Energy efficiency optimization method for multi-carrier NOMA system under non-ideal CSI and hardware impairment conditions

Abstract

The present invention claims protection for a method for optimizing the energy efficiency of a multi-carrier NOMA system under non-ideal CSI and hardware damage conditions, and relates to the technical field of wireless communication resource management. It includes: setting a user number threshold on each subcarrier, establishing a non-convex nonlinear two-layer optimization problem, finding the lower bound of the inner minimization problem by the worst-case analysis method, and converting the outer maximization problem into an optimization problem about the user rate by rewriting the power into the form of user rate, using fast dynamic resource allocation (FDRA) to determine the subcarrier allocation matrix, and then introducing new constraints to transform the problem into a convex optimization problem for solution. The present invention quickly converges to the performance of the resource allocation method based on maximizing the minimum user energy efficiency, and can significantly improve the overall energy efficiency of the system under conditions of non-ideal CSI and RHIs, with strong practicality and fairness.

Description

Technical Field

[0001] The present invention relates to the technical field of wireless communication resource management, and in particular to an energy efficiency optimization algorithm for a multi-carrier non-orthogonal multiple access (NOMA) system under conditions of non-ideal channel state information (CSI) and hardware impairment. Background Art

[0002] The 5G era is accelerating, and 5G networks have become a part of our lives. However, high energy consumption and spectrum scarcity remain prominent challenges. Therefore, research on efficient resource allocation algorithms for non-orthogonal multiple access (NOMA) systems to improve system performance is urgent. Compared to single-carrier NOMA systems, multi-carrier NOMA systems support more users, achieve higher spectrum efficiency, and are more robust against frequency-selective fading. Consequently, multi-carrier NOMA systems have become a research hotspot in next-generation wireless network access technologies.

[0003] After searching the prior art, Zhu Zhengyu, Lu Yapei, Wang Zixuan and others disclosed "A multi-carrier NOMA resource allocation method" in 2021, which maximizes the system sum rate under the conditions of ensuring the minimum data rate and the total base station transmission power limit under the service quality constraints of all system access users. Pan Peisheng and Han Wenhao disclosed "A multi-carrier NOMA resource allocation method and device" in 2020, calculated the optimal power allocation scheme on each subcarrier, and improved the total transmission rate of the system. In 2018, Sun Y, Ng DWK, Zhu J and others published a paper entitled "Robust and Secure Resource Allocation for Full-Duplex MISO Multicarrier NOMA Systems" in IEEE T.COMMUN., which considered the use of a full-duplex base station in a multiple-input single-output multicarrier non-orthogonal multiple access system to simultaneously provide services to multiple half-duplex uplink and downlink users on the same subcarrier, and optimize resource allocation to maximize the weighted system throughput. Zeng M, Nguyen NP, Dobre OA, et al., in their 2019 paper “Spectral-and Energy-Efficient Resource Allocation for Multi-Carrier Uplink NOMA Systems,” published in IEEE T.VEH.TECHNOL., considered the resource allocation problem of multi-carrier uplink non-orthogonal multiple access systems and proposed the system sum rate maximization problem.

[0004] As can be seen from the aforementioned studies, existing research on multicarrier NOMA systems has primarily focused on outage probability, throughput, and user fairness, while energy-efficiency-based resource allocation has been largely unexplored. Furthermore, existing studies have primarily considered ideal hardware scenarios. However, in practical communication systems, to control costs and achieve low-power communication, the hardware precision of each communication node is limited, making the entire system susceptible to numerous factors. Although existing studies have proposed calibration or compensation algorithms to mitigate these effects, due to non-ideal compensation schemes and the inherent time-invariance of hardware, residual hardware impairments (i.e., residual impairments of communication nodes after algorithmic compensation) still exist. These impairments can arise from nonlinear distortion of the transmitter amplifier, in-phase / quadrature-phase imbalance (IQI), and carrier frequency offset at the receiver, which also have a certain impact on system performance. Supported by existing research and experimental verification, this effect can be quantified and modeled as a form of distortion noise. In practical communications, the effects of distortion noise can lead to a non-ideal system state, namely, residual hardware impairments (RHIs). To realize the practical application of energy efficiency optimization algorithms for multi-carrier NOMA systems, it is necessary to study these algorithms under hardware impairment conditions. Furthermore, in real-world channel environments, channel state information (CSI) is affected by channel estimation errors, channel feedback errors, and quantization errors. Ideal CSI is also difficult to obtain in actual communications, and the actual situation is non-ideal. Therefore, energy efficiency optimization algorithms for multi-carrier NOMA systems that jointly consider non-ideal CSI and system RHIs have great theoretical and practical significance.

