A distributed joint signal detection and noise parameter estimation method and device for a cell-free massive MIMO system
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SOUTHEAST UNIV
- Filing Date
- 2026-05-11
- Publication Date
- 2026-06-26
Smart Images
Figure CN122293231A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of wireless communication signal processing, specifically relating to a distributed joint signal detection and noise parameter estimation method and apparatus for cell-free massive multiple-input multiple-output (CMIMO) systems. Background Technology
[0002] Cellular-free massive MIMO is a novel network architecture proposed in recent years for sixth-generation (6G) mobile communication. In this architecture, a large number of distributed access points (APs) are connected to the central processing unit (CPU) via fronthaul links. All APs cooperate to serve all user terminals within the coverage area, eliminating traditional cellular boundaries. Compared to traditional centralized massive MIMO systems, cellular-free massive MIMO systems achieve more uniform coverage performance through spatial diversity and effectively eliminate cell edge effects.
[0003] In the uplink of a non-cellular massive MIMO system Each access point is equipped with Root antenna, serving together A single-antenna user terminal. The received signal of each access point can be represented as , ;in, This is the channel matrix from the access point to all users. Send symbol vectors for all users, This is the noise vector at that access point. The task of uplink signal detection is to recover the user's transmitted symbols based on the received signals from all access points and channel information. .
[0004] Due to the distributed deployment of access points and the limited bandwidth of the fronthaul link, it is necessary to rationally allocate computing tasks between the access points and the central processing unit to balance detection performance and fronthaul overhead. Several distributed detection algorithms have been proposed in the existing technology, but all have limitations to varying degrees.
[0005] Centralized Linear Minimum Mean Square Error (LMMSE) detection is a method that aggregates channel information and received signals from all access points to a central processing unit for unified processing. This method requires the central processing unit to construct a global channel matrix and perform large-scale matrix inversion, with a fronthaul overhead of [missing information]. However, this performance becomes difficult to maintain as the system size increases. Furthermore, as a linear algorithm, its bit error rate performance is limited.
[0006] The distributed detection method based on expectation propagation (EP) divides the antenna into... Each cluster operates as an independent unit, with element-wise variable-factor node message passing within each cluster. The outer loop fuses the results from each cluster in a central processing unit. However, this method employs antenna-wise scalar factor node decomposition, which can lead to problems when the number of antennas within a cluster increases. Less than the number of users It is difficult to converge, and the computational cost of element-by-element message passing is relatively large.
[0007] The Expectation Propagation-Based Distributed Approximate Message Passing (EP-DAMP) method operates on a fully decomposed factor graph, reducing computational complexity at the access point by using aggregation parameters. Access points compute scalar statistics such as residuals and variances, while the central processing unit fuses external information. A low-complexity variant of this method (LC-dAMP) further simplifies message passing by approximating the large system, resulting in access point complexity of only [value missing]. The pre-pass cost is Scalar detection is one of the distributed detection schemes with the lowest fronthaul overhead currently available. This represents the number of EP iterations.
[0008] However, the aforementioned existing technologies all assume that the noise at each access point is spatial white Gaussian noise, i.e. The noise covariance matrix is a scalar Multiply by the identity matrix This assumption has shortcomings in practical systems, specifically in the following aspects:
[0009] (1) Hardware non-ideal: Hardware defects such as phase noise and I / Q imbalance at the access point can introduce structured residual interference. When the same oscillator drives multiple antennas, the phase noise exhibits spatial correlation among these antennas, resulting in the noise covariance matrix having off-diagonal elements.
[0010] (2) Quantization noise of low precision analog-to-digital converter (ADC): In deployment scenarios where low precision ADCs are used to reduce power consumption and cost, quantization noise has a signal-dependent spatial structure and does not satisfy the spatial white noise assumption.
[0011] (3) Uncoordinated interference: Co-channel interference from adjacent systems or uncoordinated users has a definite spatial direction of arrival and exhibits spatial correlation among multiple antennas at the access point, constituting spatial colored noise.
[0012] (4) Channel estimation error: The residual interference introduced by imperfect channel estimation has a structured covariance related to the channel space covariance matrix.
[0013] When the covariance matrix of the actual noise In situations where detection algorithms designed under the white noise assumption cannot utilize the spatial structure information of the noise to perform spatial whitening or interference suppression, this leads to a severe degradation in detection performance. In particular, the low-complexity distributed approximate message passing (LC-dAMP) algorithm exhibits an error floor phenomenon in strong interference environments, where the bit error rate cannot continue to decrease with the improvement of the signal-to-noise ratio.
[0014] Furthermore, existing distributed detection algorithms lack the ability to estimate noise parameters. In practical deployments, the noise covariance matrix is often unknown or changes over time, making algorithms lacking online noise parameter estimation mechanisms ill-suited for real-world environments.
[0015] In summary, the existing distributed detection technology for non-cellular large-scale multiple-input multiple-output systems has the following shortcomings: (1) It only supports white noise models and cannot handle spatial colored noise; (2) Its performance degrades severely under strong interference environments, resulting in a bit error rate floor; (3) It lacks the ability to estimate the noise covariance matrix online. Summary of the Invention
[0016] Purpose of the invention: The purpose of this invention is to provide a distributed joint signal detection and noise parameter estimation method and apparatus for non-cellular massive MIMO systems. Under a distributed architecture, it can realize signal detection that can handle spatial colored noise and simultaneously estimate the noise covariance matrix of each access point online, thereby improving the detection performance under strong interference environment and eliminating the bit error rate floor phenomenon.
[0017] Technical Solution: To achieve the above-mentioned objectives, in a first aspect, the present invention provides a distributed joint signal detection and noise parameter estimation method for non-cellular massive MIMO systems, comprising the following steps:
[0018] S1. The multi-antenna reception likelihood function of each AP is modeled as a vectorized factor node. The vectorized factor node uses the noise covariance matrix of the AP as the complete matrix to participate in message calculation. The noise covariance matrix is used to characterize the spatial correlation characteristics of noise at the AP.
