A relay-assisted backscattering network resource allocation method based on linear mapping

Abstract

The present disclosure relates to a relay-assisted backscattering network resource allocation method based on linear mapping. It comprises: establishing a relay-assisted backscattering network; from the perspective of frame structure, analyzing the throughput of the backscattering phase, the relay forwarding phase and the total throughput of the whole system based on linear mapping theory; taking the maximization of the total throughput of the whole system as the goal, establishing a mixed integer non-convex optimization problem model based on the backscattering coefficient, the number of subframes allocated to the backscattering phase and the relay forwarding phase, and the transmit power of the hybrid access point; introducing relaxation variables, auxiliary variables, using KKT conditions, time-sharing method and continuous convex approximation method to transform the non-convex optimization problem model into a continuous convex optimization problem model; and calculating the optimal total throughput of the whole system through a low-complexity iterative algorithm. Compared with the common continuous-time-based resource allocation strategy, the present disclosure obtains a more practical resource allocation strategy.

Description

Technical Field

[0001] The present disclosure relates to the technical field of wireless communications, and in particular to a method for allocating resources in a relay-assisted backscatter network based on linear mapping. Background Art

[0002] As an integral part of future networks, the Internet of Things (IoT) is driving a transformation in human production and lifestyle through a fully intelligent and automated approach. Simultaneously, the rapidly increasing deployment of smart devices is placing higher demands on energy supply. However, due to size and cost constraints, IoT nodes are energy-constrained. In high-risk or high-density deployment environments, accessing the power grid or frequently replacing batteries is difficult to address this bottleneck. Backscattering, a promising technology, allows IoT nodes to modulate their own information onto existing radio frequency signals and radiate the modulated signal through antennas, while simultaneously harvesting energy from the radio frequency signals to maintain their own circuitry, thereby achieving low-power passive information transmission. However, this passive information transmission method is only suitable for low-rate, short-range wireless communications. To address this issue, existing technologies have proposed relay-assisted backscatter networks. Leveraging the store-and-forward nature of relays, these networks allow IoT nodes to achieve higher communication rates and longer ranges through both backscatter and relay links. Therefore, relay-assisted backscattering networks are crucial for addressing the limited passive transmission performance of IoT nodes in backscatter networks. Existing work mainly focuses on asymmetric transmission processes and studies continuous-time resource allocation strategies based on ideal coding strategies, which is not feasible in actual communications where information transmission is performed in frames.

[0003] Therefore, it is necessary to provide a new technical solution to improve one or more problems existing in the above solutions.

[0004] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present disclosure, and therefore may include information that does not constitute prior art known to ordinary technicians in the field. Summary of the Invention

[0005] The purpose of the present disclosure is to provide a method for allocating resources in a relay-assisted backscatter network based on linear mapping, thereby overcoming one or more problems caused by limitations and defects of related technologies, at least to a certain extent.

[0006] According to an embodiment of the present disclosure, a method for allocating resources in a relay-assisted backscatter network based on linear mapping is provided, the method comprising:

[0007] Establishing a relay-assisted backscatter network, the relay-assisted backscatter network comprising: an Internet of Things node, a receiver, and a hybrid access point; wherein the Internet of Things node is equipped with an energy harvesting module and a backscatter module;

[0008] The entire transmission process of the relay-assisted backscatter network is divided into a backscattering phase and a relay forwarding phase. Based on the frame structure of the relay-assisted backscatter network, the throughput of the backscattering phase, the relay forwarding phase, and the total throughput of the entire system are analyzed based on linear mapping theory; the total throughput of the entire system;

[0009] With the goal of maximizing the total throughput of the entire system, under the energy causality constraints of the IoT nodes and the hybrid access points, a mixed integer non-convex optimization problem model is established based on the backscatter coefficient, the number of subframes allocated to the backscattering phase and the relay forwarding phase, and the transmit power of the hybrid access point; wherein the transmit power of the hybrid access point includes the transmit power in the backscattering phase and the transmit power in the relay forwarding phase;

[0010] Introducing slack variables and auxiliary variables, using KKT conditions, time-sharing methods, and continuous convex approximation methods to transform the mixed integer non-convex optimization problem model into a continuous convex optimization problem model, designing an integer conversion strategy to obtain the relevant optimal discrete solutions, and further optimizing the continuous variables in the convex optimization problem model based on the obtained discrete values;

[0011] The optimal total throughput of the entire system is calculated by a low-complexity iterative algorithm.

[0012] In an embodiment of the present disclosure, the entire transmission process of the relay-assisted backscatter network is divided into a backscattering phase and a relay forwarding phase. For the relay-assisted backscatter network, based on the frame structure, the throughput of the backscattering phase, the relay forwarding phase, and the total throughput of the entire system are analyzed based on the linear mapping theory. The total throughput of the entire system includes:

[0013] Set the duration of the transmission frame in the backscattering phase and the relay forwarding phase to T s , consisting of L subframes, wherein M subframes are used for the backscattering phase, N subframes are used for the relay forwarding phase, and M+N=L is satisfied;

[0014] In the backscattering phase, the backscattered signals received by the receiver and the hybrid access point are respectively:

[0015]

[0016]

[0017] Where, F = diag(H SR s), Represents the energy signal, represents the sending signal of the IoT node; P0 represents the power of the energy signal transmitted by the hybrid access point, β represents the backscatter coefficient of the IoT node, H SD =h SD I M 、H SR =h SR I M and H RD =h RD I N are the channel state information matrices of the links from IoT node to receiver, IoT node to hybrid access point, and hybrid access point to receiver, respectively, where h SD 、h SR 、h RD Denote the channel coefficients of the links from IoT node to receiver, IoT node to hybrid access point, and hybrid access point to receiver, respectively. LI represents the residual loop interference channel state information matrix, and are the complex Gaussian noise vector, I M represents the M-dimensional identity matrix, I N represents the N-dimensional identity matrix;

[0018]

[0019] Where η represents the energy collection efficiency, M represents the number of subframes allocated to the backscattering phase, N represents the number of subframes allocated to the relay forwarding phase, and T s Indicates the frame length of each frame;

[0020] The throughput of the link from the IoT node to the receiver and the throughput of the link from the IoT node to the hybrid access point are respectively expressed as:

[0021]

[0022]

[0023] Where W is the communication bandwidth, σ 2 Represents the noise power spectral density, Q = diag (H SR 1) and 1 represents an M×1-dimensional column vector whose elements are all 1, R SD represents the throughput from IoT node to receiver, R SR represents the throughput of the link from IoT node to hybrid access point, It represents the conjugate transpose of Q, which is an intermediate variable and has no physical meaning. represents the conjugate transpose, Indicates H SD Perform conjugate transpose.