[0005] This paper proposes an energy efficiency optimization algorithm for a multi-carrier NOMA system under non-ideal CSI and hardware damage conditions. First, a downlink multi-user multi-carrier NOMA system is established. First, the total energy efficiency maximization problem of the system is established under the joint consideration of hardware damage and non-ideal CSI conditions. Then, the original energy efficiency maximization problem is decoupled into two sub-problems: user power allocation and subcarrier allocation. The power allocation problem is converted into a convex optimization problem using the functional relationship between the user's achievable rate and power. Finally, the fast dynamic resource allocation (FDRA) method is used to obtain the optimal subcarrier allocation factor to solve the subcarrier allocation problem, and the solution to the original problem is iteratively obtained.

[0006] In 2021, Wang Zhengqiang, Du Jin, Fan Zifu and others disclosed "A method for maximizing energy efficiency of multi-carrier cooperative non-orthogonal multiple access systems", and proposed a multi-carrier NOMA system energy efficiency optimization method similar to the present invention. This invention takes into account the base station transmission power, relay transmission power and user minimum rate constraints, and maximizes the total energy efficiency of the system by controlling the base station transmission power, relay transmission power and matching factor. The difference from the present invention is that this invention does not take into account the irrational channel state information and hardware damage conditions in actual communications. Therefore, the results proposed by this invention must have errors in actual communications. Therefore, compared with the present invention, this invention cannot be directly used in actual communications and does not have the stability of the present invention when applied in actual communication scenarios. Summary of the Invention

[0007] The present invention aims to solve the above problems in the prior art. It proposes a method for optimizing the energy efficiency of a multi-carrier NOMA system under non-ideal CSI and hardware impairment conditions. The technical solution of the present invention is as follows:

[0008] A method for optimizing energy efficiency of a multi-carrier NOMA system under non-ideal CSI and hardware impairment conditions, comprising the following steps:

[0009] 101. Initialize the number of users and subcarriers, generate base station locations and user locations. The channel state information obtained by the user is non-ideal. The actual channel state information obtained by the user is derived from the estimated channel gain and estimation error. Sort the users in descending order of estimated channel gain, and consider the RHIs generated by distortion noise to establish a system model.

[0010] 102. Construct an optimization problem with the objective function of maximizing the total energy efficiency of the system. Decouple the target optimization problem into the subcarrier allocation problem and the power allocation problem. Solve the problem in layers and use the worst-case analysis method to solve the inner-layer minimization problem.

[0011] 103. For the outer maximization problem of the original optimization problem, the user power is rewritten in the form of user achievable rate, the objective function optimization object is replaced, and the fractional objective function is rewritten using the Dinkelbach method. The objective function is converted to a linear objective function, and the original optimization problem is converted to a linear optimization problem. The subcarrier allocation matrix is set to all 1s, making the objective optimization problem a convex optimization problem. The user achievable rate is then solved using the convex optimization interior point algorithm.

[0012] 104. Calculate the user rate and the benefit function of each node in the subcarrier allocation matrix, sort each subcarrier in descending order according to the benefit function, and determine whether the number of users on each subcarrier is greater than or equal to the subcarrier user number threshold. If so, eliminate an equal number of users according to the sorting based on the subcarrier user number threshold D, and update the subcarrier allocation factor matrix. Otherwise, do not update the matrix.

