Mode selection and resource allocation method for underwater sensor networks assisted by relay

Abstract

The present invention relates to the technical field of underwater sensor network relay resource allocation, and in particular to a relay-assisted underwater sensor network mode selection and resource allocation method. The relay-assisted underwater sensor network consists of a sink node (SN) and an underwater sensor node (USN), wherein the USN is randomly deployed in the sea to sense necessary information, and the SN is usually deployed on the sea surface to collect information sensed by all underwater sensor nodes. In order to avoid interference, the entire collection cycle is evenly divided into multiple time slots by using a time division multiple access method. In each time slot, the USN can use an acoustic signal to send corresponding information to the SN. If direct transmission is used, a user node far away from the SN consumes more energy than a user node close to the SN, resulting in node energy imbalance and reduced network life. Further considering the relay transmission mode through an amplification and forwarding protocol, the user network can not only transmit its own information, but also act as a relay to help other user networks.

Description

Technical field:

[0001] The present invention relates to the technical field of underwater sensor network relay resource allocation, and in particular to a relay-assisted underwater sensor network mode selection and resource allocation method that can determine a suitable relay set by balancing energy consumption between nodes, thereby improving system communication performance. Background technology:

[0002] People are very interested in exploring the ocean environment and have never stopped exploring, including temperature, ocean currents, target detection and other work. In order to collect this data, a large number of sensors need to be deployed in some ocean areas to sense the necessary information, which also brings a key challenge, that is, how to efficiently transmit the information collected by each sensor to the ground control center. Therefore, underwater acoustic sensor networks have received more and more attention, and some related technologies have also been well studied, mainly involving multiple access control protocols, resource optimization and network architecture design. Although the existing work on marine networks has made great achievements, it must be mentioned that network life has always been a key factor restricting the development of networks. Generally speaking, a network with a specific function consists of dozens to hundreds of sensor nodes, and all sensor nodes need to work together to ensure the integrity of the collected information. As long as a node does not work because of energy exhaustion, the network will be considered invalid. However, due to the high cost, it is very difficult to charge or replace invalid sensor nodes. Therefore, such a plan is uneconomical, and the huge waste caused is unacceptable. How to effectively use network resources to improve network life and cost performance has become a meaningful issue. Although underwater acoustic communication has the advantages of stable and reliable transmission over long distances, energy consumption increases with the increase of transmission distance. In particular, the deployment of sensor nodes in the network is almost impossible to be uniform. Sensor nodes far away from the sink node will suffer large signal attenuation and thus have to spend more energy to transmit data.

[0003] Furthermore, due to the unbalanced energy consumption, the network life will also be shortened. At this point, deploying relay nodes is a feasible and effective way to overcome this shortcoming. The relays currently used are almost all fixed relays or mobile relays based on underwater drones. On the one hand, additional fixed relay deployments will also bring additional costs. On the other hand, these relay nodes are difficult to manage because they are easily affected by rapidly changing environments. Mobile relays based on underwater robots can overcome the above shortcomings well due to their flexibility. However, the long path delay caused by the low speed of underwater robots is difficult to overcome. Summary of the invention:

[0004] In view of the shortcomings and deficiencies in the prior art, the present invention proposes a method for selecting a mode and allocating resources of a relay-assisted underwater sensor network that is applicable to a general underwater sensor network and can improve the life of the network.

[0005] The present invention is achieved by the following measures:

[0006] A relay-assisted underwater sensor network mode selection and resource allocation method, characterized in that it includes the following steps:

[0007] Step 1: Establish a relay-assisted underwater sensor network model. The system consists of a sink node SN and underwater sensor nodes USN. USN is randomly deployed in the sea to sense the necessary information, while SN is usually deployed on the sea surface to collect the information sensed by all underwater sensor nodes. In order to avoid interference, the entire collection cycle is evenly divided into multiple time slots using time division multiple access (TDMA). In each time slot, USN uses acoustic signals to send corresponding information to SN. When direct transmission is used, user nodes far away from SN will consume more energy than user nodes close to SN, resulting in node energy imbalance and reduced network life. Therefore, this system considers the relay transmission mode through the amplification and forwarding protocol, that is, the user network can not only transmit its own information, but also act as a relay to help other user networks. In the relay transmission mode, USN only needs to transmit the signal to the closer relay node instead of the distant SN, and then the relay node forwards the amplified signal to the SN, where the definition As a set of USNs, where M is the total number of USNs, the total collection period is assumed to be T, the length of each time slot is correspondingly ΔT = T / M, the bandwidth used by the network is represented by B, and the central carrier frequency is f; the attenuation of the underwater acoustic signal mainly depends on the central carrier frequency and the communication distance between the sensor nodes. The Urick model is used to simulate the attenuation of the underwater acoustic signal, and the attenuation is expressed as:

[0008]

[0009] Where d is the communication distance between sensor nodes. λ is a constant and ranges between 1 and 2. For convenience, λ is usually equal to 1.5. α(f) represents the absorption coefficient, which is a function of the carrier frequency. By applying the Thorp empirical formula, the absorption coefficient α(f) is given as follows:

[0010]

[0011] According to the Thorp empirical formula, the noise of underwater acoustic communication is affected by turbulence N1(f), waves N2(f), wind N3(f) and thermal noise N4(f) (in decibels / Pa / Hz), and the total noise N(f) is the sum of these elements:

[0012] N(f)=N1(f)+N2(f)+N3(f)+N4(f) (3)

[0013] Specifically, the calculation formula for each component is as follows:

[0014] 10log N1(f)=17-30log f (4)

[0015] 10log N2(f)=40+20(s-0.5)+26log f-60log(f+0.03) (5)

[0016]

[0017] 10log N4(f)=-15+20log f (7)

[0018] Among them, s represents the transport activity coefficient, which is between 0 and 1, and w represents the wind speed in meters per second;

[0019] In order to facilitate further analysis of the acoustic signal transmission process and energy consumption, the unit conversion formula for acoustic and electrical signals is given below:

[0020]

[0021] In direct transmission mode, the SN will directly receive the signal from the mth USN in the form of:

[0022]

[0023] in and Indicates the distance between SN and the mth USN. m represents the transmission power of the mth USN, is the signal to be reconstructed by SN, represents the signal noise,

[0024] Then, the total amount of data received by the SN can be expressed as:

[0025]

[0026] where h m =H m / (BN(f)), Indicates the actual transmission time;

[0027] In the relay transmission mode, the transmission process is divided into two stages. In the first stage, the mth USN sends its signal to the relay node instead of the SN. If the nth USN is selected as the relay, the corresponding signal it receives from the mth USN is:

[0028]

[0029] Among them G m,n =1 / A(d m,n ,f) and d m,n Indicates the distance between the nth USN and the mth USN. represents the signal noise, and the total amount of data received by the mth USN can be expressed as:

[0030]

[0031] where g m,n =G m,n / (BN(f)),

[0032] In the second stage, the nth USN amplifies the received signal and forwards it to the SN. Then, the SN receives the corresponding signal from the nth USN.

