System and method for throughput optimization of ts-swipt multi-hop relay based on greedy binary search

Abstract

The system comprises a source node, a relay node adopting a DF protocol and a destination node; the source node has a fixed power supply, the transmission power of the source node is fixed and recorded as P s, and each relay node, wherein the energy collected from the radio frequency signal of the direct predecessor node through the TS-SWIPT protocol is used for operation; the purpose of the application is to solve the technical problems that the existing TS-SWIPT multi-hop network has high calculation complexity and is difficult to be deployed in real time when processing throughput maximization, lacks a special and efficient processing method for the TS protocol, the exponential complexity of the exhaustive search is unacceptable, and the performance loss of the heuristic method is significant.

Description

Technical Field

[0001] This invention relates to the field of electronic information technology, and in particular to a TS-SWIPT multi-hop relay throughput optimization system and method based on greedy binary search. Background Technology

[0002] Wireless multi-hop relay networks are a key technology for extending communication coverage and improving transmission reliability. They achieve hop-by-hop signal forwarding by deploying multiple relay nodes between the source and destination nodes. This system has wide applications in wireless sensor networks (WSNs), the Internet of Things (IoT), and emergency communications, and is particularly suitable for situations where node energy is limited, deployment environments are complex, or physical obstructions exist (see the existing technology "RIS-Assisted Seamless Connectivity in Wireless Multi-Hop Relay Networks"). Traditional relay nodes mostly rely on battery power, and their limited energy reserves and frequent maintenance requirements severely restrict the long-term reliable operation of the network. To overcome this bottleneck, simultaneous wireless information and power transfer (SWIPT) technology has emerged. This technology enables relay nodes to simultaneously decode information and collect energy from received radio frequency signals, thereby achieving self-sufficiency in power (see the existing technology "Green Operations of SWIPT Networks: The Role of End-User Devices").

[0003] Among the various implementation protocols of SWIPT, the time-switching (TS) protocol has become one of the mainstream solutions due to its simple hardware implementation and flexible control (see the existing technology "Robust Transceiver Design for SWIPT DF MIMO Relay Systems With Time-Switching Protocol"). In a TS-SWIPT multi-hop decode-and-forward (DF) relay network, each relay node divides the transmission time slot into an energy harvesting phase and an information decoding and forwarding phase, and the time allocation ratio is called the TS ratio. One of the core optimization problems of the system is: under the condition that the source node's transmit power is fixed, how to jointly optimize the TS ratio of each relay node to maximize end-to-end throughput. This problem is directly related to the network's energy utilization, data transmission efficiency, and service quality, and is a key issue in the fields of green communication and sustainable Internet of Things (see the existing technology "Throughput Maximization for Multi-Hop Decode-and-Forward Relay Network With Wireless Energy Harvesting").

[0004] Existing research on maximizing throughput in TS-SWIPT multi-hop networks mainly follows these technical paths: First, transforming the original non-convex problem into a convex optimization problem through variable substitution (such as logarithmic transformation), and then using iterative algorithms such as the interior-point method (IPM) to solve it, for example, the schemes disclosed in existing technologies such as "ThroughputMaximization for Multi-Hop Decode-and-Forward Relay Network With WirelessEnergy Harvesting" or "Interior Point-Driven Throughput Maximization for TS-SWIPT Multi-Hop DF Relays: A Log Barrier Approach"; second, using an exhaustive search strategy to perform global optimization in a discrete parameter space; and third, using a heuristic method with a fixed TS ratio to reduce implementation complexity. Specifically, existing technologies have the following defects and shortcomings: 1) High computational complexity and difficulty in real-time deployment: Existing solution methods based on convex optimization frameworks, such as the interior-point method and other general convex optimization solvers, require multiple iterations and complex matrix operations (such as inverting the Hessian matrix), and their time complexity is typically on the order of the cube to the 3.5th power of the problem size. ~ ,in The high number of relays results in excessive computational latency in IoT scenarios with multiple relays and high real-time requirements, failing to meet the needs of rapid resource scheduling in dynamic channel environments. This type of algorithm is particularly difficult to deploy directly for edge nodes with limited computing power. 2) Lack of dedicated and efficient methods for the TS protocol: Although the throughput maximization problem of TS-SWIPT multi-hop relay networks has been proven to be transformable into a convex problem, academia and industry still rely on general iterative solvers (such as the scheme disclosed in the existing technology "Interior Point-Driven Throughput Maximization for TS-SWIPT Multi-HopDF Relays: A Log Barrier Approach"). There is no dedicated algorithm that can directly utilize the problem structure and obtain the optimal TS ratio without iterative optimization. This gap forces system designers to make a difficult trade-off between algorithm accuracy and computational efficiency, lacking a solution that can guarantee global optimality while achieving linear complexity. 3) The exponential complexity of exhaustive search is unacceptable: Although exhaustive search can serve as a benchmark for verifying optimality, its computational complexity increases with the number of relays. Exponential growth ( , (the number of discretization steps for each TS ratio), even for For medium-sized networks, the computation time is already beyond practical use. This method cannot be scaled to scenarios with a greater number of relay nodes that may arise in real-world deployments. 4) Significant performance loss with heuristic methods: Heuristic methods with fixed TS ratios (such as setting the TS ratio of all relays to the same constant) are extremely fast in calculation, but they completely ignore the dynamic changes in channel conditions and the differences in the quality of each hop link. Existing research shows that the throughput performance of such methods is far lower than the optimal solution. When channel conditions are poor or the number of relays increases, the performance gap can be more than an order of magnitude, failing to meet the quality of service requirements. Summary of the Invention