[0013] 105. Determine whether the number of users on each subcarrier is less than or equal to the subcarrier user number threshold. If so, output the subcarrier allocation matrix and calculate the system energy efficiency. If so, return to step 104 until the number of users on each subcarrier is less than the subcarrier user number threshold, so that the result converges to the optimal solution.

[0014] The advantages and beneficial effects of the present invention are as follows:

[0015] The present invention mainly considers the resource allocation problem based on energy efficiency in the downlink transmission multi-carrier NOMA system. A resource allocation method based on energy efficiency in the multi-carrier NOMA system considering non-ideal CSI and RHIs is proposed. This method decouples the original problem into two sub-problems: user power allocation and subcarrier allocation, and constructs a mathematical problem with maximizing the total energy efficiency of the system as the objective function. Since the objective function is nonlinear and non-convex, the present invention solves the two sub-problems by converting the functional relationship between the user's achievable rate and the allocated power and iteratively solving the two sub-problems using the FDRA algorithm. It has the characteristics of low computational complexity, high energy efficiency, and is suitable for downlink transmission multi-carrier NOMA systems.

[0016] On the basis of the existing technology, the present invention considers non-ideal CSI and residual hardware damage conditions in a multi-carrier NOMA system, and sets a user number threshold on each subcarrier to establish a non-convex nonlinear two-layer optimization problem, such as step 101 and step 102 in claim 1, and also includes the combination of claim 2 and claim 3. Existing research and inventions have not yet considered irrational CSI and hardware damage conditions in a multi-carrier NOMA system, that is, the combination of the above claims is innovative. For such an NP-hard problem as described in claim 2, the present invention optimizes and solves the original problem through the worst-case analysis method and convex optimization theory, so that the system performance far exceeds the unoptimized energy efficiency maximization baseline solution, and the FDRA algorithm is used to make the result converge quickly to the optimal value. The present invention verifies from the model level that hardware damage of the communication node and irrational CSI will reduce system performance, making the present invention more applicable to actual situations. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1The present invention provides a flow chart of an energy efficiency optimization algorithm for a multi-carrier NOMA system considering non-ideal CSI and hardware damage conditions in a preferred embodiment;

[0018] Figure 2 This is a comparative relationship diagram of the FDRA energy-efficiency resource allocation algorithm proposed in the present invention and the energy-efficiency maximization baseline algorithm under different channel estimation errors and hardware damage levels;

[0019] Figure 3 This is a comparative relationship diagram of the FDRA energy efficiency resource allocation algorithm proposed in the present invention and the energy efficiency maximization baseline algorithm under different HI conditions;

[0020] Figure 4 The maximum transmission power P of the algorithm proposed in this invention is different from that of the base station. max The total energy efficiency convergence speed of the system under

[0021] Figure 5 This is a comparative relationship diagram of the FDRA-based energy-efficiency resource allocation algorithm proposed in the present invention and the energy-efficiency maximization baseline algorithm under different non-ideal channel estimation error upper bounds. DETAILED DESCRIPTION

[0022] The following will describe the technical solutions in the embodiments of the present invention in detail with reference to the accompanying drawings. The described embodiments are only a part of the embodiments of the present invention.

[0023] The technical solution of the present invention to solve the above technical problems is:

[0024] This implementation case is an energy-efficiency-based resource allocation method for a downlink multi-carrier NOMA system considering non-ideal CSI and RHIs conditions.

[0025] The specific implementation cases are as follows:

[0026] In the first step, the number of users is initialized to K, the number of subcarriers is N, the user set of the kth user is: k∈{1,2,…,K}, and the subcarrier set of the nth subcarrier is: C∈{C1,C2,…,C N For subcarrier C n The channel gain of the kth user on can be expressed as: in, represents the Rayleigh fading coefficient, d k represents the distance from the kth user to the base station, and α represents the path fading coefficient. Considering the non-ideal channel, the real channel gain is modeled as: in, Denotes the estimated channel gain, Δh k，nDenotes the estimated channel error. The SIC decoding sequence uses the following estimated channel gain instead: π(k) is the corresponding index of the decoding order of user k. The set of estimated channel errors is expressed as: Subcarrier C n The received signal of the kth user on is: Among them, η n Represents the system aggregate distortion noise, satisfying The system hardware damage level is evaluated, which represents the total distortion power received by the receiver, w π(k)，n Represents additive white Gaussian noise (AWGN). After the user decodes his own signal through SIC and eliminates the interference between users according to the channel sorting, the user k can be placed on the subcarrier C n The SINRs on are expressed as: in, represents the aggregate interference from other users, including strong user interference that cannot be eliminated by SIC and estimated channel error interference from non-ideal channels. According to Shannon’s formula, user k has n The achievable rate on is expressed as: R π(k)，n =log2(1+γ π(k)，n ). Accumulating all users on all subcarriers, the system achievable sum rate is expressed as:

[0027] In the second step, assume that the system has a fixed circuit power loss of P c , so the system energy efficiency can be expressed as: The minimum energy efficiency maximization problem is decoupled into an optimization problem regarding subcarrier allocation and power allocation. The target problem is divided into two layers. The internal layer is the minimization problem regarding the estimation error, and the outer layer is the maximization problem regarding the decoupled sub-problems of the original problem, namely subcarrier allocation and power allocation. For the number of users on the same subcarrier, due to hardware limitations and too many users on the same subcarrier leading to reduced decoding efficiency at the receiving end, the SIC algorithm has high complexity. Therefore, a threshold D for the number of users needs to be set on each subcarrier. The number of users on any subcarrier cannot exceed this limit. Under a series of constraints, the energy efficiency optimization problem of the multi-carrier NOMA system under non-ideal CSI and hardware damage conditions is established as:

[0028]

[0029]

[0030]

[0031]

[0032]

[0033] C5:R π(k)，n ≥R min ,ρ π(k)，n =1

[0034]

[0035] Among them, P max Indicates the maximum system power, R t represents the minimum user rate, D represents the maximum number of users that can be accommodated on subcarrier n, and R min Indicates the minimum rate requirement on subcarrier n when user k accesses the subcarrier, Δh π(k)，n represents the channel estimation error, Represents a set of estimated error values. Constraint C1 represents the total system power constraint, constraint C2 is the user minimum rate constraint, constraint C3 represents the maximum number of users on a single subcarrier, indicating that up to D users can be multiplexed to the same subcarrier, C4 represents the subcarrier selection factor constraint, and C5 represents the minimum rate limit of the selected user on the subcarrier. If the channel condition of the node does not support the minimum rate R min , the node will also be discarded because it cannot complete the decoding of the SIC algorithm. C6 represents the channel estimation error set, which is also the upper bound constraint of the channel estimation error.

[0036] The third step is about user rate R π(k)，n The minimization problem can be expressed as:

[0037]

[0038]

[0039] For this problem, the following inequality relationship can be derived:

[0040]

[0041] in Therefore, the minimum rate of user k on subcarrier n can be obtained:

[0042]

[0043] Through the above derivation, the inner layer minimization problem of the original problem is solved, and the following deterministic energy efficiency optimization problem can be obtained:

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050] In the fourth step, based on the Dinkelbach method, the objective function of the above optimization problem can be rewritten into the following subtraction function form f(η) through fractional programming:

[0051]

[0052] Among them, function η represents the system energy efficiency value, η * The system has the best energy efficiency if and only if η=η * When , the formula satisfies f(η)=0.

[0053] According to the system model, user k is on subcarrier C n By changing the independent variables and function positions, we can obtain the accessible rate of p in the matrix F. π(k),n The expression:

[0054]

[0055] According to the above formula, the total power expression of the user on a single subcarrier can be obtained as:

[0056]

[0057] Assumptions as well as So in subcarrier C n The total power of all users on the network is: Assume that when j>K, S j,n =0 and G j,n =1. So the above formula can be rewritten as follows:

[0058]

[0059] Multiply both sides of the above equation by The following formula can be obtained:

[0060]

[0061] By recursive method, we can get:

[0062]

[0063] in, It is represented as a constant part without variables. In summary, we can get the subcarrier C n The total power expression of all users on (1≤n≤N):

[0064]

[0065] So the total system power is:

[0066]

[0067] For a given subcarrier allocation matrix F, the optimization problem can be updated as follows:

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074] because It's about The problem is still non-convex. According to the objective function of the above problem, the function is about the variable It is a monotonically decreasing function of , so when resource allocation is not optimal, there is a fifth step.