[0033]

[0034] Then, the total amount of data received by the SN can be calculated as

[0035]

[0036] Where T m,n and q m,n They represent the actual transmission time and transmission power of the nth USN to assist the mth USN. Since the transmission process is divided into two stages, the final amount of data received by the SN depends on the minimum value of the two links, that is,

[0037] Step 2: According to the system model established in step 1, USN has two modes to choose from: relay transmission mode and direct transmission mode. A binary variable a is defined. m,n ∈{0,1} to represent relay selection and mode selection, a m,n =1 means the nth USN is the relay of the mth USN. If not, a m,n = 1. For the special case m = n, a m,m =1 indicates that the mth USN selects the direct transmission mode, then the remaining energy of the mth USN in the kth collection cycle can be expressed as:

[0038]

[0039] The second term on the right represents the energy consumption required by the mth USN to transmit its own information, and the third term refers to the energy consumption caused by acting as a relay. Due to the long propagation delay, the actual transmission time depends on the communication distance. For the direct transmission mode, the actual transmission time of the mth USN can be calculated as

[0040]

[0041] Where v is the speed of sound. For the relay transmission mode and assuming that the nth USN acts as a relay, the actual transmission time of the mth USN can be expressed as

[0042]

[0043] Typically, once the first USN runs out of energy, the network is considered to be dead. Therefore, the network lifetime is defined as the number of data collection rounds before the network fails. In each round of data collection, our goal is to maximize the minimum remaining energy of the user network, thereby further improving the network lifetime. The main optimization variables include relay selection and mode selection variables. Transmission time variable Power allocation variables and The final optimization problem is expressed as follows:

[0044]

[0045] stC1:

[0046] C2:

[0047] C3:

[0048] C4:

[0049] C5:

[0050] C6:

[0051] C7:

[0052] C8:

[0053] C9:

[0054] C10:

[0055] In this optimization problem, C1 indicates that each USN must choose between the relay transmission mode and the direct transmission mode. In addition, if the relay transmission mode is selected, only one relay node can be selected. C2 indicates that a USN can only serve as a relay for another USN when its own data is directly transmitted. The reason is that if a USN can act as a relay, its remaining energy must be sufficient to at least ensure that its own data is directly transmitted without any relay help. C3 and C4 indicate that regardless of the relay transmission mode or the direct transmission mode, all user networks can successfully transmit the amount of data they sense. C5 and C6 indicate that the actual transmission time is limited by the given time slot length. C7 and C8 ensure that the transmission power of each USN is less than the maximum transmission power. C9 ensures that the actual transmission time is non-negative. C10 indicates a m,n is a binary variable;

[0056] Step 3: Determine the optimal resource allocation strategy:

[0057] Under the premise that the mode and relay selection are given in step 2, for the direct mode, the optimal resource allocation strategy is easy to obtain. For the relay mode, the optimization problem (18) is reformulated as a non-convex problem, and the Lagrangian dual decomposition method is applied to obtain the optimal solution. Specifically, assum- ing that the mode selection and relay selection results have been given, the group of user networks is divided into three subsets, namely, USNs using direct transmission mode, USNs using relay transmission mode, and USNs acting as relays. Specifically, we let represents the set of USNs acting as relays, where s is the number of relays, so the relay r i The set of assisting USNs is represented as The user network set of direct transmission mode is represented as Analyze the energy consumption of all user networks and find the optimal resource allocation strategy:

[0058] For USNs in direct transmission mode, there will be no interference between USNs due to the application of time division multiple access frames. Then, the optimization problem (18) can be solved according to each is divided into many sub-problems. Then, the sub-problems can be expressed as

[0059]

[0060] stC1:

[0061] C2: According to formula (10), constraint (19.C1) can be equivalent to In addition, note that before the kth round of data collection begins, the remaining energy of the USN is known. Therefore, the optimization problem (19) can be transformed into the following form.

[0062] for The derivative of is always negative, and the consumption function increases with the transmission time. And decreases, so the optimal solution is For USNs adopting relay transmission mode, energy consumption is jointly determined by USN and relay. The same relay may assist multiple USNs, which means that they will compete for the resources of the relay. However, since their time slots are independent, there is no interference between them. According to the optimization problem (18), each relay The optimization problem can be written as

[0063]

[0064] stC1:

[0065] C2:

[0066] C3:

[0067] C4:

[0068] C5: Because the relay selection result has been given, the energy consumption and It can be expressed as

[0069] Due to the non-convexity of constraints (21.C1) and (21.C2), the optimization problem (21) is difficult to solve. In order to improve the solution efficiency, the optimal solution of the optimization problem (21) always holds therefore, It can be used as an additional constraint for the optimization problem (21). In order to further deal with the non-convex constraints (21.C1) and (21.C2), we also need to use the following theorem.

[0070] For the optimal solution of problem (21), constraints (21.C1-21.C3) always hold in equality;

[0071] Based on this, make the following variable substitutions.

[0072]

[0073] in, Then, according to Theorem 1 and formula (28), constraint (21.C3) is equivalent to

[0074] T c / 2≤T m,r ≤T c (29), further, the original optimization problem (21) can be rewritten as

[0075]

[0076] stC1:T c / 2≤T m,r ≤T c

[0077] C2:

[0078] C3: By introducing auxiliary variables, problem (30) can be equivalently transformed into

[0079] max s

[0080] stC1:T c / 2≤T m,r ≤T c

[0081] C2:

[0082] C3:

[0083] C4:

[0084] C5: To further process problem (31), the optimization problem (31) is equivalent to the following convex optimization problem:

[0085] max s

[0086] stC1:

[0087] C2:

[0088] C3: in, And T upper = min{T c ,T1 *}, due to the convexity of the optimization problem (41), the dual gap between the original problem and the dual problem is zero, so the Lagrangian dual decomposition method is applied to solve the optimization problem (41), and the Lagrangian function can be written as

[0089]

[0090] in and μ are the Lagrange multipliers corresponding to constraints (41.C1) and (41.C2).

[0091] Then the dual function can be expressed as

[0092] For a given Lagrange multiplier and μ, problem (43) is equivalent to solving the following two optimization problems:

[0093]

[0094] According to the existing technology, Always holds true, so for the optimization problem s can be any non-negative number. It is a one-dimensional convex optimization problem that can be solved efficiently using gradient descent;

[0095] The dual problem is as follows:

[0096] minD(λ,μ)

[0097] stC1:λ≥0,μ≥0

[0098] C2: The dual problem (46) can be solved by the subgradient method, where the subgradient is defined as: Then, the update rule for the Lagrange multipliers is given as follows:

[0099]

[0100] in ρ(k) and τ(k) are the step sizes for the kth iteration.

