A distributed multi-sensor detection fusion method based on aerial computing

Abstract

The application belongs to the technical field of wireless communication, and particularly relates to a distributed multi-sensor detection fusion method based on aerial computation. First, binary source information is observed and judged by I local sensors independently, and the judgment result of each local sensor is forwarded by a plurality of relay nodes, and the received signals of the I relay transmission links after forwarding are subjected to aerial computation on a binary add multiple access channel to reach a fusion center; then, the fusion center extracts a decision metric value based on a log-likelihood ratio criterion according to the aerial computation result, and further determines a final decision result according to the decision metric value. The binary add multiple access channel is used between the last relay node and the fusion center, so no matter how many sensor sensing data, they can be accessed at one time, and the resources consumed by the channel will not increase with the increase of the number of local sensors, and compared with the prior art, the channel access pressure is reduced.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, specifically relating to a distributed multi-sensor detection and fusion method based on over-the-air computing. Background Technology

[0002] The development of smart cities requires a widely covered information sensing network as a key infrastructure to achieve digitalization, networking, and intelligence. In this network, the sensing layer is at the bottom layer, responsible for the wireless access of local smart terminal devices in the smart city. To ensure the accuracy of data processing at the application layer and the precision of data mining conclusions, the quality of the sensing layer data is crucial. Therefore, ensuring the reliable transmission of sensing layer data in the ubiquitous sensing network is the most effective way to achieve reliable spatiotemporal information sensing in smart cities, making its research extremely important.

[0003] Smart cities have diverse application scenarios. For example, in the field of remote traffic detection, to collect typical data such as traffic flow in fixed areas like urban intersections, numerous sensor nodes need to be deployed within these areas, requiring distributed multi-sensor detection fusion technology. In traditional research, multiple sensor nodes mostly use orthogonal multiple access channels (such as time division multiple access, frequency division multiple access, or code division multiple access technologies) to connect to the fusion center. The aim is to ensure that data sensed by each local sensor can be transmitted to the fusion center without interference. The fusion center then uses certain detection fusion rules to process this data and arrive at a decision. In other words, traditional research often adopts a separate architecture of "communication first, then computation." However, in future smart cities, the number of connected intelligent terminal nodes such as sensors will reach hundreds of millions, with a deployment density of millions per square kilometer. If the traditional "communication first, then computation" "separate architecture" is still adopted, the fusion center needs to recover massive amounts of individual sensor perception data before performing computation, which will occupy a huge amount of channel bandwidth resources. Under the condition that channel resources do not increase significantly, it will undoubtedly put enormous pressure on urban wireless channel access. Summary of the Invention

[0004] The purpose of this invention is to provide a distributed multi-sensor detection and fusion method based on over-the-air computing, in order to solve the problem of high wireless channel access pressure caused by the separate architecture of prior communication followed by computing in the prior art.

[0005] To address the aforementioned technical problems, this invention provides a distributed multi-sensor detection fusion method based on over-the-air computing, comprising the following steps:

[0006] 1) After the binary source information is independently observed and decided by I local sensors, the decision result of each local sensor is forwarded by several relay nodes. After forwarding, the received signal of I relay transmission links reaches the fusion center through air computing on the binary plus multiple access channel.

[0007] 2) Based on the aerial calculation results, the fusion center calculates the decision metric extracted based on the log-likelihood ratio criterion, and then determines the final decision result based on the decision metric.

[0008] The beneficial effects of the above technical solution are as follows: This invention is based on a "communication and computing integration" architecture. It uses a binary plus multiple access channel between the last relay node and the fusion center. This channel performs signal processing and transmission based on over-the-air computing. Therefore, no matter how many sensor data channels there are, they can all be accessed at once. It has the characteristics of low channel resource consumption and high channel utilization. The resources consumed by the channel will not increase with the increase of the number of local sensors. Compared with the "communication first, then computing" architecture in the prior art, it reduces the channel access pressure and is suitable for future applications in scenarios with massive sensor node access.