[0019] S2. Each AP performs local computation in parallel, including: constructing a full parameter matrix based on the cavity message parameters sent by each user variable node, the AP's channel matrix, and the current noise covariance matrix; performing a matrix inversion operation on the full parameter matrix to obtain the inverse matrix; and using the inverse matrix to calculate external information parameters for all users respectively.
[0020] S3. Each AP uploads the calculated external information parameters to the CPU via the fronthaul link;
[0021] S4. The CPU collects all external information parameters uploaded by all APs and calculates the global posterior estimate of each user according to the Gaussian product fusion rule.
[0022] S5. The CPU calculates new cavity message parameters based on the global posterior estimate and sends them to each AP via the forward link.
[0023] S6. Repeat S2 to S5 to perform inner layer iterations of expectation propagation until the preset expectation propagation convergence condition is met.
[0024] S7. After the expected propagation converges, each AP independently updates its own noise covariance matrix locally using the current global posterior estimate.
[0025] S8. Replace the current noise covariance matrix with the updated noise covariance matrix, and repeat S2 to S7 to perform the expectation maximization outer iteration until the preset outer iteration termination condition is met, and obtain the detection results of each user and the noise covariance matrix estimate of AP.
[0026] Preferably, in step S2, the first The full parameter matrix of each AP equal to the The noise covariance matrix of each AP The sum of a cumulative sum matrix over all users; the cumulative sum matrix over all users is the sum of the first... The user sent to the first The cavity message variance parameter of the AP, the first AP to the first The matrix is obtained by summing the products of the channel vector and its conjugate transpose for each user.
[0027] Preferably, in step S2, the extrinsic information parameters include the extrinsic information mean and the extrinsic information variance. The AP uses the inverse matrix to... External information parameters are calculated for each user, specifically including:
[0028] Calculate the intermediate scalar, which is equal to the first... AP to the first The conjugate transpose of the channel vector of the i-th user, the inverse matrix, and the i-th user AP to the first The product of the channel vectors of each user;
[0029] Calculate the extrinsic information variance, the reciprocal of which is equal to the intermediate scalar divided by one minus the first scalar. The user sent to the first The difference between the cavity message variance parameter of each AP and the product of the intermediate scalar;
[0030] Calculate the residual vector, the residual vector being equal to the first... Subtract a summation vector over all users from the received signal vector of the first AP, where the summation vector over all users is the sum of the received signal vector of the first AP. AP to the first The channel vector of the i-th user and the i-th The user sent to the first The vector is obtained by summing the products of the mean parameters of the cavity messages of each AP;
[0031] Calculate the extrinsic mean, which is equal to the first... The user sent to the first The sum of the mean cavity message parameter of each AP and an intermediate term, wherein the intermediate term is the... AP to the first The product of the conjugate transpose of the channel vector of each user, the inverse matrix, and the residual vector, divided by the intermediate scalar.
[0032] Preferably, in step S7, the first The noise covariance matrix after the AP update is equal to the sum of the first matrix and the second matrix; the first matrix is the product of the residual vector calculated based on the global posterior estimate and its conjugate transpose, wherein the residual vector calculated based on the global posterior estimate is the... The received signal vector of the AP minus the first AP The product of the channel matrix of the first AP and the posterior mean estimate vector of all users; the second matrix is the product of the channel matrix of the first AP and the posterior mean estimate vector of all users. The channel matrix of the first AP, the diagonal matrix composed of the posterior variances of each user, and the first... The product of the conjugate transpose of the channel matrix of each AP.
[0033] Furthermore, step S7 also includes performing regularization processing on the updated noise covariance matrix. The regularized noise covariance matrix is equal to the sum of the first term and the second term. The first term is the product of the difference between the regularization coefficient and the updated noise covariance matrix. The second term is the product of the regularization coefficient, the initial noise power estimate, and the identity matrix.
[0034] Preferably, the outer iteration termination condition is one or more of the following combinations: the number of outer iterations reaches a preset maximum value; the noise covariance matrix update amount is less than a preset first threshold between two adjacent outer iterations; the change amount of the user detection result is less than a preset second threshold between two adjacent outer iterations.
[0035] Further, in step S1, given that the structure of the interference covariance matrix is known, the noise covariance matrix is parameterized as a combination of scalar power parameters and the known structured interference covariance matrix; in step S7, only the scalar power parameters are updated, including: each access point first calculates the noise sufficient statistics matrix in the same way as the full matrix estimation; then, by taking the least squares projection of the difference between the statistics matrix and the structured interference covariance matrix in the direction of the unit matrix, the updated value of the scalar power parameters is extracted; or the updated value is further regularized.
[0036] In a second aspect, the present invention provides a distributed joint signal detection and noise parameter estimation apparatus for non-cellular massive MIMO systems, used to implement the method described in the first aspect, comprising:
[0037] The access point processing module, deployed on each AP, is used to model the multi-antenna reception likelihood function of the AP as a vectorized factor node. This vectorized factor node uses the AP's noise covariance matrix as the complete matrix in message calculation. The noise covariance matrix characterizes the spatial correlation of noise at the AP. Local calculations include: constructing a full parameter matrix based on the cavity message parameters sent by each user variable node, the AP's channel matrix, and the current noise covariance matrix; performing a matrix inversion operation on the full parameter matrix to obtain the inverse matrix; calculating extrinsic information parameters for all users using the inverse matrix; uploading the calculated extrinsic information parameters to the CPU via the fronthaul link; and, after expected propagation convergence, independently updating each user's noise covariance matrix locally using the current global posterior estimate.
[0038] The central fusion module, deployed on the CPU, is used to collect external information parameters uploaded by all APs, calculate the global posterior estimate of each user according to the Gaussian product fusion rule, and calculate new cavity message parameters based on the global posterior estimate, and send them to each AP through the fronthaul link.
[0039] The iterative control module is used to control the inner iterative process of the desired propagation, and terminate the inner iterative process when the preset convergence condition is met; and to control the outer iterative process of the noise covariance matrix update, and output the detection results of each user and the noise covariance matrix estimate of AP when the preset termination condition is met.
[0040] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the distributed joint signal detection and noise parameter estimation method for non-cellular massive MIMO systems described in the first aspect.