[0024] In an embodiment of the present disclosure, the entire transmission process of the relay-assisted backscatter network is divided into a backscattering phase and a relay forwarding phase. For the relay-assisted backscatter network, based on the frame structure, the throughput of the backscattering phase, the relay forwarding phase, and the total throughput of the entire system are analyzed based on the linear mapping theory. The total throughput of the entire system includes:

[0025] In the relay forwarding stage, the forwarding signal received by the receiver is expressed as:

[0026]

[0027] Where, Represents the coded signal; at the same time, a linear mapping matrix is ​​introduced as the actual coding strategy, that is, x = Gc, P1 represents the power of the signal forwarded by the hybrid access point; is a complex Gaussian noise vector with zero mean;

[0028] The signals received by the receiver in the backscattering stage and the relay forwarding stage are expressed as:

[0029]

[0030] Formula (7) can be further simplified as:

[0031] y D =H D c+n D (8)

[0032] Where y D Represents the total received signal at the receiver, H D It is an intermediate variable defined and has no physical meaning. c represents the information of the IoT node. Then the throughput at the receiver can be expressed as:

[0033]

[0034] The total throughput of the entire system is expressed as:

[0035] R sum =max{R SD ,min(R SR ,R D )} (10)

[0036] Where R D2 Indicates an intermediate variable defined, which has no physical meaning. Indicates H D Perform conjugate transpose.

[0037] In an embodiment of the present disclosure, the step of maximizing the total throughput of the entire system, under the energy causality constraint of the IoT node and the hybrid access point, establishing a mixed integer non-convex optimization problem model based on the backscatter coefficient, the number of subframes allocated to the backscattering stage and the relay forwarding stage, and the transmit power of the hybrid access point to maximize the total throughput of the entire system includes:

[0038] The mixed integer non-convex optimization problem model is:

[0039]

[0040] Where, represents a mixed integer non-convex optimization problem, st represents the constraint, E represents the total energy transmitted by the hybrid access point in one frame, P c represents the circuit power consumption when the IoT node performs backscattering, P max Represents the maximum transmit power of the hybrid access point, C1 and C2 represent the energy causal constraints of the hybrid access point and the IoT node, respectively; C3 and C4 constrain the number of subframes allocated in the two phases; C5 is derived from the power constraint; C6 and C7 set the range of the hybrid access point's transmit power and backscatter coefficient in the two phases, λ1…λ N They represent the eigenvalues ​​of the linear mapping matrix respectively.

[0041] In an embodiment of the present disclosure, the steps of introducing slack variables, auxiliary variables, converting the mixed integer non-convex optimization problem model into a continuous convex optimization problem model using KKT conditions, time-sharing methods, and continuous convex approximation methods, designing an integer conversion strategy to obtain relevant optimal discrete solutions, and further optimizing the continuous variables in the convex optimization problem model based on the obtained discrete values ​​include:

[0042] Introducing the slack variable t=min(R SR ,R D ), the mixed integer non-convex optimization problem model Convert to optimization problem model Introduce Lemma 1 to explain the optimization problem and equivalence.

[0043] Lemma 2 is introduced to illustrate that the KKT condition can be used to obtain Will Substitution Eliminate some optimization variables to obtain the optimization problem model in, They represent the optimal solutions of eigenvalues ​​respectively;

[0044] Based on the time-sharing method, the slack variable ρ∈[0,1] and the slack discrete variable M / L are introduced to transform the optimization problem model Transformed into the optimization problem model

[0045] Introduction Lemma 3: Optimization Problem Model When obtaining the optimal solution, the equality of constraints C1-1 and C2-1 must hold, and the optimal backscattering coefficient obtained from C2-1 is expressed as Substitution Derive the model

[0046] In the embodiment of the present disclosure, the optimization problem model There are two situations:

[0047] When R SD ≤t, that is, h SD ≤h SR , the optimization problem model Can be transformed into an optimization problem model

[0048] Introducing auxiliary variables, using continuous convex approximation method, the optimization problem model Convert to optimization problem model

[0049] When R SD >t, that is, h SD <h SR , t=R″ SR , the optimization problem model Convert to optimization problem model And continue to transform into an optimization problem model

[0050] In the embodiment of the present disclosure, based on the continuous optimal solution, an integer conversion strategy is designed to obtain the corresponding optimal discrete solution; wherein, the integer conversion strategy is: in and Represents rounding down and rounding up respectively;

[0051] Based on the obtained optimal discrete values, the continuous variables in the optimization problem are further optimized.

[0052] In an embodiment of the present disclosure, the step of calculating the optimal total throughput of the entire system by using a low-complexity iterative algorithm includes:

[0053] The low-complexity algorithm is expressed as:

[0054] Algorithm 1: Solution

[0055] Input: coordinates of the IoT node, the hybrid access point, and the receiver;

[0056] Output: P0 * 、P1 * , ρ * , β * ;

[0057] Initialization: ρ 0 、a 0 ;

[0058] Repeat: Solve Get {a * ,b * ,ρ *};

[0059] Update the obtained continuous optimal variables;

[0060] Until: * ,b * ,ρ *}convergence;

[0061] pass and Calculate {P0 * ,P1 * ,β *};

[0062] Among them, P0 * is the optimal value of P0, P1 * is the optimal value of P1, ρ * is the optimal value of ρ, β * is the optimal value of β.

