Orthogonal frequency division multiplexing communication deterministic time delay resource allocation method

Abstract

The invention discloses an orthogonal frequency division multiplexing communication deterministic time delay resource allocation method, and belongs to the field of wireless communication. A system model of OFDM hard cut-off time delay is established in a system modeling stage, and the problem that in an OFDM system, a certain amount of data needs to be transmitted in the hard cut-off time and expected total energy needs to be optimized is solved. In the expectation value function approximation stage, the expectation value function is approximated, and a deterministic optimization problem is obtained. In the two-layer optimization stage, an auxiliary variable is introduced, a closed-form solution of an optimal value of a subproblem under the given auxiliary variable is obtained through derivation, the optimal auxiliary variable is determined through finite times of search, and then the data transmission rate of each subcarrier is analyzed and calculated based on the optimal auxiliary variable. In the performance analysis stage, the performance upper bound of the method when special values of the deterministic parameters are taken and the progressive performance upper bound when general values of the deterministic parameters are taken are analyzed. The performance of the method is superior to that of a baseline method, and better performance can be obtained by adjusting deterministic parameters.

Description

Technical Field

[0001] The present invention relates to the technical field of wireless communications, and in particular to a method for allocating deterministic delay resources in orthogonal frequency division multiplexing communications. Background Art

[0002] In wireless communication networks, latency assurance plays a crucial role in applications with high real-time requirements, such as the Internet of Things. In particular, in industrial control, the real-time transmission of control instructions and feedback information is crucial for ensuring the normal production of products. The communication needs of a large number of sensor devices in the Internet of Things necessitate conserving energy consumed by communications. However, the time-varying fading characteristics of wireless channels make it difficult to achieve both low energy consumption and low latency, necessitating a compromise between the two. Orthogonal Frequency Division Multiplexing (OFDM) technology, with its parallel transmission over frequency-selective channels, provides additional optimization resources for delay-constrained energy optimization.

[0003] Because the channel state in future time slots is causally unknown, optimizing the expected energy consumption for transmitting a certain amount of data before a deadline in an OFDM system is a stochastic dynamic optimization problem. This problem requires dynamically adjusting the data transmission rate of each subcarrier based on the state. Existing solutions for stochastic dynamic optimization problems include Lyapunov optimization, reinforcement learning, and dynamic programming. However, Lyapunov optimization and reinforcement learning are suitable for solving infinite-dimensional problems and are therefore not suitable for guaranteeing hard deadline delay constraints. For dynamic programming, these methods use Bellman recursion to determine decision rules. If the state is discretized, dynamic programming suffers from the curse of dimensionality when the number of states is large, and lacks precision when the number of states is small. Furthermore, using dynamic programming to handle continuous states complicates the calculation of the expected value. Summary of the Invention

[0004] This paper addresses the problem of delay-constrained energy optimization in OFDM systems and provides a deterministic delay resource allocation method for orthogonal frequency division multiplexing communications. By using a deterministic approximation of the expected optimal value function, the inverse recursive problem is transformed into an efficiently solvable single-slot optimization problem. A two-layer optimization solution is then employed, combining closed-form solution derivation with auxiliary variable optimization to significantly reduce computational complexity. Finally, the performance of the proposed method is analyzed, establishing a theoretical foundation for deterministic parameter adjustment.

[0005] An embodiment of the present invention provides a method for allocating deterministic delay resources in orthogonal frequency division multiplexing communication, comprising the following steps:

[0006] Step 1, system modeling phase: Establish a system model for OFDM hard-cutoff delay, define energy consumption and delay constraints, and formulate a stochastic dynamic optimization problem;

[0007] Step 2, expected value function approximation stage: based on the stochastic dynamic optimization problem, the expected optimal value function is approximated using deterministic approximation, and the reverse recursive problem is transformed into a single-slot deterministic optimization problem;

[0008] Step 3, two-level optimization phase: Introduce auxiliary variables to construct an equivalent problem to the single-slot deterministic optimization problem. Derivate a closed-form solution to the optimal value of the subproblem under a given auxiliary variable. Determine the optimal auxiliary variable through a finite search. Analytically calculate the data transmission rate of each subcarrier based on the optimal auxiliary variable.

[0009] Step 4, performance analysis phase: The optimal solution of the state and single-slot deterministic optimization problem forms a decision rule, and the performance upper bound when the deterministic parameter takes a special value and the asymptotic performance upper bound when the deterministic parameter takes a general value are analyzed.