[0005] The purpose of this invention is to address the technical problems of existing TS-SWIPT multi-hop networks in maximizing throughput, such as high computational complexity making real-time deployment difficult, lack of dedicated and efficient processing methods for the TS protocol, unacceptable exponential complexity of exhaustive search, and significant performance loss of heuristic methods. These problems restrict the performance of TS-SWIPT multi-hop networks in practical applications. Therefore, the applicant proposes a TS-SWIPT multi-hop relay throughput optimization system and method based on greedy binary search.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A TS-SWIPT multi-hop relay throughput optimization system based on greedy binary search, including source node , A relay node using the DF protocol and destination node ;Source node It has a fixed power supply, source node The transmission power is fixed and denoted as And each relay node ,in via the TS-SWIPT protocol from its direct predecessor node It uses energy collected from radio frequency signals to operate.

[0007] Each relay node Transmit block time Divided into a duration of The energy harvesting phase and a subsequent duration are The information decoding and forwarding stage, in which Time switching ratio; destination node Throughout the time Internally, only information decoding is performed; all relays operate in half-duplex mode, assuming the first... Channel gain of jump In a coherent time block The internal structure remains unchanged.

[0008] set up Represents a node ,in The information symbol at that location has a unit average power, i.e. ;No. The complex channel coefficients of the hop are denoted as The corresponding channel gain is Therefore, node The received signal at the location is: ,(1); in yes The transmission power, express The noise at the aggregation receiver is modeled as additive white Gaussian noise, and its distribution is as follows: Noise power It includes inherent antenna thermal noise and noise introduced by the information decoding circuitry; relay node ,in The collected energy is used entirely for its own signal transmission; therefore, its transmission power is given by the following formula: (2); in express The rectification efficiency; node The signal-to-noise ratio at this point is: (3); in And it is agreed that the empty product equals 1; No. Jump, among them The achievable rate is: (4); in Indicates the transmission bandwidth for destination nodes that do not perform energy harvesting. Its rate simplifies to: (5); End-to-end throughput is determined by the minimum hop rate and normalized by the number of hops: (6).

[0009] The goal of the above system is to increase the transmit power at the source node. Maximize end-to-end throughput under fixed conditions Simultaneously, jointly optimize the TS ratio of each relay. The optimization problem can be expressed as: (7a); st , (7b); To process equation (6) The nonsmoothness of the operator defines the minimum per-hop rate of the normalization. .maximize Equivalent to maximizing Problem (7) can be rewritten in the following equivalent form: (8a); st , ,(8b); ,(8c); , (8d); Constraints (8b) to (8d) are smooth, because They are coupled in a product form within the logarithm, and there exists a factor. The optimization problem is inherently non-convex; existing techniques typically transform it into a convex problem by replacing logarithmic variables and then calling general iterative solvers such as the interior-point method. However, such methods have excessively high computational complexity and are not suitable for resource-constrained IoT nodes.