[0063] In an embodiment of the present disclosure, the step of calculating the optimal total throughput of the entire system by using a low-complexity iterative algorithm includes:

[0064] The low-complexity algorithm is expressed as:

[0065] Algorithm 2: Solution

[0066] Input: coordinates of the IoT node, the hybrid access point, and the receiver;

[0067] Output: ρ * 、P0 * ;

[0068] if:

[0069] but:

[0070] Otherwise: If:

[0071] but:

[0072] Otherwise: obtain ρ by bisection * ,

[0073] In an embodiment of the present disclosure, the step of calculating the optimal total throughput of the entire system by using a low-complexity iterative algorithm includes:

[0074] The low-complexity algorithm is expressed as:

[0075] Algorithm 3: Algorithm for maximizing the total throughput of the entire system

[0076] Input: coordinates of the IoT node, the hybrid access point, and the receiver;

[0077] Output: M + 、N + , β + 、P0 + 、P1 + ;

[0078] If: h SD ≤h SR ;

[0079] Then: by solving Get {P0 * , P1 * , ρ * , β *};

[0080] Otherwise: by solving Get {P0 * ,ρ *};

[0081] Obtaining the discrete optimal solution {M + ,N +};

[0082] If: h SD ≤h SR ;

[0083] Then: By re-optimizing {P0,P1}, we can obtain {P0 + ,P1 +},

[0084] Otherwise: recalculate {P0+ ,P1 + ,β +};

[0085] Among them, M + is the optimal value of M, N + is the optimal value of N, β + is the optimal value of β, P0 + is the optimal value of P0, P1 + is the optimal value of P1.

[0086] The technical solutions provided by the embodiments of the present disclosure may have the following beneficial effects:

[0087] In one embodiment of the present disclosure, through the above method, from the perspective of frame structure, the linear mapping method is used as the actual relay coding strategy analysis system workflow, and a precise capacity expression is obtained compared to existing work. At the same time, based on the precise capacity expression, a resource allocation strategy based on asymmetric discrete time is explored, and a more practical resource allocation strategy is obtained compared to the common resource allocation strategy based on continuous time.

[0088] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] The accompanying drawings are incorporated into and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the specification, are used to explain the principles of the present disclosure. Obviously, the drawings described below are only some embodiments of the present disclosure, and those skilled in the art can derive other drawings based on these drawings without inventive effort.

[0090] Figure 1 A flowchart schematically illustrates a method for allocating resources in a relay-assisted backscatter network based on linear mapping in an exemplary embodiment of the present disclosure;

[0091] Figure 2 Schematically illustrates a schematic diagram of a relay-assisted backscatter network model in an exemplary embodiment of the present disclosure;

[0092] Figure 3 A diagram schematically illustrates the relationship between iteration variables and iteration times in an exemplary embodiment of the present disclosure;

[0093] Figure 4 A diagram schematically illustrates a comparison between the resource allocation scheme in an exemplary embodiment of the present disclosure and three other fixed time allocation schemes;

[0094] Figure 5The diagram schematically shows a comparison between the resource allocation scheme in the exemplary embodiment of the present disclosure and the traditional continuous-time optimization scheme. DETAILED DESCRIPTION

[0095] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be embodied in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete and will fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0096] This example embodiment first provides a method for allocating resources in a relay-assisted backscatter network based on linear mapping. Figure 1 As shown in , the method may include:

[0097] Step S101: establishing a relay-assisted backscatter network, wherein the relay-assisted backscatter network includes: an Internet of Things node, a receiver, and a hybrid access point; wherein the Internet of Things node is equipped with an energy collection module and a backscatter module.

[0098] Step S102: The entire transmission process of the relay-assisted backscatter network is divided into a backscattering stage and a relay forwarding stage. For the relay-assisted backscatter network, from the perspective of frame structure, the throughput of the backscattering stage, the relay forwarding stage, and the total throughput of the entire system are analyzed based on linear mapping theory.

[0099] Step S103: With the goal of maximizing the total throughput of the entire system, under the energy causality constraint of the IoT node and the hybrid access point, a mixed integer non-convex optimization problem model is established based on the backscatter coefficient, the number of subframes allocated to the backscattering stage and the relay forwarding stage, and the transmit power of the hybrid access point; wherein the transmit power of the hybrid access point includes the transmit power of the backscattering stage and the transmit power of the relay forwarding stage.

[0100] Step S104: Introduce slack variables and auxiliary variables, use KKT conditions, time-sharing method and continuous convex approximation method to transform the mixed integer non-convex optimization problem model into a continuous convex optimization problem model, design an integer conversion strategy to obtain the relevant optimal discrete solution, and further optimize the continuous variables in the convex optimization problem model based on the obtained discrete values.

[0101] Step S105: Calculate the optimal total throughput of the entire system by using a low-complexity iterative algorithm.

[0102] Through the above method, starting from the perspective of frame structure, the linear mapping method is used as the actual relay coding strategy analysis system workflow, and a precise capacity expression is obtained compared with existing work. At the same time, based on the precise capacity expression, a resource allocation strategy based on asymmetric discrete time is explored. Compared with the common resource allocation strategy based on continuous time, a more practical resource allocation strategy is obtained.

[0103] Below, we will refer to Figures 1 to 5 Each step of the above method in this exemplary embodiment is described in more detail.

[0104] In step S101, a relay-assisted backscatter network is established. The relay-assisted backscatter network includes IoT nodes, receivers, and hybrid access points. The IoT nodes are equipped with energy harvesting modules and backscatter modules. Specifically, the hybrid access points function as both RF energy stations and relays, and are equipped with two antennas for simultaneously transmitting energy signals and receiving backscatter signals.

[0105] In step S102, the entire transmission process of the relay-assisted backscatter network is divided into a backscattering stage and a relay forwarding stage. For the relay-assisted backscatter network, from the perspective of frame structure, the throughput of the backscattering stage, the relay forwarding stage and the total throughput of the entire system are analyzed based on linear mapping theory.