[0010] Optionally, in one embodiment of the present invention, step 1 specifically includes:

[0011] Step 1-1: For an OFDM communication system, both the transmitter and the receiver are single-antenna users. Represents a time slot set, using the first T time slots for transmission, and the time variable t∈{1,...,T+1} is used to count the time slots The starting time; First, establish the wireless communication transmission model in the system model, time slot The received signal y on subcarrier k t,k Expressed as:

[0012]

[0013] Among them, s t,k Indicates time slot and the user's transmitted symbol on subcarrier k, p t,k and h t,k Respectively represent the time slot The transmit power on subcarrier k and the channel coefficient, n t,k Indicates time slot Noise on subcarrier k; noise n t,k Modeled as independent and identically distributed Gaussian random variables on each subcarrier in each time slot, the probability distribution satisfies σ 2 =N0W represents the noise power, N0 represents the noise power spectral density. W represents the subcarrier bandwidth;

[0014] Step 1-2: Channel model adoption Among them, η and represent the large-scale and small-scale fading coefficients respectively;

[0015] Step 1-3: Use the block fading channel model and assume that the channel coefficient h t,k The independent and identically distributed (IID) distribution is followed in each time slot, and it is assumed that for the online scheduling problem, perfect channel state information of the current time slot can be obtained before the start of the time slot;

[0016] Step 1-4: Define the residual performance queue in the system model and define the communication transmission cumulative rate requirement ρ = B / T s , B is the size of the data packet to be transmitted, T s Indicates the length of each time slot, and the residual performance state is recorded as C t , and model the residual performance state C t State transfer;

[0017] Steps 1-5: R t,k Indicates time slot The data rate borne by subcarrier k is to achieve the data rate R t,k , the required transmission power p t,k Expressed as:

[0018]

[0019] Among them, g t,k =|h t,k | 2 Indicates that the user is in the time slot The channel power gain of the kth subcarrier;

[0020] Step 1-6: The transmitter needs to send T packets of length T s In a time slot, communication with users is carried out through K subcarriers, and B bits of data need to be transmitted. Therefore, the delay constraint that the cumulative communication transmission rate should meet is expressed as:

[0021]

[0022] Steps 1-7: Give state variables, action variables, and decision rules;

[0023] Steps 1-8: The stochastic dynamic optimization problem for finding the strategy π is expressed as:

[0024]

[0025] μ t,k (C t ,g t )≥0,t=1,...,T

[0026]

[0027] in, represents the expected operation, g tis the channel state vector of time slot t, whose kth element is g t,k , μ t,k is the decision rule for time slot t, subcarrier k, μ t,k (C t ,g t ) is given by C t With g t The data rate of subcarrier k in time slot t is μ T,k is the decision rule for time slot T, subcarrier k, C T is the residual performance state at time T, g T is the channel state vector of time slot T, μ T,k (C T ,g T ) is given by C T With g T The data rate of subcarrier k in time slot T is C t+1 is the residual performance state at time t+1.

[0028] Optionally, in one embodiment of the present invention, step 2 specifically includes:

[0029] Step 2-1: Define the optimal value function for the subproblem starting from t = T

[0030] Step 2-2: Define the optimal value function of the subproblem at stage t=1,...,T-1

[0031] Steps 2-3: t=1,...,T-1 satisfies the following Bellman recursion:

[0032]

[0033] R t,k ≥0

[0034] Among them, g t+1 is the channel state vector at time t+1, represents the conditional expectation operation, At time t+1, the residual performance state is The channel state is g t+1 The optimal value function when ; is the residual performance state C at a given time t t and each subcarrier data rate R t,k Under the conditions, expectations;

[0035] Step 2-4: Using the multi-carrier deterministic approximation method, first calculate the expected optimal value function Make approximations, approximate results for:

[0036]

[0037] Where K represents the number of subcarriers and g represents the deterministic parameter;

[0038] Step 2-5: Use the approximation of the expected optimal value function to replace the expectation of the optimal value function, and transform the reverse recursive problem into a single-time-slot deterministic optimization problem. Therefore, when t < T, the deterministic optimization problem to be solved is:

[0039]

[0040] Optionally, in one embodiment of the present invention, step 3 specifically includes:

[0041] Step 3-1: By introducing auxiliary variables Transform the deterministic optimization problem in steps 2-5 into the following joint optimization problem:

[0042]

[0043] Step 3-2: Given auxiliary variable r t , transforming the joint optimization problem into the following sub-optimization problems:

[0044]

[0045] Step 3-3: Derive the optimal solution to the sub-optimization problem in step 3-2 and the equations satisfied by its solution parameter β;

[0046] Step 3-4: Given the channel state g of each subcarrier t,1 ,...,g t,K , let G t,k =log2(1 / g t,k ), for G t,k Sort in ascending order, merge the same values, and form N reference levels β t,1 <β t,2 ...<β t,N , and let β t,N+1 =+∞;

[0047] Step 3-5: Define subcarrier set

[0048] Step 3-6: Define segmentation point α t,n-1 , each segment point satisfies 0=α t,0 <α t,1 <α t,2 ...<α t,N-1 ;

[0049] Step 3-7: Using α t,n , divided into N segment intervals I t,n ;

[0050] Step 3-8: Derive the closed-form solution for the horizontal plane within each segmented interval;

[0051] Step 3-9: Get the given r t ∈I t,n When the optimal solution R of the sub-optimization problem in step 3-2 is t,k (r t );

[0052] Step 3-10: The optimal solution R t,k (r t ) is substituted into the joint optimization problem in step 3-1 to obtain the optimization problem for the auxiliary variables:

[0053]

[0054] st0≤r t ≤C t

[0055] Step 3-11: Based on the residual performance state C t The interval where the segmented interval is located is adjusted to obtain the adjusted closed interval I t,n ;

