Large-scale MIMO-OFDM downlink channel state information feedback method and system based on rate distortion theory

Abstract

The invention discloses a large-scale MIMO-OFDM (Multiple Input Multiple Output-Orthogonal Frequency Division Multiplexing) downlink channel state information (CSI) feedback method and a large-scale MIMO-OFDM downlink channel state information (CSI) feedback system based on a rate-distortion theory, and solves the problems that in the prior art, the high-dimensional CSI feedback overhead is large, and the feedback precision and the transmission efficiency are difficult to According to the method, a downlink channel state information (CSI) compression feedback problem is modeled into a data compression problem, CSI is regarded as a high-dimensional random information source, a downlink CSI feedback optimality condition is established based on a rate distortion theory, and then a deep neural network is constructed through an approximate optimality condition; the deep neural network comprises an encoder and a decoder, the encoder is deployed at a user equipment end, and the decoder is deployed at a base station end; the user equipment side estimates a channel matrix from the downlink pilot signal, compresses and encodes the channel matrix by using an encoder, and feeds back a code word to the base station side; and in the operation stage, the base station side reconstructs the channel matrix from the feedback code word by using the decoder. The method can ensure the feedback precision and remarkably reduce the feedback overhead.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of communication, and particularly relates to a large-scale MIMO-OFDM downlink channel state information feedback method and system based on a rate distortion theory. BACKGROUND

[0002] Large-scale Multiple-Input Multiple-Output (MIMO) technology achieves great improvement in spectrum efficiency and energy efficiency by deploying large-scale antenna arrays at the base station end. The core premise of its performance gain is that the transmitting end obtains high-precision channel state information (CSI). In a frequency division duplex (FDD) system, since the uplink and downlink channels lack reciprocity, user equipment (UE) needs to feed back the downlink CSI to the base station. However, when OFDM technology is combined with a large-scale MIMO system, the large number of antennas and subcarriers leads to a dramatic increase in the dimension of the channel matrix, directly causing a dramatic increase in the overhead of CSI feedback, which becomes a key bottleneck restricting the performance improvement of the system.

[0003] Most of the existing deep learning (DL) based CSI feedback schemes adopt a two-stage compression feedback strategy: first, the downlink spatial frequency domain channel matrix is converted into an angle-delay domain channel matrix (ADCM) through two-dimensional inverse discrete Fourier transform (2D-IDFT), and then it is truncated; on this basis, a deep neural network is used to further compress the truncated angle-delay domain channel matrix (T-ADCM). Although this kind of scheme has achieved certain results, its inherent defects are still quite prominent: first, most of the existing schemes focus on the design of the neural network module and architecture, ignoring the theoretical exploration of the feedback performance limit, which not only restricts the further improvement of performance, but also reduces the theoretical explainability of the technical scheme; second, the existing feedback schemes based on T-ADCM restrict the feedback accuracy. Specifically, these schemes use a DFT-based channel model, which considers that the non-zero values of the channel matrix are concentrated in the first few columns. However, when the number of effective subcarriers is not sufficiently large, the DFT-based angle-delay domain channel matrix (DFT-ADCM) will have significant spectral leakage, causing the truncation method to bring about non-negligible information loss, which in turn affects the feedback accuracy.

[0004] In a large-scale MIMO-OFDM system, to further improve the performance of the deep learning based downlink CSI feedback method and enhance its model explainability, systematic research and mathematical characterization of the optimal feedback strategy are needed; at the same time, in view of the inherent error introduced by the truncation operation in the feedback method based on T-ADCM, a more accurate channel modeling method needs to be explored to reduce or eliminate the error caused by the traditional truncation method. SUMMARY

[0005] The application aims at the deficiencies in the existing downlink CSI feedback scheme of large-scale MIMO-OFDM system based on deep learning, and provides a large-scale MIMO-OFDM downlink CSI feedback method and system based on rate-distortion theory, so as to realize more efficient downlink CSI feedback.

[0006] The technical scheme is as follows:

[0007] In the first aspect, the application provides a large-scale MIMO-OFDM downlink CSI feedback method based on rate-distortion theory, which comprises the following steps:

[0008] The downlink CSI compression feedback problem is modeled as a data compression problem, and the CSI is regarded as a high-dimensional random source, and the rate-distortion theory is used to establish the optimality condition of the downlink CSI feedback, and then a deep neural network is constructed by approximating the optimality condition, wherein the deep neural network comprises an encoder and a decoder, and the encoder is deployed at the user equipment end, and the decoder is deployed at the base station end.

[0009] The user equipment end estimates the channel matrix from the downlink pilot signal, and uses the encoder to compress and encode the channel matrix, and then feeds back the code word to the base station end, and the base station end uses the decoder to reconstruct the channel matrix from the feedback code word.

