Uplink power control method for cell-free massive MIMO supporting URLLC

Abstract

A method for uplink power control in a cell-free massive MIMO system supporting URLLC is disclosed, comprising: 1: constructing a cell-free massive MIMO system supporting URLLC; 2: establishing a channel model; 3: all users sending pilot signals to all access points for pilot training; 4: performing channel estimation to obtain an estimated channel coefficient vector; 5: all users simultaneously transmitting uplink data to all access points, with each access point preprocessing the data signals of all users; 6: a central processing unit jointly decoding the preprocessed signals to obtain user signals corresponding to the users; 7: calculating the user's signal-to-noise ratio and the user's uplink achievable rate; 8: establishing problem P1; 9: transforming problem P1 into problem P2; 10: transforming problem P2 into problem P3; and 11: solving problem P3 to obtain a local optimal solution to the user weighted sum rate maximization problem. The method reduces the adverse effects of channel aging on the cell-free massive MIMO system supporting URLLC.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a method for controlling uplink power of a non-cell massive MIMO network supporting URLLC. Background Art

[0002] Ultra-reliable low-latency communication (URLLC) is a key application in 5G and future wireless communication networks, primarily used in scenarios with extremely high requirements for latency and reliability, such as industrial automation and telemedicine. However, the implementation of URLLC faces two major challenges: latency and reliability.

[0003] In traditional URLLC designs, time diversity can enhance reliability, but this approach increases transmission time, leading to latency issues. Furthermore, existing standardization rules restrict the transmission of coded packets over discontinuous spectrum resources, further limiting the application of frequency diversity in URLLC.

[0004] To address this issue, Massive Multiple-Input Multiple-Output (MIMO) technology has become a research focus. Massive MIMO utilizes spatial diversity by deploying a large number of antennas at the base station and receiver to improve spectral and energy efficiency. This technology has been proven to significantly increase system capacity and effectively reduce interference. However, cellular Massive MIMO systems still face challenges such as high path loss and inter-cell interference, which affect communication reliability and stability.

[0005] To address these issues of massive MIMO, a cell-free massive MIMO architecture was proposed, in which multiple access points are distributed throughout the coverage area and connected to a central processor via forward links, which is responsible for distributing the workload to serve users.

[0006] Shortcomings of Existing Technologies: Cell-free massive MIMO based on short packet transmission not only achieves higher spectral efficiency and reliability than cellular massive MIMO, but its performance can be further enhanced through resource allocation. However, several practical factors remain unaddressed. One is channel correlation, and the other is user mobility. When an access point is equipped with multiple antennas, the channel exhibits coherent characteristics. Furthermore, user mobility causes channel aging, a phenomenon that cannot be described using block fading models. Both channel aging and spatial correlation can lead to significant performance degradation and should be considered in cell-free massive MIMO systems. Summary of the Invention

[0007] The present invention provides a method for controlling uplink power of a non-cell massive MIMO system supporting URLLC, which effectively reduces the adverse effects of channel aging on the non-cell massive MIMO system supporting URLLC.

[0008] To achieve the above objectives, the present invention provides a method for controlling uplink power of a cell-free massive MIMO network supporting URLLC, the key of which is to include the following steps:

[0009] Step 1: Build a cell-free massive MIMO system supporting URLLC. The cell-free massive MIMO system is configured with M access points, which simultaneously serve K single-antenna users in the same time-frequency resources. Each access point is equipped with N antennas, and all access points are connected to the same central processor via a forward link.

[0010] Step 2: Establishing a channel model based on the cell-free massive MIMO system;

[0011] Step 3: The central processor allocates pilot signals to each user, and all users simultaneously send pilot signals to all access points for pilot training. The pilots are randomly allocated to each user, and different users may reuse the same pilots.

[0012] Step 4: During the pilot training process, performing channel estimation on the pilot signal to obtain an estimated channel coefficient vector;

[0013] Step 5: All users simultaneously transmit uplink data to all access points. Each access point pre-processes the data signals of all users and transmits the pre-processed signals to the central processor via a backhaul link.

[0014] Step 6: The central processor jointly decodes the pre-processed signal to obtain a user signal corresponding to the user;

[0015] Step 7: Calculate the signal-to-noise ratio of the corresponding user according to the user signal, and calculate the uplink achievable rate of the corresponding user according to the signal-to-noise ratio;

[0016] Step 8: Optimize the uplink data transmission power of each user to maximize the weighted sum rate of all users while satisfying the minimum rate constraint and the maximum transmission power constraint, and establish the weighted sum rate maximization problem P1 for all users.