[0056] Step 3-12: Using the segmented intervals, decompose the optimization problem on the auxiliary variables in step 3-10 into the following segmented sub-problems:

[0057]

[0058] in, is the adjusted closed interval;

[0059] Step 3-13: Derive the optimal solution to the segmented subproblem in step 3-12

[0060] Step 3-14: Compare the optimal solutions of each sub-problem to obtain the optimal solution of the optimization problem in step 3-10

[0061] Step 3-15: Determine the optimal solution to the optimization problem with respect to the auxiliary variables The interval in which it is located;

[0062] Step 3-16: Then given Calculate the horizontal plane

[0063]

[0064] Among them, n ＊ for The index of the interval, Indicates time slot t, the nth in ascending order ＊ a reference level;

[0065] Step 3-17: Calculate the data rate of each subcarrier

[0066]

[0067] Step 3-18: Given the channel state vector g T and the residual performance state C T Calculate the optimal solution of the optimization problem in step 2-1 when t=T.

[0068] Optionally, in one embodiment of the present invention, step 4 specifically includes:

[0069] Step 4-1: Policy evaluation for policy π

[0070] Step 4-2: Assuming that the channel state distribution of each subcarrier is the same, the deterministic parameter is expressed as The performance upper bound of the strategy evaluation is obtained by determining the deterministic parameters The strategy evaluation at this time satisfies:

[0071]

[0072] in, For the deterministic parameters The strategy evaluation at time , the right side of the above formula is the deterministic parameter The upper bound of performance when is the set of feasible solutions to the single-slot deterministic optimization problem when t = 1 and the residual performance state is C1, C1 is the residual performance state at t = 1, and g1 is the channel state vector at t = 1;

[0073] Step 4-3: Express the asymptotic performance upper bound of the deterministic parameter g when it is generally taken as a value, and obtain that the policy evaluation of the deterministic parameter g when it is generally taken as a value satisfies:

[0074]

[0075] Among them, V1(C1,g1,g) represents the policy evaluation when the deterministic parameter is g, and the right side of the above formula is the asymptotic performance upper bound when the deterministic parameter g takes a general value.

[0076] The deterministic delay resource allocation method for OFDM communications in this embodiment of the present invention utilizes state information to dynamically adjust the transmission rate of each subcarrier, meeting hard deadline constraints and reducing the system's average energy consumption. Appropriately adjusting deterministic parameters can further improve algorithm performance.

[0077] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0079] Figure 1 A flowchart of a method for allocating deterministic delay resources in orthogonal frequency division multiplexing communication according to an embodiment of the present invention;

[0080] Figure 2 The average energy consumption of the embodiment of the present invention varies with the size of the data packet;

[0081] Figure 3 When the data packet size B=6kbits, the average energy consumption changes with the total number of time slots in the embodiment of the present invention;

[0082] Figure 4 When the data packet size B=1.5 kbits, the average energy consumption varies with the total number of time slots in the embodiment of the present invention;

[0083] Figure 5 The average energy consumption of the embodiment of the present invention varies with the deterministic parameters;

[0084] Figure 6 is the Empirical Cumulative Distribution Function (ECDF) of the transmission completion time of an embodiment of the present invention. DETAILED DESCRIPTION

[0085] The following describes embodiments of the present invention in detail, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and are not to be construed as limiting the present invention.

[0086] Figure 1 The present invention provides a flowchart of a method for allocating deterministic delay resources in orthogonal frequency division multiplexing communication according to an embodiment of the present invention.

[0087] like Figure 1 As shown, the orthogonal frequency division multiplexing communication deterministic delay resource allocation method includes the following steps:

[0088] Step 1, system modeling phase: Establish a system model of OFDM hard cutoff delay, define energy consumption and delay constraints, and construct a stochastic dynamic optimization problem.

[0089] Step 2, expected value function approximation stage: Based on the random dynamic optimization problem, the expected optimal value function is approximated using deterministic approximation, and the reverse recursive problem is transformed into a single-slot deterministic optimization problem.

[0090] Step 3, two-layer optimization stage: Introduce auxiliary variables to construct an equivalent problem to the single-time-slot deterministic optimization problem, derive a closed-form solution to the optimal value of the subproblem under the given auxiliary variables, determine the optimal auxiliary variables through a finite search, and analytically calculate the data transmission rate of each subcarrier based on the optimal auxiliary variables.

[0091] Step 4, performance analysis phase: The optimal solution of the state and single-slot deterministic optimization problem forms a decision rule. The performance upper bound of the proposed method when the deterministic parameter takes a special value and the asymptotic performance upper bound of the proposed method when the deterministic parameter takes a general value are analyzed.

[0092] In an embodiment of the present invention, step 1 specifically includes the following steps:

[0093] Step 1-1: For an OFDM communication system, both the transmitter and the receiver are single-antenna users. Represents a time slot set, and the present invention uses the first T time slots for transmission. The time variable t∈{1,...,T+1} is used to count the time slots The starting time of the time slot. First, the wireless communication transmission model in the system model is given. The received signal y on subcarrier k t,k Expressed as:

[0094]

[0095] Among them, s t,k Indicates time slot And the user's transmitted symbol on subcarrier k. t,k and h t,k Respectively represent the time slot The transmit power and channel coefficient on subcarrier k, n t,k Indicates time slot Noise on subcarrier k. Noise n t,k Modeled as independent and identically distributed Gaussian random variables on each subcarrier in each time slot, its probability distribution satisfies σ 2=N0W represents noise power, N0 represents noise power spectral density, and W represents subcarrier bandwidth.