[0106] In one embodiment, from the perspective of frame structure, the total throughput of the entire system is analyzed based on the linear mapping method, specifically including: the entire transmission process is divided into two stages: backscattering and relay forwarding. Assume that the duration of each transmission frame is T s , consisting of L subframes, where M subframes are used for the backscattering phase and N subframes are used for the relay forwarding phase, and M+N=L;

[0107] In one embodiment, during the backscattering phase, the hybrid access point acts as an energy station and broadcasts an energy signal. The IoT node modulates its own information onto the energy signal and backscatters it to the receiver and the hybrid access point. During the backscattering phase, the backscattered signals received by the receiver and the hybrid access point are:

[0108]

[0109]

[0110] Where, F = diag(H SR s), Represents the energy signal, represents the sending signal of the IoT node; P0 represents the power of the energy signal transmitted by the hybrid access point, β represents the backscatter coefficient of the IoT node, H SD =h SD I M 、H SR =h SR I M and H RD =h RD I N are the channel state information matrices of the links from IoT node to receiver, IoT node to hybrid access point, and hybrid access point to receiver, respectively, where h SD 、h SR 、h RD Denote the channel coefficients of the links from IoT node to receiver, IoT node to hybrid access point, and hybrid access point to receiver, respectively. LI represents the residual loop interference channel state information matrix, and are the complex Gaussian noise vector, I M represents the M-dimensional identity matrix, I N represents the N-dimensional identity matrix;

[0111]

[0112] Where η represents the energy collection efficiency, M represents the number of subframes allocated to the backscattering phase, N represents the number of subframes allocated to the relay forwarding phase, and T s Indicates the frame length of each frame;

[0113] The throughput of the link from the IoT node to the receiver and the throughput of the link from the IoT node to the hybrid access point are respectively expressed as:

[0114]

[0115]

[0116] Where W is the communication bandwidth, σ 2 Represents the noise power spectral density, Q = diag (H SR 1) and 1 represents an M×1-dimensional column vector whose elements are all 1, R SD represents the throughput from IoT node to receiver, R SR represents the throughput of the link from IoT node to hybrid access point, It represents the conjugate transpose of Q, which is an intermediate variable and has no physical meaning. represents the conjugate transpose, Indicates H SD Perform conjugate transpose.

[0117] Specifically, during the backscattering phase, the hybrid access point acts as an energy station and broadcasts an energy signal. The IoT node modulates its own information onto the energy signal and backscatters it to the receiver and the hybrid access point. Based on this, during the backscattering phase, the backscattered signal of the receiver can be obtained, as shown in Formula (1), and the backscattered signal received by the hybrid access point can be obtained, as shown in Formula (2). At the same time, the energy collected by the IoT node is obtained, as shown in Formula (3). Based on this, the throughput from the IoT node to the receiver is calculated, as shown in Formula (4), and the throughput of the link from the IoT node to the hybrid access point is calculated, as shown in Formula (5).

[0118] In one embodiment, in the relay forwarding stage, the forwarding signal received by the receiver is represented as:

[0119]

[0120] Where, Represents the coded signal; at the same time, a linear mapping matrix is ​​introduced as the actual coding strategy, that is, x = Gc, P1 represents the power of the signal forwarded by the hybrid access point; is a complex Gaussian noise vector with zero mean;

[0121] The signals received by the receiver in the backscattering stage and the relay forwarding stage are expressed as:

[0122]

[0123] Formula (7) can be further simplified as:

[0124] y D =H D c+n D (8)

[0125] Where y D Represents the total received signal at the receiver, H D It is an intermediate variable defined and has no physical meaning. c represents the information of the IoT node. Then the throughput at the receiver can be expressed as:

[0126]

[0127] The total throughput of the entire system is expressed as:

[0128] R sum =max{R SD ,min(R SR ,R D )} (10)

[0129] Where R D2Indicates an intermediate variable defined, which has no physical meaning. Indicates H D Perform conjugate transpose.

[0130] Specifically, during the relay forwarding phase, the hybrid access point acts as a relay and sends the received backscattered signal to the receiver according to the decoding and forwarding strategy. The forwarded signal received by the receiver is shown in Equation (6). Furthermore, the signals received by the receiver in the two phases (i.e., the backscattering phase and the relay forwarding phase) are shown in Equation (7), which is simplified to Equation (8). The throughput at the receiver is then shown in Equation (9), which is further calculated to obtain Equation (11), which is as follows:

[0131]

[0132] In order to facilitate the processing of R D2 , under the power constraint Tr(GG H )≤N, introduce the characteristic decomposition GG H =U H ΛU, where U is a unitary matrix, Λ=diag(λ1,…,λ N ) and eigenvalues ​​λ1,…,λ N are non-negative, then R D2 Converted into formula (12), formula (12) is as follows:

[0133]

[0134] Then, based on the throughput from the IoT node to the receiver, the throughput from the IoT node to the hybrid access point link, and the throughput at the receiver, the total throughput of the entire system is obtained, as shown in formula (10).

[0135] In step S103, with the goal of maximizing the total throughput of the entire system, a mixed integer non-convex optimization problem model is established based on the backscatter coefficient, the number of subframes allocated to the backscattering and relay forwarding phases, and the hybrid access point transmit power, subject to energy causality constraints of the IoT node and the hybrid access point. The hybrid access point transmit power includes the transmit power in the backscattering phase and the transmit power in the relay forwarding phase. Specifically, with the goal of maximizing the total throughput of the entire system, a mixed integer non-convex optimization problem model is established based on the backscatter coefficient, the backscattering and relay forwarding time, and the hybrid access point transmit power, subject to several constraints.

[0136] In one embodiment, the mixed integer non-convex optimization problem model is:

[0137]

[0138] Where, represents a mixed integer non-convex optimization problem, st represents the constraint, E represents the total energy transmitted by the hybrid access point in one frame, P c represents the circuit power consumption when the IoT node performs backscattering, P max Represents the maximum transmit power of the hybrid access point, C1 and C2 represent the energy causal constraints of the hybrid access point and the IoT node, respectively; C3 and C4 constrain the number of subframes allocated in the two phases; C5 is derived from the power constraint; C6 and C7 set the range of the hybrid access point's transmit power and backscatter coefficient in the two phases, λ1…λ N They represent the eigenvalues ​​of the linear mapping matrix respectively.