[0075] Step 5: For subcarrier C n Total power of all users The power obtained can be made less than or equal to As shown in the following formula:

[0076]

[0077] This formula can be understood as follows: when resource allocation reaches the optimal level, the inequality takes the equal sign; when resource allocation has not yet reached the optimal level, the obtained subcarrier C n The total power on Therefore, the above formula always holds true under the constraints of the above optimization problem. Introducing this inequality as a new constraint into the above optimization problem, the new optimization problem can be expressed as:

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085] This issue has been added constraint The newly added subcarrier C n The total power constraint on the power grid is given in the following text, and its role will be described in detail through the transformation of the following inequality.

[0086] Through mathematical transformation, we can get the following formula:

[0087]

[0088] make as well as Take the log function on both sides of the inequality sign, so the above formula can be written as:

[0089]

[0090] Therefore, the target optimization problem can be transformed into:

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098] At this point, since the log function must be convex, it is a convex function, so this problem is a convex optimization problem. When F is determined, it can be solved by the interior point method. Finally, we can obtain the closed-form solution of power:

[0099]

[0100] Therefore, given the subcarrier allocation matrix F, the user allocated power p π(k),n It can be obtained according to the above formula.

[0101] In this embodiment, Figure 2 The comparison diagram of the proposed FDRA-based energy efficiency resource allocation algorithm and the energy efficiency maximization baseline algorithm under different channel estimation errors and hardware damage levels is given. Figure 2 It can be seen that the total system energy efficiency of the proposed algorithm is superior to that of the comparison algorithm in all dimensions. Moreover, when considering different channel estimation errors and hardware damage levels, it can be seen that the energy efficiency is lower than that of the ideal channel and ideal hardware conditions when considering two interferences. Figure 3 The comparison diagram of the proposed FDRA-based energy efficiency resource allocation algorithm and the energy efficiency maximization baseline algorithm under different HI conditions is given. Figure 3 It can be seen that for both the proposed algorithm and the comparison algorithm, the total system energy efficiency is always a monotonically decreasing function of the upper bound ε of the non-ideal channel estimation error. The proposed algorithm outperforms the comparison algorithm due to its better resource allocation scheme. As the hardware damage level increases, the system energy efficiency also decreases, indicating that hardware damage has a negative impact on the total system energy efficiency. Figure 4 The proposed algorithm is given at different base station maximum transmission power P max The total energy efficiency convergence speed of the system under Figure 4 It can be seen that as the maximum transmission power of the base station P max As increases, the total energy efficiency of the system increases, and the energy efficiency converges after 5 iterations to obtain the optimal energy efficiency value; Figure 5 The comparison diagram of the proposed FDRA-based energy-efficient resource allocation algorithm and the energy-efficient maximization baseline algorithm under different non-ideal channel estimation error upper bounds is given. Figure 5 It can be seen that the proposed algorithm has better system overall energy efficiency than the comparison algorithm under the joint consideration of hardware damage and non-ideal channel conditions.

[0102] It should also be noted that the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, commodity, or apparatus that includes a series of elements includes not only those elements but also other elements not explicitly listed, or includes elements inherent to such process, method, commodity, or apparatus. In the absence of further limitations, an element defined by the phrase "comprises a ..." does not exclude the presence of other identical elements in the process, method, commodity, or apparatus that includes the element.

[0103] The above embodiments should be understood as merely illustrating the present invention and not as limiting the scope of protection of the present invention. After reading the contents of the present invention, technicians may make various changes or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A method for optimizing energy efficiency of a multi-carrier NOMA system under non-ideal CSI and hardware impairment conditions, characterized in that: The following steps are involved:

101. Initialize the number of users and subcarriers, generate base station locations and user locations. The channel state information obtained by the user is non-ideal. The actual channel state information obtained by the user is derived from the estimated channel gain and estimation error. Sort the users in descending order of estimated channel gain, and consider the RHIs generated by distortion noise to establish a system model.