[0010] Further, the beam-domain channel matrix is estimated from the downlink pilot signal based on the beam-based channel model, and the user equipment end uses the encoder to compress and encode the beam-domain channel matrix, wherein the beam-based channel model is a beam matrix multiplied by a beam-domain channel vector, and the beam matrix is a matrix composed of a group of spatial-frequency domain direction vectors corresponding to the direction cosine and the time delay sampling grid point, and each spatial-frequency domain direction vector is called a beam.

[0011] Further, the establishment of the optimality condition is based on a tight upper bound of the rate-distortion function of the compression problem of the channel matrix, and specifically, the compression problem of the channel matrix is converted into a compression problem containing a hidden space by introducing a hidden space and defining a mapping from the hidden space to the channel matrix reconstruction space, and the rate-distortion function of the converted problem is a tight upper bound of the rate-distortion function of the original problem.

[0012] Further, the rate-distortion function tight upper bound is equivalent to the loss function of a variational autoencoder, and solving the rate-distortion function tight upper bound is realized by training a variational autoencoder.

[0013] Further, the deep neural network adopts a variational autoencoder structure, and when the variational autoencoder satisfies the following three conditions, optimal downlink CSI feedback can be achieved: (1) the decoder of the variational autoencoder is a bijection; (2) the probability representation space of the variational autoencoder contains the optimal solution of the optimization problem corresponding to the rate distortion function; and (3) the encoding length of any downlink channel matrix is equal to the relative entropy of the transfer kernel and the prior distribution of the variational autoencoder.

[0014] Further, the deep neural network RDFI-Net is constructed by approximating the optimality condition; the RDFI-Net adopts a variational autoencoder structure, residual blocks are introduced in the feature extraction module to strengthen the nonlinear representation capability of high-dimensional CSI features, and an up-sampling module is designed based on a sub-pixel rearrangement technology to reduce the information loss of the decoder; the RDFI-Net introduces a hierarchical autoregressive probability model, uses the hidden space of a multi-layer autoregressive structure to improve the probability representation capability, and reduces the suboptimality when solving the rate distortion optimization problem; the RDFI-Net uses an entropy encoding technology to approximate the optimal code length; specifically, the RDFI-Net discretizes the hidden space, and encodes the obtained discrete symbols based on the statistical characteristics of the CSI.

[0015] Further, the deep neural network adopts a quantization-compatible end-to-end training framework; for a fixed code rate training framework, the hidden variable is approximated by additive uniform noise; for a variable code rate training framework, an adaptive quantization factor is introduced, and is coupled with a Lagrange multiplier used to solve a rate distortion function of a channel matrix compression problem containing a hidden space, the adaptive quantization factor is used to directly adjust the quantization precision of the hidden variable, so that low-complexity rate adjustment is achieved; the coupling relationship between the adaptive quantization factor and the Lagrange multiplier is learned by the variable code rate training framework.

[0016] In a second aspect, the present application provides a downlink CSI feedback system for a large-scale MIMO-OFDM system based on rate distortion theory, which is used to implement the downlink CSI feedback method for a large-scale MIMO-OFDM system based on rate distortion theory, and the system comprises:

[0017] A network model construction unit is configured to model the downlink CSI compression feedback problem as a data compression problem, and to regard the CSI as a high-dimensional random source, to establish a downlink CSI feedback optimality condition based on rate distortion theory, and to further construct a deep neural network by approximating the optimality condition; the deep neural network comprises an encoder and a decoder, wherein the encoder is deployed at a user equipment end, and the decoder is deployed at a base station end;

[0018] A user equipment end processing unit is configured to estimate a channel matrix from a downlink pilot signal, to compress and encode the channel matrix by using the encoder, and to feed back a code word to the base station end.

[0019] A base station end processing unit is configured to reconstruct the channel matrix from the feedback codeword by using a decoder.

[0020] In a third aspect, the present application provides a computer system, comprising a memory, a processor and a computer program stored in the memory and executable in the processor, wherein the computer program is configured to implement the processing steps of the user equipment end or the base station end in the rate-distortion theory based downlink CSI feedback method for massive MIMO-OFDM system.

[0021] In a fourth aspect, the present application provides a computer program product, comprising a computer program, wherein the computer program is configured to implement the processing steps of the user equipment end or the base station end in the rate-distortion theory based downlink CSI feedback method for massive MIMO-OFDM system when executed in a processor.

[0022] Beneficial effects: Compared with the prior art, the present application proposes a downlink channel feedback method and system based on rate-distortion theory by deep fusion theory derivation and neural network architecture design. Firstly, the optimal CSI feedback theoretical condition system is established based on the rate-distortion function, and then the deep neural network for downlink CSI feedback is designed through the approximate optimal feedback condition, so as to realize the efficient compression and reconstruction of CSI. Furthermore, a low complexity rate adjustment mechanism is proposed, which uses the Lagrange multiplier as the control parameter to dynamically adjust the trade-off between the feedback overhead and the channel reconstruction accuracy. Experiments show that the present application can significantly improve the feedback accuracy and reduce the feedback overhead. BRIEF DESCRIPTION OF DRAWINGS

[0023] Figure 1 FIG. 1 is a diagram of the downlink CSI feedback system based on RDFI-Net in the embodiment of the present application.