[0009] Furthermore, a decision metric is determined based on the channel quality from the source to the local sensor. If the channel quality from the source to the local sensor is superior, then the decision metric is:

[0010] Λ=2r-I

[0011] Where Λ represents the decision metric; r represents the result of the calculation in the air.

[0012] The beneficial effects of the above technical solution are as follows: As can be seen from the above formula, the calculation of the decision metric eliminates all multiplication and logarithmic operations, and does not require channel state information, thus having low complexity.

[0013] Furthermore, a decision metric is determined based on the channel quality between relay nodes. If the channel quality between relay nodes is relatively good, then the decision metric is:

[0014]

[0015] Where Λ represents the decision metric; z i P represents the received signal of the i-th relay transmission link after forwarding, 1≤i≤1; di P represents the detection probability of the i-th local sensor; fi This represents the false alarm probability of the i-th local sensor;

[0016] Otherwise, the decision metric is:

[0017] Λ=2r-I

[0018] Where r represents the result of the calculation in the air.

[0019] The beneficial effects of the above technical solution are as follows: As can be seen from the above formula, when the channel quality between relay nodes is good, the decision metric can be obtained with only a small amount of prior information, including parameters reflecting the performance of local sensors (detection probability and false alarm probability) and received signals, which greatly reduces the computational burden; otherwise, the calculation of the decision metric eliminates all multiplication and logarithmic operations and does not require channel state information, thus having low complexity.

[0020] Furthermore, the final judgment result is calculated using the following formula:

[0021]

[0022] in, Λ represents the final judgment result; τ represents the judgment metric; and τ represents the judgment threshold.

[0023] The beneficial effect of the above technical solution is that the final judgment result can be accurately determined by setting a judgment threshold.

[0024] Furthermore, the channels between local sensors and relay nodes, and between relay nodes, are all binary symmetric channels.

[0025] The beneficial effects of the above technical solution are: using a binary symmetric channel for transmission ensures the reliability of signal transmission.

[0026] Furthermore, the relay node forwards information using an amplification forwarding method, with an amplification factor of 1.

[0027] The beneficial effects of the above technical solution are: setting the amplification factor to 1 means that the relay does not need to do any processing, but only forwards the data, which improves the processing efficiency.

[0028] Furthermore, the decision result of the local sensor is the binary information obtained by the local sensor after a single-bit hard decision. The relationship between the binary information and the received signal of the relay transmission link is as follows:

[0029]

[0030] Among them, z i This represents the received signal of the i-th relay transmission link after forwarding, 1≤i≤1; x i Represents the binary information of the i-th relay transmission link; e i,j This represents the channel transmission error corresponding to the j-th binary symmetric channel of the i-th relay transmission link; J represents the total number of binary symmetric channels from the local sensor to the fusion center. This represents modulo-2 addition, also known as XOR operation.

[0031] The beneficial effect of the above technical solution is that the above formula accurately represents the relationship between binary information and the received signal of the link. Attached Figure Description

[0032] Figure 1-1 This is a diagram illustrating the application of the present invention in a remote medical testing scenario;

[0033] Figure 1-2 This is a flowchart of the communication system in an embodiment of the present invention;

[0034] Figure 2 This is a flowchart of the method of the present invention;

[0035] Figure 3 This is a diagram showing the impact of the number of relays on the channel error probability performance of the suboptimal fusion rule (10) based on the log-likelihood ratio in this embodiment of the invention.

[0036] Figure 4 This is a diagram showing the impact of the number of relays on frame error rate performance in the suboptimal fusion rule (10) based on log-likelihood ratio in this embodiment of the invention.

[0037] Figure 5 This is a diagram showing the impact of the number of routes on the channel error probability performance of the suboptimal fusion rule (10) based on the log-likelihood ratio in this embodiment of the invention.

[0038] Figure 6 This is a diagram showing the impact of the number of routes on frame error rate performance in the suboptimal fusion rule (10) based on log-likelihood ratio in this embodiment of the invention.