[0017] Step 9: Convert the user's minimum rate constraint into the user's minimum signal-to-interference-and-noise ratio constraint and introduce the auxiliary variable χ k (t), transform the weighted sum rate maximization problem P1 into the weighted sum rate maximization problem P2;

[0018] Step 10: Analyze the function properties of the weighted sum rate maximization problem P2, and use the best local approximation function to approximate the objective function of the weighted sum rate maximization problem P2 into a series of sub-problems, and transform these sub-problems into geometric programming problems P3 based on the properties of the logarithmic function;

[0019] Step 11: Solve the geometric programming problem P3 through the continuous convex optimization iteration method to obtain the local optimal solution of the user's weighted sum rate maximization problem.

[0020] Through the above design, the URLLC-supported cell-free massive MIMO system adopts a time division duplex working mode, and each coherent time block is divided into two processing stages: pilot training and data transmission. In addition, the time-frequency block resources are divided into multiple coherent intervals. Each coherent interval is composed of τ c symbols, each short packet contains L symbols, L = τ p +τ u , where τ p and τ u They represent the pilot sequence length and uplink data sequence length respectively.

[0021] This paper studies the impact of channel aging on the performance of cell-free massive multiple-input multiple-output MIMO systems supporting ultra-reliable low-latency communication (URLLC), and takes into account spatial correlation and pilot contamination. Under the conditions of short packet transmission and maximum ratio combining, a closed-form expression for the achievable uplink rate is derived. In order to maximize the weighted sum rate of all users, a maximum power optimization problem is proposed. Two approximate functions are introduced to transform the original non-convex problem into a series of geometric programming problems, which are then iteratively solved using continuous convex optimization. Channel aging greatly degrades the performance of cell-free massive MIMO systems supporting URLLC. Compared with the system without power control, the proposed maximum power allocation strategy improves the uplink spectrum efficiency per user by 95%, effectively mitigating the adverse effects of channel aging.

[0022] Preferably, in step 2, the channel model is a Rayleigh fading channel with channel aging and spatial correlation, and the expression of the Rayleigh fading channel is:

[0023]

[0024] Among them, g m,k (t) represents the channel coefficient between the m-th access point and the k-th user at the t-th symbol index, and It means a complex Gaussian distribution with a mean of 0 and a variance of R. is the spatial correlation matrix; h m,k(t) represents the small-scale fading between the mth access point and the kth user at symbol index t, and It means that it obeys a complex Gaussian distribution with a mean of 0 and a variance of 1;

[0025] There is relative motion between the user and the access point, and the channel exhibits aging characteristics. The standard channel aging model is used to analyze the impact of channel aging. The expression is:

[0026]

[0027] Among them, g m，k (t in ) represents the tth in The initial channel vector at symbols, ξ m，k (t) represents the new component vector at the t-th symbol, and

[0028] ρ k (tt in ) represents the symbol index t and the symbol index t in The normalized correlation of the channel coefficients between k (tt in )=J0(2πf D，k T s |tt in |), and 0≤ρ k (tt in )≤1, where, where, f D，k is the Doppler shift of the kth user, T S is the sampling time, J0 represents the zero-order Bessel function of the first kind;

[0029] The expression is

[0030] Preferably, in step 3, all users send pilot signals to all access points at the beginning of the uplink training phase, and the mth access point receives the pilot signals of all users. The expression is:

[0031]

[0032] in, represents the pilot signals of all users received by the mth access point, Denotes the normalized signal-to-noise ratio for the pilot symbol, G m (0)=[g m，1 (0), g m，2 (0),…,g m，K(0)] represents the channel coefficient vector between the mth access point and all users at the 0th symbol; is the pilot sequence of the kth user, τ p is the pilot sequence length, and is the additive white Gaussian noise at the mth access point, the superscript p indicates that the current signal is a pilot signal, and the superscript H indicates the transpose of the vector;

[0033] In step 4, at time τ p +1, and then use the obtained channel estimate as the initial state to obtain the channel estimate at all other times; define λ = τ p +1, the channel coefficient between the mth access point and the kth user at the 0th symbol is expressed as:

[0034]

[0035] In order to estimate the channel coefficient vector of the kth user, and Multiplying them, we get the pilot signal of the kth user at the 0th symbol received by the mth access point:

[0036]

[0037] in, Indicates that the mth access point receives the pilot signal of the kth user, N m，k (0) represents the Gaussian white noise when the mth access point receives the data of the kth user;

[0038] Using the minimum mean square error method, the p The channel is estimated at +1 symbol, and the estimated channel coefficient vector is:

[0039]

[0040] Among them, Φ m，k The expression is:

[0041]