[0101] The present invention also includes a method for processing mode selection and relay selection, specifically, firstly designing a preference function by analyzing basic constraints to obtain a potential relay set, and then considering the priority of the user network, using a many-to-one matching method to process the relay selection problem, wherein the relay selection and the acquisition of the preference function specifically include the following steps:

[0102] According to the optimization goal, if USN is used as a relay, the following two criteria need to be met:

[0103] Let USN and relay be represented as m and n respectively, then the first criterion is the distance constraint: if the nth USN can be a candidate relay for the mth USN, then the distance between the mth USN and the nth USN should be less than the distance from the mth USN to the sink node to ensure that the relay mode is better than the direct mode. This constraint can be expressed as:

[0104] The second criterion is energy constraint: First, the premise of acting as a relay is that the remaining energy of this USN is sufficient to ensure that its own data is transmitted in a direct manner. The second rule is that the remaining energy is still sufficient to relay data from other USNs. To ensure the second rule, the energy consumption of the mth USN in relay mode is calculated to be equal to the energy consumption in direct mode.

[0105] in is very easy to calculate. This is because the function about is decreasing and is a constant. According to Theorem 1, if Then the relay mode is not feasible; if The conditions for the relay mode to be feasible are:

[0106]

[0107] in The above constraint (51) means that the residual energy of the nth USN has the potential to reduce the energy consumption of the mth USN; then, in order to evaluate the importance of each relay, based on the residual energy and energy consumption, we design the preference function V m,n To express the preference of the mth USN for the nth USN. According to the relay r and the matching USN set on relay r The optimal objective function value of the optimization problem (41) is defined as Then, the gain function V m,n Defined as:

[0108]

[0109] in, is the set of all feasible relays of the mth USN;

[0110] The acquisition of the preference function can be achieved in the following ways:

[0111] Initialize the relay collection and preference function V m,n =0;

[0112] According to the remaining energy Sort USNs in ascending order;

[0113] Execute the loop of i=1:M-1, j=i+1:M. If formula (49) holds, calculate the time according to formula (50). If formula (51) holds and Then solve the optimization problem (52) and update the preference function V m,nThe matching process mainly includes three stages: request stage, decision stage and role conversion stage. Represents a set of USNs that cannot act as relays. To complement, first, The USNs in are sorted in ascending order of residual energy. Then, for each Value V according to your preference m,n Relay Set Sort the elements in ;

[0114] 1) Request phase: In this phase, USN m with the smallest remaining energy has priority in sending a matching request. Then, USN m sends If the relay set is empty, direct mode is the only option for USN m. Otherwise, the next stage further determines whether to adopt relay mode.

[0115] 2) Decision-making stage: For each relay in, if no other USN has been matched, the relay will directly accept the request. Otherwise, the requested USN will compete with the matched USN. Unless the relay gain can be improved, USN m will be rejected. Assume that USN m has been matched with relay n, and define Combined with the matched nodes on relay n, the gain function is expressed as:

[0116]

[0117] For the case where USN m has no matching relay n, the gain function is expressed as:

[0118]

[0119] if Because the relay does not have sufficient resources to support the request, USN m will be rejected. Then, relay n will be removed from the set If The relay will agree to USN m's request. Note that USN m may not create a match with relay n even if relay n agrees to its request. The reason is that there may be multiple relays to choose from. Therefore, the final decision returns to USN m, and it will choose the relay with the largest gain, that is,

[0120]

[0121] 3) Role Transformation Stage: The USN in is a potential relay, not an actual relay. Therefore, there may be some nodes that are not connected to Because the remaining relays do not match any USN, these relays are converted from Go to is reasonable because they are not real relays. Therefore, the unmatched relays are sorted in descending order of residual energy. Then, the relay with the smallest residual energy is removed from Remove and add to Newly added USN participation request phase and decision phase.

[0122] The optimization problem (41) in step 3 of the present invention can be solved by the following method:

[0123] Get the initial Lagrange multiplier and μ, maximum number of iterations K max and convergence threshold ε, calculate the optimal time allocation First calculate the lower bound T lower and upper bound T upper , execute k=1:K max For a given Lagrange multiplier, solve the optimization problem and To obtain the optimal solution The gradient is calculated according to equations (47a)-(47b), and the gradient is updated according to equations (48a)-(48b). If ||λ(k)-λ(k-1)||<ε, |μ(k)-μ(k-1)|<ε, the loop is terminated.

[0124] Compared with the prior art, the present invention is superior to the traditional time division multiple access frame, especially when facing a large-scale network, the improvement is more obvious, has better adaptability to different intermediate deployments, and can significantly improve the network life. Description of the drawings:

[0125] Attached Figure 1 It is a schematic diagram of the relay-assisted underwater sensor network model of the present invention.

[0126] Attached Figure 2 It is a curve diagram showing the relationship between network life and USN quantity in an embodiment of the present invention.

[0127] Attached Figure 3 It is a curve diagram showing the relationship between network life and USN energy in an embodiment of the present invention.

[0128] Attached Figure 4 It is a curve diagram of the relationship between network lifetime and time slot length in an embodiment of the present invention.

[0129] Attached Figure 5 It is a curve diagram showing the relationship between the network life and the maximum transmission power of the USN in the embodiment of the present invention.

[0130] Attached Figure 6 It is a curve diagram showing the relationship between network life and network scale in an embodiment of the present invention.

[0131] Attached Figure 7 It is a curve diagram showing the relationship between network life and USN data volume in an embodiment of the present invention. Specific implementation method:

[0132] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0133] Embodiment 1:

[0134] like Figure 1 As shown in Figure 1, a relay-assisted underwater sensor network is considered in this example. The network consists of sink nodes (SN) and underwater sensor nodes (USN). Among them, USNs are randomly deployed in the sea to sense the necessary information, while SNs are usually deployed on the sea surface to collect the information sensed by all underwater sensor nodes. In order to avoid interference, the entire collection period is evenly divided into multiple time slots using time division multiple access (TDMA). In each time slot, USN can use acoustic signals to send corresponding information to SN. However, if direct transmission is adopted, user nodes far away from SN will consume more energy than user nodes close to SN, resulting in node energy imbalance and reduced network life. Therefore, we further consider the relay transmission mode through the amplification and forwarding protocol. In other words, the user network can not only transmit its own information, but also act as a relay to help other user networks. In the relay transmission mode, USN only needs to transmit the signal to the closer relay node instead of the distant SN, and then the relay node forwards the amplified signal to the SN.

[0135] definition As the set of USNs, M is the total number of USNs. The total collection period is assumed to be T, and the length of each time slot is correspondingly ΔT=T / M. The bandwidth used by the network is denoted as B, and the central carrier frequency is f.

[0136] 1) Signal attenuation and noise model

[0137] The attenuation of underwater acoustic signals mainly depends on the central carrier frequency and the communication distance between sensor nodes. Urick model

[23] It is widely considered to be the most convincing model for simulating the attenuation of underwater acoustic signals. Specifically, the attenuation is expressed as:

[0138]

[0139] Where d is the communication distance between sensor nodes. λ is a constant and ranges between 1 and 2. For convenience, λ is usually equal to 1.5. α(f) represents the absorption coefficient, which is a function of the carrier frequency. By applying the Thorp empirical formula

[23] , the absorption coefficient α(f) is given as follows:

[0140]

[0141] According to the study in

[23] , the noise of underwater acoustic communication is affected by turbulence N1(f), waves N2(f), wind N3(f) and thermal noise N4(f) (in decibels / Pa / Hz). The total noise N(f) is the sum of these elements:

[0142] N(f)=N1(f)+N2(f)+N3(f)+N4(f) (3)

[0143] Specifically, the calculation formula for each component is as follows:

[0144] 10log N1(f)=17-30log f (4)

[0145] 10log N2(f)=40+20(s-0.5)+26log f-60log(f+0.03) (5)

[0146]

[0147] 10log N4(f)=-15+20log f (7)

[0148] Among them, s represents the transport activity coefficient, which is between 0 and 1. w represents the wind speed in meters per second.

