A Precoding Method Applicable to URLLC Short Packet Communication in a Cell-Free System

Abstract

The present invention provides a precoding method applicable to cell-free system URLLC short-packet communication, including: establishing a mathematical model of a cell-free system based on access point selection; establishing an objective function and constraint conditions for the URLLC weighted sum rate optimization problem; based on the idea of semidefinite relaxation and successive convex approximation, converting the non-convex weighted sum rate optimization problem into a convex optimization problem; using an iterative convergence method and an SDP solver to solve the converted convex optimization problem. The present invention can optimize system precoding, effectively balance the weighted sum rate of the system and the computational complexity of the system, optimize system performance, so that the cell-free URLLC short-packet communication system can maximize the system weighted sum rate under the conditions of meeting certain delay and reliability requirements, as well as system backhaul capacity and power requirements, and has broad application prospects.

Description

Technical Field

[0001] The present invention relates to the technical field of wireless communication, and particularly relates to a precoding method applicable to URLLC short-packet communication in a cell-free system. Background Art

[0002] Next-generation mobile communication faces the explosive growth of Internet of Things (IoT) devices, followed by a sharp increase in data traffic. To meet the increasing traffic volume and quality-of-service requirements, the cell-free network is considered a key technical architecture for the next-generation mobile communication network. Among them, baseband processing is centralized in the central processing unit, and access points are connected to the baseband processing unit through backhaul links to share channel state information, achieving cooperative transmission between multiple-antenna access points, with strong scalability and flexibility. Compared with traditional centralized antennas, it can achieve a good improvement in transmission performance. In addition, these IoT devices need to meet strict latency and reliability requirements. Ultra-Reliable and Low-Latency Communication (URLLC), as one of the key technologies for next-generation mobile communication, has received extensive attention. To address the phenomenon of the sharp increase in the number and traffic of these latency- and reliability-sensitive IoT devices, it is necessary to comprehensively consider the relationship among latency, reliability, and rate. On the premise of meeting latency and reliability, it is necessary to maximize the rate to the greatest extent.

[0003] Currently, most existing studies focus on precoding optimization in the scenario of infinite code length to improve the system spectral efficiency, while there are few studies on precoding design in the scenario of finite code length. In fact, when the code length is very short, the bit error rate will also increase accordingly, which will affect the reliable transmission of data. However, to meet the latency requirements, short packet lengths must be used. Therefore, the three key performance indicators of URLLC, namely latency, reliability, and rate, cannot be optimized simultaneously, and there is a trade-off problem among them. Since the data traffic scale generated by devices with strict requirements for reliability and latency in the IoT is also very large, it has become very difficult to ensure both high-reliability and low-latency transmission and meet high-rate transmission to avoid network congestion, which also poses a great challenge to the optimal allocation of system resources in the network. Moreover, there is little research on the system rate in the existing technology under short packet length transmission. Summary of the Invention

[0004] To solve the above problems, the present invention provides a precoding method applicable to URLLC short-packet communication in a cell-free system, which maximizes the weighted sum rate of the system on the premise of meeting ultra-low latency and high-reliability transmission. And considering the user-centric access point selection scheme can reduce the computational complexity within an acceptable performance loss range.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A precoding method applicable to cell-free system URLLC short-packet communication, comprising:

[0007] S1. Establish a cell-free system mathematical model based on access point selection;

[0008] S2. Establish the objective function and constraint conditions of the URLLC weighted sum rate optimization problem;

[0009] S3. Based on the idea of semidefinite relaxation and successive convex approximation, convert the non-convex weighted sum rate optimization problem into a convex optimization problem;

[0010] S4. Use the iterative convergence method and SDP solver to solve the converted convex optimization problem.

[0011] Further, the specific steps of step 1 include the following sub-steps:

[0012] S11. Configure a cell-free system with 1 central processing unit, N multi-antenna access points, each access point equipped with M antennas and K single-antenna users, where the central processing unit is connected to all access points through a backhaul link, and all statistical channel state information is shared at each access point, so there is cooperation between access points;

[0013] S12. Establish an access point selection process. The channel gain vector of user k is h k , h k = [h k1 ,..., h kN H . According to the power magnitude of the channel gain vector, select the first I access points corresponding to the channels with the largest channel gain to serve user k. We use a selection matrix D k to represent the access points serving user k. D k is a block diagonal matrix, and the block matrices on the non-block diagonal are 0. If base station i serves the user, the i-th block diagonal matrix is I M , otherwise the block diagonal matrix is 0 M . Where k ∈ {1,..., K}, (·) H is the conjugate transpose operation.