102. Construct an optimization problem with the objective function of maximizing the total energy efficiency of the system. Decouple the target optimization problem into the subcarrier allocation problem and the power allocation problem. Solve the problem in layers and use the worst-case analysis method to solve the inner-layer minimization problem.

103. For the outer maximization problem of the original optimization problem, the user power is rewritten in the form of user achievable rate, the objective function optimization object is replaced, and the fractional objective function is rewritten using the Dinkelbach method. The objective function is converted to a linear objective function, and the original optimization problem is converted to a linear optimization problem. The subcarrier allocation matrix is set to all 1s, making the objective optimization problem a convex optimization problem. The user achievable rate is then solved using the convex optimization interior point algorithm.

104. Calculate the user rate and the benefit function of each node in the subcarrier allocation matrix, sort each subcarrier in descending order according to the benefit function, and determine whether the number of users on each subcarrier is greater than or equal to the subcarrier user number threshold. If so, eliminate an equal number of users according to the sorting based on the subcarrier user number threshold D, and update the subcarrier allocation factor matrix. Otherwise, do not update the matrix.

105. Determine whether the number of users on each subcarrier is less than or equal to a subcarrier user number threshold. If so, output a subcarrier allocation matrix and calculate system energy efficiency. If it is greater than the threshold, return to step 104 until the number of users on each subcarrier is lower than the subcarrier user number threshold, so that the result converges to the optimal solution; The step 101 specifically includes: Initialize the number of users to K, the number of subcarriers to N, the user set of the kth user is: k∈{1,2,...,K}, the subcarrier set of the nth subcarrier is: C∈{C1,C2,…,C N }; For subcarrier C n The channel gain of the kth user on can be expressed as: in, represents the Rayleigh fading coefficient, d k represents the distance from the kth user to the base station, and α represents the path fading coefficient. Considering the non-ideal channel, the real channel gain is modeled as: in, Denotes the estimated channel gain, Δh k,n Represents the estimated channel error; the SIC decoding order is: π(k) is the corresponding index of the decoding order of user k; the estimated channel gain is used Instead of representing the true channel gain, the set of estimated channel errors is expressed as: ε k,n represents the normalized upper bound of the estimated channel error, h π(k),n Indicates the real channel gain; subcarrier C n The received signal of the kth user on is: Among them, η n represents the system aggregate distortion noise, s π(k),n Represents a data transmission symbol that satisfies The system hardware damage level is evaluated, which represents the total distortion power received by the receiver, w π(k),n represents additive white Gaussian noise AWGN; p π(k),n represents the received power of user k on subcarrier n; after the user decodes its own signal through SIC and eliminates the interference between users according to the channel sorting, the received power of user k on subcarrier C is n The SINRs on are expressed as: in, represents the aggregate interference from other users, ρ π(i),n represents the subcarrier allocation factor, Δh π(k),n Represents the estimated channel error; including strong user interference that SIC cannot eliminate and estimated channel error interference of non-ideal channels; According to Shannon's formula, user k is on subcarrier C n The achievable rate on is expressed as: R π(k),n =log2(1+γ π(k),n ), accumulating all users on all subcarriers, the system achievable sum rate is expressed as: The step 102 specifically includes: Assume that the system has a fixed circuit power loss of P c , the system energy efficiency can be expressed as: The minimum energy efficiency maximization problem is decoupled into an optimization problem involving subcarrier allocation and power allocation. The objective problem is divided into two layers: the internal layer is the minimization problem of estimation error, and the external layer is the maximization problem of subcarrier allocation and power allocation, which are the decoupled subproblems of the original problem. A user number threshold D is set on each subcarrier, and the number of users on any subcarrier cannot exceed this limit. Under a series of constraints, the energy efficiency optimization problem of the multi-carrier NOMA system under non-ideal CSI and hardware impairment conditions is established as follows: Among them, P max Indicates the maximum system power, R t represents the minimum user rate, D represents the maximum number of users that can be accommodated