[0039] Figure 7 This is a diagram showing the impact of the number of relays on the channel error probability performance in the simplified decision metric extraction method (18) when the channel from the information source to the local sensor is ideal in this embodiment of the invention.

[0040] Figure 8 This is a graph showing the impact of the number of relays on frame error rate performance under the ideal channel from the information source to the local sensor in this embodiment of the invention, based on the simplified decision metric extraction method (18).

[0041] Figure 9 This is a diagram showing the impact of the number of routes on the channel error probability performance under the ideal condition that the channel from the information source to the local sensor is ideal, based on the simplified decision metric extraction method (18).

[0042] Figure 10 This is a diagram showing the impact of the number of routes on frame error rate performance under the ideal channel from the information source to the local sensor in this embodiment of the invention, based on the simplified decision metric extraction method (18).

[0043] Figure 11 This is a comparison diagram of the channel error probability performance of the suboptimal fusion rule (10) based on log-likelihood ratio and the simplified decision metric extraction method (18) in this embodiment of the invention.

[0044] Figure 12 This is a comparison chart of the frame error rate performance of the suboptimal fusion rule (10) based on log-likelihood ratio and the simplified decision metric extraction method (18) in this embodiment of the invention.

[0045] Figure 13 This is a diagram showing the impact of the number of relays on the channel error probability performance in the case of a high error transfer probability in the relay transmission channel, based on the simplified decision metric extraction method (26).

[0046] Figure 14 This is a diagram showing the impact of the number of routes on the channel error probability performance when the error transfer probability of the relay transmission channel is high, based on the simplified decision metric extraction method (26).

[0047] Figure 15 This is a comparison diagram of the channel error probability performance of the suboptimal fusion rule (10) based on log-likelihood ratio and the simplified decision metric extraction method (26) in this embodiment of the invention;

[0048] Figure 16 This is a diagram showing the impact of the number of relays on the channel error probability performance under the condition that the error transfer probability of the relay transmission channel is low, based on the simplified decision metric extraction method (27).

[0049] Figure 17 This is a diagram showing the impact of the number of relays on frame error rate performance under the condition that the error transfer probability of the relay transmission channel is low in this embodiment of the invention;

[0050] Figure 18 This is a diagram showing the impact of the number of routes on the channel error probability performance under the condition that the error transfer probability of the relay transmission channel is low in this embodiment of the invention;

[0051] Figure 19 This is a diagram showing the impact of the number of routes on frame error rate performance under the condition that the error transfer probability of the relay transmission channel is low in this embodiment of the invention;

[0052] Figure 20 This is a comparison diagram of the channel error probability performance of the suboptimal fusion rule (10) based on log-likelihood ratio and the simplified decision metric extraction method (27) in this embodiment of the invention;

[0053] Figure 21This is a comparison chart of frame error rate performance between the suboptimal fusion rule (10) based on log-likelihood ratio and the simplified decision metric extraction method (27) in this embodiment of the invention. Detailed Implementation

[0054] This invention proposes a distributed multi-sensor detection fusion method based on over-the-air computation within a "communication and computing integration" architecture. The basic concept is that after source information is independently observed and decided by multiple local sensors, the decision result of each local sensor is forwarded by multiple relays. After forwarding, the received signals from multiple links undergo over-the-air computation (i.e., signal superposition) on a Binary Adder Multiple-access Channel (BAMAC) to reach the fusion center. The fusion center directly extracts a decision metric based on the log-likelihood ratio criterion from the signal superposition result, and then derives the final fusion decision result based on the decision metric. In other words, this invention uses BAMAC between the last relay node and the fusion center, enabling one-time access regardless of the number of sensor data streams. It features low channel resource consumption and high channel utilization, achieving low complexity and high channel utilization even in scenarios with limited communication channel capacity. To make the objectives, technical solutions, and advantages of this invention clearer, the following detailed description is provided in conjunction with the accompanying drawings.