[0014] S13. Establish the model of the received signal and signal-to-interference-plus-noise ratio at the user end. The precoding vector of user k is u k , after passing through the channel h k , the received signal is expressed as Furthermore, the signal-to-interference-plus-noise ratio can be expressed as where s k is the symbol sent to the target user k, satisfying |·| represents the absolute value operation, ​denotes the expectation operation, ∑(·) denotes the summation operation, and n k is additive white Gaussian noise with noise variance σ k 2 .

[0015] S14. Establish a URLLC rate model, where c k = log2(1 + γ k ) is the Shannon capacity, n is the codeword length, is the channel dispersion, Q -1 (·) is the inverse of the Q function, and ∈ is the error probability.

[0016] Further, the specific steps of step 2 include the following sub-steps:

[0017] S21. Establish an objective function for URLLC short-packet communication:

[0018]

[0019] where represents optimizing the precoding vector u to maximize the subsequent function value, and α k is the rate weighting coefficient of user k;

[0020] S22. Establish constraint conditions that include both backhaul capacity and power, and QoS constraint conditions, as follows:

[0021]

[0022] where p i is the maximum transmit power of access point i, b i is the maximum backhaul capacity of access point i, 1{·} is the representation method of the indicator function. If · is not 0, the value of the indicator function is 1, otherwise it is 0, is the rate result calculated in the previous iteration, is the minimum signal-to-interference-plus-noise ratio requirement that user k needs to achieve.

[0023] Further, the specific steps of step 3 include the following sub-steps:

[0024] S31. Approximate the indicator function, where is the approximation coefficient of the indicator function, c1 represents a constant term, θ is the regularization constant factor, is the precoding obtained in the previous iteration.

[0025] S32. Convert the original problem into a semidefinite relaxation problem:

[0026]

[0027] where represents the optimized allocation of U k to maximize the subsequent function value, s.t. means to satisfy the following conditions, and tr{·} represents the trace operation represents U k is a positive semi - definite matrix, and Rank(·) represents the rank operation G i is a block - diagonal matrix and can be expressed as where diag{·} is the diagonalization operation represent the vector of (j - 1)M all - zero elements and the vector of M all - one elements respectively

[0028] S33. Convert the positive semi - definite relaxation problem into a convex optimization problem:

[0029]

[0030] where φ k , π k , ω k are the introduced auxiliary variables and are the results obtained from the previous iteration

[0031] Furthermore, in step S31, the indicator function is approximated by using the l0 - norm and the re - weighted l1 - norm in sequence

[0032] Furthermore, in step S32, the original problem is transformed by using the positive semi - definite relaxation transformation

[0033] Furthermore, in step S33, the non - convex original problem is transformed into a convex problem by using the continuous convex approximation transformation

[0034] Furthermore, step 4 specifically includes the following sub - steps

[0035] S41. Initialize the parameters of the system scenario, including initializing the positions of users and access points, the channel gain matrix of users, the selection matrix D k , initialize precoding, the initial values of auxiliary variables, the convergence threshold, and the initial value of the weighted sum rate to 0

[0036] S42. At the beginning of the t - th iteration, solve the convex optimization problem in S33 to obtain the allocation scheme of system resources, and the system resources are the precoding matrix

[0037] S43. Calculate and update the optimal weighted sum rate at this time Update the variable t. Compare and the size of the convergence threshold. If the value of the former is less than the latter, it is considered that the iterative algorithm converges at this time, and then jumps to step S44; otherwise, enter the next iteration t+1, and repeat steps S42-S43;

[0038] S44. The loop iteration ends, and through Gaussian randomization or eigenvalue decomposition the recovered precoding vector u is obtained k , and the weighted sum rate value is calculated

[0039] Furthermore, it also includes the following steps:

[0040] During the communication process, the remote access points and user locations are randomly generated within a circular area with a radius of r. The large-scale fading information of the channel changes according to the path, and the small-scale fading of the channel follows a Gaussian distribution. The system dynamically implements the inner iteration and outer update algorithms in the resource allocation method of step S4 according to different statistical channel state information.