[0139] Step S104: Introducing slack variables and auxiliary variables, the mixed-integer non-convex optimization problem model is converted into a continuous convex optimization problem model using KKT conditions, time-sharing methods, and continuous convex approximation. An integer conversion strategy is designed to obtain the relevant optimal discrete solutions. Based on the obtained discrete values, the continuous variables in the convex optimization problem model are further optimized. Specifically, the mixed-integer non-convex optimization problem model is converted into a continuous convex optimization problem to facilitate the subsequent determination of the optimal total throughput of the entire system.

[0140] In one embodiment, in step S104, step S401: introduce a slack variable t=min(R SR ,R D ), simplify the complex form of the objective function and get the optimization problem Introduce Lemma 1 to explain the problem and equivalence.

[0141] Step S402: Introduce Lemma 2 to illustrate the use of KKT conditions to obtain Substitute the conclusion into Eliminate some optimization variables to get the optimization problem

[0142] Step S403: Based on the time-sharing method, introduce the slack variable ρ∈[0,1] and the slack discrete variable M / L to solve the non-convex mixed integer optimization problem Transformed into a non-convex continuous optimization problem

[0143] Step S404: Introduce Lemma 3 to illustrate the problem When obtaining the optimal solution, the equality of constraints C1-1 and C2-1 must hold, and the optimal backscattering coefficient obtained from C2-1 is expressed as Substituting the above conclusion into Conclusion

[0144] Step S405: Optimization problem For case 1, we introduce auxiliary variables to deal with the existing coupled variable constraints, and then use the continuous convex approximation method to transform the non-convex constraints into convex constraints to obtain the optimization problem For case 2, we obtain the linear optimization problem

[0145] Step S406: Based on the obtained continuous optimal solution, an integer conversion strategy is designed to obtain a corresponding optimal discrete solution.

[0146] Step S407: Based on the obtained optimal discrete values, further optimize the continuous variables in the optimization problem model.

[0147] In a specific embodiment, the above method is:

[0148] Since the objective function of the optimization problem is a complex form of max-min, a slack variable t=min(R SR ,R D ), simplify the objective function to obtain the following optimization problem:

[0149]

[0150] Lemma 1: Optimization Problem When the optimal solution is obtained, one of the equality signs of constraints C8 and C9 always holds true, then and The conversion is an equivalent conversion.

[0151] Proof of Lemma 1: Proof by contradiction from R SR ≥R D and R SR <R D Two cases are proved. SR ≥R D When, assuming The optimal solution is The solution satisfies all constraints and C9 There is another set of feasible solutions All constraints are met and R in C9 D =t * Established, of which At this time, since the objective function is a non-decreasing function of the variable t, the objective function obtains a larger value. SR ≥R D In this case, the optimal solution must make the equality of C9 hold. At this time, the optimization problem Can be degraded to A situation when R SR <RD By the same token, it can be proved that the optimal solution must make the equality of C8 hold. At this time, the optimization problem Can be degraded to Another case of . Lemma 1 is proved.

[0152] Lemma 2: Using the KKT condition, we can conclude

[0153] Proof of Lemma 3: For For example, some Lagrangian functions can be written as

[0154]

[0155] where μ1, μ2, μ3, μ4, μ5 and μ6 are non-negative Lagrange multipliers with respect to constraints C1, C2, C3, C5, C8, C9, Then the Lagrangian function with respect to λ i The partial derivative of make Get the optimal λ i The necessary condition is because The optimal right For , there is only one solution that satisfies the KKT condition, then the problem The optimal solution satisfies λ i =1,i=1,…,N.

[0156] Will Substitution The optimization problem is transformed into:

[0157]

[0158] in

[0159] Due to the problem Still a non-convex mixed integer optimization problem, based on the time-sharing method, the slack variable ρ∈[0,1] and the slack discrete variable M / L are introduced to transform the non-convex mixed integer optimization problem into Transformed into a continuous optimization problem

[0160]

[0161] in,

[0162]

[0163] Lemma 3: Problem When obtaining the optimal solution, the equality of constraints C1-1 and C2-1 must hold, and the optimal backscattering coefficient obtained from C2-1 is expressed as

[0164] Proof of Lemma 3: Assumption Problem The optimal solution is {P0 + ,P1 + ,β + ,ρ + ,t +}, the solution satisfies all constraints and ρ + P0 + +(1-ρ + )P1 + <P,η(1-β + )P0 + |h SR | 2 >P c . And we can find another set of solutions {P0 * ,P1 * ,β * ,ρ + ,t +} satisfies all constraints and ρ + P0 * +(1-ρ + )P1 * =P,η(1-β * )P0 * |h SR | 2 =P c , where P0 * >P0 + , P1 * >P1 + , β * >β + . At this time, the objective function can obtain a better value. Therefore, the problem The optimal solution must make the equality of constraints C1-1 and C2-1 hold. From this, we can deduce that the optimal power reflection coefficient is

[0165] Substituting the above conclusion into Optimization problem model Translates to:

[0166]

[0167] in,

[0168] because The objective function contains the max function and the optimization problem is non-convex, so we discuss the following two cases.

[0169] Case 1: R″ SD ≤t, that is, h SD ≤h SR , optimization problem can be transformed into:

[0170]

[0171] Define a=P0(1-ρ), b=P1(1-ρ), and and Substitution have to:

[0172]

[0173] in

[0174] Based on the continuous convex approximation method, the The non-convex terms on the left side of the inequality signs in C8-3 and C9-4 are subjected to binary Taylor expansion, and the optimization problem model is Translates to:

[0175]

[0176] stC1-4:f1(ρ j ,a j )+b=P,

[0177] C6-1,C7-2,C10,

[0178] C8-4:g1(ρ j ,a j )≥t,

[0179] C9-5:q(ρ,a)+w1(ρ j ,a j )≥t.