[0055] This embodiment applies the distributed multi-sensor detection fusion method based on over-the-air computing of the present invention to, for example, Figure 1-1 The remote medical testing system shown includes local sensors, relay nodes, and a fusion center. Its workflow is as follows: Figure 1-2 As shown. Furthermore, all routes are independent and non-uniformly distributed in a multi-hop, multi-access parallel distributed access channel system. The specific fusion method, implemented through the cooperation between local sensors, relay nodes, and the fusion center, is as follows: Figure 2 as follows:

[0056] Step one: Binary information H0 and H1 from the same source are observed by I local sensors and subjected to single-bit hard decision. The decision results are then forwarded by multiple relay nodes. The received signals from multiple links ultimately reach the fusion center via the binary plus multiple access channel. During transmission on the BAMAC, the received signals from multiple links are automatically superimposed; that is, multiple signals undergo in-flight computation before reaching the fusion center. Specifically:

[0057] 1) After the binary information H0 and H1 from the information source are transmitted through a noisy channel, they are independently observed by the i-th (1≤i≤1) local sensor, and then converted into binary information x after a single-bit hard decision. i Pdi =P(x i =1|H1) and P fi =P(x i =1|H0) represent the detection probability and false alarm probability of the i-th local sensor, respectively, which are used to characterize the channel quality between the source and the local sensor.

[0058] 2) Each local sensor independently forwards its hard decision result to a multi-relay transmission link, which then forwards it through J relay nodes before reaching the fusion center. Let z be the received value obtained by the last relay node (i.e., the Jth relay node). i Subsequently, all received values ​​z i After being transmitted via a binary plus multiple access channel, the data is sent to the fusion center, and the received value at the fusion center is denoted as r.

[0059] The channels between local sensors and relay nodes, as well as between relay nodes, are all binary symmetric channels (BSCs). Furthermore, the relay forwarding method is amplified forwarding with an amplification factor of 1.

[0060] x i and z i The relationship is shown in equation (1), and the binary information z of I relay transmission links i After the binary real number addition operation, the fusion center is reached, and the specific formula is shown in equation (2).

[0061]

[0062]

[0063] Among them, e i,j Let I represent the channel transmission error corresponding to the j-th BSC in the i-th relay transmission link, I represent the total number of parallel relay transmission links, and J represent the total number of BSCs from the local sensor to the last relay node (i.e., the j-th relay node). This represents modulo-2 addition, also known as XOR operation.

[0064] Step 2: The fusion center directly extracts the decision metric based on the log-likelihood ratio from the signal superposition results (i.e., the aerial calculation results).

[0065] In this step, there are two methods for extracting the fusion center decision metric:

[0066] Method 1: Determine the decision metric expression based on the channel quality from the source to the local sensor. Specifically, when the channel from the source to the local sensor is ideal, the fusion center decision metric expression is:

[0067] Λ=2r-I (3)

[0068] Method 2: Determine the decision metric expression based on the channel quality between relay nodes. When the error transfer probability of the relay transmission channel BSC is high (i.e., the channel quality between relay nodes is poor), the decision metric expression of the fusion center is as shown in equation (3); when the error transfer probability of the relay transmission channel BSC is low (i.e., the channel quality between relay nodes is good), the decision metric expression of the fusion center is:

[0069]

[0070] The specific derivation process is as follows:

[0071] A1: For the transmission link from the local sensor to the fusion center, J serial BSCs can be equivalently processed to obtain an equivalent BSC with an error transition probability ε. i It can be written as:

[0072]

[0073] Where, ε i,j =P r (e i,j =1) represents the error transition probability of the j-th BSC in the i-th transmission link. This represents modulo-2 addition, also known as XOR operation.

[0074] A2: Based on equation (5), the received value z of the last relay node can be obtained. i have:

[0075]

[0076] The proof is as follows:

[0077]

[0078] In the derivation from the second to the third line of equation (6), the aftereffect-free property of the Markov chain relation P(z) is used. i =1|x i =1,H1)=P(z i =1|x i =1), similarly prove that P(z) in equation (6) i =0|H1), P(z) i =1|H0) and P(z i =0|H0) result.