[0010] Suppose that for a given TS ratio sequence If the normalized rate ( r (Also known as candidate rate) is feasible, that is, it exists. If (8b)-(8c) are satisfied, then any value less than The speed must also be feasible, a property that allows it to be possible to... Perform a binary search on the interval to efficiently locate the maximum feasible rate. ; Therefore, a throughput maximization algorithm based on greedy binary search is proposed to test a given candidate rate. Does a set of TS ratios exist? All constraints are satisfied; Define cumulative variables (set up ),but ;Will Before substitution The jump constraint (8b) yields information about Upper bound: , . (9); The constraint (8c) for the last jump is given The lower bound: (10); To maximize the final value To satisfy the lower bound (10), the most greedy strategy is to take the equality sign of equation (9) at each step, that is: , ,(11); from Begin recursive calculation. It can be proven that the function... In satisfying The time is strictly increasing, therefore the sequence generated by equation (11) is... It is the sequence that maximizes the maximum value among all feasible sequences. The sequence. Therefore, if and only if the sequence obtained by equation (11) is... At that time, candidate rate It is feasible.

[0011] Based on the above feasibility criteria, it can be determined by adjusting the normalization rate. The maximum feasible rate is determined by performing a binary search within the range of values ​​of . This is the Greedy Binary Search (GBS) algorithm, and its specific steps are summarized as follows: Step 1: Initialize the binary search interval for the normalized rate; Step 2: Within the search interval, perform an iterative binary search based on the preset search precision; in each iteration, call the feasibility check subroutine to check the current midpoint candidate rate, and dynamically update the search interval according to the check result until the precision condition is met, thereby determining the optimal normalized rate. Step 3: Based on the optimal normalization rate, calculate the cumulative variable sequence of intermediate relay nodes, and recover the optimal time-switching (TS) ratio for each hop accordingly, and output the final optimization result.

[0012] Step 1 specifically includes the following sub-steps: Step 1-1: Set the lower bound of the search interval Initialize to 0; Step 1-2: Generate a conservative upper bound based on the constraints of the last hop, and set the upper bound of the search interval accordingly. Initialize to ;in, Preset parameters for the system. K This represents the number of relay nodes.

[0013] Step 2 specifically includes the following sub-steps: Step 2-1: Determine the difference between the upper and lower bounds of the current search interval. Is the search precision greater than the preset value? ,in If so, then calculate the midpoint of the current interval as a candidate rate. If yes, proceed to step 2-2; otherwise, stop the iteration and proceed to step 2-4. Step 2-2: The candidate rates The data is input into the feasibility check subroutine for verification. This feasibility check subroutine specifically includes the following execution process: Step 2-2-1: Initialize the cumulative variables for the first hop. ; Step 2-2-2: For the relay node sequence number k =1 to K The following judgments and updates are executed sequentially: like If it fails, it is directly judged as "infeasible" and the subroutine is terminated; otherwise, it is handled according to the formula. Calculate and update the cumulative variable for the next hop. ; Step 2-2-3: After completion K After the first iteration, determine the final accumulated variable. Does it meet the lower bound condition? If the condition is met, the subroutine returns "feasible"; otherwise, it returns "infeasible". Step 2-2-4: Update the binary search interval based on the subroutine's return result: if it returns "feasible", then let If the return value is "not feasible", then let Return to step 2-1; Steps 2-3: Set the current lower bound after satisfying the search precision condition. Set to optimal normalization rate .

[0014] Step 3 specifically includes the following sub-steps: Step 3-1: Determine the optimal normalization rate Substitute the values ​​back into the recursive formula of step 2-2-2, and record the complete cumulative variable sequence generated during the calculation process. ,Right now ; Step 3-2: For k=1 to K, use the formula Recover each one and calculate the optimal TS ratio. ; Step 3-3: Output the obtained optimal normalized rate and the optimal TS ratio sequence As the ultimate resource allocation strategy.

[0015] Compared with the prior art, the present invention has the following technical effects: 1) The method of this invention is based on the inherent monotonicity of the problem (if a certain rate) If feasible, then all lower rates are also feasible. The maximum feasible normalized rate is precisely located using binary search. The optimal time switching ratio is directly recovered by constructing a greedy sequence; theoretical analysis proves that the greedy update maximizes the final accumulated variable among all feasible sequences. This ensures the necessity and sufficiency of the feasibility determination and its global optimality. Simulation results (Table I) verify that the relative errors of the throughput and TS ratio obtained by this algorithm and exhaustive search are within the acceptable range. to The magnitude was determined to confirm that it had reached the global optimum.

