A Cell-Free Massive MIMO Resource Allocation Method

Abstract

This invention discloses a non-cellular massive MIMO resource allocation method. By introducing a parameter representing AP selection, AP selection and downlink power are jointly optimized. Both downlink data power allocation and uplink pilot power control utilize the Lagrange dual function method, which imposes minimal restrictions on the objective function characteristics and offers a low solution difficulty. In summary, the invention simultaneously solves for AP selection and downlink data power allocation with the goal of maximizing user sum and rate, and further improves user sum and rate through uplink pilot power control.

Description

Technical Field

[0001] The present invention relates to the field of network communication technology, and in particular to a cell-free large-scale MIMO resource allocation method based on Lagrangian dual gradient descent. Background Art

[0002] In the 4G era and earlier, due to the low density of base stations and users, edge effects were not the primary factor limiting network performance. However, as base station / access point density increases (the distance between base stations in 5G has been reduced to tens of meters), the trend of intensified wireless communications will lead to more inter-cell interference, and edge effects will become a bottleneck limiting future network performance. De-cellularization is an inevitable trend in the evolution of access network architecture.

[0003] Cell-free massive multiple-input multiple-output (MIMO) is a new network architecture that aligns with the decellularization trend of access networks. This system deploys a large number of access points (APs) distributed throughout the service area, using the same time-frequency resources to serve a far smaller number of user equipment (UE) than the total number of antennas in the system. The concept of cells is eliminated within the service area, eliminating inter-cell interference and handover issues. The antennas distributed across each AP significantly reduce the average distance between the AP and the user, significantly improving the system's macrodiversity gain. Furthermore, each AP is connected to the central processing unit (CPU) via a fronthaul link, enabling joint signal processing to achieve additional signal processing gain. Despite the large number of antennas, channel hardening still exists in cell-free massive MIMO. Depending on whether the uplink and downlink are separated in time or frequency, cell-free massive MIMO systems can operate in time-division duplex (TDD) or frequency-division duplex (FDD) mode.

[0004] Cell-Free Massive MIMO (CF mMIMO) combines the characteristics of massive MIMO and distributed antenna systems, can simultaneously obtain the gains of both systems, and provides users in the service area with impressive performance and wide coverage based on simple signal processing technology. It is a promising network architecture.

[0005] However, in a non-cellular massive MIMO system, there are many APs and they are widely distributed. In the traditional fully connected mode (each user is served by all APs), there will be some inefficient connections. These connections contribute little to the desired signal and bring strong inter-user interference, affecting the overall performance of the system.

[0006] On the other hand, uplink power control and downlink power allocation are key technologies for overcoming the near-far effect, reducing inter-user interference, and improving system performance. Power control / allocation should aim to optimize a system-wide utility function. While downlink data power allocation is a well-studied problem in centralized massive MIMO systems, the situation is quite different in cell-free massive MIMO due to the larger number of optimization variables and their tight coupling, resulting in a fundamentally different problem structure. Regarding AP selection and downlink data power allocation, existing solutions either first determine the UE-AP connection relationship based on certain criteria and then allocate downlink data power based on this relationship; or, in fully connected scenarios, first determine the downlink data power allocation scheme based on certain criteria and then disconnect certain UE-AP connections based on this power allocation scheme according to certain criteria. Because step-by-step optimization cannot achieve the optimal solution for the given goal, system performance is compromised.

[0007] Furthermore, in cell-free massive MIMO systems, the AP serves a large number of users, but due to the limited coherence time of the channel, the system can only provide a limited number of orthogonal pilot resources. This inevitably causes different users to reuse the same pilots, resulting in pilot contamination and inaccurate channel estimation between users and the AP. Existing technologies focus on allocating orthogonal pilots to reduce pilot contamination, while ignoring the role of uplink pilot power control in suppressing pilot contamination. Furthermore, existing downlink data power allocation schemes are often modeled as convex optimization problems with a given objective. Due to the large number of users and access points in cell-free massive MIMO systems, the computational complexity of convex optimization algorithms is very high.

[0008] Based on the above analysis, we propose a transmission scheme for joint AP selection and downlink data power allocation based on the Lagrangian dual function. Combined with the proposed uplink pilot power control scheme based on the Lagrangian dual function, the system spectral efficiency is optimized. Summary of the Invention

[0009] In view of the existing deficiencies, the present invention proposes a non-cellular large-scale MIMO resource allocation method.