[0149] In order to facilitate further analysis of the acoustic signal transmission process and energy consumption, we give the following formula for converting acoustic and electrical signal units:

[13] .

[0150]

[0151] In direct transmission mode, the SN will directly receive the signal from the mth USN in the form of:

[0152]

[0153] in and Indicates the distance between SN and the mth USN. m Indicates the transmit power of the mth USN. is the signal to be reconstructed by SN. Represents signal noise.

[0154] Then, the total amount of data received by the SN can be expressed as:

[0155]

[0156] in Indicates the actual transmission time.

[0157] In the relay transmission mode, the transmission process is divided into two stages. In the first stage, the mth USN sends its signal to the relay node instead of the SN. If the nth USN is selected as the relay, the corresponding signal it receives from the mth USN is:

[0158]

[0159] Among them G m,n =1 / A(d m,n ,f) and d m,n Indicates the distance between the nth USN and the mth USN. Represents signal noise.

[0160] The total amount of data received by the mth USN can be expressed as:

[0161]

[0162] where g m,n =G m,n / (BN(f)).

[0163] In the second stage, the nth USN amplifies the received signal and forwards it to the SN. Then, the SN can receive the corresponding signal from the nth USN.

[0164]

[0165] Then, the total amount of data received by the SN can be calculated as

[0166]

[0167] Where T m,n and q m,n They represent the actual transmission time and transmission power of the nth USN to assist the mth USN. Since the transmission process is divided into two stages, the final amount of data received by the SN depends on the minimum value of the two links, that is, As mentioned above, USN has two modes to choose from: relay transmission mode and direct transmission mode. To describe it, we define a binary variable a m,n ∈{0,1} to represent relay selection and mode selection. m,n=1 means that the nth USN is the relay of the mth USN. If not, a m,n = 1. For the special case m = n, a m,m =1 indicates that the mth USN selects direct transmission mode.

[0168] Then, the remaining energy of the mth USN in the kth collection cycle can be expressed as:

[0169]

[0170] The second term on the right represents the energy consumption required by the mth USN to transmit its own information. The third term refers to the energy consumption caused by acting as a relay.

[0171] Due to the long propagation delay, the actual transmission time depends on the communication distance. For the direct transmission mode, the actual transmission time of the mth USN can be calculated as

[0172]

[0173] Where v is the speed of sound. For the relay transmission mode and assuming that the nth USN acts as a relay, the actual transmission time of the mth USN can be expressed as

[0174]

[0175] Typically, once the first USN runs out of energy, the network is considered dead. Therefore, the network lifetime is defined as the number of data collection rounds before the network fails. In each round of data collection, our goal is to maximize the minimum remaining energy of the user network, thereby further improving the network lifetime. The main optimization variables include relay selection and mode selection variables Transmission time variable Power allocation variables and The final optimization problem is expressed as follows:

[0176]

[0177] stC1:

[0178] C2:

[0179] C3:

[0180] C4:

[0181] C5:

[0182] C6:

[0183] C7:

[0184] C8:

[0185] C9:

[0186] C10:

[0187] In this optimization problem, (C1) indicates that each USN must choose between relay transmission mode and direct transmission mode. In addition, if the relay transmission mode is selected, only one relay node can be selected. (C2) indicates that a USN can only act as a relay for another USN when its own data is transmitted directly. The reason is that if a USN can act as a relay, its remaining energy must be sufficient to at least ensure that its own data is transmitted directly without any relay assistance. (C3) and (C4) indicate that regardless of whether it is relay transmission mode or direct transmission mode, all user networks can successfully transmit the amount of data they sense. (C5) and (C6) indicate that the actual transmission time is limited by the given time slot length. (C7) and (C8) ensure that the transmission power of each USN is less than the maximum transmission power. (C9) ensures that the actual transmission time is non-negative. (C10) indicates a m,n is a binary variable.

[0188] Obviously, the proposed optimization problem (18) is a non-convex mixed integer programming. The optimal solution of problem (18) is difficult to obtain, and the difficulty mainly includes two parts. One is how to deal with the binary variable a m,n Although the exhaustive method can find the optimal solution, it is only suitable for the case of a small number of variables. The second point is that even if a binary variable a is given m,n ,constraint C4 and the non-convexity of the objective function. Therefore, to reduce the complexity, we propose a suboptimal but effective joint mode selection and resource allocation algorithm in the following;

[0189] Given the mode and relay selection, the optimal resource allocation strategy is provided. For the direct mode, the optimal resource allocation strategy is easy to obtain. However, for the relay mode, the optimization problem (18) is reformulated as a non-convex problem. Then, we prove that it can be equivalent to a convex optimization problem through some transformations. Finally, the Lagrangian dual decomposition method is applied to obtain the optimal solution.

[0190] Assuming that the mode selection and relay selection results have been given, the group of user networks can be divided into three subsets, namely, USNs using direct transmission mode, USNs using relay transmission mode, and USNs acting as relays. Specifically, we let represents the set of USNs acting as relays, where s is the number of relays. i The set of assisting USNs is represented as The user network set of direct transmission mode is represented as Then, we will analyze the energy consumption of all user networks and find the optimal resource allocation strategy.

[0191] 1) Direct transfer mode

[0192] For USNs in direct transmission mode, there will be no interference between USNs due to the application of time division multiple access frames. Then, the optimization problem (18) can be solved according to each is divided into many sub-problems. Then, the sub-problems can be expressed as

[0193]

[0194] stC1:

[0195] C2:

[0196] According to formula (10), constraint (19.C1) can be equivalent to In addition, note that before the kth round of data collection begins, the remaining energy of the USN is known. Therefore, the optimization problem (19) can be transformed into the following form.

[0197]

[0198]

[0199] for The derivative of , we can prove that it is always negative. Therefore, the energy consumption function increases with the transmission time Therefore, the optimal solution is

[0200] 2) Relay transmission mode

[0201] For USNs adopting relay transmission mode, the energy consumption is determined by both USN and relay. The same relay may assist multiple USNs, which means that they will compete for the relay's resources. However, since their time slots are independent, there is no interference between them. According to the optimization problem (18), the corresponding time slots of each relay are The optimization problem can be written as

[0202]

[0203] stC1:

[0204] C2:

[0205] C3:

[0206] C4:

[0207] C5:

[0208] Because the relay selection result has been given, the energy consumption and It can be expressed as

[0209]

[0210]

[0211] Due to the non-convexity of constraints (21.C1) and (21.C2), the optimization problem (21) is difficult to solve. In order to improve the solution efficiency, we first provide a Theorem 1 to reduce the feasible set space.