[0016] 2) The time complexity of the method of this invention is: ,in For the number of relays, For search accuracy, a single feasibility check only requires... After performing arithmetic and logarithmic operations, the binary search iterations are... The complexity is linearly related to the number of relays. In contrast, the complexity of general convex optimization solvers such as the interior-point method is typically O(n log n). to Simulation results ( Figure 4 This indicates that when At that time, the computation time of this algorithm (0.027 ms) is more than three orders of magnitude shorter than that of the interior-point method (78.9 ms), and the advantage becomes more significant as the number of relays increases. Furthermore, this algorithm does not require storing large matrices, and its space complexity is only [missing information]. It is ideal for IoT nodes with limited computing power and scarce memory resources.

[0017] 3) Existing TS-SWIPT throughput maximization methods mostly rely on general iterative solvers such as interior-point methods, requiring repeated matrix inversion and line search. The method of this invention constructs the optimal TS ratio in one go through the greedy recursive formula (11), completely avoiding the iterative optimization process. This not only eliminates the risk of uncertain algorithm convergence, but also reduces implementation complexity, making it easy to solidify into a deterministic process in embedded systems.

[0018] 4) The linear logarithmic complexity of the method of this invention enables it to efficiently handle a large number of relays. For multi-hop networks (reaching tens or even hundreds of hops), this algorithm exhibits significantly better scalability than traditional methods (interior point method, exhaustive search) whose computational complexity increases exponentially or even exponentially. Furthermore, the monotonicity-based search mechanism of this algorithm is inherently robust to different channel implementations; in simulations using a Rician fading channel, the algorithm consistently and stably obtains the optimal solution after 5000 independent implementations.

[0019] 5) By jointly optimizing the TS ratio of each relay, the method of this invention maximizes the end-to-end normalized throughput under a fixed source power. This is in contrast to heuristic methods with a fixed TS ratio (such as...). Compared to [previous algorithm], this algorithm [is superior to] [previous algorithm]. , The throughput can reach 135.23 kbps at dBm, while the fixed throughput... The method achieves a throughput of only 2.43 kbps, representing a performance improvement of over 50 times. This significant throughput gain directly translates into higher network data transmission efficiency and lower energy consumption per bit. For energy-harvesting IoT networks, this means a longer network lifespan and lower maintenance costs.

[0020] In summary, this invention provides a throughput optimization solution that combines global optimality, ultra-low computational complexity, direct constructibility, high scalability, and significant performance gains. It can effectively promote the practical deployment and application of TS-SWIPT multi-hop relay networks in energy-sensitive IoT and other wireless communication systems with limited computing power. Attached Figure Description

[0021] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is the TS-SWIPT multi-hop DF relay network topology diagram in this invention; Figure 2 In the embodiment, the source power is fixed. At dBm, the average end-to-end throughput of each algorithm varies with the number of relays. A schematic diagram illustrating the changes; Figure 3 In the embodiment, a fixed number of relays Below, the average throughput varies with the source power. A schematic diagram illustrating the changes; Figure 4 This is a comparison chart of the computational efficiency of each algorithm in the embodiments; Figure 5 This is a flowchart of the method of the present invention. Detailed Implementation

[0022] like Figure 1 As shown, a TS-SWIPT multi-hop relay throughput optimization system based on greedy binary search includes a source node. , A relay node using the DF protocol and destination node ;Source node It has a fixed power supply, source node The transmission power is fixed and denoted as And each relay node ,in via the TS-SWIPT protocol from its direct predecessor node It uses energy collected from radio frequency signals to operate.

[0023] Each relay node Transmit block time Divided into a duration of The energy harvesting phase and a subsequent duration are The information decoding and forwarding stage, in which Time switching ratio; destination node Throughout the time Internally, only information decoding is performed; all relays operate in half-duplex mode, assuming the first... Channel gain of jump In a coherent time block The internal structure remains unchanged.

[0024] set up Represents a node ,in The information symbol at that location has a unit average power, i.e. ;No. The complex channel coefficients of the hop are denoted as The corresponding channel gain is Therefore, node The received signal at the location is: ,(1); in yes The transmission power, express The noise at the aggregation receiver is modeled as additive white Gaussian noise, and its distribution is as follows: Noise power It includes inherent antenna thermal noise and noise introduced by the information decoding circuitry; relay node ,in The collected energy is used entirely for its own signal transmission; therefore, its transmission power is given by the following formula: (2); in express The rectification efficiency; node The signal-to-noise ratio at this point is: (3); in And it is agreed that the empty product equals 1; No. Jump, among them The achievable rate is: (4); in Indicates the transmission bandwidth for destination nodes that do not perform energy harvesting. Its rate simplifies to: (5); End-to-end throughput is determined by the minimum hop rate and normalized by the number of hops: (6).