[0041] Fourthly, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the distributed joint signal detection and noise parameter estimation method for non-cellular massive MIMO systems described in the first aspect.
[0042] Beneficial effects: Compared with the prior art, the present invention has the following beneficial effects:
[0043] (1) Support for spatial colored noise processing: This invention uses vectorized factor node modeling to embed the noise covariance matrix into the construction process of the full parameter matrix in the form of a complete matrix, so that message calculation naturally contains spatial information related to noise, realizing implicit spatial whitening, and solving the problem that the scalar factor node structure decomposed by antenna in the prior art cannot introduce the off-diagonal noise covariance matrix.
[0044] (2) Possesses online noise covariance matrix estimation capability: This invention uses expectation maximization outer iteration, and each access point updates the noise covariance matrix locally using the posterior statistics after expectation propagation convergence, without needing to know the noise statistical characteristics in advance. Furthermore, the noise covariance update is performed locally at each access point, without generating additional forward propagation overhead.
[0045] (3) Elimination of the bit error rate floor phenomenon: Addressing the issue that existing distributed detection algorithms based on the white noise assumption suffer from a bit error rate floor in spatially colored noise environments, meaning the bit error rate cannot continue to decrease with increasing signal-to-noise ratio, this invention effectively eliminates the bit error rate floor phenomenon by jointly performing signal detection and noise parameter estimation. Under colored noise conditions, it achieves approximately [missing information - likely a missing word or phrase]. The signal-to-noise ratio gain.
[0046] (4) Maintaining fronthaul overhead comparable to existing technologies: In each inner layer iteration of this invention, the uplink overhead of each access point is... Each scalar (external information mean and variance) is sent to the central processing unit, which then issues the following: Each scalar (cavity message parameter) is sent to each access point, and the total forward overhead for each iteration is... The scalar overhead is on the same order of magnitude as the fronthaul overhead of existing low-complexity distributed detection schemes.
[0047] (5) Theoretical Guarantee: Analysis based on the hybrid Fisher information matrix shows that, under the Gaussian assumption, the cross-information between signal and noise parameters is strictly zero, and the theoretical limit of signal detection performance is not directly affected by noise parameter estimation errors. This theoretical result supports the effectiveness of the detection-estimation alternating iterative architecture, enabling a small number of outer iterations ( The detection performance can be approximated by the known true noise covariance matrix in one pass. Attached Figure Description
[0048] Figure 1 The flowchart illustrates the distributed joint signal detection and noise parameter estimation method provided in this embodiment of the invention.
[0049] Figure 2 The diagram shows the pseudocode of the algorithm provided in the embodiment of the present invention.
[0050] Figure 3 This is a block diagram of a distributed joint signal detection and noise parameter estimation system provided in an embodiment of the present invention.
[0051] Figure 4 The graph shows the change in bit error rate with signal-to-noise ratio in the simulation comparison experiment provided for the embodiments of the present invention.
[0052] Figure 5 The graph shows the change in bit error rate with interference-to-noise ratio in the simulation comparison experiment provided for the embodiments of the present invention. Detailed Implementation
[0053] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0054] The following is a further explanation of the distributed joint signal detection and noise parameter estimation method for non-cellular massive MIMO systems involved in the embodiments of the present invention.
[0055] This embodiment discloses a distributed joint signal detection and noise parameter estimation method for a non-cellular massive MIMO system. The non-cellular massive MIMO system includes multiple distributed access points (APs) and a central processing unit (CPU). Each AP is connected to the CPU via a fronthaul link to jointly serve multiple user terminals.
[0056] Specifically, let the cellular-free massive MIMO system in this embodiment include Distributed access points (denoted as) A central processing unit (CPU) and A single-antenna user terminal (denoted as) Each access point is connected to the central processing unit via a fronthaul link. Each access point is equipped with... One antenna, all access points cooperate to serve all user terminals within the coverage area.
[0057] The user terminal sends an uplink signal to the access point. As described in the background section, the first... The received signal of each access point is represented as In real-world deployment environments, noise levels are high due to factors such as hardware impairment, low-precision ADC quantization noise, uncoordinated interference, and channel estimation errors. covariance matrix It is usually a non-diagonal positive definite matrix, that is This characterizes the spatial correlation characteristics of noise between antennas.
[0058] like Figure 1 As shown, the distributed joint signal detection and noise parameter estimation method for non-cellular massive MIMO systems specifically includes the following steps:
[0059] Step S1, Vectorized Factor Graph Modeling: The multi-antenna reception likelihood function of each AP is modeled as a vectorized factor node. The vectorized factor node uses the noise covariance matrix of the AP as the complete matrix to participate in message calculation. The noise covariance matrix is used to characterize the spatial correlation characteristics of noise at the AP.
[0060] In this embodiment, the multi-antenna reception likelihood function of each AP is modeled as a vectorized factor node. Vectorized factor nodes with the noise covariance matrix of AP It participates in message computation as a complete matrix, in which Characterizing the first Spatial correlation characteristics of noise at each AP.
[0061] It should be noted that one of the core aspects of this embodiment lies in the change in the factor graph modeling method. In the prior art, the received signal of each access point is decomposed antenna by antenna. scalar observation Establish accordingly scalar factor nodes Each scalar factor node contains only the scalar noise variance. It is impossible to introduce spatial information related to noise between antennas. Scalar factor nodes and Generate between user variable nodes A message on the side.
[0062] This embodiment uses a vectorized factor graph to represent each access point. The likelihood function of the antenna received The overall model is a vectorized factor node. This factor node is observed as a vector. As input, the noise covariance matrix Participate in message computation as a complete matrix. Vectorized factor node. Connect all User variable nodes Each user variable node is connected to a prior factor node. The total number of message edges is only The number of bars is far less than that of element-wise methods. strip.
[0063] The corresponding joint distribution decomposition is:
[0064]
[0065] in, For all The joint vector of signals received by each access point. For the first Prior distribution of symbols sent by each user For the first The receive likelihood function of each access point.