[0010] In order to achieve the above object, the present invention provides the following technical solutions:

[0011] A non-cellular massive MIMO resource allocation method, wherein before AP selection and downlink data power allocation, τ is allocated to K users. p orthogonal pilots; the AP selection and downlink data power allocation process aims to maximize the user and rate, and introduces a continuous variable {c mk} is used to characterize the connection relationship between UE and AP, and the AP selection and downlink data power allocation are jointly optimized. The Lagrangian dual gradient descent method is used to solve the problem, and the AP selection scheme {c mk} and downlink data power allocation scheme {p mk The uplink pilot power control process aims to maximize the sum of the variances of all user channel estimates. The uplink pilot power coefficient is solved based on the Lagrangian dual gradient descent method to obtain the uplink pilot power control scheme {p k}.

[0012] Furthermore, the user and rate are related to the UE-AP connection {c mk} and downlink data power {p mk The function expression of} is as follows:

[0013]

[0014] in, is the variance of the additive Gaussian noise in the uplink channel, {p mk} is the downlink data power, {c mk} is the characterization quantity of the UE-AP connection relationship, {γ mk} is the variance of the channel estimate, which is only related to the user pilot power control coefficient {p k} is related to the pilot allocation result, and the calculation formula is as follows:

[0015]

[0016] in, is the channel model between AP and UE, τ p is the length of the pilot sequence, p k is the pilot power sent by the kth user, β mk is the large-scale fading coefficient.

[0017] Furthermore, the following constraints are applied when jointly optimizing AP selection and downlink data power allocation:

[0018]

[0019]

[0020]

[0021]

[0022] Taking 0.5 as the hard threshold, the continuous variables {c mk} is set to 1, indicating that a UE-AP connection is established. mk}The result remains unchanged; the {c mk} is set to 0, indicating that the UE-AP connection is disconnected. mk}The result is also set to 0.

[0023] Furthermore, the following constraints are applied when jointly optimizing AP selection and downlink data power allocation:

[0024]

[0025]

[0026]

[0027]

[0028]

[0029] Taking advantage of the fact that the sine function takes on the value of zero at integer multiples of π, the continuous variable {c mk} is directly restricted to 0-1 variables.

[0030] Furthermore, the objective function of the uplink pilot power control process is:

[0031]

[0032] Constraints:

[0033]

[0034]

[0035] Among them, p ulnk is the power used by each user to send the pilot when performing average uplink pilot power control, {γ mk} is the variance of the channel estimate, which is only related to the user pilot power control coefficient {p k} is related to the pilot allocation result, and the calculation formula is as follows:

[0036]

[0037] in, is the channel model between AP and UE, τ p is the length of the pilot sequence, pk is the pilot power sent by the kth user, β mk is the large-scale fading coefficient.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] First, the proposed method for cellular-free massive MIMO resource allocation introduces a parameter representing AP selection. Based on the Lagrange dual function method, it designs a transmission scheme that combines AP selection with downlink data power allocation. This method selects the appropriate serving AP for each user and allocates power for the AP to transmit downlink data. Compared to previous step-by-step optimization methods based on convex optimization, the proposed method imposes fewer restrictions on the optimization objective function and simplifies the solution. This not only compensates for the performance loss caused by the step-by-step solution, but also reduces the computational complexity and eases the solution. Simulations have demonstrated that the proposed method for combining AP selection with downlink data power allocation can further improve user and data rates.

[0040] Secondly, existing solutions for uplink pilot power control typically transform the original non-convex problem into a convex one before solving it. This transformation requires considerable skill and difficulty. This method, based on the Lagrangian dual function, solves the uplink pilot power control coefficient with the goal of maximizing the sum of the system channel estimate variances. This overcomes this problem and allocates appropriate power to user uplink pilots. This further improves the system's spectral efficiency compared to using equal power for uplink pilots. Simulations demonstrate that incorporating uplink pilot power control further improves the sum of users and rates.

[0041] In summary, the method of the present invention introduces a parameter representing AP selection to jointly optimize AP selection and downlink power. The proposed uplink pilot power control method further suppresses pilot contamination, improving system performance. Both downlink data power allocation and uplink pilot power control utilize the Lagrange dual function method, which imposes minimal constraints on the objective function characteristics and offers a low solution complexity. With the goal of maximizing user sum and rate, the method simultaneously solves for AP selection and downlink data power allocation, and further improves user sum and rate through uplink pilot power control. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments described in the present invention. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0043] Figure 1 Transmission block diagram of a cell-free massive MIMO system.