[0025] The goal of the system is to increase the transmit power at the source node. Maximize end-to-end throughput under fixed conditions Simultaneously, jointly optimize the TS ratio of each relay. The optimization problem can be expressed as: (7a); st , (7b); To process equation (6) The nonsmoothness of the operator defines the minimum per-hop rate of the normalization. .maximize Equivalent to maximizing Problem (7) can be rewritten in the following equivalent form: (8a); st , ,(8b); ,(8c); , (8d); Constraints (8b) to (8d) are smooth, because They are coupled in a product form within the logarithm, and there exists a factor. The optimization problem is inherently non-convex; existing techniques typically transform it into a convex problem by replacing logarithmic variables and then calling general iterative solvers such as the interior-point method. However, such methods have excessively high computational complexity and are not suitable for resource-constrained IoT nodes.

[0026] Suppose that for a given TS ratio sequence If the normalized rate ( r (Also known as candidate rate) is feasible, that is, it exists. If (8b)-(8c) are satisfied, then any value less than The speed must also be feasible, a property that allows it to be possible to... Perform a binary search on the interval to efficiently locate the maximum feasible rate. ; Therefore, a throughput maximization algorithm based on greedy binary search is proposed to test a given candidate rate. Does a set of TS ratios exist? All constraints are satisfied; Define cumulative variables (set up ),but ;Will Before substitution The jump constraint (8b) yields information about Upper bound: , . (9); The constraint (8c) for the last jump is given The lower bound: (10); To maximize the final value To satisfy the lower bound (10), the most greedy strategy is to take the equality sign of equation (9) at each step, that is: , ,(11); from Begin recursive calculation. It can be proven that the function... In satisfying The time is strictly increasing, therefore the sequence generated by equation (11) is... It is the sequence that maximizes the maximum value among all feasible sequences. The sequence. Therefore, if and only if the sequence obtained by equation (11) is... At that time, candidate rate It is feasible.

[0027] Based on the above feasibility criteria, it can be determined by adjusting the normalization rate. The maximum feasible rate is determined by performing a binary search within the range of values ​​of . This is the Greedy Binary Search (GBS) algorithm, and its specific steps are summarized as follows: Step 1: Initialize the binary search interval for the normalized rate; Step 2: Within the search interval, perform an iterative binary search based on the preset search precision; in each iteration, call the feasibility check subroutine to check the current midpoint candidate rate, and dynamically update the search interval according to the check result until the precision condition is met, thereby determining the optimal normalized rate. Step 3: Based on the optimal normalization rate, calculate the cumulative variable sequence of intermediate relay nodes, and recover the optimal time-switching (TS) ratio for each hop accordingly, and output the final optimization result.

[0028] Step 1 specifically includes the following sub-steps: Step 1-1: Set the lower bound of the search interval Initialize to 0; Step 1-2: Generate a conservative upper bound based on the constraints of the last hop, and set the upper bound of the search interval accordingly. Initialize to ;in, Preset parameters for the system. K This represents the number of relay nodes.

[0029] Step 2 specifically includes the following sub-steps: Step 2-1: Determine the difference between the upper and lower bounds of the current search interval. Is the search precision greater than the preset value? ,in If so, then calculate the midpoint of the current interval as a candidate rate. If yes, proceed to step 2-2; otherwise, stop the iteration and proceed to step 2-4. Step 2-2: The candidate rates The data is input into the feasibility check subroutine for verification. This feasibility check subroutine specifically includes the following execution process: Step 2-2-1: Initialize the cumulative variables for the first hop. ; Step 2-2-2: For the relay node sequence number k =1 to K The following judgments and updates are executed sequentially: like If it fails, it is directly judged as "infeasible" and the subroutine is terminated; otherwise, it is handled according to the formula. Calculate and update the cumulative variable for the next hop. ; Step 2-2-3: After completion K After the first iteration, determine the final accumulated variable. Does it meet the lower bound condition? If the condition is met, the subroutine returns "feasible"; otherwise, it returns "infeasible". Step 2-2-4: Update the binary search interval based on the subroutine's return result: if it returns "feasible", then let If the return value is "not feasible", then let Return to step 2-1; Steps 2-3: Set the current lower bound after satisfying the search precision condition. Set to optimal normalization rate .