[0180] where f1(ρ j ,a j )=f(ρ j ,a j )+f′ ρ (ρ j ,a j )×(ρ-ρ j )+f′ a (ρ j ,a j )(aa j )

[0181] g1(ρ j ,a j )=g(ρ j ,a j )+g′ ρ (ρ j ,a j )×(ρ-ρ j )+g′ a (ρ j ,a j )×(aa j )

[0182] w1(ρ j ,a j )=w(ρ j ,a j )+w′ ρ (ρ j ,a j )×(ρ-ρ j )+w′ a (ρ j ,a j )×(aa j )

[0183]

[0184]

[0185] At this time, the optimization problem The CVX tool can be used to solve it, see Algorithm 1 for details.

[0186] Case 2: R″ SD >t, that is, h SD <h SR , t=R″ SR , the optimization problem model is can be transformed into:

[0187]

[0188] Will Substitution have to:

[0189]

[0190] definition It can be observed that its second-order derivative is negative, so the first-order derivative is monotonically decreasing. The objective function is concave and has only one optimal solution. Therefore, this problem can be solved using monotonicity or bisection method, see Algorithm 2 for details.

[0191] Based on the optimal continuous solution solved for each case, an integer conversion strategy is designed to obtain the corresponding optimal discrete value, which is expressed as: in and Indicates floor and ceiling, respectively.

[0192] The discrete solution M obtained by the integer conversion strategy + and N + Substitute the known variables into the problem or Further optimization of other continuous variables was performed.

[0193] Optimization problem model For case 1, we introduce auxiliary variables to deal with the existing coupled variable constraints, and then use the continuous convex approximation method to transform the non-convex constraints into convex constraints to obtain the optimization problem model For case 2, the linear optimization problem model is obtained

[0194] Step S105: Calculate the optimal total throughput of the entire system by using a low-complexity iterative algorithm.

[0195] In one embodiment, the design of the low-complexity algorithm specifically includes:

[0196] The low-complexity algorithm is expressed as:

[0197] Algorithm 1: Solution

[0198] Input: coordinates of the IoT node, the hybrid access point, and the receiver;

[0199] Output: P0 * 、P1 * , ρ * , β * ;

[0200] Initialization: ρ 0 、a 0 ;

[0201] Repeat: Solve Get {a * ,b * ,ρ *};

[0202] Update the obtained continuous optimal variables;

[0203] Until: * ,b * ,ρ *}convergence;

[0204] pass and Calculate {P0 * ,P1 * ,β *};

[0205] Among them, P0 * is the optimal value of P0, P1 * is the optimal value of P1, ρ * is the optimal value of ρ, β * is the optimal value of β.

[0206] Algorithm 2: Solution

[0207] Input: coordinates of the IoT node, the hybrid access point, and the receiver;

[0208] Output: ρ * 、P0 * ;

[0209] if:

[0210] but:

[0211] Otherwise: If:

[0212] but:

[0213] Otherwise: obtain ρ by bisection * ,

[0214] Algorithm 3: Algorithm for maximizing the total throughput of the entire system

[0215] Input: coordinates of the IoT node, the hybrid access point, and the receiver;

[0216] Output: M + 、N + , β + 、P0 + 、P1 + ;

[0217] If: h SD ≤h SR ;

[0218] Then: by solving Get {P0 * ,P1 * ,ρ * ,β *};

[0219] Otherwise: by solving Get {P0 * ,ρ *};

[0220] Obtaining the discrete optimal solution {M + ,N +};

[0221] If: h SD ≤h SR ;

[0222] Then: By re-optimizing {P0,P1}, we can obtain {P0 + ,P1 +},

[0223] Otherwise: recalculate {P0 + ,P1 + ,β +};

[0224] Among them, M + is the optimal value of M, N + is the optimal value of N, β + is the optimal value of β, P0 + is the optimal value of P0, P1 + is the optimal value of P1.

[0225] The following is a simulation experiment to further illustrate the embodiment of the present disclosure.

[0226] The embodiment of the present disclosure simulates and verifies a method for allocating resources in a relay-assisted backscatter network based on linear mapping under the following simulation parameters. 2 In a two-dimensional network, it is assumed that the coordinate positions of the IoT node, hybrid access point HAP and receiver are (0,0), (20m,20m), (100m,0) respectively, and the frame length of each frame is T s =10ms, bandwidth is set to W=10kHz, noise power spectral density σ 2 =-100dBm / Hz, energy conversion efficiency η = 0.5, backscatter circuit power consumption P c = 200μW, the total energy transmitted by HAP in each frame is E = 200mW. In this simulation, the channel is modeled as ξ i and d i Represent the power gain and distance of small-scale fading of the i-th link, respectively, where i∈{SD,SR,RD}, α1, α2, α3 represent the path loss factors of SD, SR and RD links, respectively. Figure 3The relationship between the iteration variables ρ and a and the number of iterations is described. The above-mentioned iterative algorithm can converge to a constant value after a relatively small number of iterations, which shows that the proposed iterative algorithm can converge quickly. In addition, it can be observed that P max = 20W, the convergence speed is faster than P max =30W, which shows that the convergence performance of the continuous convex approximation algorithm depends to a large extent on the setting of the initial value. Figure 4 The proposed solution was compared with three fixed-time allocation schemes: a backscatter network, a relay-assisted backscatter network, and an opportunistic relay-assisted backscatter network. The throughput for each strategy was plotted against the SD link loss factor. The proposed solution consistently outperformed the other schemes in terms of throughput. This is because the other schemes consider a fixed-time strategy and fail to fully utilize system parameters to improve system performance. Figure 5 The proposed solution is compared with a traditional relay-assisted backscatter network solution that optimizes continuous time allocation, and curves are plotted between throughput and SD link loss factor under different strategies. This figure shows the throughput curves under different total subframe numbers, namely L = 20 (actual) and L = 1000 (simulation). It is observed that when L = 20, the throughput obtained by the proposed solution is lower than the throughput of the traditional solution. The main reasons are: the traditional solution uses the upper bound formula of the precise throughput obtained in this disclosure to design the optimal resource allocation strategy. In addition, the traditional solution optimizes the continuous time to obtain a more ideal throughput, which is not feasible in reality.