[0024] Figure 2 FIG. 2 is a network structure diagram of RDFI-Net in the embodiment of the present application.

[0025] Figure 3 FIG. 3 is a data flow diagram of the training phase of RDFI-Net in the embodiment of the present application.

[0026] Figure 4 FIG. 4 is a data flow diagram of the encoding phase of RDFI-Net in the embodiment of the present application.

[0027] Figure 5 FIG. 5 is a data flow diagram of the decoding phase of RDFI-Net in the embodiment of the present application.

[0028] Figure 6 FIG. 6 is a data flow diagram of the optimal feedback evaluation phase of RDFI-Net in the embodiment of the present application.

[0029] Figure 7 A reconstruction error comparison chart of T-ADCM and BDCM in the embodiment of the present application.

[0030] Figure 8 A compression performance comparison chart of RDFI-Net and baseline model in the outdoor scene in the embodiment of the present application.

[0031] Figure 9 A compression performance comparison chart of RDFI-Net and baseline model in the indoor scene in the embodiment of the present application. DETAILED DESCRIPTION

[0032] The technical solutions provided by the present application will be described in detail below in combination with specific embodiments, and it should be understood that the following specific embodiments are only used to illustrate the present application and not to limit the scope of the present application.

[0033] As shown in Figure 1 The embodiment of the present application discloses a large-scale MIMO-OFDM system downlink CSI feedback method based on rate distortion theory. The method models the downlink CSI compression feedback problem as a data compression problem, and regards the CSI as a high-dimensional random source. Based on the rate distortion theory, the downlink CSI feedback optimality condition is established, and then a deep neural network (Rate-Distortion-Function-Inspired-Net) RDFI-Net is constructed by approximating the optimality condition. The RDFI-Net includes an encoder and a decoder. The encoder is deployed at the user equipment end, and the decoder is deployed at the base station end. The user equipment end estimates the channel matrix from the downlink pilot signal, and uses the RDFI-Net encoder to compress and encode the channel matrix, and then feeds the code word to the base station end. The base station end uses the RDFI-Net decoder to reconstruct the high-dimensional channel matrix from the feedback code word.

[0034] In this embodiment, the user equipment end estimates the beam domain channel matrix using the beam basis channel model, compresses and encodes the estimated beam domain channel matrix based on the RDFI-Net proposed by the present application, and feeds the code word to the base station. The base station decodes the code word fed back by the user based on the RDFI-Net, and reconstructs the high-dimensional CSI. It should be noted that the neural network architecture design idea of the present application is not limited to the application of the beam basis channel model. The beam basis channel model is a beam matrix multiplied by a beam domain channel vector. The beam matrix is a matrix composed of a group of spatial-frequency domain direction vectors corresponding to the direction cosine and time delay sampling grid points. Each spatial-frequency domain direction vector is called a beam. In some embodiments, it can also be used for other channel models.

[0035] The following will be specifically explained in detail in combination with a specific communication system example. It should be noted that the method of the present application is applicable not only to the specific system model shown in the following example, but also to other system models.

[0036] I. System configuration

[0037] In this embodiment, a massive MIMO-OFDM system working in FDD mode is considered. The base station is equipped with N t uniform linear arrays, serving K single-antenna users with user index set The carrier frequency is denoted as f c , and the antenna spacing of the array is d = λ c / 2, where λ c = c / f c and c is the speed of light. In OFDM modulation, the number of carriers is N c , the length of the cyclic prefix is N g , the subcarrier spacing is Δ f , and the sampling interval is T s = 1 / N c Δ f . Among them, N p subcarriers are used to transmit pilot channels for downlink channel estimation, and the index set is The duration of each OFDM symbol with CP is T sym = (N c +N g )T s . Define N×N unit matrix as I N ; I N,M represents: when N < M, I N,M = [I N 0 N,M-N ] (where 0 N,M-N is an N×(M-N) zero matrix); when N > M, I N,M = [I M 0 M,N-M ] T (where 0 M,N-M is an M×(N-M) zero matrix, and the N-order normalized discrete Fourier transform (DFT) matrix is denoted as F N .

[0038] II. Beam-based channel model

[0039] Define the spatial domain direction steering vector and the frequency domain direction steering vector as

[0040]

[0041] where and denote the start and end indices of the training subcarriers. The downlink space-frequency domain channel matrix between the base station and the kth UE may be expressed as

[0042]

[0043] where P k is the number of paths for the kth user, is the direction cosine corresponding to θ p,k , τ p,k denotes the time delay of the pth path for user k, denotes the corresponding complex gain. Further, let and be defined as

[0044]

[0045] where u i and τ j are the sampled direction cosine and time delay, satisfying and N v = F v N t , N τ = F τ N f , where F v and F τ are the fine factors. Thus, may be rewritten as

[0046]