[0066] In this embodiment, the following message is defined on the vectorized factor graph:
[0067] No. User variable nodes To the Access point factor nodes Message: , by parameter pair The descriptions, and , represent the mean and variance of the cavity message, respectively; where, Indicates the first User variable nodes Send to the Access point factor nodes The cavity message function reflects, except for the first Apart from the likelihood of the access point, all other factors are... The overall confidence level.
[0068] No. Access point factor nodes To the User variable nodes Message: , by parameter pair The descriptions, represent the mean and variance of the external information, respectively; where, Indicates the first Access point factor nodes Send to the User variable nodes The external information function reflects the first Each access point, based on its received signals and channel information, The estimate.
[0069] Step S2, AP-side vectorized message calculation: Each AP performs local calculations in parallel, including: constructing a full parameter matrix based on the cavity message parameters sent by each user variable node, the AP's channel matrix, and the current noise covariance matrix; performing a matrix inversion operation on the full parameter matrix to obtain the inverse matrix; and using the inverse matrix to calculate extrinsic information parameters for all users, wherein the extrinsic information parameters include the extrinsic information mean and extrinsic information variance.
[0070] In this embodiment, when each AP performs local calculations, it first calculates based on the cavity message parameters sent to the AP by each user variable node. The channel matrix of the AP and the current noise covariance matrix Construct the full parameter matrix Then, perform a matrix inversion operation on the full parameter matrix to obtain... Finally utilize For all Calculate the extrinsic parameters for each user, including the extrinsic mean. External information variance .
[0071] Preferably, the first The full parameter matrix of each AP equal to the The noise covariance matrix of each AP The sum of a cumulative sum matrix over all users; the cumulative sum matrix over all users is the sum of the first... The user sent to the first The cavity message variance parameter of the AP, the first AP to the first The matrix is obtained by summing the products of the channel vectors and their conjugate transposes of each user. The AP uses the inverse matrix to... External information parameters are calculated for each user, specifically including:
[0072] Calculate the intermediate scalar, which is equal to the first... AP to the first The conjugate transpose of the channel vector of the i-th user, the inverse matrix, and the i-th user AP to the first The product of the channel vectors of each user;
[0073] Calculate the extrinsic information variance, the reciprocal of which is equal to the intermediate scalar divided by one minus the first scalar. The user sent to the first The difference between the cavity message variance parameter of each AP and the product of the intermediate scalar;
[0074] Calculate the residual vector, the residual vector being equal to the first... Subtract a summation vector over all users from the received signal vector of the first AP, where the summation vector over all users is the sum of the received signal vector of the first AP. AP to the first The channel vector of the i-th user and the i-th The user sent to the first The vector is obtained by summing the products of the mean parameters of the cavity messages of each AP;
[0075] Calculate the extrinsic mean, which is equal to the first... The user sent to the first The sum of the mean cavity message parameter of each AP and an intermediate term, wherein the intermediate term is the... AP to the first The product of the conjugate transpose of the channel vector of each user, the inverse matrix, and the residual vector, divided by the intermediate scalar.
[0076] It should be noted that vectorized message computation at the AP end is the core of the E-Step (steps S2 to S6, i.e., the inner iteration of EP) in this embodiment. Taking the first... Taking an AP as an example, it receives three sets of inputs: (1) local channel matrix and received signals (2) Cavity message parameters issued by the central processing unit (3) Current noise covariance matrix The specific calculation may include the following steps:
[0077] Step S21, Construction of the full parameter matrix: Construct the full parameter matrix according to the following formula:
[0078]
[0079] The dimension of this matrix is Noise covariance matrix Directly embedded in the form of a complete matrix This is key to supporting spatial colored noise processing.
[0080] Step S22, Matrix Inversion: Perform a matrix inversion on the full parameter matrix:
[0081]
[0082] The complexity of this step is... It only needs to be executed once to serve all One user.
[0083] Step S23, Residual Vector Calculation: Calculate the residual vector:
[0084]
[0085] Step S24, Calculation of external information parameters: using And the Sherman-Morrison lemma, for each user Calculate external information parameters.
[0086] First, calculate the intermediate scalar:
[0087]
[0088] Then, the inverse of the external information variance is derived using the Sherman-Morrison lemma:
[0089]
[0090] The mean of external information is:
[0091]
[0092] Each user The computational complexity is , Shared by individual users The total complexity is .
[0093] Step S3, AP to CPU upload: Each AP uploads the calculated external information parameters to the CPU via the fronthaul link.
[0094] Specifically, each access point will calculate the external information parameters. Uploaded to the central processing unit via the fronthaul link. Each access point uploads per iteration. A scalar.
[0095] Step S4, CPU Global Fusion: The CPU collects the external information parameters uploaded by all APs and calculates the global posterior estimate of each user according to the Gaussian product fusion rule. The global posterior estimate includes the global posterior mean and the global posterior variance.
[0096] Specifically, the CPU global fusion processing flow may include the following steps:
[0097] Step S41, External Information Collection: Collect all External information parameters uploaded by each access point.
[0098] Step S42, Gaussian product fusion: For each user The global posterior variance and global posterior mean are calculated according to the Gaussian product fusion rule:
[0099]
[0100]
[0101] in Let be the prior power of the transmitted symbol. The fusion complexity is O(n). .
[0102] In an alternative implementation, a nonlinear moment matching step is also included: utilizing the discrete constellation prior distribution of the user-transmitted symbols. The global posterior estimate is nonlinearly corrected, and the posterior mean under the discrete prior is calculated. and posterior variance To replace the linear fusion results under the Gaussian assumption.
[0103] Step S5, CPU to AP Feedback: The CPU calculates new cavity message parameters based on the global posterior estimate and sends them to each AP via the forward link. Specifically, this may include:
[0104] Step S51, Cavity Message Calculation: For each user and each access point Calculate the new cavity message parameters:
[0105] The variance of cavity messages is approximated: ;
[0106] The mean value of the cavity message is:
[0107]
[0108] Step S52 (optional), Damping treatment: To improve the numerical stability of the desired propagation iteration, when updating the cavity message parameters in each iteration, the new parameters are weighted and averaged with the parameters from the previous iteration.
[0109]
[0110]
[0111] in The damping coefficient is... This is the index for the current iteration.