[0042] Among them, I N represents the identity matrix;

[0043] Channel Estimation and channel estimation error are independent and uncorrelated complex Gaussian random variables, obey distributed, obey distribution, where Q m，k The expression is:

[0044]

[0045] As a preference: in step 5, the user sets (L-τ p ) symbols are allocated for uplink data transmission, and the data signals received by the mth access point from all users at the tth symbol are:

[0046]

[0047] Among them, λ≤t≤L, the superscript d indicates that the current signal is a data signal, p k is the uplink data transmission power of the kth user, And X d The elements in (t) are independent of each other, that is, E(|[X d (t)] kl | 2 )=1, (1≤k≤K,1≤l≤(L-τ p )), and E([X d (t)] kl [X d (t)] ij )=0, (i≠k or j≠l), E represents the expectation;

[0048] Using the maximum ratio combining method, each access point uses the maximum ratio combining MRC coefficient Process the received data signal; the mth access point preprocesses the data signals of all users at the tth symbol, and the expression of the preprocessed signal is:

[0049]

[0050] in, represents the transpose of the estimated channel coefficient vector between the mth access point and all users at symbol index λ.

[0051] Preferably, in step 6, each access point performs local channel estimation and multi-user detection, and then transmits the signal to the central processor via the backhaul link. The central processor then performs joint decoding. The user signal of the k-th user at the t-th symbol obtained by decoding in the central processor is:

[0052]

[0053] Among them, each δ m,k The value of (t) is equal to and is the inverse of the number of access points; DS k,t represents the expected signal of the kth user at the tth symbol, LS k,trepresents the leakage signal of the kth user at the tth symbol, CA k,t represents the channel aging effect of the kth user at the tth symbol, UI k,i,t represents the inter-user interference of the kth user at the tth symbol, ZN k,t represents the additive white Gaussian noise of the k-th user at the t-th symbol.

[0054] Preferably, in step 7, the signal-to-noise ratio expression of the k-th user at the t-th symbol is:

[0055]

[0056]

[0057] Where δ is the coefficient of large-scale fading decoding, is an M-dimensional complex vector, tr(Q) means finding the trace of the matrix Q, diag(.) means extracting the vector composed of the elements on the main diagonal of the matrix, Indicates the definition of the equal sign.

[0058] Under short packet transmission, the uplink achievable data rate of the kth user at the tth symbol is expressed as follows:

[0059]

[0060] Wherein, η represents the ratio of the pilot sequence length to the length of the short data packet, C(t)=log2(1+γ k (t)) is based on the traditional Shannon formula, represents the correction factor due to the FCBL mechanism, represents dispersion, Q -1 (ε k ) is Q(ε k ) function, L represents the length of a short data packet, ε k represents the decoding error probability.

[0061] Preferably, in step 8, the weighted sum rate maximization problem P1 is expressed as follows:

[0062]

[0063] Among them, R k (t) is the uplink achievable data rate of the k-th user at the t-th symbol; w k represents the weight assigned to the k-th user to reflect its priority or importance, which is assumed to be randomly generated in the range [0,1];

[0064] In step 9, the weighted sum rate maximization problem P1 is transformed into the weighted sum rate maximization problem P2, which is expressed as follows:

[0065]

[0066] in,

[0067] Among them, χ k (t) represents an auxiliary variable, represents the inverse of the function, is the achievable rate threshold for each user, is the maximum transmit power of each user.

[0068] Preferably, in step 10, by analyzing the properties of the objective function in the weighted sum rate maximization problem P2 and introducing two approximate functions, the weighted sum rate maximization problem P2 is transformed into a series of sub-problems;

[0069] The expressions of the two approximate functions are ln(1+z)≥a ln(z)+b and in, z represents a variable;

[0070] Based on the above two approximate functions, the lower bound of the objective function of the weighted sum rate maximization problem P2, that is, the expression of a series of sub-problems, is obtained as follows:

[0071]

[0072] According to the properties of the logarithmic function, the expression of the geometric programming problem P3 to be solved in the i-th iteration is as follows:

[0073]

[0074] in, The superscript i indicates the number of iterations.

[0075] Initialize the data transmission power of the kth user to and calculate the corresponding set up Then, in the i-th iteration, two approximation functions are used to obtain ln(1+χ k (t)) and G(χ k (t)). In addition, using calculate and

[0076] As a preference: in said step 11, the geometric programming problem P3 is solved by using a continuous convex optimization iteration method, and before the alternating iterative solution, an auxiliary variable is introduced. If and only if When is always greater than or equal to 1, the initial feasible solution of the user's transmit power is obtained by solving problem P4, which is expressed as:

[0077]

[0078] Solving problem P4, the initial feasible solution for the user's transmission power is: Then the geometric programming problem P3 is solved by continuous convex optimization iteration method.