[0079] A3: The derivation of the expression for the optimal decision metric of the fusion center is as follows:

[0080] First, define S1 = {z}i :z i =1}, k=|S1|, that is, S1 represents all z values ​​that are 1 out of I received values. i The set formed by these elements, k represents the number of elements in set S1. From equation (2), we know that k = r. Correspondingly, we define S0 = {z} i :z i If =0}, then Ik=|S0|, that is, S0 represents all z values ​​that are 1 out of I received values. i The set constituted. Therefore, the fusion center decision metric can be expressed as:

[0081]

[0082] Where s1:|s1|=k represents all I received values ​​{z i There are k sets S1 corresponding to the values ​​of 1 in}. Thus, the optimal decision metric expression for the fusion center is obtained. From equation (2), it can be seen that the numerator of equation (8)... and denominator Both are probability density functions of the Poisson binomial random variable r.

[0083] A4: In the process of implementing the optimal decision metric, in order to calculate the numerator and denominator in equation (8), it is necessary to exhaustively enumerate the I received values ​​{z} when r = k. i All possible combinations of} result in high computational complexity even with a small number of transmission paths I. For example, when I = 6 and k = 3, the summation terms in the numerator and denominator of equation (8) contain respectively Furthermore, the fusion center also needs to have perfect knowledge of the Channel State Information (CSI) for each path. i Equation (8) involves a large number of complex operations such as multiplication, which results in high implementation complexity and makes it difficult to apply in engineering. Therefore, it is very necessary to simplify and approximate Equation (8) to reduce the implementation complexity in engineering applications.

[0084] A5: A core reason for the high computational complexity of equation (8) is that both its numerator and denominator are probability density functions of the Poisson binomial random variable r. To address the high computational complexity of the Poisson binomial distribution, we consider using the binomial distribution to approximate it. Using the probability average to approximate equation (6), we have:

[0085]

[0086] Substituting equation (9) into equation (8), the suboptimal decision fusion statistic based on the log-likelihood ratio (LLR) can be transformed into:

[0087]

[0088] A6: Compared with the optimal fusion statistics given in Equation (8), the suboptimal fusion statistics given in Equation (10) no longer require exhaustive enumeration of all elements, making the system user-friendly and easy to implement. However, it can be seen that there are still a large number of logarithmic and multiplication operations in Equation (10), and the implementation of the summation term requires the CSI of each relay channel. Therefore, it is necessary to continue to simplify Equation (10).

[0089] The theoretical derivation process of method 1, i.e. formula (3), is given below:

[0090] A7: For an ideal channel from the source to the local sensor, then P di =1 and P fi =0, therefore equation (10) can be modified to:

[0091]

[0092] make Then the logarithmic term in equation (11) can be further written as:

[0093]

[0094] Next, define Equation (12) can then be modified as follows:

[0095]

[0096] In equation (13), the following definitions apply:

[0097]

[0098] use The approximate formula, equation (13), can be expressed as:

[0099]

[0100] Since Φ(θ) decays rapidly with increasing θ, equation (15) can be further expressed as:

[0101]

[0102] Substituting equation (16) into equation (11), the final decision metric can be written as:

[0103]

[0104] Especially when the threshold τ = 0, remove This will not affect the test results. Then, equation (17) can be transformed into:

[0105] Λ=2r-I (18)

[0106] As shown in equation (18), all multiplication and logarithmic operations are successfully eliminated, and CSI is not required.

[0107] Thus, the derivation process of the fusion center detection metric under the ideal condition of the channel from the information source to the local sensor is obtained, namely, the derivation process of equation (3).

[0108] Secondly, the derivation process of Method 2 is given.

[0109] The following is the derivation of equation (3) when the error transfer probability of the relay transmission channel BSC is relatively high.