[0047] where When N v and N τ are large enough, the subsets and are small enough such that the steering vector v(u) in and u(τ) in may be well approximated by the sampled spatial steering vector v(u i ) and the sampled frequency steering vector u(τ j ), respectively. Thus, the SFDCM in (2) can be approximated as

[0048]

[0049] where

[0050] Let then the space-frequency domain channel matrix may be expressed as

[0051]

[0052] where (6) is referred to as the beam-domain channel matrix (BDCM), and (6) is referred to as the beam-based channel model. It is worth noting that when the refinement factor is reduced to 1, (6) degenerates to the DFT-based angular delay-domain channel model widely adopted in existing research, which can be expressed as

[0053]

[0054] where denotes the T-ADCM, denotes the DFT-ADCM, N f denotes the minimum number of columns required to cover the delay spread. In particular, the channel model in (7) is the theoretical basis of the truncation scheme adopted in previous work, as it indicates that only the first N f contains non-zero coefficients. However, when the refinement factor is small, (7) only has sufficient accuracy when the number of subcarriers is sufficiently large. In practical scenarios where the number of effective subcarriers is limited, spectral leakage causes non-zero coefficients in the DFT-ADCM to spread to the tail. Therefore, simple truncation of these tail columns introduces significant reconstruction error, thus restricting the CSI feedback performance. Unlike existing methods, higher reconstruction accuracy can be achieved using the BDCM.

[0055] First, it is assumed that the UE can accurately estimate from the downlink pilot signals through a channel estimation algorithm. is encoded into a codeword v k This process can be represented as

[0056]

[0057] where f en (·) denotes the encoding function corresponding to the encoder. When v k is fed back to the base station, the decoder recovers from v k This process can be represented as

[0058]

[0059] where f de (·) denotes the decoding function corresponding to the decoder. Finally, based on the beam-based channel model, can be recovered from

[0060] ​

[0061] The definitions of V and F here are consistent with equation (6). Typically, when the refinement factor is set to 2, the beam-based channel model in equation (6) usually achieves accurate channel representation. Therefore, It can achieve N t ×N p arrive Near-lossless dimensionality reduction. This significant dimensionality reduction not only reduces the dimension by several orders of magnitude compared to SFDCM, but also preserves key channel features that are often lost in the T-ADCM method.

[0062] III. Optimal CSI Feedback

[0063] To simplify the notation, the subscript k and superscript in the channel matrix notation are omitted. Let H be the value space. for The regeneration space. Based on the assumption that the UE independently feeds back downlink CSI and that the feedback codeword is transmitted to the base station without error, the feedback process can be modeled as a memoryless high-dimensional information source. Therefore, the minimum feedback overhead required to achieve distortion not exceeding D is characterized by the RD function, which is defined as...

[0064]

[0065] in Indicates H and Mutual information, ρ: Indicates distortion measurement. Indicates from arrive The transfer kernel. The rate-distortion function in equation (11) establishes the fundamental limit of the CSI feedback system: any rate-distortion pair (R,D) satisfying R>R(D) can be achieved by a certain CSI feedback scheme, and there is no scheme that can break through this theoretical limit. Therefore, accurately characterizing the rate-distortion function is crucial when studying optimal downlink CSI feedback. However, the analytical expression of this function is usually unknown, and the calculation of the rate-distortion function for CSI feedback scenarios is more challenging. Given the difficulty in calculating the rate-distortion function of downlink CSI feedback, this embodiment instead uses a tight upper bound of an RD function, which can provide a computationally feasible approximation method for characterizing the performance limit of CSI feedback while ensuring mathematical rigor.

[0066] remember For the hidden space, ω: Let be any mapping from the latent space to the reconstructed space. Therefore, in the new distortion function ρ ω : Next, a new compression problem Induced. The distortion function can be expressed as

[0067] ρω (H, Z) = p(H, ω(Z)), (12)

[0068] where p is the distortion measure defined in (11). Furthermore, let the decoder-induced rate-distortion function corresponding to ω be defined as

[0069]

[0070] where Q Z|H is the transition kernel from to It has been proved that (13) is a tight upper bound of the rate-distortion function, and the equality holds when the decoder ω is bijective, i.e., for any D ≥ 0, R ω (D) ≥ R(D). Further, (13) is reformulated as

[0071]

[0072] where P Z denotes the prior distribution of Z. For the computation of (14), it is concluded that for a fixed Lagrangian multiplier λ > 0, the rate-distortion point lies on the R ω (D) curve, where

[0073]

[0074] Here is the solution to the following optimization problem

[0075]

[0076] where the objective function is expressed as

[0077]

[0078] Although computing the upper bound of the rate-distortion function in (13) is equivalent to solving the unconstrained optimization problem with the objective function in (17), the optimization of (16) is still challenging due to the variables lying in the probability metric space. To this end, the present embodiment proposes to parameterize the distributions Q Z|H and P Z using deep neural networks (DNNs). And it can be proved that the computation of R ω (D) is equivalent to training a variational autoencoder (VAE). Therefore, the optimization problem in (16) can be translated into a VAE training problem. Further, the present embodiment gives three optimality sufficient conditions. Specifically, the optimal CSI feedback can be achieved when there exists a variational autoencoder satisfying the following conditions:

[0079] (1) ω is a bijective.