[0096] Step 1-2: Channel model adoption Among them, η and represent the large-scale and small-scale fading coefficients respectively.

[0097] Step 1-3: Use the block fading channel model, that is, the channel of each time slot is changing, but it remains unchanged within each time slot. Assume that the channel coefficient h t,k The independent and identically distributed (IID) is followed in each time slot, and it is assumed that for the online scheduling problem under study, perfect channel state information of the current time slot can be obtained before the start of the time slot.

[0098] Step 1-4: Next, define the residual performance queue in the system model. Define ρ = B / T s represents the cumulative communication transmission rate requirement, B is the size of the data packet to be transmitted, T s Indicates the length of each time slot, R t,k Indicates time slot The data rate on subcarrier k. The residual performance state C is t , which means that in the time slot Start receiving the user's unfinished cumulative rate requirements. C t+1 By C t and time slots The data transmission rate and C t The state transition model is:

[0099]

[0100] Wherein, C1=ρ, which means that C1 is equal to the communication transmission cumulative rate requirement.

[0101] Steps 1-5: To achieve rate R t,k , the required transmission power p t,k Satisfies the following expression:

[0102]

[0103] Among them, g t,k =|h t,k | 2 Indicates that the user is in the time slot Channel power gain of the kth subcarrier.

[0104] Step 1-6: The transmitting station needs to send T packets of length T sIn the time slot of , communication with the user is carried out through K subcarriers. To meet the delay constraint, the communication process needs to transmit B bits of data. Therefore, the delay constraint that the cumulative communication transmission rate should meet is expressed as:

[0105]

[0106] Step 1-7: Give state variables, action variables, and decision rules; the state variables are the residual performance state C of the user at time t t , channel status Its kth element is g t,k The action variable is the rate R of each subcarrier in each time slot. t,k Therefore, the decision rule can be expressed as in, represents the user's residual performance state space, represents the channel state space, represents the action space. The decision rule determines the action based on the state, which means μ t,k (C t ,g t )=R t,k . represents the set of non-negative real numbers, represents a set of strictly positive N-dimensional real vectors. Strategy π consists of a decision rule for each time slot, which dynamically determines the data transmission rate of each subcarrier.

[0107] Steps 1-8: The goal is to find a strategy π that satisfies the user's cumulative rate requirements while minimizing the expected total energy consumption in the OFDM system. Therefore, the stochastic dynamic optimization problem is expressed as:

[0108]

[0109] μ t,k (C t ,g t )≥0,t=1,...,T,

[0110]

[0111] in, represents the expected operation, g t is the channel state vector of time slot t, whose kth element is g t,k , μ t,k is the decision rule for time slot t, subcarrier k, μ t,k (C t ,g t ) is given by C t With g t The data rate of subcarrier k in time slot t is μT,k is the decision rule for time slot T, subcarrier k, C T is the residual performance state at time T, g T is the channel state vector of time slot T, μ T,k (C T ,g T ) is given by C T With g T The data rate of subcarrier k in time slot T is C t+1 is the residual performance state at time t+1; the first constraint in the above formula means that when t<T, in the time slot The transmission rate should not exceed the residual performance state C t The second constraint means that in the time slot The transmission rate should be equal to the residual performance. The third constraint means that the rate is non-negative. The fourth constraint describes the transition of the residual performance state.

[0112] In an embodiment of the present invention, step 2 specifically includes the following steps:

[0113] Step 2-1: Define the optimal value function for the subproblem starting from t = T First, the Bellman recursive solution method for dynamic programming is given. The optimal value function of the subproblem starting from stage t is defined as t=1,...,T. When t=T, is the optimal value for the following optimization problem:

[0114]

[0115] R T,k ≥0

[0116] Given the residual performance state C at time T T With the channel state g T , for the optimal solution of the above optimization problem, the state and the optimal solution form a mapping relationship, which is the time slot The optimal decision rule.

[0117] Step 2-2: Define the optimal value function of the subproblem at stage t=1,...,T-1 When t=1,...,T-1, is the optimal value for the following optimization problem:

[0118]

[0119] μ i,k (C i ,g i )≥0,i=1,...,T

[0120] Among them, π t ={μ t ,...,μ T} represents the truncation strategy starting from time t, where μ i Indicates time slot The vector composed of the decision rules of each subcarrier, whose kth element is the decision rule μ i,k .

[0121] Steps 2-3: t=1,...,T-1 satisfies the following Bellman recursion:

[0122]

[0123] R t,k ≥0

[0124] Among them, g t+1 is the channel state vector at time t+1, represents the conditional expectation operation, At time t+1, the residual performance state is The channel state is g t+1 The optimal value function when ; is the residual performance state C at a given time t t and each subcarrier data rate R t,k Under the conditions, The expectation of the residual performance state C at time t t With the channel state g t ,For the optimal solution of the above optimization problem, the state and the optimal solution form a mapping relationship, which is the optimal decision rule for time slot t.