[0227] Those skilled in the art will readily appreciate other embodiments of the present disclosure after considering the specification and practicing the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the present disclosure that follow the general principles of the present disclosure and include common knowledge or customary techniques in the art not disclosed herein. The description and examples are to be considered as exemplary only, with the true scope and spirit of the present disclosure being indicated by the appended claims.

Claims

1. A method for allocating resources in a relay-assisted backscatter network based on linear mapping, characterized in that: The method includes: Establishing a relay-assisted backscatter network, the relay-assisted backscatter network comprising: an Internet of Things node, a receiver, and a hybrid access point; wherein the Internet of Things node is equipped with an energy harvesting module and a backscatter module; The entire transmission process of the relay-assisted backscatter network is divided into a backscattering phase and a relay forwarding phase. Based on the frame structure of the relay-assisted backscatter network, the throughput of the backscattering phase, the relay forwarding phase, and the total throughput of the entire system are analyzed based on linear mapping theory. The entire transmission process of the relay-assisted backscatter network is divided into a backscattering phase and a relay forwarding phase. For the relay-assisted backscatter network, based on the frame structure, the throughput of the backscattering phase, the relay forwarding phase, and the total throughput of the entire system are analyzed based on the linear mapping theory. The total throughput of the entire system includes: Set the duration of the transmission frame in the backscattering phase and the relay forwarding phase to T s , consisting of L subframes, wherein M subframes are used for the backscattering phase, N subframes are used for the relay forwarding phase, and M+N=L is satisfied; In the backscattering phase, the backscattered signals received by the receiver and the hybrid access point are respectively: Where, F = diag(H SR s), Represents the energy signal, represents the sending signal of the IoT node; P0 represents the power of the energy signal transmitted by the hybrid access point, β represents the backscatter coefficient of the IoT node, H SD =h SD I M 、H SR =h SR I M and H RD =h RD I N are the channel state information matrices of the links from IoT node to receiver, IoT node to hybrid access point, and hybrid access point to receiver, respectively, where h SD 、h SR 、h RD Denote the channel coefficients of the links from IoT node to receiver, IoT node to hybrid access point, and hybrid access point to receiver, respectively. LI represents the residual loop interference channel state information matrix, and are the complex Gaussian noise vector, I M represents the M-dimensional identity matrix, I N represents the N-dimensional identity matrix; The energy collected by the IoT node is expressed as: Where η represents the energy collection efficiency, M represents the number of subframes allocated to the backscattering phase, N represents the number of subframes allocated to the relay forwarding phase, and T s Indicates the frame length of each frame; The throughput of the link from the IoT node to the receiver and the throughput of the link from the IoT node to the hybrid access point are respectively expressed as: Where W is the communication bandwidth, σ 2 Represents the noise power spectral density, Q = diag (H SR 1) and 1 represents an M×1-dimensional column vector whose elements are all 1, R SD represents the throughput from IoT node to receiver, R SR represents the throughput of the link from IoT node to hybrid access point, It represents the conjugate transpose of Q, which is an intermediate variable and has no physical meaning. represents the conjugate transpose, Indicates H SD Perform conjugate transpose; In the relay forwarding stage, the forwarding signal received by the receiver is expressed as: Where, Represents the coded signal; at the same time, a linear mapping matrix is ​​introduced as the actual coding strategy, that is, x = Gc, P1 represents the power of the signal forwarded by the hybrid access point; is a complex Gaussian noise vector with zero mean; The signals received by the receiver in the backscattering stage and the relay forwarding stage are expressed as: Formula (7) can be further simplified as: y D =H D c+n D (8) Where y D Represents the total received signal at the receiver, H D It is an intermediate variable defined and has no physical meaning. c represents the information of the IoT node. Then the throughput at the receiver can be expressed as: The total throughput of the entire system is expressed as: R sum =max{R SD ,min(R SR ,R D )} (10) Where R D2 Indicates an intermediate variable defined, which has no physical meaning. Indicates H D Perform conjugate transpose; With the goal of maximizing the total throughput of the entire system, under the energy causality constraints of the IoT nodes and the hybrid access points, a mixed integer non-convex optimization problem model is established based on the backscatter coefficient, the number of subframes allocated to the backscattering phase and the relay forwarding phase, and the transmit power of the hybrid access point; wherein the transmit power of the hybrid access point includes the transmit power in the backscattering phase and the transmit power in the relay forwarding phase; The step of maximizing the total throughput of the entire system, and establishing a mixed integer non-convex optimization problem model based on the backscatter coefficient, the number of subframes allocated to the backscattering stage and the relay forwarding stage, and the transmit power of the hybrid access point under the energy causality constraint of the IoT node and the hybrid access point, includes: The mixed integer non-convex optimization problem model is: Where, represents the mixed integer non-convex optimization problem model, st represents the constraint, E represents the total energy transmitted by the hybrid access point in one frame, P c represents the circuit power consumption when the IoT node performs backscattering, P max Represents the maximum transmit power of the hybrid access point, C1 and C2 represent the energy causal constraints of the hybrid access point and the IoT node, respectively; C3 and C4 constrain the number of subframes allocated in the two phases; C5 is derived from the power constraint; C6 and C7 set the range of the hybrid access point's transmit power and backscatter coefficient in the two phases, λ1…λ N Respectively represent the eigenvalues ​​of the linear mapping matrix; Introducing slack variables and auxiliary variables, using KKT conditions, time-sharing methods, and continuous convex approximation methods to transform the mixed integer non-convex optimization problem model into a continuous convex optimization problem model, designing an integer conversion strategy to obtain the relevant optimal discrete solutions, and further optimizing the continuous variables in the convex optimization problem model based on the obtained discrete values; The optimal total throughput of the entire system is calculated by a low-complexity iterative algorithm.