[0080] (2) The probability representation space of the variational autoencoder contains the optimal solution of the optimization problem corresponding to the rate-distortion function.

[0081] (3) The encoding code length of H i is equal to the relative entropy of the transition kernel of the variational autoencoder and the prior distribution where and are consistent with the definitions in (16).

[0082] However, it is still difficult to satisfy these conditions: first, the decoder in the VAE does not guarantee bijectivity; second, the optimization problem in (16) needs to traverse all possible distributions Q Z|H and P Z , and only a suboptimal solution can be obtained by parameterizing through DNNs; third, it is significantly difficult to implement the encoding of each downlink CSI sample H i with a code length exactly equal to the feedback amount . Despite this, the derived optimality conditions still provide key insights for the design of specific CSI feedback, and the approximation of these conditions through VAEs can construct a near-optimal scheme.

[0083] Four, RDFI-Net

[0084] First, the overall design method of RDFI-Net is introduced. The design of RDFI-Net follows the proposed optimality conditions. To approximately satisfy the bijectivity requirement (condition 1), the modules of RDFI-Net are specially designed to maximize the representation capacity, thereby minimizing the information loss in the decoding process. This design strategy has a solid theoretical basis - according to the universal approximation theorem, a well-designed neural network can approximate a bijective mapping. To approximately satisfy the global optimality requirement (condition 2), RDFI-Net uses a hierarchical autoregressive probability model (HAPM) to enhance the probability modeling capability of the model. HAPM introduces structured hierarchical dependencies between latent variables through an autoregressive structure, thereby improving modeling capability. Given that the optimality of the stable point in (16) depends on the expressiveness of the probability distribution, the autoregressive property of HAPM expands the feasible distribution space. This improvement enables more accurate approximation of the optimal distribution set, thereby alleviating the performance degradation caused by limited modeling flexibility. To approximately satisfy the KL code length condition (the third condition), RDFI-Net discretizes the latent space by quantization and approximates the optimal code length using entropy coding. In the discrete scenario, the term can be reconstructed as

[0085]

[0086] where and maintain the definitions in (16), Indicates and The corresponding encoding function (18) shows that, using entropy coding technology, any CSI sample H i The feedback cost can closely approximate Meanwhile, considering the impact of the non-differentiability of quantization on gradient-based optimization methods, this embodiment constructs a quantization-compatible training framework to achieve end-to-end training—approximate quantization using additive uniform noise during the training phase and precise quantization applied during the inference phase.

[0087] The overall structure of RDFI-Net is as follows Figure 2 As shown, the encoder extracts hierarchical features of different sizes from the input, which are then fed into the latent variables of each layer. The modules of RDFI-Net are specifically designed to approximate the proposed optimal conditions. Specifically, to enhance the network's expressive power, residual blocks are integrated into each feature extraction module. Given the efficient feature extraction capabilities of the ConvNeXt architecture, these are used as residual blocks. Downsampling employs convolutional layers with a stride equal to the kernel size. Furthermore, upsampling operations implement subpixel rearrangement techniques, whose reversible nature ensures lossless information reconstruction, effectively narrowing the gap between the upper bound and the theoretical rate-distortion function.

[0088] To enhance probabilistic modeling capabilities, RDFI-Net is based on HAPM and introduces a set of N layers of latent variables connected in an autoregressive manner. Wherein, the i-th hidden variable Z i Conditional Dependency In this hierarchical structure, the transfer kernel and prior distribution are represented as:

[0089]

[0090] in Z represents i The j-th component, d i Z represents i The dimensions of probabilistic models are limited. Existing methods mainly employ single-layer or two-layer probabilistic models, but these methods have limited probabilistic modeling capabilities due to the shallowness of their probabilistic models. HAPM improves probabilistic modeling capabilities by explicitly introducing dependencies between latent variables. Unlike simple stacking, which is prone to deep collapse, HAPM's autoregressive hierarchical structure achieves cross-layer information fusion through residual jump connections between latent layers.

[0091] Furthermore, this embodiment proposes a quantization-compatible training framework, such as... Figure 3 As shown. This framework includes a fixed bitrate training framework and a variable bitrate training framework. For the fixed bitrate training framework, this embodiment uses additive uniform noise approximation quantization, which is expressed as:

[0092]

[0093] where To fit this approximation, the transition kernel is chosen as a conditionally uniform distribution in each dimension, which can be expressed as

[0094]

[0095] where g a,b (·) denotes a function that takes value 1 on (a, b) and 0 elsewhere, z i,j is the j-th component of z i , and μ i,j denotes the mean of z . Regarding the choice of the prior, the present embodiment is based on the theoretical property that, given as the optimal transition kernel that minimizes the objective in (16), the corresponding optimal prior distribution is