[0030] Step 3 specifically includes the following sub-steps: Step 3-1: Determine the optimal normalization rate Substitute the values ​​back into the recursive formula of step 2-2-2, and record the complete cumulative variable sequence generated during the calculation process. ,Right now ; Step 3-2: For k=1 to K, use the formula Recover each one and calculate the optimal TS ratio. ; Step 3-3: Output the obtained optimal normalized rate and the optimal TS ratio sequence As the ultimate resource allocation strategy.

[0031] The time complexity analysis of the above GBS algorithm is as follows: One feasibility check (Algorithm 1) only requires traversal Each relay performs a constant number of arithmetic and logarithmic operations, so the complexity is O(n log n). Binary search (Algorithm 2) requires iteration. Next, because The constant is the number of iterations. Therefore, the total time complexity of GBS is O(n log n). , and the number of relays They form a linear relationship. The space complexity is only [missing information]. It is used to store the sequence of accumulated variables.

[0032] Compared to existing technologies: General convex optimization solvers such as the interior-point method typically have a time complexity of O(n log n). to [6], and requires the storage of large data structures such as the Hessian matrix, resulting in high space complexity. In the tested scenario, compared with the interior point method, the computation time was reduced by more than three orders of magnitude on average (see Figure 4 ).

[0033] Exhaustive search: exponential complexity ( (Number of discretization steps for each TS ratio) is only applicable to very small numbers. .

[0034] Fixed TS ratio heuristic method: Although computation is fast, it cannot guarantee optimality and suffers significant performance loss.

[0035] Furthermore, the GBS algorithm directly obtains the global optimal solution over the continuous domain (this can be proven through the optimality of monotonic and greedy updates). Simulation results (see...) Figure 2 –4 and Table I) verify that GBS achieves a high degree of agreement with the results of exhaustive search and interior point methods, and remains stable under different channel implementations. These characteristics indicate that this method can meet the real-time resource scheduling requirements of IoT nodes with limited computing power and latency sensitivity.

[0036] Example: To verify the performance of the proposed Greedy Binary Search (GBS) algorithm, simulations were performed in a typical low-power IoT scenario. The system operates in the 2.4 GHz ISM band, with the following specific parameter settings: transmission bandwidth... MHz, source node transmit power is fixed at dBm (excluding) Figure 3 (External). Receiver noise power dBm, this value takes into account The thermal noise power spectral density is dBm / Hz, the receiver noise figure is 10 dB, and the system bandwidth is [data missing]. The rectification efficiency of all relay nodes is [data missing]. The source node and destination node are 5 m apart, and the relays are evenly spaced. Therefore, the first... The jump distance is m.

[0037] Regarding channel models, the first The composite channel gain model of the hop is as follows The reference gain Path loss index , To accommodate the channel coefficients of Rice fading, the Rice factor is 3 dB.

[0038] All simulation results were obtained by averaging 5000 independent Monte Carlo experiments (random channel implementation) on the MATLAB R2025a platform, with an Intel Core i7-9750H processor and 16 GB of memory. The search precision of Algorithm 2 (binary search) was set to... .

[0039] Comparison with benchmark: The proposed GBS algorithm is compared with the following three benchmark schemes: 1. Exhaustive Search (ES): Discretized exhaustive search of the TS ratio space with a step size of 0.01 (due to exponential complexity, it is only applicable to...) The result serves as the global optimal performance benchmark.

[0040] 2. Interior-Point Method (IPM): Using a general convex optimization solver (such as the interior-point method based on the logarithmic barrier function) to solve the convex problem after logarithmic transformation (8), the continuous optimal TS ratio and the corresponding maximum throughput are obtained.

[0041] 3. Fixed TS Ratio (FTS): All trunks use a uniform fixed TS ratio. No optimization is performed. This approach represents a zero-complexity heuristic.

[0042] Performance evaluation and chart analysis: Figure 2 Table 1 shows the results under a fixed source power. At dBm, the average end-to-end throughput of each algorithm varies with the number of relays. The throughput of all algorithms changes with... The increase followed by a sharp decrease reflects the significant impact of accumulated energy loss on performance in multi-hop networks. For The proposed GBS algorithm perfectly matches the curve of exhaustive search (ES); for all The curves of GBS and the Interior Point Method (IPM) are consistent, preliminarily verifying the global optimality of GBS. The Fixed TS Ratio Strategy (FTS) exhibits severe performance degradation, for example, when... , At that time, the throughput was only 2.43 kbps, far lower than GBS's 135.23 kbps, highlighting the necessity of jointly optimizing the TS ratio.