[0041] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0042] The present invention can optimize the allocation of system precoding resources, and maximize the weighted sum rate of the system on the premise of meeting ultra-low latency and high-reliability transmission. And the user-centric access point selection scheme can reduce the computational complexity within an acceptable performance loss range, and has broad application prospects. Brief Description of the Drawings

[0043] Figure 1 It is a flowchart of the precoding method for URLLC short packet communication in a cell-free system provided by the present invention.

[0044] Figure 2 It is a schematic diagram of the precoding resource allocation optimization algorithm provided by an embodiment of the present invention.

[0045] Figure 3 It is a performance comparison diagram between the precoding design of the present invention and the traditional linear precoding. Detailed Embodiments

[0046] The following will combine specific embodiments to detail the technical solutions provided by the present invention. It should be understood that the following specific embodiments are only used to illustrate the present invention and not to limit the scope of the present invention.

[0047] A precoding method applicable to URLLC short packet communication in a cell-free system provided by the present invention has a process as Figure 1 shown, and includes the following steps:

[0048] S1. Establish a mathematical model of a cell-free system based on access point selection, including models for the access point selection process, the received signal at the user end, the signal-to-interference-plus-noise ratio, and the URLLC rate model;

[0049] Specifically, in this example, the mathematical model of the cell-free system based on access point selection is established according to the following steps:

[0050] S11. Configure a cell-free system with 1 central processing unit, N multi-antenna access points, each access point equipped with M antennas and K single-antenna users, where the central processing unit is connected to all access points through a backhaul link, and all statistical channel state information is shared at each access point, so there is cooperation between access points;

[0051] S12. Establish the access point selection process. The channel gain vector of user k is h k , h k = [h k1 ,..., h kN H . According to the power magnitude of the channel gain vector, select the first I access points corresponding to the channels with the largest channel gain to serve user k. We use a selection matrix D k to represent the access points serving user k. D k is a block diagonal matrix, and the block matrices on the non-block diagonal are 0. If base station i serves the user, the i-th block diagonal matrix is I M , otherwise the block diagonal matrix is 0 M . Where k ∈ {1,..., K}, (·) H is the conjugate transpose operation.

[0052] S13. Establish the model of the received signal at the user end and the signal-to-interference-plus-noise ratio. The precoding vector of user k is u k , after passing through the channel h k , the received signal is expressed as Furthermore, the signal-to-interference-plus-noise ratio can be expressed as where s k is the symbol sent to the target user k, satisfying |·| represents the absolute value operation, represents the expectation operation, ∑(·) represents the summation operation, n k is additive white Gaussian noise, and the noise variance is σ k 2 .

[0053] S14. Establish the URLLC rate model, where c k = log2(1 + γ k ) is the Shannon capacity, n is the codeword length, ​is the channel dispersion, Q -1 (·) is the inverse of the Q function, and ∈ is the bit error probability.

[0054] S2. Establish the objective function and constraint conditions of the URLLC weighted sum rate optimization problem;

[0055] In this example, the objective function and constraint conditions of the URLLC weighted sum rate optimization problem are established according to the following steps:

[0056] S21. Establish the objective function of URLLC short packet communication:

[0057]

[0058] where means to optimize the precoding vector u to maximize the subsequent function value, and α k is the rate weighting coefficient of user k;

[0059] S22. Establish the constraint conditions that include both the backhaul capacity and power, and the QoS constraint conditions, as follows:

[0060]

[0061] where p i is the maximum transmit power of access point i, b i is the maximum backhaul capacity of access point i, 1{·} is the representation method of the indicator function. If · is not 0, the value of the indicator function is 1, otherwise it is 0. is the rate result calculated in the previous iteration, is the minimum signal-to-interference-plus-noise ratio requirement that user k needs to achieve.