[0125] Step 2-4: Due to the complexity of dynamic programming and expectation calculation, it is difficult to obtain a closed-form solution to the expected value function. Approximate dynamic programming is used. Specifically, the following multi-carrier deterministic approximation method is used. First, the expected optimal value function The approximate result is It is expressed as:

[0126]

[0127] Where K represents the number of subcarriers and g represents the deterministic parameter. For t=T and t<T, Respectively represent the channel g of each subcarrier in the stage subproblems in step 2-1 and step 2-2 i,k Fixed to the calculated energy consumption in g.

[0128] Step 2-5: Use the approximation of the expected optimal value function to replace the expectation of the optimal value function to obtain a deterministic optimization problem. Therefore, when t < T, the following deterministic optimization problem needs to be solved:

[0129]

[0130] The set of feasible solutions to the above optimization problem is Since deterministic approximation eliminates randomness, the above optimization problem is a deterministic problem. Given the residual performance state C at time t, t And the channel status of each subcarrier g t,k , we can get the optimal solution R of the above optimization problem t,k This forms the decision rule of the present invention

[0131] Next, a corresponding solution method is designed for the deterministic optimization problem in steps 2-5. In an embodiment of the present invention, step 3 specifically includes the following steps:

[0132] Step 3-1: First, introduce auxiliary variables Transform the optimization problem in steps 2-5 into the following joint optimization problem:

[0133]

[0134] Step 3-2: Next, given the auxiliary variable r t , transforming the above joint optimization problem into the following sub-optimization problem:

[0135]

[0136] Note that the above sub-problem solutions are also applicable to the solution of the optimization problem in step 2-1. The solution of the optimization problem in step 2-1 will be specifically given in steps 3-18 to 3-23. Next, the solution of the sub-problem in step 3-2 will be introduced in steps 3-3 to 3-9.

[0137] Step 3-3: Derive the optimal solution to the sub-optimization problem in step 3-2 The equations satisfied by its solution parameter β. The optimal solution to the subproblem in step 3-2 for:

[0138]

[0139] Among them, β needs to be solved by the following equation:

[0140]

[0141] Optimal solution The parameter β in rt Therefore, we can determine the given r t When β is written as β(r t ). Parameter β is called the horizontal plane. Parameter β further determines the optimal solution R of the optimization problem in step 3-2 t,k (r t ) and the optimal value E(r t ).

[0142] Step 3-4: Given the channel state g of each subcarrier t,1 ,...,g t,K , let G t,k =log2(1 / g t,k ), then G t,k Sort in ascending order, merge the same values, and get the sorted value G t,(n) Let β t,n =G t,(n) , forming N reference horizontal planes β t,1 <β t,2 ...<β t,N , and let β t,N+1 = +∞. Note that, in general, N = K, because the channel state values ​​are generally different.

[0143] Step 3-5: Define subcarrier set

[0144] Step 3-6: Define segmentation points Each segment point satisfies 0=α t,0 <α t,1 <α t,2 ...<α t,N-1 Here Representing a collection The number of elements in .

[0145] Step 3-7: Next, use α t,n , divided into N intervals I t,n . The nth interval is:

[0146]

[0147] Step 3-8: Derive the closed-form solution for the horizontal plane in each segment interval. t ∈I t,n When β satisfies β∈[β t,n ,β t,n+1 ), we can get:

[0148]

[0149] Step 3-9: Get the given r t ∈It,n When the optimal solution R of the sub-optimization problem in step 3-2 is t,k (r t )for:

[0150]

[0151] Step 3-10: R t,k (r t ) is substituted into the joint optimization problem in step 3-1 to obtain the optimization problem for the auxiliary variables:

[0152] st0≤r t ≤C t

[0153] Step 3-11: Based on the residual performance state C t The interval where the segmented interval is located is adjusted to obtain the adjusted closed interval Since we get E(r t ) is represented by a segmented representation, and in each segment, the objective function of the above optimization problem is a convex function, so the segmented solution is adopted next. Before the segmented solution, according to the constraint 0≤r t ≤C t For segmented interval I t,n Specifically, if C t ∈I t,n' , modify I t,n' The right endpoint is C t , and delete the interval I where j>n' t,j , and then modify the remaining intervals to closed intervals

[0154] Step 3-12: Next, using interval segmentation, decompose the optimization problem on the auxiliary variables in step 3-10 into the following segmented sub-problems:

[0155]

[0156] Step 3-13: Derive the optimal solution to the segmented subproblem in step 3-12

[0157]

[0158] Among them, I n,left with I n,right The intervals The left and right endpoints of The operation is defined as:

[0159]

[0160] Step 3-14: Next, compare the optimal solutions of each segment to obtain the optimal solution r of the optimization problem in step 3-10. t *:

[0161]

[0162] Step 3-15: Determine the optimal solution r of the optimization problem with respect to the auxiliary variables t Specifically, the interval where the above formula is minimized is The interval is It is the optimal solution r t *The interval where it is located.