[0112] Step S6, Expectation Propagation Inner Layer Iteration: Repeat steps S2 to S5 to perform expectation propagation inner layer iteration until the preset expectation propagation convergence condition is met.
[0113] Specifically, after obtaining the cavity message parameters in step S5, it can be determined whether the expected propagation inner layer iteration has converged. If it has not converged, the new cavity message parameters are transmitted through the forward link. Distribute the data to each access point and return to step S2 to continue iteration. If convergence has been achieved, output the posterior statistic. This data is then fed back to each access point for noise covariance updates.
[0114] Step S7, Noise Covariance Update: After the expected propagation converges, each AP independently updates its own noise covariance matrix locally using the current global posterior estimate.
[0115] In this embodiment, the first Taking the first AP as an example, the first The noise covariance matrix after the AP update is equal to the sum of the first matrix and the second matrix; the first matrix is the product of the residual vector calculated based on the global posterior estimate and its conjugate transpose, wherein the residual vector calculated based on the global posterior estimate is the... The received signal vector of the AP minus the first AP The product of the channel matrix of the first AP and the posterior mean estimate vector of all users; the second matrix is the product of the channel matrix of the first AP and the posterior mean estimate vector of all users. The channel matrix of the first AP, the diagonal matrix composed of the posterior variances of each user, and the first... The product of the conjugate transpose of the channel matrix of each AP.
[0116] Preferably, after updating the noise covariance matrix, the process further includes performing regularization on the updated noise covariance matrix. The regularized noise covariance matrix is equal to the sum of the first term and the second term. The first term is the product of the difference between the regularization coefficient and the updated noise covariance matrix. The second term is the product of the regularization coefficient, the initial noise power estimate, and the identity matrix.
[0117] It should be noted that the noise covariance update is the core of the M-Step in this embodiment. (The rest of the text appears to be a fragment and doesn't translate directly.) Taking one access point as an example, the specific calculation may include the following steps:
[0118] Step S71, Residual Estimation: Calculate the residual vector:
[0119]
[0120] in This is the posterior mean estimation vector for all users.
[0121] Step S72, Initial Update of Noise Covariance: Update the noise covariance matrix according to the M-Step formula of the expectation-maximization algorithm:
[0122]
[0123] The first matrix term The first term is the outer product of the residuals, reflecting the covariance of the noisy samples under the current posterior mean estimate; the second matrix term... This is a posterior uncertainty compensation term, used to correct the underestimation of noise covariance caused by signal estimation uncertainty. This is the diagonal matrix of the posterior variance. The complexity of this step is O(log n). It is executed locally at the access point and does not incur forwarding overhead.
[0124] Step S73, Regularization: Perform regularization on the updated noise covariance matrix:
[0125]
[0126] in The regularization coefficient is . This represents the initial noise power estimate. Regularization prevents overfitting of the noise covariance estimate under finite sample conditions and ensures... The positive definiteness of .
[0127] After regularization As a new Substitute this into the expected propagation calculation for the next round of EM outer layer iteration.
[0128] Step S8, Outer Iteration: Replace the current noise covariance matrix with the updated noise covariance matrix, and repeat steps S2 to S7 to perform expectation-maximizing outer iteration until the preset outer iteration termination condition is met, thus obtaining the detection results for each user. Noise covariance matrix estimation with AP .
[0129] Based on one or more of the above embodiments, the distributed joint signal detection and noise parameter estimation method for non-cellular massive MIMO systems described in this invention, based on the key innovation of a two-layer nested iterative architecture of vectorized expectation propagation and expectation maximization, is denoted as Vec-EP-EM. During a complete execution of the Vec-EP-EM algorithm, the message interaction between the access point and the central processing unit follows the following timing sequence:
[0130] In the outer EM iteration, each round of the inner EP iteration includes: (1) Parallel construction of each access point. ,calculate (2) Uploaded by each access point and external information parameters; Uploaded to the central processing unit from each access point (3) The central processing unit performs global fusion and calculates cavity messages; (4) The central processing unit issues... To each access point, each access point receives A scalar.
[0131] After the expected propagation converges, the central processing unit will use the posterior statistic. The broadcast is sent to each access point. Each access point performs a noise covariance update (M-Step) locally, and the updated... M-Step is used only locally and does not require transmission over a fronthaul link, so it does not incur additional fronthaul overhead.
[0132] The forward overhead for each EP iteration is the uplink. Individual scalar plus downlink scalar, total A scalar.
[0133] In one variant implementation, given the known structure of the interference covariance matrix, the noise covariance matrix is parameterized as a combination of scalar power parameters and a known structured interference covariance matrix. In step S7, only the scalar power parameters are updated, including: each access point first calculates the noise sufficient statistics matrix in the same manner as the full matrix estimation; then, the updated value of the scalar power parameters is extracted by taking the least squares projection of the difference between the statistics matrix and the structured interference covariance matrix in the direction of the unit matrix; or the updated value is further regularized.
[0134] For example, the noise covariance matrix can be parameterized as a combination of scalar power and a known structure matrix:
[0135]
[0136] in For the estimation of the first Scalar noise power parameters of each AP Given a known structured disturbance covariance matrix, in practical applications, it can be continuously observed to determine whether a fixed covariance exists. Under this parameterization, only the scalar parameter needs to be updated in step S7. This further reduces computational complexity.
[0137] Specifically, in the parameterized case Next, in step S7 The update method is as follows:
[0138] First, the noise sufficient statistics matrix is calculated in the same manner as the full matrix estimation:
[0139]
[0140] Then, Projection to the family of parameterized models Above, through Extracting scalar components from the matrix inner product of directions:
[0141]
[0142] in A small positive number (e.g.) ), used to guarantee Thus ensure The positive definiteness of . The trace averaging operation is equivalent to... exist Perform least-squares projection in the direction.
[0143] Similarly, it is possible to Apply regularization:
[0144]
[0145] in Here are the regularization coefficients. The updated noise covariance matrix is: .
[0146] This parameter update will be in step S7 Matrix updates are simplified to single scalar updates, reducing complexity from Reduce to .