[0062] S3. Based on the idea of semidefinite relaxation and successive convex approximation, convert the non-convex weighted sum rate optimization problem into a convex optimization problem;

[0063] Specifically, the conversion is carried out according to the following steps:

[0064] S31. Successively use the l0 norm and the reweighted l1 norm to approximate the indicator function, and the approximated expression is where is the indicator function approximation coefficient, c1 represents the constant term, and θ is the regularization constant factor. is the precoding obtained in the previous iteration.

[0065] S32. Use the semidefinite relaxation transformation to convert the original problem into a semidefinite relaxation problem:

[0066]

[0067] where means to optimize the allocation of Uk Maximize the subsequent function value, where s.t. means subject to the following conditions, and tr{·} represents the trace operation. Denote U k as a positive semi - definite matrix, and Rank(·) represents the rank operation. G i is a block - diagonal matrix and can be expressed as where diag{·} is the diagonalization operation. represent the vectors of (j - 1)M all - zero elements and M all - one elements respectively.

[0068] S33. Use the successive convex approximation transformation to convert the positive semi - definite relaxation problem into a convex optimization problem:

[0069]

[0070] where φ k , π k , ω k are the introduced auxiliary variables. and are the results obtained from the previous iteration.

[0071] S4. Use the iterative convergence method and the SDP solver to solve the problem in S3.

[0072] Specifically, it includes the following steps:

[0073] S41. Initialize the parameters of the system scenario, including the positions of users and access points, the channel gain matrix of users, the selection matrix D k , the initial precoding, the initial values of auxiliary variables, the convergence threshold, and the initial value of the weighted sum rate to 0.

[0074] S42. At the beginning of the t - th iteration, solve the convex optimization problem in S33 to obtain the allocation scheme of system resources, where the system resources are the precoding matrix.

[0075] S43. Calculate and update the optimal weighted sum rate at this time Update the variable t. Compare with the convergence threshold. If the former value is less than the latter, it is considered that the iterative algorithm converges at this time, and then jump to step S44; otherwise, enter the next iteration t + 1 and repeat steps S42 - S43.

[0076] S44. After the iterative loop ends, obtain the restored precoding vector u through Gaussian randomization or eigenvalue decomposition k , and calculate the weighted sum rate value

[0077] When applying the method of the present invention,

[0078] During the communication process, the remote access point and the user location are randomly generated within a circular area with a radius of r. The large-scale fading information of the channel changes according to the path, and the small-scale fading of the channel follows a Gaussian distribution. The system dynamically implements the inner-layer iteration and outer-layer update algorithms in the resource allocation method of step S4 according to different statistical channel state information. The optimized allocation scheme of the system resources obtained based on the method of the present invention is applied to the cell-free system in the short-packet communication scenario. Under the premise of meeting the ultra-low latency and high-reliability transmission, the weighted sum rate of the system can be maximized. And considering the user-centric access point selection scheme can reduce the computational complexity within an acceptable performance loss range.

[0079] The technical means disclosed in the solution of the present invention are not limited to the technical means disclosed in the above embodiments, but also include technical solutions composed of any combination of the above technical features. It should be noted that for those of ordinary skill in the art in this technical field, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements are also regarded as the protection scope of the present invention.