[0163] Step 3-16: Then given r t *, calculate the horizontal plane β(r t *):

[0164]

[0165] Among them, n ★ for The index of the interval, Indicates time slot t, the nth in ascending order ★ a reference level;

[0166] Step 3-17: Calculate the data rate of each subcarrier

[0167]

[0168] Steps 3-18 to 3-23: Given a channel state vector g T and the residual performance state C T Calculate the optimal solution to the optimization problem in step 2-1 when t=T. The solution is similar to the solution of the subproblem in step 3-2 in steps 3-3 to 3-9. Specifically:

[0169] Step 3-18: Given the channel state g of each subcarrier T,1 ,...,g T,K , let G T,k =log2(1 / g T,k ), then G T,k Sort in ascending order, merge the same values, and obtain N reference horizontal planes β T,1 <β T,2 ...<β T,N Note that, in general, N = K. Let β T,N+1 =+∞.

[0170] Step 3-19: Utilize Beta T,n, get the subcarrier set

[0171] Step 3-20: Define r T The segmentation point Each segment point satisfies 0=α T,0 <α T,1 <α T,2 ...<α T,N-1 .

[0172] Step 3-21: Next, use α T,n , divided into N intervals, where the nth interval is:

[0173]

[0174] Step 3-22: Determine r T The interval when hour, You can get a given r T When β satisfies:

[0175]

[0176] Step 3-23: Calculate the given r T When , the optimal solution of the optimization problem in step 2-1 is for:

[0177]

[0178] So far, we have obtained the given channel state g T and the residual performance state C T Time, in the time slot The data transmission rate of each subcarrier.

[0179] In an embodiment of the present invention, step 4 specifically includes the following steps:

[0180] Step 4-1: Policy evaluation V representing policy π t π (C t ,g t ). Let the strategy evaluation of strategy π be V t π (C t ,g t ), which is the expected energy consumption under given strategy and state conditions, and its formula is:

[0181]

[0182] Step 4-2: Assuming that the channel state distribution of each subcarrier is the same, the deterministic parameters can be obtained by using the approximate dynamic programming strategy to evaluate the properties. The strategy evaluation of the proposed method satisfies when . It represents the deterministic parameter The performance upper bound of the strategy evaluation of the proposed method is obtained when the deterministic parameter When , the strategy evaluation of the proposed method satisfies:

[0183]

[0184] Among them, V1 1 (C1, g1) is the deterministic parameter of the proposed method The strategy evaluation at time , the right side of the above formula is the deterministic parameter The performance upper bound of the proposed method is, C1 is the residual performance state at t = 1, g1 is the channel state vector at t = 1, u1 (C 1) The set of feasible solutions to the optimization problem in steps 2-5 when t=1 and the residual performance state is C1.

[0185] Step 4-3: Using the properties of approximate dynamic programming strategy evaluation and combined with asymptotic analysis, we can obtain that when the deterministic parameter g takes a general value, the strategy evaluation of the proposed method satisfies . represents the asymptotic performance upper bound for the deterministic parameter g when it takes a general value, and we obtain that when the deterministic parameter g takes a general value, the strategy evaluation of the proposed method satisfies:

[0186]

[0187] Here, V1(C1,g1,g) represents the policy evaluation of the proposed method when the determinism parameter is g. The right side of the above equation is the asymptotic upper bound of the proposed method for general values ​​of the determinism parameter g. This shows that when the total number of time slots is large, that is, when the delay constraint is relatively loose, appropriately increasing the determinism parameter can achieve better performance.

[0188] The method of the present invention is simulated and verified by using specific embodiments below.

[0189] The large-scale fading of the channel model adopts logarithmic distance loss, and the small-scale fading adopts independent and identically distributed truncated exponential distribution.

[0190] This is compared with two baseline methods: the first baseline method is the equal rate method, which evenly distributes the cumulative rate requirement to each subcarrier; the second baseline method is the first time slot method, which uses the reverse water filling method to meet the cumulative rate requirement in the first time slot.

[0191] The deterministic parameter in step 4-2 is When the performance upper bound of the proposed method is statistically averaged over the channel implementation, the average result is Figure 2, Figure 3 , Figure 4 , Figure 5 The mark in the middle is the upper bound of performance. The deterministic parameter in step 4-3 is When the asymptotic performance upper bound of the proposed method is statistically averaged over the channel realization, the average result is Figure 2 , Figure 3 , Figure 4 , Figure 5 The mark in the middle is the asymptotic performance upper bound.

[0192] like Figure 2 As shown, typical values ​​of the deterministic parameters are selected as well as The proposed method is generally better than the baseline method under the deterministic parameter g1. Appropriately increasing the deterministic parameter can further reduce the average energy consumption.

[0193] like Figure 3 and Figure 4 As shown, typical values ​​of the deterministic parameters are selected as well as Under different total number of time slots, the method proposed in the present invention is generally better than the baseline method under the deterministic parameter g1. Properly increasing the deterministic parameter can further reduce the average energy consumption.