[0096]

[0097] Therefore, the prior distribution P Z needs to be sufficiently flexible to fit the transition kernel. Moreover, P Z must be strictly positive over the entire definition domain, be easily convertible into a probability mass function (PMF) to fit entropy coding, and needs to ensure numerical stability in the optimization. Therefore is chosen as

[0098]

[0099] where denotes the probability density function (PDF) of a Gaussian distribution with mean μ and variance σ 2 , and P denotes the prior distribution of z , parameterized by the ＜i parameters and that depend on Z . P can be easily converted into a PMF to support entropy coding, whose corresponding PMF is explicitly expressed as

[0100]

[0101] From the above equation, it can be seen that is obtained by evaluating on equidistant points with step size 1. In summary, the objective function in the fixed-rate training is expressed as

[0102]

[0103] where λ is pre-configured to balance the feedback overhead and reconstruction accuracy. However, the fixed-rate training strategy is controlled by a specific rate-distortion trade-off of fixed λ. Therefore, to achieve rate adaptation, multiple models with different λ values need to be trained, which is difficult in practical systems.

[0104] For the variable-rate training framework, the present embodiment introduces an adaptive quantization factor coupled with λ, which directly adjusts the quantization accuracy of the latent variable, thereby achieving low-complexity rate adjustment. The coupling relationship between the adaptive quantization factor and λ is learned by the variable-rate training framework. Specifically, the present embodiment extends the fixed-rate training framework and further proposes a low-complexity rate adjustment mechanism, which uses λ as a conditional variable with a probability distribution function P λ (·) to achieve variable-rate CSI feedback in a single model. Specifically, under this framework, the objective function of the variable-rate model is

[0105]

[0106] It is noted that making the neural network architecture conditionally dependent on λ introduces considerable complexity, so the present embodiment proposes a learnable adaptive quantization factor (AQF) to avoid additional architectural overhead. The AQF is coupled with λ and directly controls the size of the quantization step size By this method, the trade-off between feedback overhead and reconstruction accuracy can be dynamically adjusted by adjusting a, which is equivalent to adjusting λ. After introducing the AQF, equation (23) can be deformed as

[0107]

[0108] Therefore, equation (27) can be deformed as

[0109]

[0110] Further simplifying the above equation to

[0111]

[0112] This shows that quantizing z i,j with a step size of i,j is equivalent to first scaling z i,j with a(λ) and then quantizing a(λ)z BD with a rounding quantizer.

[0113] Therefore, the approximation in the training phase is

[0114]

[0115] where u is a random sample subject to a uniform distribution. The distribution of λ is set as

[0116]

[0117] This means that λ is drawn from the set Λ with equal probability, where is a predefined set, and M is the number of elements in the set Λ. The AQF set is initialized as and is optimized by the following objective function to learn the coupling relationship with Λ

[0118]

[0119] After optimization, the relationship between λ and a is learned, so that the variable-rate CSI feedback is achieved by adjusting a, which is functionally equivalent to adjusting λ. To improve the stability of training, a two-stage training strategy is implemented: first, train RDFI-Net in a fixed-rate mode with a higher λ value, and then optimize according to equation (32).

[0120] The UE compresses H BD into a binary bit stream as shown in Figure 4 . Unlike the additive uniform noise approximation quantization in the training phase, each Z i is obtained by element-wise quantization of the residual of μ i with respect to . In the fixed-rate mode, this operation is represented as

[0121]

[0122] where μ i,j is quantized to the nearest neighbor from the set . In the variable-rate mode, the hidden variables are first scaled using the AQF and then quantized, represented as

[0123]

[0124] After quantization, Z i is encoded into binary bits using the PMF represented in equation (24). Each hidden block produces an independent bit stream, so the feedback overhead consists of N bit streams corresponding to N hidden variables Z1, Z2,..., Z N . These bit streams are transmitted from the UE to the BS. After receiving the bit streams, the BS decodes them according to Figure 5 and finally obtains the reconstructed BDCM. Finally, the BS reconstructs the SFDCM according to equation (6).

[0125] In addition to being used for downlink CSI feedback, the RDFI-Net can be used to calculate the upper bound of the rate-distortion function for optimal CSI feedback performance evaluation, as shown in Figure 6 . In this process, the probability model is set as a Gaussian distribution with a diagonal covariance matrix, so the of the i-th hidden variable is KL divergence between the two distributions is

[0126]

[0127] where d i represents the dimension of the i-th hidden variable, represents the parameters of the i-th layer hidden variable. Further, the objective function of the upper bound calculation process can be reconstructed as

[0128]

[0129] V. Implementation Effects

[0130] To make the person in the technical field better understand the present application scheme, the performance results of the downlink channel state information feedback method based on rate distortion theory in the embodiment under specific configuration are given below.