[0147] In some optional implementations, the outer iteration termination condition is one or a combination of the following: (a) the number of outer iterations reaches a preset maximum value. (b) The update amount of the noise covariance matrix between two adjacent outer iterations (c) The change in the user detection result between two adjacent outer layer iterations is less than a preset first threshold. In practical applications, the above thresholds can be set according to the system's trade-off requirements for convergence accuracy and computational complexity. As a typical engineering reference, the order of magnitude of the preset first threshold can be set to 10. -4 The order of magnitude of the preset second threshold can be set to 10. -3 .
[0148] The detection-estimation alternating iterative architecture of this invention is supported by the following theoretical basis: Under the Gaussian assumption, the Hybrid Fisher Information Matrix (HFIM) of the combined system with respect to the signal parameters... and noise parameters The cross term is strictly zero:
[0149]
[0150] in Represents the mixed Fisher information matrix of the combined system with respect to the signal parameters. With noise parameters The cross-information sub-block matrix is equal to This indicates that, under the Gaussian assumption, signal parameters and noise parameters are orthogonal or decoupled in the first-order information sense. This theoretically guarantees that alternating signal detection and noise parameter estimation will not directly violate the theoretical lower bound of signal detection performance due to cross-information coupling.
[0151] The physical meaning of this theorem is: (1) the Cramer-Rao lower bound of signal detection performance is not directly affected by the noise parameter estimation error (in an asymptotic sense); (2) the Cramer-Rao lower bound of the signal mixture parameter (H-PCRB) is equivalent to the MMSE lower bound when the true noise parameter is known. The key to the proof lies in the second-order mixture partial derivative of the log-likelihood function. For noise A linear function, whose expectation is obtained by... The intersection term is zero, where the superscript is zero. Indicates conjugate.
[0152] in Let be the parameter vector of the noise covariance matrix for each AP. When the noise covariance matrix is parameterized as... In the case of general full matrix estimation, It can be extended to include all For vectors with independent parameters, the decoupling conclusion still holds.
[0153] This theorem guarantees a small number of EM outer layer iterations ( The detection performance can be approximated by the known true noise covariance matrix in one pass.
[0154] The pseudocode for the Vec-EP-EM algorithm is as follows: Figure 2 As shown.
[0155] The distributed joint signal detection and noise parameter estimation apparatus for non-cellular massive MIMO systems according to embodiments of the present invention will be further described below. The apparatus described below and the method described above can be referred to in correspondence.
[0156] like Figure 3 As shown in the figure, this embodiment discloses a distributed joint signal detection and noise parameter estimation device for non-cellular massive MIMO systems, comprising:
[0157] The access point processing module, deployed on each AP, is used to model the multi-antenna reception likelihood function of the AP as a vectorized factor node. This vectorized factor node uses the AP's noise covariance matrix as the complete matrix in message calculation. The noise covariance matrix characterizes the spatial correlation of noise at the AP. Local calculations include: constructing a full parameter matrix based on the cavity message parameters sent by each user variable node, the AP's channel matrix, and the current noise covariance matrix; performing a matrix inversion operation on the full parameter matrix to obtain the inverse matrix; calculating extrinsic information parameters for all users using the inverse matrix; uploading the calculated extrinsic information parameters to the CPU via the fronthaul link; and, after expected propagation convergence, independently updating each user's noise covariance matrix locally using the current global posterior estimate.
[0158] The central fusion module, deployed on the CPU, is used to collect external information parameters uploaded by all APs, calculate the global posterior estimate of each user according to the Gaussian product fusion rule, and calculate new cavity message parameters based on the global posterior estimate, and send them to each AP through the fronthaul link.
[0159] The iterative control module is used to control the inner iterative process of the desired propagation, and terminate the inner iterative process when the preset convergence condition is met; and to control the outer iterative process of the noise covariance matrix update, and output the detection results of each user and the noise covariance matrix of AP when the preset termination condition is met.
[0160] In a specific implementation, the access point processing module may include the following units:
[0161] Received signal buffer unit, used to buffer the received signal ;
[0162] Channel matrix storage unit, used to store local channel matrix ;
[0163] Full parameter matrix construction unit, used to construct based on Channel vector and cavity message parameter construction ;
[0164] The matrix inversion unit is used to perform... Operations;
[0165] The residual calculation unit is used to calculate... ;
[0166] External information computing unit, containing Sherman-Morrison acceleration module, utilizes calculate ;
[0167] The noise covariance update unit is used to perform M-Step updates. ;
[0168] The regularization processing unit is used to perform... ;
[0169] The noise covariance matrix storage unit is used to store the current noise covariance matrix. It is interconnected with the full parameter matrix construction unit and the noise covariance update unit to form a feedback loop.
[0170] The data flow direction between each unit is: received signal buffer Residual calculation, channel matrix storage Full parameter matrix construction / residual calculation / noise covariance update, full parameter matrix construction Matrix inversion External information calculation, residual calculation External information calculation, posterior statistic Noise covariance update Regularization Noise covariance matrix storage Constructing the full parameter matrix.
[0171] The central fusion module may include the following units:
[0172] External information collection unit, used to collect external information parameters uploaded by all access points;
[0173] Gaussian product fusion unit, used to compute global posterior according to fusion rules. ;
[0174] The cavity message calculation unit is used to calculate new cavity messages. ;
[0175] The posterior statistic broadcasting unit is used to broadcast the global posterior estimate to each access point.
[0176] Data is transmitted from the access point to the central processing unit via the uplink fronthaul link. The central processing unit transmits data to the access point via a downlink fronthaul link. After the expected propagation converges, the posterior statistic is transmitted through the forward link. .
[0177] To verify the effectiveness of the method of the present invention, a specific simulation embodiment is given below.
[0178] Simulation parameter settings: The simulation parameter settings for the non-cellular massive MIMO system are shown in the table below:
[0179] Table 1 Simulation Parameters
[0180]
[0181] The channel model employs a Rayleigh fading model based on the spatial correlation matrix. The locations of each access point are... Within a square area, user terminals are randomly and uniformly distributed, and these terminals are also randomly and uniformly distributed within the same area. The path loss model uses... (Unit: dB), where The distance is three-dimensional (access point is 10 meters above user terminal). Channel estimation uses a minimum mean square error (MMSE) estimator based on orthogonal pilots.