[0079] As a preferred method, the geometric programming problem P3 is solved by continuous convex optimization iteration. The specific steps are as follows:

[0080] Step A1: Initialization: number of iterations i = 1, error tolerance And the objective function Obj of P1 (0) ;

[0081] Step A2: Given and Calculated using the CVX toolkit and

[0082] Step A3: Obtained from step A2 To update Calculate Obj (i) ;

[0083] Step A4: When When , update i = i + 1 and return to step 2; otherwise, end and output the local optimal solution of the user's weighted sum rate maximization problem.

[0084] The beneficial effects of the present invention are as follows: for a cell-free massive MIMO system supporting URLLC, under the rate requirements and the user's maximum transmission power constraints, a power control strategy for optimizing the user data transmission power is proposed with maximizing the user's weighted total rate as the objective function. This strategy not only effectively reduces the adverse effects of channel aging on the cell-free massive MIMO system supporting URLLC, but also is very effective in devices with a low energy budget, thereby improving the system's performance and energy efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 It is a schematic diagram of the process of the present invention;

[0086] Figure 2Schematic diagram of the structure of a cell-free massive MIMO system supporting URLLC in an embodiment;

[0087] Figure 3 Graph showing the impact of channel aging on a cell-free massive MIMO system supporting URLLC in an embodiment;

[0088] Figure 4 Graph showing the impact of channel spatial correlation on a cell-free massive MIMO system supporting URLLC in an embodiment;

[0089] Figure 5 2 is a CDF diagram of the uplink achievable rate of the URLLC-supported cell-free massive MIMO system with and without power control in an embodiment. DETAILED DESCRIPTION

[0090] The present invention will be further described in detail below with reference to the accompanying drawings and specific examples. The following examples or drawings are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0091] like Figure 1 FIG. 1 shows a method for uplink power control of a cell-free massive MIMO network supporting URLLC, comprising the following steps:

[0092] Step 1: Build a cell-free massive MIMO system supporting URLLC. The cell-free massive MIMO system is configured with M access points. The M access points simultaneously serve K single-antenna users in the same time-frequency resources. Each access point is equipped with N antennas. All access points are connected to the same central processor via a forward link, as shown in Figure 1. Figure 2 As shown;

[0093] Step 2: Establishing a channel model based on the cell-free massive MIMO system;

[0094] Step 3: The central processor distributes pilot signals to each user, and all users simultaneously send pilot signals to all access points for pilot training;

[0095] Step 4: During the pilot training process, performing channel estimation on the pilot signal to obtain an estimated channel coefficient vector;

[0096] Step 5: All users simultaneously transmit uplink data to all access points. Each access point pre-processes the data signals of all users and transmits the pre-processed signals to the central processor via a backhaul link.

[0097] Step 6: The central processor jointly decodes the pre-processed signal to obtain a user signal corresponding to the user;

[0098] Step 7: Calculate the signal-to-noise ratio of the corresponding user according to the user signal, and calculate the uplink achievable rate of the corresponding user according to the signal-to-noise ratio;

[0099] Step 8: Optimize the uplink data transmission power of each user to maximize the weighted sum rate of all users while satisfying the minimum rate constraint and the maximum transmission power constraint, and establish the weighted sum rate maximization problem P1 for all users.

[0100] Step 9: Convert the user's minimum rate constraint into the user's minimum signal-to-interference-and-noise ratio constraint and introduce the auxiliary variable χ k (t), transform the weighted sum rate maximization problem P1 into the weighted sum rate maximization problem P2;

[0101] Step 10: Analyze the function properties of the weighted sum rate maximization problem P2, and use the best local approximation function to approximate the objective function of the weighted sum rate maximization problem P2 into a series of sub-problems, and transform these sub-problems into geometric programming problems P3 based on the properties of the logarithmic function;

[0102] Step 11: Solve the geometric programming problem P3 through the continuous convex optimization iteration method to obtain the local optimal solution of the user's weighted sum rate maximization problem.

