterized in that: In order to minimize the overall pilot overhead in the system, a non-orthogonal pilot scheme is adopted. Although the pilots transmitted from different antennas completely overlap in the delay-Doppler space, the complex Gaussian random sequence used as a pilot for each antenna is still independent. Therefore, in the delay-Doppler domain, the training pilot of the (p+1)-th antenna is composed of yx l,k,p Represents, where l=0,1,...,M τ -1, k = -N ν / 2,...,0,...,N ν / 2-1, p=0,1,...,N t -1, the pilot signal y received in the DD domain of the user end l，k , as shown below: In the formula, x l-l′，k-k′，p Indicates sending a signal. Indicates phase compensation, k = -N ν / 2,...,0,...,N ν / 2-1, and l=0,1,...,M τ -1, v l，k represents noise, and the channel Expressed in DFT form The formula is as follows: Substitute formula (2) into formula (1) and rearrange the expression get Among them, y l,k It is the signal received in the delay-Doppler-angle domain; For ease of analysis, we express (3) in the form of a vector matrix, y l,k Arranged into column vectors, Arrange into column vectors where h r The elements in (l′N g +k′+N g / 2+1)-th is equal to Therefore, formula (3) can be re-expressed in the form of a vector matrix as In the formula is a two-dimensional periodic convolution matrix, is a matrix with elements (lN ν +k+N ν / 2+1,l′N g +k′+N g / 2+1)-th, remember as well as The above formula can be expressed as y=Z c,W h+v (5) v represents the noise matrix; the channel h can be inversely vectorized to obtain a truncated delay-Doppler-angle channel, denoted as It consists of The non-zero part of l=0,1,...,M g -1,k=-N g / 2,...,0,...,N g / 2-1, and r=-N t / 2,...,0,...,N t / 2-1.

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