[0212] Theorem 1. For the optimal solution of the optimization problem (21), it always holds

[0213] Proof: The feasible solution to the original problem must satisfy any of these two equations, that is, and for In the following, we will prove that the optimal solution must satisfy In this way, the proof of Theorem 1 has been completed. In order to prove this fact in detail, we first explain that When This is because

[0214]

[0215] Then, combined with the conditions And the monotonicity of the log2(·) function, we can get Therefore, constraint (21.C1) can be removed. Furthermore, constraint (21.C2) is equivalent to

[0216]

[0217] p m g m,r q m,r h r ≥C(T m,r )(p m g m,r +q m,r hr +1) (24b)

[0218] q m,r h r (p m g m,r -C(T m,r ))≥C(T m,r )(p m g m,r +1) (24c)

[0219]

[0220] in The main condition for the successful conversion from step (24c) to (24d) is that p m g m,r -C(T m,r )>0. We say that this condition must be satisfied. If this condition is not satisfied, constraint (21.C1) will not be satisfied, and the whole problem is infeasible. According to the above transformation, the energy consumption of the relay node can be written as

[0221]

[0222] For any given p m , similar to the analysis of problem (20), function T m,r C(T m,r ) is about T m,r In addition, it is clear that C(T m,r ) is also about T m,r Decreasing. m,r The larger the value, the more beneficial it is to reduce the energy consumption of relay nodes. On the other hand, the energy consumption of USN is This means that the smaller It is beneficial to reduce the energy consumption of USN. Therefore, the optimal solution must be This completes the proof; according to Theorem 1, It can be used as an additional constraint for the optimization problem (21). In order to further deal with the non-convex constraints (21.C1) and (21.C2), we also need to use the following theorem.

[0223] Theorem 2. For the optimal solution of problem (21), constraints (21.C1-21.C3) always hold in equations.

[0224] Proof: Assume that constraint (21.C1) does not hold in terms of equality, then we have By further transformation, this is equivalent to

[0225]

[0226] Then, for a fixed p m , must exist So that formula (26) still holds. The energy consumption of USN can be further reduced, which may increase the objective function, which is consistent with is the optimal solution contradiction. Using a similar method, we can get constraint (21.C2) will also be equal. Then we can get the optimal transmission power p m and q m,r for:

[0227]

[0228]

[0229] Assume that constraint (21.C3) does not hold in equality. Keep time unchanged, according to equation (27a), the transmission power p m Then, according to equation (25), the energy consumption of the relay increases with time T m,r Therefore, time T m,r It will be increased until constraint (21.C3) holds true in equation, because it helps to reduce the energy consumption of the relay. This completes the proof.

[0230] The proof is complete.

[0231] According to Theorem 2, we can make the following variable substitutions.

[0232]

[0233] in,

[0234] Then, according to Theorem 1 and Formula (28), constraint (21.C3) is equivalent to T c / 2≤T m,r ≤T c (29), further, the original optimization problem (21) can be rewritten as

[0235]

[0236] stC1:T c / 2≤T m,r ≤T c

[0237] C2:

[0238] C3: By introducing auxiliary variables, problem (30) can be equivalently transformed into

[0239] max s

[0240] stC1:T c / 2≤T m,r ≤T c

[0241] C2:

[0242] C3:

[0243] C4:

[0244] C5: To further deal with problem (31), we provide Theorem 3 below.

[0245] Theorem 3: Problem (31) is equivalent to a convex optimization problem.

[0246] Proof: Order And taking its derivative we can get

[0247] Then, taking its second-order derivative we get

[0248] according to Together with formula (33), we have proved that constraint (31.C2) is convex. Then, according to (27a) and (27b), let G(T m,r )=T m,r q m,r (T m,r ), we can get:

[0249]

[0250] in

[0251] G1(T m,r )=T m,r C(T m,r )(35a),

[0252] Then, by taking G(T m,r ), we can get

[0253] Where K(T m,r )=G1′(T m,r )G2(T m,r )-G1(T m,r )G2′(T m,r ). Similar to equations (32) and (33), G1′(T m,r ) can be written as

[0254]

[0255] Obviously, the first-order derivative G′1(T m,r ) is about T m,r Increasing. Because We get G′1(T m,r )<0. On the other hand, G′2(T m,r ) can be written as

[0256] in

[0257]

[0258] Then we can get K(T m,r )<0 is true. Further, for G(T m,r ) Find the second-order derivative

[0259]

[0260] Where Z(T m,r )=2K(T m,r )G2(T m,r )G′2(T m,r ). According to equations (35b) and (38), it is obvious that Z(T m,r )<0. Therefore, in order to prove that G″(T m,r )≥0, equivalently, it can be proved that K′(T m,r )≥0. Function K′(T m,r ) is shown below

[0261] K′(T m,r )=G″1(T m,r )G2(T m,r )-G1(T m,r )G″2(T m,r )(40), according to equations (35a), (35b), (37b), K′(T m,r )≥0 is equivalent to G″2(T m,r )≤0.

[0262] Obviously, G″2(T m,r ) < 0 always holds. Therefore, we have proved that constraint (31.C3) is convex.

[0263] In addition, it is obvious that p m (T c -T m,r ) is about T m,rTherefore, constraint (31.C4) is equivalent to T c / 2≤T m,r ≤T1 * , where T1 * is an upper bound and satisfies pm(T c -T1 * )=P max Similarly, q m,r (T m,r ) is a m,r Incrementing function.

[0264] Therefore, constraint (31.C5) is equivalent to in is a lower bound and satisfies Therefore, the optimization problem (31) is equivalent to the following convex optimization problem.

[0265] max s

[0266] stC1:

[0267] C2:

[0268] C3:

[0269] in, And T upper = min{T c ,T1 *}. This completes the proof.

[0270] The proof is complete.

[0271] Due to the convexity of the optimization problem (41), the duality gap between the primal problem and the dual problem is zero. Therefore, the Lagrangian dual decomposition method is applied to solve the optimization problem (41). The Lagrangian function can be written as

[0272]

[0273] in and μ are the Lagrange multipliers corresponding to constraints (41.C1) and (41.C2).

[0274] Then the dual function can be expressed as

[0275]

[0276] For a given Lagrange multiplier and μ, problem (43) is equivalent to solving the following two optimization problems:

[0277]

[0278] According to the literature

[24] , Therefore, for the optimization problem s can be any non-negative number.

[0279] question It is a one-dimensional convex optimization problem and can be solved efficiently using gradient descent.

[0280] The dual problem is as follows:

[0281] min D(λ,μ)

[0282] stC1:λ≥0,μ≥0

[0283] C2:

[0284] The dual problem (46) can be solved by the subgradient method, where the subgradient is defined as:

[0285]

[0286] Then, the update rule for the Lagrange multipliers is given as follows:

[0287]

[0288] in ρ(k) and τ(k) are the step sizes for the kth iteration.

[0289] For the specific solution details of problem (41), please refer to Algorithm 1.

[0290]

[0291]

[0292] The above provides an optimal resource allocation method for given mode selection and relay selection results. Next, a suboptimal but effective matching algorithm is proposed to deal with the mode selection and relay selection problems. First, the corresponding preference function is designed by analyzing the basic constraints, and then the potential relay set can be obtained. Furthermore, considering the priority of the user network, a many-to-one matching method is used to deal with the relay selection problem.