[0044] Figure 2The flowchart of the joint AP selection and downlink data power allocation scheme based on Lagrangian duality is shown in Figure 2.

[0045] Figure 3 Compare the results of users and rates for different plans.

[0046] Figure 4 This is the result of further improving the uplink pilot power control and rate. DETAILED DESCRIPTION

[0047] In order to better understand the present technical solution, the method of the present invention is described in detail below with reference to the accompanying drawings.

[0048] The application scenario of the present invention is a user-centric non-cellular massive MIMO system. The system transmission block diagram is as follows: Figure 1 As shown. The technology of the present invention is implemented in TDD mode. Due to the channel reciprocity during bidirectional transmission within the same frequency band, downlink precoding can be performed based on the channel state information (CSI) obtained from sending the uplink pilot. The signaling overhead varies only with the number of service terminals and is independent of the number of APs. The present invention proposes a transmission scheme for joint AP selection and downlink data power allocation based on Lagrangian dual function, and optimizes the uplink pilot power using the Lagrangian dual gradient descent method to further suppress pilot pollution and improve user sum rate. The algorithm is executed by the CPU.

[0049] 1. System Model

[0050] We consider a CF mMIMO network consisting of M multi-antenna APs and K single-antenna UEs, randomly distributed in a square area with a side length of D, and each AP is equipped with N antennas.

[0051] The central processing unit is connected to all APs through a perfect fronthaul link. The system adopts TDD mode. A wireless frame consists of a length of τ p The uplink pilot training phase has a length of τ u The uplink data transmission phase and the length of τ d We use the block fading channel model, where τ c is the length of the channel coherence time and satisfies τ p +τ d +τ u <τ c Since this paper discusses the optimization of downlink data power allocation, the uplink data transmission phase is not elaborated in detail.

[0052] The channel model, uplink pilot training phase, and downlink data transmission phase are introduced below.

[0053] 1.1 Channel Model

[0054] Channel model between AP and UE:

[0055]

[0056] where β mk is the large-scale fading coefficient, which is related to path loss and shadow fading channel. It can be calculated as follows based on the 3GPP urban micro-cell model:

[0057] β mk =-30.5-36.7log 10 (d mk / 1m)+z mk (2)

[0058] where z m k Represents shadow fading, obeying Gaussian distribution a m Used to represent the shadow fading caused by obstacles around the m-th AP, b k Used to represent the shadow fading caused by obstacles around the k-th UE. This means that shadow fading is correlated. This is because the closer the distance between two transmitters (or receivers), the more likely they are to experience some common propagation paths or obstacles, and the stronger the correlation of their shadow fading will be. m k is the small-scale fading characteristic of the channel and is a complex Gaussian random variable that obeys independent and identical distribution. so

[0059] 1.2 Uplink Pilot Training and Channel Estimation

[0060] The pilot signal received by the mth AP is:

[0061]

[0062] N is the number of antennas configured for each AP, τ p is the length of the pilot sequence, p k is the pilot power sent by the kth user, is additive noise that follows a complex Gaussian distribution, is the pilot sequence sent by the kth user, satisfying

[0063]

[0064] represents the set of users that use the same pilot as user k.

[0065]

[0066] This is because when pilot resources are limited, different users reuse pilots to cause pollution. Using MMSE for channel estimation, we get:

[0067]

[0068] is the additive Gaussian noise variance of the uplink channel, Variance of:

[0069]

[0070] 1.3 Downlink Data Transmission

[0071] The transmitted signal at the mth AP is:

[0072]

[0073] The signal received by the kth user is:

[0074]

[0075] represents the set of APs serving k-th, Represents the set of users served by the m-th AP. Using MRT precoding, the precoding vector is r k can be written as:

[0076]

[0077] Using the derivation process of ergodic capacity, the lower bound of the ergodic channel capacity under the unit bandwidth of the kth user is obtained as:

[0078]

[0079] 2. Joint AP selection and downlink data power allocation scheme based on Lagrangian duality