[0194] exist Figure 6 In the experiment, the deterministic parameter interval δ=(g2-g1) / N δ,1 , where N δ,1 +1=5 is the number of deterministic parameters. Two subcarrier numbers K=56 and K=64 are set respectively. Figure 6 In the experiment, the deterministic parameter interval is set to (2.5g2-g1) / N δ,2 , where N δ,2 +1=14 is the number of deterministic parameters.

[0195] like Figure 5 and Figure 6 As shown, increasing the deterministic parameter can make the distribution of the transmission completion time of the method proposed in the present invention more delayed, so that the deterministic parameter can be adjusted within a certain range to reduce the average energy consumption.

[0196] According to the deterministic delay resource allocation method for orthogonal frequency division multiplexing communication proposed in an embodiment of the present invention, a system model of OFDM hard cutoff delay is established in the system modeling stage, and the problem of transmitting a certain amount of data within the hard cutoff time and optimizing the expected total energy in the OFDM system is constructed. In the expected value function approximation stage, the expected value function is approximated to obtain a deterministic optimization problem. In the two-layer optimization stage, auxiliary variables are introduced to derive the closed-form solution of the optimal value of the subproblem under the given auxiliary variables. The optimal auxiliary variables are determined through a finite number of searches, and then the data transmission rate of each subcarrier is analytically calculated based on the optimal auxiliary variables. In the performance analysis stage, the performance upper bound of the proposed method when the deterministic parameters take special values ​​and the asymptotic performance upper bound when the deterministic parameters take general values ​​are analyzed. The present invention outperforms the baseline method in performance, and better performance can be achieved by adjusting the deterministic parameters.

[0197] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or N embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and the features of different embodiments or examples without contradiction.

[0198] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of technical features indicated. Thus, a feature specified as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "N" means at least two, such as two, three, etc., unless otherwise specifically defined.

[0199] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, segment or portion of code comprising one or N executable instructions for implementing a custom logical function or step of a process, and the scope of the preferred embodiments of the present invention includes alternative implementations in which functions may be performed out of the order shown or discussed, including performing functions in a substantially simultaneous manner or in the reverse order depending on the functions involved, which should be understood by those skilled in the art to which the embodiments of the present invention pertain.

Claims

1. A method for allocating deterministic delay resources in orthogonal frequency division multiplexing communication, characterized in that: The following steps are involved: Step 1, system modeling phase: Establish a system model for OFDM hard-cutoff delay, define energy consumption and delay constraints, and formulate a stochastic dynamic optimization problem; Step 2, expected value function approximation stage: based on the stochastic dynamic optimization problem, the expected optimal value function is approximated using deterministic approximation, and the reverse recursive problem is transformed into a single-slot deterministic optimization problem; Step 3, two-level optimization phase: Introduce auxiliary variables to construct an equivalent problem to the single-slot deterministic optimization problem. Derivate a closed-form solution to the optimal value of the subproblem under a given auxiliary variable. Determine the optimal auxiliary variable through a finite search. Analytically calculate the data transmission rate of each subcarrier based on the optimal auxiliary variable. Step 4, performance analysis phase: The optimal solution of the state and single-slot deterministic optimization problem forms a decision rule, and the performance upper bound when the deterministic parameter takes a special value and the asymptotic performance upper bound when the deterministic parameter takes a general value are analyzed.

2. The method according to claim 1, characterized in that Step 1 specifically includes: Step 1-1: For an OFDM communication system, both the transmitter and the receiver are single-antenna users. Represents a time slot set, using the first T time slots for transmission, and the time variable t∈{1,...,T+1} is used to count the time slots The starting time; First, establish the wireless communication transmission model in the system model, time slot The received signal y on subcarrier k t,k Expressed as: Among them, s t,k Indicates time slot and the user's transmitted symbol on subcarrier k, p t,k and h t,k Respectively represent the time slot The transmit power and channel coefficient on subcarrier k, n t,k Indicates time slot Noise on subcarrier k; noise n t,k Modeled as independent and identically distributed Gaussian random variables on each subcarrier in each time slot, the probability distribution satisfies σ 2 =N0W represents noise power, N0 represents noise power spectral density, and W represents subcarrier bandwidth; Step 1-2: Channel model adoption Among them, η and represent the large-scale and small-scale fading coefficients respectively; Step 1-3: Use the block fading channel model and assume that the channel coefficient h t,k The independent and identically distributed (IID) distribution is followed in each time slot, and it is assumed that for the online scheduling problem, perfect channel state information of the current time slot can be obtained before the start of the time slot; Step 1-4: Define the residual performance queue in the system model and define the communication transmission cumulative rate requirement ρ = B / T s , B is the size of the data packet to be transmitted, T s Indicates the length of each time slot, and the residual performance state is recorded as C t , and model the residual performance state C t State transfer; Steps 1-5: R t,k Indicates time slot The data rate borne by subcarrier k is to achieve the data rate R t,k , the required transmission power p t,k Expressed as: Among them, g t,k =|h t,k | 2 Indicates that the user is in the time slot The channel power gain of the kth subcarrier; Step 1-6: The transmitter needs to send T packets of length T s In a time slot, communication with users is carried out through K subcarriers, and B bits of data need to be transmitted. Therefore, the delay constraint that the cumulative communication transmission rate should meet is expressed as: Steps 1-7: Give state variables, action variables, and decision rules; Steps 1-8: The stochastic dynamic optimization problem for finding the strategy π is expressed as: μ t,k (C t ,g t )≥0,t=1,...,T in, represents the expected operation, g t is the channel state vector of time slot t, whose kth element is g t,k , μ t,k is the decision rule for time slot t, subcarrier k, μ t,k (C t ,g t ) is given by C t With g t The data rate of subcarrier k in time slot t is μ T,k is the decision rule for time slot T, subcarrier k, C T is the residual performance state at time T, g T is the channel state vector of time slot T, μ T,k (C T ,g T ) is given by C T With g T The data rate of subcarrier k in time slot T is C t+1 is the residual performance state at time t+1.