[0293] Before we start the matching process, it is extremely important to decide the set of USNs that can act as relays. Therefore, it is necessary to determine the criteria for acting as relays. According to the optimization goal, if a USN can act as a relay, it needs to meet the following two criteria. For convenience, USN and relay are represented as m and n respectively.

[0294] 1) Distance constraint: If the nth USN can be a candidate relay for the mth USN, then the distance between the mth USN and the nth USN should be less than the distance from the mth USN to the sink node to ensure that the relay mode is better than the direct mode. This constraint can be expressed as:

[0295]

[0296] 2) Energy Constraints: First, the premise of acting as a relay is that the remaining energy of this USN is sufficient to ensure that its own data is transmitted in a direct manner. The second rule is that the remaining energy is still sufficient to relay data from other USNs. To ensure the second rule, the energy consumption of the mth USN in relay mode is calculated to be equal to the energy consumption in direct mode.

[0297]

[0298] in is very easy to calculate. This is because the function about is decreasing and is a constant. According to Theorem 1, if Then the relay mode is not feasible; if The conditions for the relay mode to be feasible are:

[0299]

[0300] in The above constraint (51) means that the remaining energy of the nth USN may reduce the energy consumption of the mth USN.

[0301] Then, to evaluate the importance of each relay, based on the residual energy and energy consumption, we design the preference function V m,n To express the preference of the mth USN for the nth USN. According to the relay r and the matching USN set on relay r The optimal objective function value of the optimization problem (41) is defined as Then, the gain function V m,n Defined as:

[0302]

[0303] in, is the set of all feasible relays of the mth USN. Algorithm 2 provides the specific relay discovery and preference function calculation.

[0304]

[0305] Algorithm 3 summarizes the details of the matching process between wireless sensor networks and relays. The matching process mainly includes three stages: request stage, decision stage and role conversion stage. Represents a set of USNs that cannot act as relays. is a complement set. First, The USNs in are sorted in ascending order of residual energy. Then, for each Value V according to your preference m,n Relay Set Sort the elements in .

[0306] 1) Request phase: In this phase, USN m with the smallest remaining energy has priority in sending a matching request. Then, USN m sends If the relay set is empty, direct mode is the only option for USN m. Otherwise, the next stage further determines whether to adopt relay mode.

[0307] 2) Decision-making stage: For each relay in, if no other USN has been matched, the relay will directly accept the request. Otherwise, the requested USN will compete with the matched USN. Unless the relay gain can be improved, USN m will be rejected. Assume that USN m has been matched with relay n, and define Combined with the matched nodes on relay n, the gain function is expressed as:

[0308]

[0309] For the case where USN m has no matching relay n, the gain function is expressed as:

[0310]

[0311] if Because the relay does not have sufficient resources to support the request, USN m will be rejected. Then, relay n will be removed from the set If The relay will agree to USN m's request. Note that USN m may not create a match with relay n even if relay n agrees to its request. The reason is that there may be multiple relays to choose from. Therefore, the final decision returns to USN m, and it will choose the relay with the largest gain,

[0312] Right now,

[0313]

[0314] 3) Role Transformation Stage: The USN in is a potential relay, not an actual relay. Therefore, there may be some nodes that are not connected to Because the remaining relays do not match any USN, these relays are converted from Go to is reasonable because they are not real relays. Therefore, the unmatched relays are sorted in descending order of residual energy. Then, the relay with the smallest residual energy is removed from Remove and add to Newly added USN participation request phase and decision phase.

[0315]

[0316]

[0317] In order to evaluate the performance of the proposed Joint Mode and Relay Selection Algorithm (JMRSA), some simulation results are given from the perspective of network lifetime, which is defined as the number of information collection rounds completed until the first USN runs out of energy. A three-dimensional sea area is considered, where the sink nodes are located on the sea surface and USNs are randomly distributed in the ocean. More specific simulation parameters can be found in Table 1.

[0318] Table 1 Simulation parameters

[0319]

[0320] The performance evaluation is performed from the following perspectives: time slot length, energy of USN, data volume, number of USNs, maximum transmission power and network size. The proposed algorithm is compared with the traditional TDMA

[25] . In fact, TDMA is a special case in this example, that is, all user networks choose direct mode.

[0321] In addition, this example does not study the optimized aggregation node deployment scheme. To demonstrate its effect, we provide three common deployment schemes, including the central deployment scheme, the k-means-based deployment scheme, and the fair deployment scheme. The central deployment scheme is to deploy the aggregation node at the center of the sea surface. In the k-means-based deployment scheme, the deployment of the aggregation node is based on the minimum distance sum criterion. The principle of the fair deployment scheme is to minimize the maximum distance between the USN and the aggregation node.

[0322] Figure 2The effect of the number of USNs on the network lifetime is evaluated. It is obvious that the network lifetime decreases with the increase of USNs. That is because the probability of USNs being distributed at the edge increases. The farthest USN consumes more energy than other USNs and will die first. This situation is the same as the proposed scheme. However, when the number of USNs increases, more alternative USNs can be selected for the edge USNs. Therefore, there are more opportunities to reduce the energy consumption of edge USNs. Further, by delaying the death of edge USNs, the network lifetime can be improved. In contrast, for the case of sparse network, that is, the number of USNs is small, the proposed scheme is similar to the traditional time division multiple access frame because there are almost no relays to choose from and the USN can only choose direct mode. In addition, it can be seen that the proposed scheme is always better than the traditional time division multiple access frame. This improvement is especially obvious when facing large-scale networks. On the other hand, by comparing with the other two deployment schemes, the performance of the fair aggregation node deployment scheme is the best. In particular, the impact of the deployment scheme is more obvious for the traditional TDMA method, but not for the proposed scheme. The scheme has better adaptability to different relay deployments because its core idea is to optimize relay selection.

[0323] Figure 3 Used to evaluate the impact of USN energy on network lifetime. It can be seen that the network lifetime increases linearly with the increase of USN energy. For different aggregation node deployment schemes, the performance of the algorithm is almost the same and is always better than the traditional TDMA method. When the energy of USN increases, the performance improvement is more obvious. Taking the fair deployment scheme as an example, when the energy of each USN is 1J, the proposed method can collect 10 more rounds of information than traditional TDMA. When the energy of each USN is 2J, there is about 23 rounds of improvement. The reason is that the lower limit of information collection rounds increases, and USN has more opportunities to reduce energy consumption.

[0324] Figure 4 The variation of network lifetime as the time slot length increases is shown. According to formula (20) and Theorem 2, energy consumption is a decreasing function of time. Therefore, the network lifetime can be improved by increasing the transmission time. However, for traditional TDMA, the improvement is not obvious. For the proposed scheme, the improvement rate is large at the beginning and then becomes slower. For example, when the time is increased from 2s to 3s, the network lifetime is improved by about 11%. However, when the time is increased from 3s to 4s, the improvement is reduced to 2.5%. This is because when the slot length is small, the impact of long-distance propagation delay is large.