[0080] Before AP selection and downlink data power allocation, first allocate τ to K users. p Orthogonal pilots. Define users and rates:

[0081]

[0082] The Lagrange dual function method is used to solve the objective function of the user sum rate maximization problem:

[0083]

[0084] Among them, the optimization variable is the downlink power {p mk} and UE-AP association characterization {c mk}. The constraints are:

[0085]

[0086]

[0087]

[0088]

[0089] Introducing the Lagrange multiplier λ mk ,λ m ,μ mk ,ν mk ≥0,k=1,...,K,m=1,...,M, construct the Lagrangian function:

[0090]

[0091] The original problem can be expressed as:

[0092]

[0093] stλ mk ,λ m ,μ mk ,ν mk ≥0. (16)

[0094] Prove that the combination of (13) and (14) is equivalent to (16):

[0095]

[0096]

[0097] Furthermore, the Lagrange dual function can be expressed as follows:

[0098]

[0099] The dual problem of the original problem can be expressed as:

[0100]

[0101] stλ mk ,λ m ,μ mk ,ν mk≥0.(18)

[0102] Further (18) is expressed as:

[0103]

[0104]

[0105]

[0106] λ mk ,λ m ,μ mk ,ν mk ≥0. (19)

[0107] In order to express more clearly and concisely,

[0108] g mk (p mk )=-p mk ,m=1,...,M,k=1,...,K,

[0109]

[0110] r mk (c mk )=-c mk ,m=1,...,M,k=1,...,K,

[0111] f mk (c mk )=c mk -1,m=1,...,M,k=1,...,K. (20)

[0112] From the characteristics of the dual problem, we can see that no matter whether the original problem is a convex problem or not, as long as it is converted into a dual problem, the dual problem must be a convex optimization problem. The proof is as follows:

[0113]

[0114] in, They represent the Lagrangian function as p mk ,c mk is the value of the variable when it reaches its minimum value. From formula (21), we can see that g(λ mk ,λ m ,μ mk ,ν mk ) is about λ mk ,λ m ,μ mk ,ν mkThe linear function of can be regarded as both a convex function and a concave function. Since the dual problem is to find the maximum value of the function, we can take g(λ mk ,λ m ,μ mk ,ν mk ) is considered as mk ,λ m ,μ mk ,ν mk Concave function. And because the constraint of the dual problem is λ mk ,λ m ,μ mk ,ν mk ≥0, we know that the intersection of half spaces is a convex set. So the dual problem is a convex optimization problem.

[0115] According to KKT conditions:

[0116]

[0117]

[0118]

[0119] Solving parametric equations using MATLAB under a fixed set of Lagrange multipliers

[0120]

[0121] The downlink data power allocation scheme p can be obtained m k and AP selection scheme c m k Next, we use the gradient descent method to update the Lagrange multiplier:

[0122]

[0123]

[0124]

[0125]

[0126] in,

[0127]

[0128]

[0129]

[0130]

[0131] is the iteration step of the Lagrange multiplier in the nth iteration. Afterwards, the updated Lagrange multiplier is substituted back into (23) to update the downlink data power allocation and AP selection. The above process is repeated until Or the maximum number of cycles N is reached I The algorithm flow is as follows: Figure 2 shown.

[0132] Get {c mk}, 0.5 is used as the hard threshold, and {c mk} is set to 1, indicating that a UE-AP connection is established. mk}The result remains unchanged; the {c mk} is set to 0, indicating that the UE-AP connection is disconnected. mk}The result is also set to 0.

[0133] In the comparison scheme, we use the fact that the sine function takes zero value at integer multiples of π to convert {c mk} is directly restricted to a 0-1 variable. The specific approach is to add the restriction condition in (14):

[0134]

[0135] In addition, we also compared the full connection scheme using the same downlink power, the scheme using the same downlink power and AP selection based on large-scale fading coefficients, the scheme using partial power allocation and AP selection based on large-scale fading coefficients, the scheme using max-min power allocation and AP selection based on large-scale fading coefficients, and the scheme using {c mk} is a continuous variable on [0,1] to maximize the fully connected solution of users and rate. Figure 3 The comparison of user and rate performance of different schemes under the parameters listed in Table 1 is shown.