on subcarrier n, and R min Indicates the minimum rate requirement on subcarrier n when user k accesses the subcarrier, Δh π(k),n represents the channel estimation error, Represents a set of estimated error values; constraint C1 represents the total system power constraint, constraint C2 is the user minimum rate constraint, constraint C3 represents the maximum number of users on a single subcarrier, indicating that up to D users can be multiplexed to the same subcarrier, C4 represents the subcarrier selection factor constraint, and C5 represents the minimum rate limit of the selected user on the subcarrier. If the channel condition of the node does not support the minimum rate R min , the node will also be discarded because it cannot complete the decoding of the SIC algorithm; C6 represents the channel estimation error set, which is also the upper bound constraint of the channel estimation error; The step 103 specifically includes: About user rate R π(k),n The minimization problem can be expressed as: For this problem, the following inequality relationship can be derived: in represents the ratio of noise to channel gain; therefore, the minimum rate of user k on subcarrier n can be obtained: Through the above derivation, the inner layer minimization problem of the original problem is solved, and the following deterministic energy efficiency optimization problem can be obtained: Among them, P max Indicates the maximum system power, R t represents the minimum user rate, D represents the maximum number of users that can be accommodated on subcarrier n, and R min Indicates the minimum rate requirement on subcarrier n when user k accesses the subcarrier, Δh π(k),n represents the channel estimation error, A set of values representing the estimated error; represents the minimum rate of user k on subcarrier n; The step 104 specifically includes: Based on the Dinkelbach method, the objective function of the above optimization problem can be rewritten into the following subtraction function form f(η) through fractional programming: Among them, function η represents the system energy efficiency value, η * The system has the best energy efficiency if and only if η=η * When , the formula satisfies f(η)=0; According to the system model, user k is on subcarrier C n By changing the independent variables and function positions, we can obtain the accessible rate of p in the matrix F. π(k),n The expression: According to the above formula, the total power expression of the user on a single subcarrier can be obtained as: Assumptions as well as S j,n , G j,n Represents 2 auxiliary variables; so in subcarrier C n The total power of all users on the network is: When j>K, S j,n =0 and G j,n =1; so the above formula can be rewritten as follows: Multiply both sides of the above equation by The following formula can be obtained: By recursive method, we can get: in, are two auxiliary variables, indicating the constant part that does not contain variables. In summary, we can get the subcarrier C n The total power expression of all users on (1≤n≤N): ν m,n as well as is an auxiliary variable representing a constant; so the total power of the system is: For a given subcarrier allocation matrix F, the optimization problem can be updated as follows: because It's about The problem is still non-convex. According to the objective function of the above problem, the function is about the variable A monotonically decreasing function, so when resource allocation is not optimal, step 105 is adopted; The step 105 specifically includes: For subcarrier C n Total power of all users The power obtained can be made less than or equal to As shown in the following formula: This formula can be understood as follows: when resource allocation reaches the optimal level, the inequality takes the equal sign; when resource allocation has not yet reached the optimal level, the obtained subcarrier C n The total power on Therefore, the above formula always holds true under the constraints of the above optimization problem. This inequality is introduced as a new constraint into the above optimization problem, so the new optimization problem can be expressed as: Among them, ν m,n as well as is an auxiliary variable representing a constant; this problem is newly added constraint The newly added subcarrier C n Total power constraint on ; Through mathematical transformation, we can get the following formula: make as well as Take the log function on both sides of the inequality sign, so the above formula can be written as: Therefore, the target optimization problem can be transformed into: So far, since the log function must be convex and is a convex function, the problem is a convex optimization problem; When F is determined, it can be solved by the interior point method; finally, we can obtain the closed-form solution of power: in, represents the minimum rate of user k on subcarrier n, ρ π(j),n is the subcarrier allocation factor, ν m,n as well as Auxiliary variables representing constants.

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