3. The method according to claim 2, characterized in that Step 2 specifically includes: Step 2-1: Define the optimal value function for the subproblem starting from t = T Step 2-2: Define the optimal value function of the subproblem at stage t=1,...,T-1 Steps 2-3: Satisfies the following Bellman recursion: R t,k ≥0 Among them, g t+1 is the channel state vector at time t+1, represents the conditional expectation operation, At time t+1, the residual performance state is The channel state is g t+1 The optimal value function when ; is the residual performance state C at a given time t t and each subcarrier data rate R t,k Under the conditions, expectations; Step 2-4: Using the multi-carrier deterministic approximation method, first calculate the expected optimal value function Make approximations, approximate results for: Where K represents the number of subcarriers and g represents the deterministic parameter; Step 2-5: Use the approximation of the expected optimal value function to replace the expectation of the optimal value function, and transform the reverse recursive problem into a single-time-slot deterministic optimization problem. Therefore, when t < T, the deterministic optimization problem to be solved is:

4. The method according to claim 3, characterized in that Step 3 specifically includes: Step 3-1: By introducing auxiliary variables Transform the deterministic optimization problem in steps 2-5 into the following joint optimization problem: Step 3-2: Given auxiliary variable r t , transforming the joint optimization problem into the following sub-optimization problems: Step 3-3: Derive the optimal solution to the sub-optimization problem in step 3-2 and the equations satisfied by its solution parameter β; Step 3-4: Given the channel state g of each subcarrier t,1 ,...,g t,K , let G t,k =log2(1 / g t,k ), for G t,k Sort in ascending order, merge the same values, and form N reference levels β t,1 <β t,2 ...<β t,N , and let β t,N+1 =+∞; Step 3-5: Define subcarrier set Step 3-6: Define segmentation point α t,n-1 , each segment point satisfies 0=α t,0 <α t,1 <α t,2 …<α t,N-1 ; Step 3-7: Using α t,n , divided into N segment intervals I t,n ; Step 3-8: Derive the closed-form solution for the horizontal plane within each segmented interval; Step 3-9: Get the given r t ∈I t,n When the optimal solution R of the sub-optimization problem in step 3-2 is t,k (r t ); Step 3-10: The optimal solution R t,k (r t ) is substituted into the joint optimization problem in step 3-1 to obtain the optimization problem for the auxiliary variables: s.t.0≤r t ≤C t Step 3-11: Based on the residual performance state C t The interval where the segmented interval is located is adjusted to obtain the adjusted closed interval Step 3-12: Using the segmented intervals, decompose the optimization problem on the auxiliary variables in step 3-10 into the following segmented sub-problems: in, is the adjusted closed interval; Step 3-13: Derive the optimal solution to the segmented subproblem in step 3-12 Step 3-14: Compare the optimal solutions of each sub-problem to obtain the optimal solution r of the optimization problem in step 3-10 t *; Step 3-15: Determine the optimal solution r of the optimization problem with respect to the auxiliary variables t *The interval in which it is located; Step 3-16: Then given r t *, calculate the horizontal plane β(r t *): Among them, n ＊ For r t * The index of the interval, Indicates time slot t, the nth in ascending order ＊ a reference level; Step 3-17: Calculate the data rate of each subcarrier Step 3-18: Given the channel state vector g T and the residual performance state C T Calculate the optimal solution of the optimization problem in step 2-1 when t=T.

5. The method according to claim 1, wherein Step 4 specifically includes: Step 4-1: Policy evaluation V representing policy π t π (C t ,g t ); Step 4-2: Assuming that the channel state distribution of each subcarrier is the same, the deterministic parameter is expressed as The performance upper bound of the strategy evaluation is obtained by determining the deterministic parameters The strategy evaluation at this time satisfies: Among them, V1 1 (C1, g1) is the deterministic parameter The strategy evaluation at time , the right side of the above formula is the deterministic parameter The upper bound of performance when is the set of feasible solutions to the single-slot deterministic optimization problem when t = 1 and the residual performance state is C1, C1 is the residual performance state at t = 1, and g1 is the channel state vector at t = 1; Step 4-3: Express the asymptotic performance upper bound of the deterministic parameter g when it is generally taken as a value, and obtain that the policy evaluation of the deterministic parameter g when it is generally taken as a value satisfies: Among them, V1(C1,g1,g) represents the policy evaluation when the deterministic parameter is g, and the right side of the above formula is the asymptotic performance upper bound when the deterministic parameter g takes a general value.

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