[0325] Figure 5The influence of the maximum transmission power of USN on the proposed algorithm is revealed. For traditional TDMA, USN will definitely not use the maximum transmission power. Therefore, the increase in the maximum transmission power has no effect on traditional TDMA. However, for the proposed algorithm, the effect is present and obvious. Increasing the maximum transmission power will increase the solution space of the original problem (21) and will further improve the network performance. It can be seen that by continuously increasing the maximum transmission power, the performance improvement becomes slower. Therefore, in practical applications, there is no need to blindly increase the maximum transmission power of USN.

[0326] Figure 6 The effect of network size on network lifetime is given in Figure 1. In this figure, the network size is defined as the length and width of the network. Without loss of generality, it is assumed that the length of the network is equal to the width of the network. It is obvious that the network lifetime decreases as the network size increases. In fact, due to the growth of network size, the distance between USN and the aggregation node becomes longer and longer, and it costs more for the user network to transmit the same amount of data. The algorithm outperforms the traditional TDMA method. However, for large network sizes, for example, for the case of 1000 meters, the performance improvement is small. This does not mean that the proposed algorithm is invalid. The main reason is that the network becomes sparse, resulting in a small or even no number of relays. More Figure 2 ,The network effect of the proposed algorithm is very obvious for large scale USN.

[0327] Figure 7 The effect of data volume on network lifetime is provided. As the data volume grows, the network lifetime decreases rapidly because more energy consumption is required to transmit the sensed data. Obviously, the performance of the proposed algorithm is better than that of the traditional TDMA method. The performance improvement is more obvious for low data volume. For example, from the fair deployment scheme of the aggregation node, the network lifetime is improved by nearly 40% when the data volume is 3kb. In fact, the core idea of ​​the algorithm is to achieve energy balance through relaying. This balance is obvious when the data volume is low because other constraints (such as maximum transmission power constraint and transmission time constraint) are relaxed.

[0328] The present invention proposes a relay-assisted underwater information transmission scheme to improve network life. The entire scheme can be divided into two stages: resource configuration stage; mode and relay selection stage. In the first stage, the Lagrangian dual decomposition method is used to solve an equivalent convex optimization problem to obtain the optimal resource allocation result. In the second stage, a matching-based mode and relay selection algorithm is designed according to the node priority. Simulation results show that the scheme is not affected by the aggregation node deployment scheme and has strong adaptability. In addition, the scheme is conducive to improving the network life, and the room for improvement is very obvious.

Claims

1. A relay-assisted underwater sensor network mode selection and resource allocation method, characterized in that: The following steps are involved: Step 1: Establish a relay-assisted underwater sensor network model. The system consists of a sink node SN and underwater sensor nodes USN. USNs are randomly deployed in the sea to sense information, while SNs are deployed on the sea surface to collect information sensed by all underwater sensor nodes. The entire collection cycle is evenly divided into multiple time slots using time division multiple access (TDMA). In each time slot, USN uses acoustic signals to send corresponding information to SN. In the relay transmission mode, USN only needs to transmit the signal to the closer relay node instead of the distant SN, and then the relay node forwards the amplified signal to the SN. The definition As a set of USNs, where M is the total number of USNs, the total collection period is assumed to be T, the length of each time slot is correspondingly ΔT = T / M, the bandwidth used by the network is represented by B, and the central carrier frequency is f; the attenuation of the underwater acoustic signal depends on the central carrier frequency and the communication distance between the sensor nodes. The Urick model is used to simulate the attenuation of the underwater acoustic signal, and the attenuation is expressed as: Where d is the communication distance between sensor nodes, λ is a constant and ranges between 1 and 2, α(f) represents the absorption coefficient, which is a function of the carrier frequency. By applying the Thorp empirical formula, the absorption coefficient α(f) is given as follows: According to the Thorp empirical formula, the noise of underwater acoustic communication is affected by turbulence N1(f), waves N2(f), wind N3(f) and thermal noise N4(f) (in decibels / Pa / Hz), and the total noise N(f) is the sum of these elements: N(f)=N1(f)+N2(f)+N3(f)+N4(f) (3) Specifically, the calculation formula for each component is as follows: 10logN1(f)=17-30logf (4) 10logN2(f)=40+20(s-0.5)+26logf -60log(f+0.03)(5) 10logN4(f)=-15+20logf (7) Among them, s represents the transport activity coefficient, which is between 0 and 1, and w represents the wind speed in meters per second; The following is the conversion formula for acoustic and electrical signal units: In direct transmission mode, the SN will directly receive the signal from the mth USN in the form of: in and represents the distance between SN and the mth USN; p m represents the transmission power of the mth USN, is the signal to be reconstructed by SN, represents the signal noise, Then, the total amount of data received by the SN is expressed as: where h m =H m / (BN(f)), Indicates the actual transmission time; In the relay transmission mode, the transmission process is divided into two stages. In the first stage, the mth USN sends its signal to the relay node instead of the SN. If the nth USN is selected as the relay, the corresponding signal it receives from the mth USN is: Among them G m,n =1 / A(d m,n ,f) and d m,n Indicates the distance between the nth USN and the mth USN, represents the signal noise, The total amount of data received by the mth USN is expressed as: where g m,n =G m,n / (BN(f)), In the second stage, the nth USN amplifies the received signal and forwards it to the SN. Then, the SN receives the corresponding signal from the nth USN. Then, the total amount of data received by SN is calculated as Where T m,n and q m,n They represent the actual transmission time and transmission power of the nth USN to assist the mth USN. Since the transmission process is divided into two stages, the final amount of data received by the SN depends on the minimum value of the two links, that is, Step 2: According to the system model established in step 1, USN has two modes to choose from: relay transmission mode and direct transmission mode. A binary variable a is defined. m,n ∈{0,1} to represent relay selection and mode selection, a m,n =1 means the nth USN is the relay of the mth USN. If not, a m,n = 0, for the special case m = n, a m,m =1 means the mth USN selects direct transmission mode, Then, the remaining energy of the mth USN in the kth collection cycle is expressed as: The second item on the right represents the energy consumption required by the mth USN to transmit its own information, and the third item refers to the energy consumption caused by acting as a relay. Due to the long propagation delay, the actual transmission time depends on the communication distance. For the direct transmission mode, the actual transmission time of the mth USN is calculated as Where v represents the speed of sound. For the relay transmission mode and assuming that the nth USN acts as a relay, the actual transmission time of the mth USN is expressed as Once the first USN runs out of energy, the network is considered dead. Therefore, the network lifetime is defined as the number of data collection rounds before the network fails. The transmission time variable and Power allocation variables and The final optimization problem is expressed as follows: In this optimization problem, C1 indicates that each USN must choose between the relay transmission mode and the direct transmission mode. In addition, if the relay transmission mode is selected, only one relay node can be selected. C2 indicates that a USN can only serve as a relay for another USN when its own data is directly transmitted. C3 and C4 indicate that regardless of the relay transmission mode or the direct transmission mode, all user networks can successfully transmit the amount of data they sense. C5 and C6 indicate that the actual transmission time is limited by the given time slot length. C7 and C8 ensure that the transmission power of each USN is less than the maximum transmission power. C9 ensures that the actual transmission time is non-negative. C10 indicates a m,n is a binary variable; Step 3: Determine the optimal resource allocation strategy: For the relay mode, the optimization problem (18) is reformulated as a non-convex problem, and the Lagrangian dual decomposition method is applied to obtain the optimal solution. Specifically, assuming that the mode selection and relay selection results have been given, the group of user networks is divided into three subsets, namely, USNs using direct transmission mode, USNs using relay transmission mode, and USNs acting as relays. Specifically, we let represents the set of USNs acting as relays, where s is the number of relays, so the relay r i The set of assisting USNs is represented as The user network set of direct transmission mode is represented as Analyze the energy consumption of all user networks and find the optimal resource allocation strategy: For USNs in direct transmission mode, there will be no interference between USNs due to the application of time division multiple access frames. Then, the optimization problem (18) can be solved according to each Divided into many sub-problems, then the sub-problems are expressed as According to formula (10), constraint (19.C1) is equivalent to In addition, note that before the start of the kth round of data collection, the remaining energy of the USN is known, so the optimization problem (19) is transformed into the following form: for The derivative of is always negative, and the consumption function increases with the transmission time. And decreases, so the optimal solution is For USNs adopting relay transmission mode, the energy consumption is jointly determined by USN and relay. The same relay may assist multiple USNs, which means that they will compete for the resources of the relay. However, since their time slots are independent, there is no interference between them. According to the optimization problem (18), each relay The optimization problem is written as Because the relay selection result has been given, the energy consumption and Expressed as Due to the non-convexity of constraints (21.C1) and (21.C2), for the optimal solution to the optimization problem (21) it always holds That is Theorem 1; therefore, It can be used as an additional constraint for the optimization problem (21). In order to further deal with the non-convex constraints (21.C1) and (21.C2), the following theorem is also needed: For the optimal solution of problem (21), constraints (21.C1-21.C3) always hold in equality; Based on this, make the following variable substitutions: in, Then, according to Theorem 1 and formula (28), constraint (21.C3) is equivalent to T c / 2≤T m,r ≤T c (29), the original optimization problem (21) is rewritten as By introducing auxiliary variables, problem (30) is equivalently transformed into To further process problem (31), the optimization problem (31) is equivalent to the following convex optimization problem: in, and Due to the convexity of the optimization problem (41), the dual gap between the primal problem and the dual problem is zero. Therefore, the Lagrangian dual decomposition method is applied to solve the optimization problem (41). The Lagrangian function can be written as in and μ are the Lagrange multipliers corresponding to constraints (41.C1) and (41.C2), Then the dual function is expressed as For a given Lagrange multiplier and μ, problem (43) is equivalent to solving the following two optimization problems: Always holds true, so for the optimization problem s is any non-negative number, the problem It is a one-dimensional convex optimization problem; The dual problem is as follows: The dual problem (46) is solved by the subgradient method, where the subgradient is defined as: Then, the update rule for the Lagrange multipliers is given as follows: in ρ(k) and τ(k) are the step sizes for the kth iteration.