Claims

1. A precoding method applicable to URLLC short packet communication in a cell-free system, characterized in that Including: S1. Establish a mathematical model of a cell-free system based on access point selection; S2. Establish the objective function and constraint conditions of the URLLC weighted sum rate optimization problem; S3. Based on the idea of semidefinite relaxation and successive convex approximation, convert the non-convex weighted sum rate optimization problem into a convex optimization problem; S4. Use the iterative convergence method and the SDP solver to solve the converted convex optimization problem; Step S1 specifically includes the following sub-steps: S11. Configure a cell-free system with 1 central processing unit, N multi-antenna access points, each access point equipped with M antennas and K single-antenna users, where the central processing unit is connected to all access points through a backhaul link, and all statistical channel state information is shared at each access point, so there is cooperation between access points; S12. Establish an access point selection process, where the channel gain vector of user k is h k , h k = [h k1 ,..., h kN H ; Sort according to the power magnitude of the channel gain vector, and select the first I access points corresponding to the channels with the largest channel gain to serve user k; Use the selection matrix D k to represent the access points serving user k, D k is a block diagonal matrix, and the block matrices on the non-block diagonal are 0; If base station i serves the user, the i-th block diagonal matrix is I M , otherwise the block diagonal matrix is 0 M ; where k ∈ {1,..., K}, (·) H is the conjugate transpose operation;​ S13. Establish a model for the client to receive signals and the signal-to-interference-plus-noise ratio (SINR). The precoding vector for user k is u k , through the channel h k , the received signal is expressed as Furthermore, the SINR is expressed as where s k is the symbol sent to the target user k, satisfying |·| represents the absolute value operation, represents the expectation operation, ∑(·) represents the summation operation, n k is additive white Gaussian noise, and the noise variance is σ k 2 ; S14. Establish a URLLC rate model, where c k = log2(1 + γ k ) is the Shannon capacity, n is the codeword length, is the channel dispersion, Q -1 (·) is the inverse of the Q function, and ∈ is the bit error probability; Step S2 specifically includes the following sub-steps: S21. Establish the objective function of URLLC short-packet communication: where denotes optimizing the precoding vector u to maximize the subsequent function value, and α k is the rate weighting coefficient of user k; S22. Establish the constraint conditions that include both the backhaul capacity and power and the QoS constraints as follows: where p i is the maximum transmit power of access point i, b i is the maximum backhaul capacity of access point i, 1{·} is the representation method of the indicator function. If · is not 0, the value of the indicator function is 1, otherwise it is 0. is the rate result calculated in the previous iteration, is the minimum signal-to-interference-plus-noise ratio requirement that user k needs to achieve.

2. The precoding method for cell-free system URLLC short packet communication according to claim 1, characterized in that Step S3 specifically includes the following sub-steps: S31. Indicator function approximation where c1 represents the constant term, and θ is the regularization constant factor; S32. Convert the original problem into a semidefinite relaxation problem: Among them represents the optimized allocation of U k such that the subsequent function value is maximized, s.t. means making it satisfy the following conditions, and tr{·} represents the trace operation represents U k is a positive semi - definite matrix, and Rank(·) represents the rank operation G i is a block - diagonal matrix, expressed as where diag{·} is the diagonalization operation respectively represent the vectors of (j - 1)M all - zero elements and M all - one elements S33. Convert the semidefinite relaxation problem into a convex optimization problem: Among them, φ k , π k , ω k are introduced auxiliary variables, and are the results obtained from the previous iteration.

3. The precoding method for URLLC short packet communication in a cell-free system according to claim 2, wherein Step S31 successively uses the norm and reweighting norms to approximate the indicator function.

4. The precoding method for URLLC short packet communication in a cell-free system according to claim 2, characterized in that, Step S32 transforms the original problem using semidefinite relaxation transformation.

5. The precoding method for URLLC short packet communication in a cell-free system according to claim 2, characterized in that Step S33 transforms the non-convex original problem into a convex problem using successive convex approximation transformation.

6. The precoding method for URLLC short packet communication in a cell-free system according to claim 2, characterized in that Step S4 specifically includes the following sub-steps: S41. Initialize the parameters of the system scenario, including initializing the positions of the user and the access point, the channel gain matrix of the user, and selecting the matrix D k , initializing precoding, initial values of auxiliary variables, convergence thresholds, and initial values of weighted sum rates to be 0; S42. At the beginning of the t-th iteration, solve the convex optimization problem in S33 to obtain the allocation scheme of system resources, where the system resources are precoding matrices; S43. Calculate and update the optimal weighted sum rate at this time Update variables Compare with the size of the convergence threshold. If the value of the former is less than the latter, it is considered that the iterative algorithm converges at this time, and then jump to step S44; otherwise, enter the next iteration t + 1, and repeat steps S42 - S43; S44. The loop iteration ends, and through Gaussian randomization or eigenvalue decomposition the recovered precoding vector u is obtained k , and the weighted sum rate value is calculated 7. The precoding method for URLLC short packet communication in a cell-free system according to any one of claims 1-6, characterized in that, It also includes the following steps: During the communication process, the positions of the remote access points and users are randomly generated within a circular area with a radius of r. The large-scale fading information of the channel changes according to the path, and the small-scale fading of the channel follows a Gaussian distribution. The system dynamically implements the inner iteration and outer update algorithms in the resource allocation method of Step S4 according to different statistical channel state information.

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