[0131] Considering a MIMO-OFDM communication system, the system parameter configuration is as follows: the number of antennas N t = 32, the carrier frequency f c = 4.8 GHz, the subcarrier spacing Δ f = 250 Hz, the number of subcarriers N c = 512, the number of effective subcarriers N p = 120, the length of the cyclic prefix N g = 72, the base station antenna spacing d = 0.5λ c , the fine factor F t = F τ = 2.

[0132] To evaluate the feedback performance, three indicators are used: normalized mean square error (NMSE) and bits per unit element (BPU). The NMSE is defined as The BPU is defined as where N bit represents the total number of feedback bits. NMSE is used to evaluate the reconstruction accuracy, and BPU is used to measure the feedback overhead. Open source models CsiNet, CLNet, CRNet and TransNet are used as the baseline. All baseline models use 8-bit quantization for the transmitted codewords, and the corresponding BPU is calculated as where K represents the encoding dimension in each model.

[0133] Figure 7 The reconstruction accuracy of T-ADCM is shown as a function of the number of retained columns N a . Where N a from N f= 16 to 116 with a step of 5. It can be seen from the figure that the reconstruction accuracy of the outdoor and indoor scenes is limited by the truncation effect. On the other hand, the BDCM achieves a reconstruction accuracy of -58 dB and -61 dB for the outdoor and indoor scenes, respectively. In addition, the dimension of the BDCM is 64x32, which does not introduce unacceptable dimension overhead while improving the reconstruction accuracy.

[0134] Figure 8 The performance comparison of RDFI-Net and the benchmark model in the outdoor scene under the NMSE index is shown. The results show that the benchmark model has limited CSI feedback capability. When the code rate is 0.3BPU, the reconstruction accuracy has not reached -10dB, and a large reconstruction error is introduced under a lower code rate. In contrast, under the fixed code rate mode, the feedback method proposed in the application achieves -17.04dB NMSE at 0.05BPU and further improves to -37.8dB at 0.3BPU, which achieves significant performance gain compared with the benchmark model. In addition, the feedback performance based on T-ADCM combined with RDFI-Net shows a significant truncation effect, and the reconstruction accuracy is truncated at -15.9dB, indicating that T-ADCM significantly restricts the feedback performance. In addition, the performance of RDFI-Net under the variable code rate mode maintains ideal feedback performance. Further, using SFDCM as the input to calculate the R-D function upper bound, the results show that there is a significant gap between the benchmark model and the theoretical limit, and RDFI-Net under the two working modes closely approximates the R-D upper bound, highlighting its superior performance.

[0135] Figure 9 The performance of RDFI-Net in the indoor scene is shown. In the indoor scene, the proposed feedback method still shows significant advantages compared with the benchmark model.

[0136] Based on the same inventive concept, the application embodiment discloses a large-scale MIMO-OFDM system downlink CSI feedback system based on rate distortion theory, which is used to implement the foregoing large-scale MIMO-OFDM system downlink CSI feedback method based on rate distortion theory. The system comprises: a network model construction unit, which is used to model the downlink CSI compression feedback problem as a data compression problem, and regards the CSI as a high-dimensional random source, establishes the downlink CSI feedback optimality condition based on the rate distortion theory, and then constructs a deep neural network by approximating the optimality condition; the deep neural network comprises an encoder and a decoder, wherein the encoder is deployed at the user equipment end, and the decoder is deployed at the base station end; a user equipment end processing unit is used to estimate a channel matrix from a downlink pilot signal, and to compress and encode the channel matrix by using the encoder, and then to feed back a code word to the base station end; and a base station end processing unit is used to reconstruct the channel matrix from the feedback code word by using the decoder.

[0137] The embodiment of the present application further discloses a computer system, which comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, and characterized in that the computer program is used to realize the processing steps of the user equipment end or the base station end in the large-scale MIMO-OFDM system downlink CSI feedback method based on the rate-distortion theory when the processor executes the computer program.

[0138] The embodiment of the present application further discloses a computer program product, which comprises a computer program, and the computer program is used to realize the processing steps of the user equipment end or the base station end in the large-scale MIMO-OFDM system downlink CSI feedback method based on the rate-distortion theory when the processor executes the computer program.

[0139] The part not described in the present application is the known technology of the person skilled in the art.

[0140] The preferred embodiments of the present application are described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations without creative work based on the concept of the present application. Therefore, any technical solution obtained by logical analysis, reasoning or limited experiment based on the existing technology according to the concept of the present application should be within the protection scope determined by the claims.