[0182] Colored noise model: To simulate a real-world spatial colored noise environment, the noise covariance matrix is set at each access point as follows:
[0183]
[0184] in INR is the noise floor power, and INR is the interference-to-noise ratio. This is the array steering vector corresponding to the direction of interference. For the first Each access point is located at the angle of arrival of the interfering signal. This model indicates that each access point, in addition to background white noise, is also subject to a spatially structured interference from a specific direction.
[0185] Algorithm Comparison: The detection performance of the following algorithms is compared in simulation: 1. LC-dAMP (Low Complexity Distributed Approximate Message Passing): A distributed detection algorithm with low forward overhead in the current technology, assuming white noise. 2. EP-dAMP (EP-based Distributed Approximate Message Passing): A high-performance distributed detection algorithm in the current technology, also assuming white noise. 3. Vec-EP (Genie-Aided): Uses the real noise covariance matrix. 4. Vectorized EP detector, without performing EM updates, serves as a reference curve under known noise statistics. 5. Vec-EP-EM (this invention, EM iterations = 3): A complete algorithm performing 3 outer EM iterations. 6. Vec-EP-EM (this invention, EM iterations = 5): A complete algorithm performing 5 outer EM iterations. 7. Centralized LMMSE: A linear detector that aggregates all access point information, used as a baseline reference.
[0186] Simulation results: Simulation results show that, under a fixed... conditions, Figure 4 The bit error rate versus signal-to-noise ratio curve shown indicates that:
[0187] (1) Although LC-dAMP, EP-dAMP and centralized LMMSE continuously improved with the increase of signal-to-noise ratio throughout the entire test range, their performance was significantly inferior to the Vec-EP series; within the current test range, none of the above white noise assumption baseline algorithms were reduced to the following.
[0188] (2) Vec-EP-EM (EM iterations = 3) is significantly better than the baseline algorithm under the white noise assumption; Vec-EP-EM (EM iterations = 5) is close to Vec-EP (Genie-Aided) in general, with slight overlap in some sampling points, but both are significantly better than LC-dAMP, EP-dAMP and centralized LMMSE.
[0189] (3) Within the current testing scope, Vec-EP (Genie-Aided), Vec-EP-EM (EM iterations = 3), and Vec-EP-EM (EM iterations = 5) have all been tested in approximately [missing information]. The place dropped to Below, LC-dAMP, EP-dAMP, and centralized LMMSE are... It has not yet been achieved within the specified time. This indicates that the method of the present invention has at least approximately [a certain advantage] over the aforementioned baseline algorithm. Its signal-to-noise ratio advantage.
[0190] fixed conditions, Figure 5 The figure shows the change in the interference noise ratio INR from Increase to The changes in bit error rate for each algorithm indicate that:
[0191] (1) In areas with weak interference ( Within the range, all algorithms can maintain a low bit error rate, and the white noise hypothesis algorithm and the centralized LMMSE have not yet shown a significant disadvantage.
[0192] (2) As the INR continues to increase and enters the region of strong colored noise, the BER of LC-dAMP, EP-dAMP, and centralized LMMSE increases significantly; in contrast, Vec-EP-EM, especially in the case of EM iteration number = 5, remains close to Vec-EP (Genie-Aided) and basically maintains its position at... The magnitude of the noise level indicates stronger robustness to spatial correlations.
[0193] Complexity and Forward Overhead Analysis: The computational complexity and forward overhead of the method of this invention are compared with those of existing technologies, as shown in the table below:
[0194] Table 2 Algorithm Comparison
[0195]
[0196] The computational complexity at the access point of the method of this invention is: ,in From finding the inversion of a matrix in one step. From Calculation of external information for each user. (When the number of access point antennas...) Moderate (e.g.) When the complexity is such that the forepass overhead is on the same order of magnitude as existing technologies, it is acceptable.
[0197] The method of this invention is particularly suitable for the following scenarios: (1) Strong interference environment: scenarios with spatial colored noise caused by dense access point deployment, cell edge users, and uncoordinated co-channel interference. (2) High system load: number of users With the number of effective antennas at the access point The load conditions are relatively large. (3) Block fading channel: channel coherence time Longer (4) Appropriate access point antenna size: .
[0198] This invention also discloses a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the distributed joint signal detection and noise parameter estimation method for non-cellular massive MIMO systems described in any of the above embodiments.
[0199] This invention also discloses a computer program product, including a computer program that, when executed by a processor, implements the steps of the distributed joint signal detection and noise parameter estimation method for non-cellular massive MIMO systems described in any of the above embodiments.
[0200] The program code used to implement the method of the present invention can be written in any combination of one or more programming languages. This program code can be provided to a processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the program code causes the steps of the method of the present invention to be performed.
[0201] It should be noted that the various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems or apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple, and relevant parts can be referred to the method section.
[0202] It should also be noted that relational terms such as "first" and "second" in this specification are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. The term "and / or" includes any and all combinations of one or more of the associated listed items. The terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.
[0203] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A distributed joint signal detection and noise parameter estimation method for non-cellular massive MIMO systems, characterized in that, Includes the following steps: S1. The multi-antenna reception likelihood function of each access point (AP) is modeled as a vectorized factor node. The vectorized factor node uses the noise covariance matrix of the AP as the complete matrix to participate in message calculation. The noise covariance matrix is used to characterize the spatial correlation characteristics of noise at the AP. S2. Each AP performs local computation in parallel, including: constructing a full parameter matrix based on the cavity message parameters sent by each user variable node, the AP's channel matrix, and the current noise covariance matrix; performing a matrix inversion operation on the full parameter matrix to obtain the inverse matrix; and using the inverse matrix to calculate external information parameters for all users respectively. S3. Each AP uploads the calculated external information parameters to the central processing unit (CPU) via the fronthaul link. S4. The CPU collects all external information parameters uploaded by all APs and calculates the global posterior estimate of each user according to the Gaussian product fusion rule. S5. The CPU calculates new cavity message parameters based on the global posterior estimate and sends them to each AP via the forward link. S6. Repeat S2 to S5 to perform inner layer iterations of expectation propagation until the preset expectation propagation convergence condition is met. S7. After the expected propagation converges, each AP independently updates its own noise covariance matrix locally using the current global posterior estimate. S8. Replace the current noise covariance matrix with the updated noise covariance matrix, and repeat S2 to S7 to perform the expectation maximization outer iteration until the preset outer iteration termination condition is met, and obtain the detection results of each user and the noise covariance matrix estimate of AP.