[0103] In step 2, the channel model is a Rayleigh fading channel with channel aging and spatial correlation, and the expression of the Rayleigh fading channel is:

[0104]

[0105] Among them, g m，k (t) represents the channel coefficient between the m-th access point and the k-th user at the t-th symbol index, and It means a complex Gaussian distribution with a mean of 0 and a variance of R. is the spatial correlation matrix; h m，k (t) represents the small-scale fading between the mth access point and the kth user at symbol index t, and It means that it obeys a complex Gaussian distribution with a mean of 0 and a variance of 1;

[0106] There is relative motion between the user and the access point, and the channel exhibits aging characteristics. The standard channel aging model is used to analyze the impact of channel aging. The expression is:

[0107]

[0108] Among them, g m，k (t in ) represents the tthin The initial channel vector at symbols, ξ m，k (t) represents the new component vector at the t-th symbol, and

[0109] ρ k (tt in ) represents the symbol index t and the symbol index t in The normalized correlation of the channel coefficients between k (tt in )=J0(2πf D，k T s |tt in |), and 0≤ρ k (tt in )≤1, where, where, f D，k is the Doppler shift of the kth user, T S is the sampling time, J0 represents the zero-order Bessel function of the first kind;

[0110] The expression is

[0111] In step 3, all users send pilot signals to all access points at the same time at the beginning of the uplink training phase. The mth access point receives the pilot signals of all users. The expression is:

[0112]

[0113] in, represents the pilot signals of all users received by the mth access point, Denotes the normalized signal-to-noise ratio for the pilot symbol, G m (0)=[g m，1 (0), g m，2 (0),…,g m，K (0)] represents the channel coefficient vector between the mth access point and all users at the 0th symbol; is the pilot sequence of the kth user, τ p is the pilot sequence length, and is the additive white Gaussian noise at the mth access point, the superscript p indicates that the current signal is a pilot signal, and the superscript H indicates the transpose of the vector;

[0114] In step 4, at time τ p +1, and then use the obtained channel estimate as the initial state to obtain the channel estimate at all other times; define λ = τ p+1, the channel coefficient between the mth access point and the kth user at the 0th symbol is expressed as:

[0115]

[0116] In order to estimate the channel coefficient vector of the kth user, and Multiplying them, we get the pilot signal of the kth user at the 0th symbol received by the mth access point:

[0117]

[0118] in, Indicates that the mth access point receives the pilot signal of the kth user, N m，k (0) represents the Gaussian white noise when the mth access point receives the data of the kth user;

[0119] Using the minimum mean square error method, the p The channel is estimated at +1 symbol, and the estimated channel coefficient vector is:

[0120]

[0121] Among them, Φ m,k The expression is:

[0122]

[0123] Among them, I N represents the identity matrix;

[0124] Channel Estimation and channel estimation error are independent and uncorrelated complex Gaussian random variables, obey distributed, obey distribution, where Q m,k The expression is:

[0125]

[0126] In step 5, the user sets (L-τ p ) symbols are allocated for uplink data transmission, and the data signals received by the mth access point from all users at the tth symbol are:

[0127]

[0128] Among them, λ≤t≤L, the superscript d indicates that the current signal is a data signal, p k is the uplink data transmission power of the kth user, And X d The elements in (t) are independent of each other, that is, E(|[X d (t)] kl | 2 )=1, (1≤k≤,1≤l≤(L-τ p )), and E([X d (t)] kl [X d (t)] ij )=0, (i≠k or j≠l), E represents the expectation;

[0129] Using the maximum ratio combining method, each access point uses the maximum ratio combining MRC coefficient Process the received data signal; the mth access point preprocesses the data signals of all users at the tth symbol, and the expression of the preprocessed signal is:

[0130]

[0131] in, represents the transpose of the estimated channel coefficient vector between the mth access point and all users at symbol index λ.

[0132] In step 6, each access point transmits the pre-processed signal to the central processor via the backhaul link, and the central processor then performs joint decoding. The user signal of the k-th user at the t-th symbol obtained by decoding in the central processor is:

[0133]

[0134] Among them, each δ m,k The value of (t) is equal to and is the inverse of the number of access points; DS k,t represents the expected signal of the kth user at the tth symbol, LS k,t represents the leakage signal of the kth user at the tth symbol, CA k,t represents the channel aging effect of the kth user at the tth symbol, UI k,i,t represents the inter-user interference of the kth user at the tth symbol, ZN k,t represents the additive white Gaussian noise of the k-th user at the t-th symbol.

[0135] In step 7, the signal-to-noise ratio expression of the k-th user at the t-th symbol is:

[0136]

[0137] Where δ is the coefficient of large-scale fading decoding, is an M-dimensional complex vector, tr(Q) means finding the trace of the matrix Q, diag(.) means extracting the vector composed of the elements on the main diagonal of the matrix, Indicates the definition of the equal sign.

[0138] Under short packet transmission, the uplink achievable data rate of the kth user at the tth symbol is expressed as follows:

[0139]

[0140] Wherein, η represents the ratio of the pilot sequence length to the length of the short data packet, L represents the length of a short data packet, ε k represents the decoding error probability.