[0110] A8: At this time, there is ε i →0.5 and 1-2ε i →0, then equation (10) can be rewritten as:

[0111]

[0112] Since the two terms in equation (19) have similar forms, we will first analyze the first term:

[0113]

[0114] Substituting equation (14) into equation (20), we get:

[0115]

[0116] Due to δ i,j →0, and an approximate expression can be obtained from the Taylor series expansion of the exponential function. Equation (21) can be further written as:

[0117]

[0118] Similarly, the second term of equation (19) can be modified as follows:

[0119]

[0120] By using the approximate expression log1+x≈x for the logarithmic function, equation (23) can be transformed into:

[0121]

[0122] Substituting equations (22) and (24) into equation (19), the final fusion center detection metric can be written as:

[0123]

[0124] make When the decision threshold τ is 0, it is a positive value and can be ignored. Therefore, equation (25) can be written as equation (3):

[0125]

[0126] Thus, the decision metric (3) for the fusion center to perform detection when the error transfer probability of the relay transmission channel is high is obtained.

[0127] The theoretical derivation of equation (4) is given below.

[0128] A9: When the error transfer probability of the relay transmission channel is low, i.e., when the relay channel has a high signal-to-noise ratio, then ε i ≈0. Then equation (10) can be transformed into:

[0129]

[0130] According to Equation (27), the decision metric can be obtained by combining only a small amount of prior information (such as local sensor performance and received values), which greatly reduces the computational burden.

[0131] Thus, the decision metric value shown in equation (4) is obtained.

[0132] Step 3: Input the decision metric obtained in Step 2 into the hard decision processor to obtain the final decision result.

[0133] The decision-making method in this step is as follows:

[0134]

[0135] in, τ represents the final fusion decision result, and τ represents the decision threshold.

[0136] The following simulation demonstrates the effectiveness of the method of the present invention.

[0137] Figure 3 and Figure 4 The figures show the impact of the number of relays on the Bit Error Rate (BER) and Frame Error Rate (FER) of the fusion center decision when equipped with the suboptimal rule (10) based on LLR. The number of routes I is fixed at 7, and the number of relays J is changed from 1 to 5. The horizontal axis represents the channel crossover probability. A threshold phenomenon is clearly observed in the figures; when the horizontal axis is below the threshold, the performance changes rapidly, while when it is above the threshold, the change is slow. Furthermore, it can be seen that performance decreases as the number of relays increases. The impact of the number of routes on decision performance is shown in... Figure 5 and Figure 6 As shown in the figure, where the number of relays J is fixed at 2 and the number of routes I changes from 1 to 7, it can be observed that the channel error probability and frame error rate both improve with the increase of the number of routes.

[0138] Figures 7 to 10 The effects of the number of relays and routes on the channel error probability and frame error rate of the fusion center decision are shown when the channel from the source to the local sensor is ideal, equipped with a simplified decision metric extraction method (18). The simulation conditions are set as follows: a fixed number of routes I of 7, the number of relays J changing from 1 to 5, and a fixed number of relays of 2, the number of routes changing from 1 to 7. It can be seen that the trend of system performance is similar to the suboptimal rule (10) based on LLR. That is, the performance will decrease with the increase of the number of relays and improve with the increase of the number of routes. Figure 11 and Figure 12 The performance of the fusion center is compared with that of the suboptimal rule (10) based on LLR and the simplified decision metric extraction method (18) respectively. It can be seen that under the same simulation conditions, the curves of the two have almost the same trend. This shows that although the complexity of the fusion method (18) is greatly reduced, the performance degradation of the system is very small and can be ignored.

[0139] Figure 13 and Figure 14 The paper demonstrates the performance trend of the system channel error probability extraction method (Equation (26)) with the number of routes and relays when the error transfer probability of the relay transmission channel is high. Setting the relay channel error transfer probability to 0.2, it can be seen from the figure that due to the high probability of crossover, especially when there are multiple relays, the system performance loss is greater. Furthermore, the system performance will improve with the increase in the number of routes. The paper also compares the suboptimal LLR-based rule (Equation (10) with Equation (26) in... Figure 15 A comparison was conducted, and the results showed that the performance difference between the two methods was minimal.