2. The method for relay-assisted backscatter network resource allocation based on linear mapping according to claim 1, wherein the steps of introducing slack variables, auxiliary variables, converting the mixed integer non-convex optimization problem model into a continuous convex optimization problem model using KKT conditions, time-sharing methods, and continuous convex approximation methods, designing an integer conversion strategy to obtain relevant optimal discrete solutions, and further optimizing the continuous variables in the convex optimization problem model based on the obtained discrete values ​​include: Introducing the slack variable t=min(R SR ,R D ), the mixed integer non-convex optimization problem model Convert to optimization problem model Lemma 1 introduces the mixed integer non-convex optimization problem model and optimization problem model equivalence; Among them, the optimization problem model The expression is as follows: Lemma 1: Optimization problem model When obtaining the optimal solution, one of the equality signs of constraints C8 and C9 always holds, then the mixed integer non-convex optimization problem model is and optimization problem model The conversion into equivalent conversion; Introduce Lemma 2: Using the KKT condition, we can get Will Substitute into the optimization problem model Eliminate some optimization variables to obtain the optimization problem model in, They represent the optimal solutions of eigenvalues ​​respectively; Optimization problem model The expression is as follows: Based on the time-sharing method, the slack variable ρ∈[0,1] and the slack discrete variable M / L are introduced to transform the optimization problem model Transformed into the optimization problem model Optimization problem model The expression is as follows: Where P = E / T s , Introduction Lemma 3: Optimization Problem Model When obtaining the optimal solution, the equality of constraints C1-1 and C2-1 must hold, and the optimal backscattering coefficient obtained from C2-1 is expressed as is the optimal value of P0, substitute Derive the optimization problem model Optimization problem model The expression is as follows: in, 3. The method for allocating resources in a relay-assisted backscatter network based on linear mapping according to claim 2, wherein: The optimization problem model There are two situations: When R SD ≤t, that is, h SD ≤h SR , the optimization problem model Can be transformed into an optimization problem model Among them, the optimization problem model The expression is as follows: Introducing auxiliary variables, using continuous convex approximation method, the optimization problem model Convert to optimization problem model Define a=P0(1-ρ), b=P1(1-ρ), and and Substitution have to: in Based on the continuous convex approximation method, the The non-convex terms on the left side of the inequality signs in C8-3 and C9-4 are subjected to binary Taylor expansion, and the optimization problem model is Convert to optimization problem model Optimization problem model The expression is as follows: s.t.C1-4:f1(ρ j ,a j )+b=P, C6-1,C7-2,C10, C8-4:g1(p j ,a j )≥t, C9-5:q(ρ,a)+w1(ρ j ,a j )≥t. where, f1(ρ j , a j ) = f(ρ j , a j ) + f′ ρ (ρ j , a j ) × (ρ - ρ j ) + f′ a (ρ j , a j )(a - a j ) g1(r j ,a j )=g(ρ j ,a j )+g′ ρ (r j ,a j )×(r-r j )+g′ a (r j ,a j )×(aa j ) w1(ρ j ,a j )=w(ρ j ,a j )+w′ ρ (ρ j ,a j )×(ρ-ρ j )+w′ a (ρ j ,a j )×(a-a j ) When R SD >t, that is, h SD <h SR , t=R″ SR , the optimization problem model Convert to optimization problem model And continue to transform into an optimization problem model Optimization problem model The expression is as follows: Will Substitute into the optimization problem model Optimization problem model Optimization problem model The expression is as follows: definition 4. The linear mapping-based relay-assisted backscatter network resource allocation method according to claim 3, characterized in that: Based on the continuous optimal solution, an integer conversion strategy is designed to obtain the corresponding optimal discrete solution; wherein the integer conversion strategy is: in and Represents rounding down and rounding up, M + is the optimal discrete solution, M * is a continuous optimal solution, is the optimal value of P0, P1 * is the optimal value of P1; Based on the obtained optimal discrete values, the continuous variables in the optimization problem are further optimized.

5. The method for allocating resources in a relay-assisted backscatter network based on linear mapping according to claim 4, characterized in that: The step of calculating the optimal total throughput of the entire system by using a low-complexity iterative algorithm includes: The low-complexity iterative algorithm is expressed as: Algorithm 1: Solving the optimization problem model Input: coordinates of the IoT node, the hybrid access point, and the receiver; Output: P1 * , ρ * , β * ; Initialization: ρ 0 、a 0 ; Repeat: Solve the optimization problem model Get {a * ,b * ,ρ * }; Update the obtained continuous optimal variables; Until: * ,b * ,ρ * }convergence; pass and calculate in, is the optimal value of P0, P1 * is the optimal value of P1, ρ * is the optimal value of ρ, β * is the optimal value of β.

6. The method for allocating resources in a relay-assisted backscatter network based on linear mapping according to claim 5, characterized in that: The step of calculating the optimal total throughput of the entire system by using a low-complexity iterative algorithm includes: The low-complexity iterative algorithm is expressed as: Algorithm 2: Solving the optimization problem model Input: coordinates of the IoT node, the hybrid access point, and the receiver; Output: ρ * 、 if: but: Otherwise: If: but: Otherwise: obtain ρ by bisection * , 7. The method for allocating resources in a relay-assisted backscatter network according to claim 6, wherein: The step of calculating the optimal total throughput of the entire system by using a low-complexity iterative algorithm includes: The low-complexity iterative algorithm is expressed as: Algorithm 3: Algorithm for maximizing the total throughput of the entire system Input: coordinates of the IoT node, the hybrid access point, and the receiver; Output: M + 、N + , β + 、 P1 + ; If: h SD ≤h SR ; Then: By solving the optimization problem model get Otherwise: by solving the optimization problem model get Obtaining the discrete optimal solution {M + ,N + }; If: h SD ≤h SR ; Then: By re-optimizing {P0, P1}, we can obtain Otherwise: recalculate Among them, M + is the optimal value of M, N + is the optimal value of N, β + is the optimal value of β, is the optimal value of P0, P1 + is the optimal value of P1.

Images