Claims

1. A downlink CSI feedback method for large-scale MIMO-OFDM systems based on rate distortion theory, characterized in that, The method comprises the following steps: The downlink channel state information (CSI) compression feedback problem is modeled as a data compression problem, and the CSI is regarded as a high-dimensional random source, and an optimality condition of downlink CSI feedback is established based on rate-distortion theory, and a deep neural network is constructed by approximating the optimality condition; wherein the deep neural network comprises an encoder and a decoder, wherein the encoder is deployed at a user equipment end, and the decoder is deployed at a base station end; The user equipment end estimates a channel matrix from a downlink pilot signal, and compressively encodes the channel matrix by using the encoder, and then feeds a code word to the base station end; the base station end reconstructs the channel matrix from the feedback code word by using the decoder. 2.The rate-distortion theory based downlink CSI feedback method for massive MIMO-OFDM systems according to claim 1, characterized in that, A beam-domain channel matrix is estimated from a downlink pilot signal based on a beam-based channel model, and the user equipment end compressively encodes the beam-domain channel matrix by using the encoder; The beam-based channel model is a product of a beam matrix and a beam-domain channel vector, the beam matrix is a matrix composed of a selected group of spatial-frequency domain direction steering vectors corresponding to direction cosine and time delay sampling points, and each spatial-frequency domain direction steering vector is referred to as a beam. 3.The optimal downlink CSI feedback method for large-scale MIMO-OFDM systems based on rate-distortion theory of claim 1, wherein, The establishment of the optimality condition is based on a tight upper bound of a rate-distortion function of the compression problem of the channel matrix; by introducing a latent space and defining a mapping from the latent space to a channel matrix reconstruction space, the compression problem of the channel matrix is converted into a compression problem involving the latent space; The rate-distortion function of the converted problem is a tight upper bound of the rate-distortion function of the original problem. 4.The method of Claim 3, wherein, The constructed tight upper bound of the rate-distortion function is equivalent to a loss function of a variational autoencoder, and solving the tight upper bound of the rate-distortion function is realized by training a variational autoencoder. 5.The rate-distortion theory based downlink CSI feedback method for massive MIMO-OFDM systems of claim 1, wherein, The deep neural network adopts a variational autoencoder structure, and when the variational autoencoder satisfies the following three conditions, the optimal downlink CSI feedback can be realized: the decoder of the variational autoencoder is a bijective function; the probability representation space of the variational autoencoder contains the optimal solution of the optimization problem corresponding to the rate-distortion function; the encoding length of any downlink channel matrix is equal to the relative entropy of the transfer kernel and the prior distribution of the variational autoencoder. 6.The rate-distortion theory based downlink CSI feedback method for massive MIMO-OFDM systems according to claim 1, characterized in that, A deep neural network RDFI-Net is constructed by approximating the optimality condition; RDFI-Net adopts a variational autoencoder structure, residual blocks are introduced in a feature extraction module to enhance the nonlinear representation capability of high-dimensional CSI features, and an upsampling module is designed based on a sub-pixel rearrangement technology to reduce the information loss of the decoder; RDFI-Net introduces a hierarchical autoregressive probability model, uses the hidden space of a multi-layer autoregressive structure to improve the probability representation capability, and reduces the suboptimality when solving the rate-distortion optimization problem; RDFI-Net uses entropy encoding technology to approximate the optimal code length, RDFI-Net discretizes the latent space, and encodes the obtained discrete symbols based on the statistical characteristics of the CSI. 7.The rate-distortion theory based downlink CSI feedback method for massive MIMO-OFDM systems according to claim 1, characterized in that, The deep neural network adopts a quantization-compatible end-to-end training framework, for a fixed code rate training framework, a hidden variable uses additive uniform noise to approximate quantization; for a variable code rate training framework, an adaptive quantization factor is introduced, and is coupled with a Lagrange multiplier of a rate distortion function for solving a channel matrix compression problem containing a hidden space by using a Lagrange multiplier method, the adaptive quantization factor is used to directly adjust the quantization precision of the hidden variable, so as to realize low complexity rate adjustment; the coupling relationship between the adaptive quantization factor and the Lagrange multiplier is learned by the variable code rate training framework.

8. A large-scale MIMO-OFDM system downlink CSI feedback system based on rate-distortion theory, for implementing the large-scale MIMO-OFDM system downlink CSI feedback method based on rate-distortion theory according to any one of claims 1-7, characterized in that, Comprise: A network model construction unit is configured to model a downlink channel state information (CSI) compression feedback problem as a data compression problem, and to regard the CSI as a high-dimensional random source, to establish a downlink CSI feedback optimality condition based on rate distortion theory, and to further construct a deep neural network by approximating the optimality condition; the deep neural network comprises an encoder and a decoder, wherein the encoder is deployed at a user equipment end, and the decoder is deployed at a base station end; A user equipment end processing unit is configured to estimate a channel matrix from a downlink pilot signal, and to compress and encode the channel matrix by using the encoder, and to further feed back a code word to the base station end; A base station end processing unit is configured to reconstruct the channel matrix from the feedback code word by using the decoder.

9. A computer system comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The computer program is executed by a processor to realize the processing steps of the user equipment end or the base station end in the downlink CSI feedback method of the large-scale MIMO-OFDM system based on the rate distortion theory according to any one of claims 1-7.

10. A computer program product comprising a computer program, characterized in that, The computer program is executed by a processor to realize the processing steps of the user equipment end or the base station end in the downlink CSI feedback method of the large-scale MIMO-OFDM system based on the rate distortion theory according to any one of claims 1-7.

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