[0136] Table 1

[0137]

[0138] 3. Uplink pilot power control scheme based on Lagrange dual function

[0139] Objective function:

[0140]

[0141] Constraints:

[0142]

[0143]

[0144] Among them, p u l n k is the power used by each user to send the pilot signal when performing average uplink pilot power control. The Lagrange multiplier λ, {μ k}, construct the Lagrangian function:

[0145]

[0146] The original problem can be expressed as:

[0147]

[0148]

[0149] Furthermore, the Lagrange dual function can be expressed as follows:

[0150]

[0151] The dual problem of the original problem (30) can be expressed as:

[0152]

[0153] stλ,{μ k}≥0. (32)

[0154] Further (32) is expressed as:

[0155]

[0156]

[0157] λ,{μ k}≥0. (33)

[0158] In order to express more clearly and concisely,

[0159]

[0160] s k (p k )=-p k ,k=1,...,K,34

[0161] According to KKT conditions:

[0162] Feasibility conditions of the original problem

[0163] Dual feasibility conditions

[0164] Complementary slack conditions (35)

[0166] Under a fixed set of Lagrange multipliers, use MATLAB to solve the parametric equation:

[0167]

[0168] The uplink pilot power control scheme {p k}.

[0169] Next, the Lagrange multiplier is updated using the gradient descent method:

[0170]

[0171]

[0172] in,

[0173]

[0174]

[0175] is the iteration step size of the Lagrange multiplier in the nth iteration. Then, the updated Lagrange multiplier is substituted back into (36) to update the uplink pilot power control coefficient {p k Repeat the above process until Or the maximum number of cycles is reached. Get the uplink pilot power control coefficient {p k}, then resubstitute into (12) to calculate the user and rate. Figure 4 The figure shows the system performance and rate improvement after adding uplink pilot power control under the parameters listed in Table 2.

[0176] Table 2

[0177]

[0178] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A non-cellular massive MIMO resource allocation method, including AP selection and downlink data power allocation process and uplink pilot power control process, characterized in that: Before AP selection and downlink data power allocation, allocate τ to K users. p orthogonal pilots; the AP selection and downlink data power allocation process aims to maximize the user and rate, and introduces a continuous variable {c mk } is used to characterize the connection relationship between UE and AP, and the AP selection and downlink data power allocation are jointly optimized. The Lagrangian dual gradient descent method is used to solve the problem, and the AP selection scheme {c mk } and downlink data power allocation scheme {p mk The uplink pilot power control process aims to maximize the sum of the variances of all user channel estimates. The uplink pilot power coefficient is solved based on the Lagrangian dual gradient descent method to obtain the uplink pilot power control scheme {p k }; Users and Rates About UE-AP Connections {c mk } and downlink data power {p mk The function expression of} is as follows: in, is the variance of the additive Gaussian noise in the uplink channel, {p mk } is the downlink data power, {c mk } is the characterization quantity of the UE-AP connection relationship, {γ mk } is the variance of the channel estimate, which is only related to the user pilot power control coefficient {p k } is related to the pilot allocation result, and the calculation formula is as follows: in, is the channel model between AP and UE, τ p is the length of the pilot sequence, p k is the pilot power sent by the kth user, β mk is the large-scale fading coefficient.

2. The method for allocating non-cellular massive MIMO resources according to claim 1, wherein: The following constraints are used when jointly optimizing AP selection and downlink data power allocation: Taking 0.5 as the hard threshold, the continuous variables {c mk } is set to 1, indicating that a UE-AP connection is established. mk }The result remains unchanged; the {c mk } is set to 0, indicating that the UE-AP connection is disconnected. mk }The result is also set to 0.

3. The method for allocating non-cellular massive MIMO resources according to claim 1, wherein: The following constraints are used when jointly optimizing AP selection and downlink data power allocation: Taking advantage of the fact that the sine function takes on the value of zero at integer multiples of π, the continuous variable {c mk } is directly restricted to 0-1 variables.

4. The method for allocating cellular-free massive MIMO resources according to claim 1, wherein: The objective function of the uplink pilot power control process is: Constraints: Among them, p ulnk is the power used by each user to send the pilot when performing average uplink pilot power control, {γ mk } is the variance of the channel estimate, which is only related to the user pilot power control coefficient {p k } is related to the pilot allocation result, and the calculation formula is as follows: in, is the channel model between AP and UE, τ p is the length of the pilot sequence, p k is the pilot power sent by the kth user, β mk is the large-scale fading coefficient.

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