[0043] Table 1 System Throughput and Number of Relays Relationship:

[0044] Table 2 lists further details Figure 2 middle Comparison data of average throughput and optimal TS ratio between GBS and ES. For example, when At that time, the GBS throughput was 4797.38 kbps, the ES throughput was 4795.77 kbps, and the relative error was [missing information]. The TS ratios were 0.4840 and 0.4832, respectively, with relative errors of [missing information]. .for and The relative error of throughput is as low as and The relative error of the TS ratio is within Within this range. These results conclusively demonstrate that GBS can achieve the globally optimal solution.

[0045] Table 2 Global Optimality Verification (GBS vs. ES):

[0046] Figure 3 This demonstrates the number of relays. Below, the average throughput varies with the source power. The changes. With As the energy is increased, the throughput of all algorithms increases because more energy is available for information transmission. For all tests... The values ​​of GBS and ES curves are completely coincident and consistent with the IPM curve, further confirming its global optimality. Optimal fixed TS ratio ( )exist The speed at dBm is only 1469 kbps, which is about 11% lower than GBS's 1657 kbps, further demonstrating the necessity of joint optimization.

[0047] Table 3 System Throughput and Source Power Relationship:

[0048] Figure 4 The computational efficiency of each algorithm was compared. The running time of the proposed GBS algorithm varies with... It grows linearly: from The time increased from 0.015ms to The time taken is 0.027 ms. In contrast, the time taken by the interior-point method (IPM) increases superlinearly from... The time spiked from 11.5 ms to At 78.9 ms. At that time, GBS reduces computation time by more than three orders of magnitude compared to IPM. Exhaustive search (ES), due to its exponential complexity, ... The time had already exceeded 282 ms, making it impossible to scale to larger networks. While the fixed TS ratio (FTS) had an extremely short processing time (<0.003 ms), it came at the cost of sacrificing optimality. This result fully demonstrates that GBS possesses both low complexity and... Its outstanding advantages include real-time performance.

[0049] Table 4 Calculation Time and Number of Relays Relationship:

[0050] Analysis of the simulation results and accompanying figures demonstrates that the greedy binary search algorithm proposed in this invention can efficiently obtain the globally optimal end-to-end throughput and corresponding time switching ratio under the premise of fixed source power. It significantly outperforms traditional interior-point methods and fixed-ratio schemes in terms of optimality, computational efficiency (linear logarithmic complexity), and robustness under fading channels. This provides a practical throughput optimization solution for the actual deployment of TS-SWIPT multi-hop relay networks in the energy- and computationally constrained Internet of Things (IoT).

Claims

1. A TS-SWIPT multi-hop relay throughput optimization system based on greedy binary search, characterized in that, Including source node , A relay node using the DF protocol and destination node ;Source node It has a fixed power supply, source node The transmission power is fixed and denoted as And each relay node ,in via the TS-SWIPT protocol from its direct predecessor node It uses energy collected from radio frequency signals to operate.

2. The system according to claim 1, characterized in that, Each relay node Transmit block time Divided into a duration of The energy harvesting phase and a subsequent duration are The information decoding and forwarding stage, in which Time switching ratio; destination node Throughout the time Internally, only information decoding is performed; all relays operate in half-duplex mode, assuming the first... Channel gain of jump In a coherent time block The internal structure remains unchanged.

3. The system according to claim 2, characterized in that, set up Represents a node ,in The information symbol at that location has a unit average power, i.e. ;No. The complex channel coefficients of the hop are denoted as The corresponding channel gain is Therefore, node The received signal at the location is: ,(1)； in yes The transmission power, express The noise at the aggregation receiver is modeled as additive white Gaussian noise, and its distribution is as follows: Noise power It includes inherent antenna thermal noise and noise introduced by the information decoding circuitry; relay node ,in The collected energy is used entirely for its own signal transmission; its transmission power is given by the following formula: ,(2)； in express The rectification efficiency; node The signal-to-noise ratio at this point is: ,(3)； in And it is agreed that the empty product equals 1; No. Jump, among them The achievable rate is: ,(4)； in Indicates the transmission bandwidth for destination nodes that do not perform energy harvesting. Its rate simplifies to: ，(5)； End-to-end throughput is determined by the minimum hop rate and normalized by the number of hops: (6)。 4. The system according to claim 3, characterized in that, The goal of the system is to increase the transmit power at the source node. Maximize end-to-end throughput under fixed conditions Simultaneously, jointly optimize the TS ratio of each relay. The optimization problem can be expressed as: (7a)； st , (7b) To process equation (6) The nonsmoothness of the operator defines the minimum per-hop rate of the normalization. ;maximize Equivalent to maximizing Problem (7) can be rewritten in the following equivalent form: (8a)； s.t. , ,(8b); ,(8c)； , .(8d)。 5. The system according to claim 4, characterized in that, Constraints (8b) to (8d) are smooth, because They are coupled in a product form within the logarithm, and there exists a factor. The optimization problem is inherently non-convex; existing techniques typically transform it into a convex problem by replacing logarithmic variables and then calling general iterative solvers such as the interior-point method. However, such methods have excessively high computational complexity and are not suitable for resource-constrained IoT nodes.