[0141] In step 8, the weighted sum rate maximization problem P1 is expressed as follows:

[0142]

[0143] Among them, R k (t) is the uplink achievable data rate of the k-th user at the t-th symbol; w k represents the weight assigned to the k-th user to reflect its priority or importance, and is assumed to be randomly generated between [0,1];

[0144] In step 9, the weighted sum rate maximization problem P1 is transformed into the weighted sum rate maximization problem P2, which is expressed as follows:

[0145]

[0146] in,

[0147] Among them, χ k (t) represents an auxiliary variable, represents the inverse of the function, is the achievable rate threshold for each user, is the maximum transmit power of each user.

[0148] In step 10, by analyzing the properties of the objective function in the weighted sum rate maximization problem P2 and introducing two approximate functions, the weighted sum rate maximization problem P2 is transformed into a series of sub-problems;

[0149] The expressions of the two approximate functions are ln(1+z)≥a ln(z)+b and in, z represents a variable;

[0150] Based on the above two approximate functions, the lower bound of the objective function of the weighted sum rate maximization problem P2, that is, the expression of a series of sub-problems, is obtained as follows:

[0151]

[0152] According to the properties of the logarithmic function, the expression of the geometric programming problem P3 to be solved in the i-th iteration is as follows:

[0153]

[0154] in, The superscript i indicates the number of iterations.

[0155] In step 11, the geometric programming problem P3 is solved by using the continuous convex optimization iteration method. Before the alternating iterative solution, the auxiliary variable If and only if When is always greater than or equal to 1, the initial feasible solution of the user's transmit power is obtained by solving problem P4, which is expressed as:

[0156]

[0157] Solving problem P4, the initial feasible solution for the user's transmission power is: Then the geometric programming problem P3 is solved by continuous convex optimization iteration method.

[0158] The geometric programming problem P3 is solved by continuous convex optimization iteration method. The specific steps are as follows:

[0159] Step A1: Initialization: number of iterations i = 1, error tolerance And the objective function Obj of P1 (0) ;

[0160] Step A2: Given and Calculated using the CVX toolkit and

[0161] Step A3: Obtained from step A2 To update Calculate Obj (i) ;

[0162] Step A4: When When , update i = i + 1 and return to step 2; otherwise, end and output the local optimal solution of the user's weighted sum rate maximization problem.

[0163] To better demonstrate the effectiveness of the present invention, a simulation experiment was conducted to analyze the performance of the resource allocation method proposed in the present invention. The system includes 20 access points and 15 users. All access points and users are randomly distributed in a square area with a side length of D = 0.5 km.

[0164] Figure 3 The average spectral efficiency of the uplink for the first 500 symbol indices with infinite and finite block lengths is shown. D T s = 0, the spectrum efficiency of the uplink always remains constant. However, the average spectrum efficiency based on Shannon's theorem is always greater than the average spectrum efficiency based on short packet transmission, which is caused by the penalty term introduced in the achievable rate of short packet transmission. In addition, as f D T s As the channel bandwidth increases, the peak value of the average uplink spectral efficiency decreases, and the first zero shifts to the left for both the Shannon rate and the short packet rate. However, the short packet rate reaches the zero faster than the Shannon rate. This occurs because URLLC transmission sacrifices performance to ensure a certain degree of reliability and latency. This trade-off further amplifies the effects of channel aging, degrading system performance.

[0165] exist Figure 4 In the case of σ, the user’s uplink achievable rate increases with σ ASD The first zero point of the uplink average spectral efficiency shifts to the left as it decreases gradually. This indicates that the spatial correlation of the channel also affects the average uplink SE. In order to minimize the impact of channel aging and spatial aging, the short packet length L does not exceed the first zero value of the uplink average SE. Therefore, the following simulation is based on f D T s =0.002,σ ASD =30°, L=200.

[0166] Figure 5 The CDF of the achievable uplink rate for a cell-free massive MIMO system supporting URLLC with and without power control is plotted. The proposed maximum power control algorithm ensures that the achievable uplink rate is higher than 4 bits / s / Hz, thereby guaranteeing the rate requirement for each user. Furthermore, when the system has no power control, that is, when all users transmit uplink data at maximum transmit power, the 95% probability of the achievable uplink rate per user is 3.01 bits / s / Hz. With maximum power control, the 95% probability of the achievable uplink rate per user reaches 6.02 bits / s / Hz, more than double that of the system without power control.