2. A relay-assisted underwater sensor network mode selection and resource allocation method according to claim 1, characterized in that: The invention also includes a method for processing mode selection and relay selection, specifically, firstly, by analyzing basic constraints to design a preference function, obtain a potential relay set, and then consider the priority of the user network, adopt a many-to-one matching method to handle the relay selection problem, wherein the relay selection and the acquisition of the preference function specifically include the following steps: According to the optimization goal, if USN is used as a relay, the following two criteria need to be met: Let USN and relay be represented as m and n respectively, then the first criterion is the distance constraint: if the nth USN can be used as a candidate relay for the mth USN, then the distance between the mth USN and the nth USN should be less than the distance from the mth USN to the sink node to ensure that the relay mode is better than the direct mode. This constraint is expressed as: The second criterion is energy constraint: First, the premise of acting as a relay is that the remaining energy of this USN is sufficient to ensure that its own data is transmitted in a direct manner. The second rule is that the remaining energy is still sufficient to relay data from other USNs. To ensure the second rule, the energy consumption of the mth USN in relay mode is calculated to be equal to the energy consumption in direct mode. This is because the function about is decreasing and is a constant. According to Theorem 1, if Then the relay mode is not feasible; if The conditions for the relay mode to be feasible are: in The above constraint (51) means that the remaining energy of the nth USN may reduce the energy consumption of the mth USN; then, based on the remaining energy and energy consumption, the preference function V is designed m,n To express the preference of the mth USN for the nth USN, according to the relay r and the matching USN set on relay r The optimal objective function value of the optimization problem (41) is defined as Then, the gain function V m,n Defined as: in, is the set of all feasible relays of the mth USN; The acquisition of the preference function is implemented in the following way: Initialize the relay collection and preference function V m,n =0; According to the remaining energy Sort USNs in ascending order; Execute the loop of i=1:M-1, j=i+1:M. If formula (49) holds, calculate the time according to formula (50). If formula (51) holds and Then solve the optimization problem (52) and update the preference function V m,n ; The matching process includes three stages: request stage, decision stage and role conversion stage. Represents a set of USNs that cannot act as relays. To complement, first, The USNs in are sorted in increasing order of residual energy, and then, for each Value V according to your preference m,n Relay Set Sort the elements in ; 1) Request phase: In this phase, USN m with the smallest remaining energy has priority in sending a matching request. Then, USN m sends All relays in send matching requests. If the relay set is empty, direct mode is the only option for USN m. Otherwise, it is further decided in the next stage whether to adopt relay mode. 2) Decision-making stage: For each relay in, if no other USN has been matched, the relay will directly accept the request, otherwise, the requested USN will compete with the matched USN. Unless the gain of the relay can be improved, USN m will be rejected. Assume that USN m has been matched on relay n, and define Combined with the matched nodes on relay n, the gain function is expressed as: For the case where USN m has no matching relay n, the gain function is expressed as: if Because relay resources are insufficient to support the request, USN m will be rejected, and relay n will be removed from the set Remove if The relay will agree to USN m's request, so the final decision returns to USN m, which will choose the relay with the largest gain, that is, 3) Role Transformation Stage: The USN in is a potential relay, not an actual relay, and has no The remaining relays do not match any USN. Therefore, the unmatched relays are sorted in descending order according to the remaining energy. Then, the relay with the smallest remaining energy is removed from Remove and add to Newly added USN participation request phase and decision phase.

3. The method for selecting a mode and allocating resources of a relay-assisted underwater sensor network according to claim 1, characterized in that: The optimization problem (41) in step 3 can be solved by the following method: Get the initial Lagrange multiplier and μ, maximum number of iterations K max and convergence threshold ε, calculate the optimal time allocation First, calculate the lower bound T lower and upper bound T upper , execute k=1:K max For a given Lagrange multiplier, solve the optimization problem and To obtain the optimal solution The gradient is calculated according to equations (47a)-(47b), and the gradient is updated according to equations (48a)-(48b). If ||λ(k)-λ(k-1)||<ε, |μ(k)-μ(k-1)|<ε, the loop is terminated.

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