6. The system according to claim 4 or 5, characterized in that, Suppose that for a given TS ratio sequence If the normalized rate , r Also known as the candidate rate, it is feasible; That is, it exists If (8b)-(8c) are satisfied, then any value less than The speed must also be feasible, a property that allows it to be possible to... Perform a binary search on the interval to efficiently locate the maximum feasible rate. ; Therefore, a throughput maximization algorithm based on greedy binary search is proposed to test a given candidate rate. Does a set of TS ratios exist? All constraints are satisfied; Define cumulative variables ,set up ,but ;Will Before substitution The jump constraint (8b) yields information about Upper bound: , . (9)； The constraint (8c) for the last jump is given The lower bound: .(10)； To maximize the final value To satisfy the lower bound (10), the most greedy strategy is to take the equality sign of equation (9) at each step, that is: , ,(11)。 7. The system according to claim 6, characterized in that, The throughput maximization algorithm based on greedy binary search specifically includes the following steps: Step 1: Initialize the binary search interval for the normalized rate; Step 2: Within the search interval, perform an iterative binary search based on the preset search precision; in each iteration, call the feasibility check subroutine to check the current midpoint candidate rate, and dynamically update the search interval according to the check result until the precision condition is met, thereby determining the optimal normalized rate. Step 3: Based on the optimal normalized rate, calculate the cumulative variable sequence of intermediate relay nodes, and restore the optimal time switching (TS) ratio for each hop accordingly, and output the final optimization result.

8. The system according to claim 7, characterized in that, Step 1 specifically includes the following sub-steps: Step 1-1: Set the lower bound of the search interval Initialize to 0; Step 1-2: Generate a conservative upper bound based on the constraints of the last hop, and set the upper bound of the search interval accordingly. Initialize to ;in, Preset parameters for the system. K This represents the number of relay nodes.

9. The system according to claim 8, characterized in that, Step 2 specifically includes the following sub-steps: Step 2-1: Determine the difference between the upper and lower bounds of the current search interval. Is the search precision greater than the preset value? ,in If so, then calculate the midpoint of the current interval as a candidate rate. If yes, proceed to step 2-2; otherwise, stop the iteration and proceed to step 2-4. Step 2-2: The candidate rates The data is input into the feasibility check subroutine for verification. This feasibility check subroutine specifically includes the following execution process: Step 2-2-1: Initialize the cumulative variables for the first hop. ; Step 2-2-2: For the relay node sequence number k =1 to K The following judgments and updates are executed sequentially: like If it fails, it is directly judged as "infeasible" and the subroutine is terminated; otherwise, it is handled according to the formula. Calculate and update the cumulative variable for the next hop. ; Step 2-2-3: After completion K After the first iteration, determine the final accumulated variable. Does it meet the lower bound condition? If the condition is met, the subroutine returns "feasible"; otherwise, it returns "infeasible". Step 2-2-4: Update the binary search interval based on the subroutine's return result: if it returns "feasible", then let... If the return value is "not feasible", then let ; Return to step 2-1; Steps 2-3: Set the current lower bound after satisfying the search precision condition. Set to optimal normalization rate .

10. The system according to claim 9, characterized in that, Step 3 specifically includes the following sub-steps: Step 3-1: Determine the optimal normalization rate Substitute the values ​​back into the recursive formula of step 2-2-2, and record the complete cumulative variable sequence generated during the calculation process. ,Right now ; Step 3-2: For k=1 to K, use the formula Recover each one and calculate the optimal TS ratio. ; Step 3-3: Output the obtained optimal normalized rate and the optimal TS ratio sequence As the ultimate resource allocation strategy.

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