[0167] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A method for controlling uplink power of a cell-free massive MIMO network supporting URLLC, characterized in that: The following steps are involved: Step 1: Build a cell-free massive MIMO system supporting URLLC. The cell-free massive MIMO system is configured with M access points, which simultaneously serve K single-antenna users in the same time-frequency resources. Each access point is equipped with N antennas, and all access points are connected to the same central processor via a forward link. Step 2: Establishing a channel model based on the cell-free massive MIMO system; Step 3: The central processor distributes pilot signals to each user, and all users simultaneously send pilot signals to all access points for pilot training; Step 4: During the pilot training process, performing channel estimation on the pilot signal to obtain an estimated channel coefficient vector; Step 5: All users simultaneously transmit uplink data to all access points. Each access point pre-processes the data signals of all users and transmits the pre-processed signals to the central processor via a backhaul link. Step 6: The central processor jointly decodes the pre-processed signal to obtain a user signal corresponding to the user; Step 7: Calculate the signal-to-noise ratio of the corresponding user according to the user signal, and calculate the uplink achievable rate of the corresponding user according to the signal-to-noise ratio; Step 8: Optimize the uplink data transmission power of each user to maximize the weighted sum rate of all users while satisfying the minimum rate constraint and the maximum transmission power constraint, and establish the weighted sum rate maximization problem P1 for all users. Step 9: Convert the user's minimum rate constraint into the user's minimum signal-to-interference-and-noise ratio constraint and introduce the auxiliary variable χ k (t), transform the weighted sum rate maximization problem P1 into the weighted sum rate maximization problem P2; Step 10: Analyze the function properties of the weighted sum rate maximization problem P2, and use the best local approximation function to approximate the objective function of the weighted sum rate maximization problem P2 into a series of sub-problems, and transform these sub-problems into geometric programming problems P3 based on the properties of the logarithmic function; Step 11: Solve the geometric programming problem P3 through the continuous convex optimization iteration method to obtain the local optimal solution of the user's weighted sum rate maximization problem.

2. The method for controlling uplink power of a cell-free massive MIMO network supporting URLLC according to claim 1, wherein: In step 2, the channel model is a Rayleigh fading channel with channel aging and spatial correlation, and the expression of the Rayleigh fading channel is: Among them, g m,k (t) represents the channel coefficient between the m-th access point and the k-th user at the t-th symbol index, and is the spatial correlation matrix; h m,k (t) represents the small-scale fading between the mth access point and the kth user at symbol index t, and There is relative motion between the user and the access point, and the channel exhibits aging characteristics. The standard channel aging model is used to analyze the impact of channel aging. The expression is: Among them, g m,k (t in ) represents the tth in The initial channel vector at symbols, ξ m,k (t) represents the new component vector at the t-th symbol, and ρ k (tt in ) represents the symbol index t and the symbol index t in The normalized correlation of the channel coefficients between k (tt in )=J0(2πf D,k T s |tt in |), and 0≤ρ k (tt in )≤1, where, where, f D,k is the Doppler shift of the kth user, T s is the sampling time, J0 represents the zero-order Bessel function of the first kind; The expression is 3. The method for controlling uplink power of a cell-free massive MIMO network supporting URLLC according to claim 1, wherein: In step 3, all users send pilot signals to all access points at the same time at the beginning of the uplink training phase. The mth access point receives the pilot signals of all users. The expression is: in, represents the pilot signals of all users received by the mth access point, Denotes the normalized signal-to-noise ratio for the pilot symbol, G m (0)=[g m,1 (0),g m,2 (0),…,g m,K (0)] represents the channel coefficient vector between the mth access point and all users at the 0th symbol; is the pilot sequence of the kth user, τ p is the pilot sequence length, and is the additive white Gaussian noise at the mth access point, the superscript p indicates that the current signal is a pilot signal, and the superscript H indicates the transpose of the vector; In step 4, at time τ p +1, and then use the obtained channel estimate as the initial state to obtain the channel estimate at all other times; define λ = τ p +1, the channel coefficient between the mth access point and the kth user at the 0th symbol is expressed as: In order to estimate the channel coefficient vector of the kth user, and Multiplying them, we get the pilot signal of the kth user at the 0th symbol received by the mth access point: in, Indicates that the mth access point receives the pilot signal of the kth user, N m,k (0) represents the Gaussian white noise when the mth access point receives the data of the kth user; Using the minimum mean square error method, the p The channel is estimated at +1 symbol, and the estimated channel coefficient vector is: Among them, Φ m,k The expression is: Among them, I N represents the identity matrix; Channel Estimation and channel estimation error are independent and uncorrelated complex Gaussian random variables, obey distributed, obey distribution, where Q m,k The expression is:

4. The method for controlling uplink power of a cell-free massive MIMO network supporting URLLC according to claim 1, wherein: In step 5, the user sets (L-τ p ) symbols are allocated for uplink data transmission, and the data signals received by the mth access point from all users at the tth symbol are: Among them, λ≤t≤L, the superscript d indicates that the current signal is a data signal, p k is the uplink data transmission power of the kth user, And X d The elements in (t) are independent of each other, that is, and E means seeking expectation; Using the maximum ratio combining method, each access point uses the maximum ratio combining MRC coefficient Process the received data signal; the mth access point preprocesses the data signals of all users at the tth symbol, and the expression of the preprocessed signal is: in, represents the transpose of the estimated channel coefficient vector between the mth access point and all users at symbol index λ.

5. The method for controlling uplink power of a cell-free massive MIMO network supporting URLLC according to claim 1, wherein: In step 6, each access point transmits the pre-processed signal to the central processor via the backhaul link, and the central processor then performs joint decoding. The user signal of the k-th user at the t-th symbol obtained by decoding in the central processor is: Among them, each δ m,k The value of (t) is equal to and is the inverse of the number of access points; DS k,t represents the expected signal of the kth user at the tth symbol, LS k,t represents the leakage signal of the kth user at the tth symbol, CA k,t represents the channel aging effect of the kth user at the tth symbol, UI k,i,t represents the inter-user interference of the kth user at the tth symbol, ZN k,t represents the additive white Gaussian noise of the k-th user at the t-th symbol.

6. The method for controlling uplink power of a cell-free massive MIMO network supporting URLLC according to claim 1, wherein: In step 7, the signal-to-noise ratio expression of the k-th user at the t-th symbol is: Where δ is the coefficient of large-scale fading decoding, is an M-dimensional complex vector, tr(Q) means finding the trace of the matrix Q, diag(.) means extracting the vector composed of the elements on the main diagonal of the matrix, Indicates the definition of the equal sign; Under short packet transmission, the uplink achievable data rate of the kth user at the tth symbol is expressed as follows: Wherein, η represents the ratio of the pilot sequence length to the length of the short data packet, L represents the length of a short data packet, ε k represents the decoding error probability.

7. The method for controlling uplink power of a cell-free massive MIMO network supporting URLLC according to claim 1, wherein: In step 8, the weighted sum rate maximization problem P1 is expressed as follows: Among them, R k (t) is the uplink achievable data rate of the k-th user at the t-th symbol; w k represents the weight assigned to the k-th user; In step 9, the weighted sum rate maximization problem P1 is transformed into the weighted sum rate maximization problem P2, which is expressed as follows: in, Among them, χ k (t) represents an auxiliary variable, represents the inverse of the function, is the achievable rate threshold for each user, is the maximum transmit power of each user.

8. The method for controlling uplink power of a cell-free massive MIMO network supporting URLLC according to claim 1, wherein: In step 10, by analyzing the properties of the objective function in the weighted sum rate maximization problem P2 and introducing two approximate functions, the weighted sum rate maximization problem P2 is transformed into a series of sub-problems; The expressions of the two approximate functions are ln(1+z)≥a ln(z)+b and in, z represents a variable; Based on the above two approximate functions, the lower bound of the objective function of the weighted sum rate maximization problem P2, that is, the expression of a series of sub-problems, is obtained as follows: According to the properties of the logarithmic function, the expression of the geometric programming problem P3 to be solved in the i-th iteration is as follows: in, The superscript i indicates the number of iterations.

9. The method for controlling uplink power of a cell-free massive MIMO network supporting URLLC according to claim 8, wherein: In step 11, the geometric programming problem P3 is solved by using the continuous convex optimization iteration method. Before the alternating iterative solution, the auxiliary variable If and only if When is always greater than or equal to 1, the initial feasible solution of the user's transmit power is obtained by solving problem P4, which is expressed as: Solving problem P4, the initial feasible solution for the user's transmission power is: Then the geometric programming problem P3 is solved by continuous convex optimization iteration method.

10. The method for controlling uplink power of a cell-free massive MIMO network supporting URLLC according to claim 9, wherein: The geometric programming problem P3 is solved by continuous convex optimization iteration method. The specific steps are as follows: Step A1: Initialization: number of iterations i = 1, error tolerance And the objective function Obj of P1 (0) ; Step A2: Given and Calculated using the CVX toolkit and Step A3: Obtained from step A2 To update Calculate Obj (i) ; Step A4: When When , update i = i + 1 and return to step 2; otherwise, end and output the local optimal solution of the user's weighted sum rate maximization problem.

Images