[0140] Figures 16 to 19 This demonstrates the trend of system channel error probability and frame error rate performance as a function of the number of routes and relays when the error transition probability of the relay transmission channel is low, based on the simplified decision metric extraction method (27) configured in the fusion center. The channel transition probability of each relay is set to 10. -4 By changing the detection probability P of the local sensor di Let's observe the performance changes. The values ​​are evenly distributed between 0.7 and 1, with the number of routes I set from 1 to 9, and the number of relays at 1, 2, 3, and 4. From... Figures 16 to 17 It can be seen that there is a relatively obvious threshold phenomenon. When the local sensor's P... diBelow 0.94, system performance does not significantly degrade with increasing values, while above this value, performance changes are more pronounced. Figure 20 and Figure 21 In the simulation, the rules of (10) and (27) were demonstrated to be equipped with small crossover probability in the relay channel. It can be found that the system performance obtained by using the two methods is almost the same.

[0141] In summary, the distributed multi-sensor detection fusion method based on over-the-air computing of this invention uses a binary plus multiple access channel between the last relay node and the fusion center. Therefore, regardless of the number of sensor data streams, it can achieve one-time access, featuring low channel bandwidth resource consumption and high channel utilization. That is, the channel bandwidth resources consumed by this method do not increase with the increase in the number of local sensors, making it particularly suitable for future applications in scenarios with massive sensor node access. Furthermore, the designed calculation method based on the log-likelihood ratio for the decision metric features high reliability, strong robustness, and low computational complexity.

Claims

1. A distributed multi-sensor detection fusion method based on over-the-air computing, characterized in that, Includes the following steps: 1) After the binary source information is independently observed and decided by I local sensors, the decision result of each local sensor is forwarded by several relay nodes. After forwarding, the received signal of I relay transmission links reaches the fusion center through air computation on the binary plus multiple access channel; the air computation result... for: , This is the received signal of the i-th relay transmission link after forwarding; 2) The fusion center calculates the results from the air. The decision metric based on the log-likelihood ratio criterion is extracted using either method 1 or method 2. : Method 1: Determine based on the channel quality from the source to the local sensor If the channel quality from the information source to the local sensor is good, then for: ; Method 2: Determine based on channel quality between relay nodes If the channel quality between relay nodes is relatively good, then for: , , Let represent the detection probability and false alarm probability of the i-th local sensor, respectively; Otherwise, the decision metric is: ; 3) Determine the final judgment result based on the judgment metric.

2. The distributed multi-sensor detection and fusion method based on over-the-air computing according to claim 1, characterized in that, The final judgment result is calculated using the following formula: ； in, Indicates the final judgment result; Indicates the judgment metric; Indicates the threshold for judgment.

3. The distributed multi-sensor detection fusion method based on over-the-air computing according to claim 1 or 2, characterized in that, The channels between local sensors and relay nodes, and between relay nodes, are all binary symmetric channels.

4. The distributed multi-sensor detection fusion method based on over-the-air computing according to claim 1, characterized in that, In step 1), the decision made by the local sensor is a single-bit hard decision.

5. The distributed multi-sensor detection fusion method based on over-the-air computing according to claim 1 or 2, characterized in that, The relay node forwards information using amplified forwarding, with an amplification factor of 1.

6. The distributed multi-sensor detection fusion method based on over-the-air computing according to claim 4, characterized in that, The decision result of the local sensor is the binary information obtained after the local sensor performs a single-bit hard decision. The relationship between the binary information and the received signal of the relay transmission link is as follows: ； in, This represents the received signal of the i-th relay transmission link after forwarding. ; This represents the binary information of the i-th relay transmission link; This represents the channel transmission error corresponding to the j-th binary symmetric channel of the i-th relay transmission link; J represents the total number of binary symmetric channels from the local sensor to the fusion center. This represents modulo-2 addition, also known as XOR operation.

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