2. The distributed joint signal detection and noise parameter estimation method for non-cellular massive MIMO systems according to claim 1, characterized in that, In step S2, the first The full parameter matrix of each AP equal to the The noise covariance matrix of each AP The sum of a cumulative sum matrix over all users; the cumulative sum matrix over all users is the sum of the first... The user sent to the The cavity message variance parameter of the AP, the first AP to the first The matrix is obtained by summing the products of the channel vector and its conjugate transpose for each user.
3. The distributed joint signal detection and noise parameter estimation method for non-cellular massive MIMO systems according to claim 2, characterized in that, In step S2, the extrinsic information parameters include the extrinsic information mean and the extrinsic information variance. The AP uses the inverse matrix to... External information parameters are calculated for each user, specifically including: Calculate the intermediate scalar, which is equal to the first... AP to the first The conjugate transpose of the channel vector of the i-th user, the inverse matrix, and the i-th user AP to the first The product of the channel vectors of each user; Calculate the extrinsic information variance, the reciprocal of which is equal to the intermediate scalar divided by one minus the first scalar. The user sent to the The difference between the cavity message variance parameter of each AP and the product of the intermediate scalar; Calculate the residual vector, the residual vector being equal to the first... Subtract a summation vector over all users from the received signal vector of the first AP, where the summation vector over all users is the sum of the received signal vector of the first AP. AP to the first The channel vector of the i-th user and the i-th The user sent to the The vector is obtained by summing the products of the mean parameters of the cavity messages of each AP; Calculate the extrinsic mean, which is equal to the first... The user sent to the The sum of the mean cavity message parameter of each AP and an intermediate term, wherein the intermediate term is the... AP to the first The product of the conjugate transpose of the channel vector of each user, the inverse matrix, and the residual vector, divided by the intermediate scalar.
4. The distributed joint signal detection and noise parameter estimation method for non-cellular massive MIMO systems according to claim 1, characterized in that, In step S7, the first The noise covariance matrix after the AP update is equal to the sum of the first matrix and the second matrix; the first matrix is the product of the residual vector calculated based on the global posterior estimate and its conjugate transpose, wherein the residual vector calculated based on the global posterior estimate is the... The received signal vector of the AP minus the first The product of the channel matrix of the first AP and the posterior mean estimate vector of all users; the second matrix is the product of the channel matrix of the first AP and the posterior mean estimate vector of all users. The channel matrix of the first AP, the diagonal matrix composed of the posterior variances of each user, and the first... The product of the conjugate transpose of the channel matrix of each AP.
5. The distributed joint signal detection and noise parameter estimation method for non-cellular massive MIMO systems according to claim 4, characterized in that, Step S7 further includes performing regularization processing on the updated noise covariance matrix. The regularized noise covariance matrix is equal to the sum of the first term and the second term. The first term is the product of the difference between the regularization coefficient and the updated noise covariance matrix. The second term is the product of the regularization coefficient, the initial noise power estimate, and the identity matrix.
6. The distributed joint signal detection and noise parameter estimation method for non-cellular massive MIMO systems according to claim 1, characterized in that, The outer iteration termination condition is one or more of the following combinations: the number of outer iterations reaches a preset maximum value; the noise covariance matrix update amount is less than a preset first threshold between two adjacent outer iterations; the change amount of the user detection result is less than a preset second threshold between two adjacent outer iterations.
7. The distributed joint signal detection and noise parameter estimation method for non-cellular massive MIMO systems according to claim 1, characterized in that, In step S1, given that the structure of the interference covariance matrix is known, the noise covariance matrix is parameterized as a combination of scalar power parameters and the known structured interference covariance matrix. In step S7, only the scalar power parameters are updated, including: each access point first calculates the noise sufficient statistics matrix in the same way as the full matrix estimation; Then, the updated value of the scalar power parameter is extracted by taking the least squares projection of the difference between the statistical matrix and the structured interference covariance matrix in the direction of the unit matrix; or the updated value is further regularized.
8. A distributed joint signal detection and noise parameter estimation device for non-cellular massive MIMO systems, used to implement the method according to any one of claims 1 to 7, characterized in that, include: The access point processing module, deployed in each AP, is used to model the overall likelihood function of the AP's multi-antenna reception as a vectorized factor node. The vectorized factor node uses the AP's noise covariance matrix as the complete matrix to participate in message calculation. The noise covariance matrix is used to characterize the spatial correlation characteristics of noise at the AP. Performing local computation includes: constructing a full parameter matrix based on the cavity message parameters sent by each user variable node, the AP's channel matrix, and the current noise covariance matrix; performing a matrix inversion operation on the full parameter matrix to obtain the inverse matrix; calculating extrinsic information parameters for each user using the inverse matrix; uploading the calculated extrinsic information parameters to the CPU via the fronthaul link; and, after expected propagation convergence, independently updating each user's noise covariance matrix locally using the current global posterior estimate. The central fusion module, deployed on the CPU, is used to collect external information parameters uploaded by all APs, calculate the global posterior estimate of each user according to the Gaussian product fusion rule, and calculate new cavity message parameters based on the global posterior estimate, and send them to each AP through the fronthaul link. The iterative control module is used to control the inner iterative process of the desired propagation, and terminate the inner iterative process when the preset convergence condition is met; and to control the outer iterative process of the noise covariance matrix update, and output the detection results of each user and the noise covariance matrix estimate of AP when the preset termination condition is met.
9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the distributed joint signal detection and noise parameter estimation method for non-cellular massive MIMO systems as described in any one of claims 1 to 7.
10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the distributed joint signal detection and noise parameter estimation method for non-cellular massive MIMO systems as described in any one of claims 1 to 7.