CN118200162A - A CSMA/CA network energy efficiency modeling method and system in industrial Internet of Things scenarios - Google Patents

Abstract

The invention provides a CSMA/CA network energy efficiency modeling method and system in an industrial Internet of things scene. According to the scheme, the CSMA/CA network node behaviors are modeled by using a two-dimensional Markov chain to obtain heterogeneous node steady-state transmission probability and collision probability, and the maximum single transmission power distribution boundary condition of the network node is described by analyzing hidden site problems caused by path loss due to wireless propagation effect in the industrial Internet of things field production scene, so that a set of CSMA/CA network node average energy efficiency model is provided, the calculation complexity is low, and the application value is good.

Description

A CSMA/CA network energy efficiency modeling method and system in industrial Internet of Things scenarios

Technical Field

The present invention belongs to the field of industrial Internet of Things, and in particular relates to a CSMA/CA network energy efficiency modeling method and system in an industrial Internet of Things scenario.

Background Art

At present, there are some energy efficiency optimization strategies for field communication networks using the CSMA/CA (Carrier-Sense Multiple Access with Collision Avoidance, CSMA/CA) protocol in the Industrial Internet of Things (IIoT) scenario. Among them, some technical solutions adopt an adaptive listening strategy, adaptively adjust the maximum contention window size through network nodes, and dynamically adjust it according to the real-time channel occupancy to reduce the energy consumption during the channel listening process. Some technical means adopt a dynamic power control method to dynamically adjust the transmission power of a single data transmission according to the distance between network nodes and environmental noise, while meeting the QoS (Quality of Service, QoS) indicators of communication and reducing the overall energy consumption of the network. Other technical means adopt an energy-saving node sleep-wake-up scheduling mechanism, shut down or reduce radio power consumption during non-transmission time periods, activate the node's radio state through a predetermined wake-up mechanism, and reduce the energy consumption of the node during the empty cache period. In addition, there are also some technical means to reduce the probability of collision and retransmission by introducing a non-uniformly distributed backoff algorithm, such as using a dynamic backoff algorithm based on network conditions. Although the above technical solutions have a certain degree of performance improvement on the overall energy efficiency of the network in the CSMA/CA network communication scenario, there has not yet been a targeted optimization design for the field of industrial Internet field communication. In actual industrial production applications, it may be necessary to combine multiple production environment influencing factors with network resource allocation strategies to achieve the best energy efficiency performance. Therefore, the energy efficiency modeling method for CSMA/CA networks based on Markov chains in the industrial Internet of Things scenario is still an open research problem.

Summary of the invention

Aiming at the application scenario of industrial Internet of Things field communication system based on CSMA/CA protocol, and aiming at the performance analysis of CSMA/CA protocol and the design requirements of node power and code length joint allocation strategy for industrial Internet of Things scenario, the present invention provides a CSMA/CA network energy efficiency modeling method and system in industrial Internet of Things scenario.

The present invention proposes a CSMA/CA network energy efficiency modeling method in an industrial Internet of Things scenario, which includes the following steps:

To achieve the above object, the technical solution of the method of the present invention is:

A CSMA/CA network energy efficiency modeling method based on Markov chain in an industrial Internet of Things scenario includes the following steps:

Step 1: Based on the CSMA/CA control protocol, the node state is abstracted into a two-dimensional Markov chain to construct a CSMA/CA network equivalent Markov chain model, and the single-step transition probability of the two-dimensional Markov chain is obtained;

Step 2: Based on the single-step transfer probability of the two-dimensional Markov chain obtained in step 1 and the closed-form solution of the steady-state probability distribution in discrete queuing theory, a closed-form solution of the steady-state probability distribution of the equivalent two-dimensional Markov model of the CSMA/CA network node described in step 1 is obtained; at the same time, based on the closed-form solution of the steady-state probability distribution, the steady-state transmission probability of any CSMA/CA network node in any system time slot is obtained;

Step 3: Based on the closed-form solution of the steady-state probability distribution obtained in step 2 and the steady-state transmission probability of the CSMA/CA network node obtained in step 2, the boundary conditions of the channel listening busy probability for the industrial Internet of Things field communication system scenario and the maximum transmission power of the CSMA/CA network node for a single transmission are derived based on probability theory;

Step 4: Based on the two types of nonlinear equations about the boundary conditions of the node transmission power allocation strategy obtained in step 3, the normalized network throughput model and network average energy efficiency model of the CSMA/CA network in the industrial Internet of Things scenario are derived based on probability theory.

Furthermore, the two-dimensional Markov chain in step 1 constructs an equivalent Markov chain model of the CSMA/CA network as a two-dimensional Markov chain with backoff level i and backoff timer remaining value j as state variables, and each state of the Markov chain is represented by two random variables {s(t), v(t)}, wherein the random variable s(t) of the first dimension represents the backoff level i of the node at time t, and i∈[-1,m], wherein m represents the maximum backoff order of the CSMA/CA network; the random variable v(t) of the second dimension represents the backoff timer remaining value j of the node at time t, and j∈[-1,w _m -1]; wherein w _m represents the contention window size when the CSMA/CA network reaches the maximum backoff order m, and w _i =2 ⁱ ·w ₀ ,i∈[0,m]; wherein w _i represents the maximum contention window size when the backoff order is i, w ₀ represents the contention window size when the backoff order is 0; when the backoff class i and the remaining value j of the backoff timer are both -1, it means that the node is in an idle state, that is, the sending queue of the node is empty. The first state parameter i of the two-dimensional Markov chain represents the current backoff class of the CSMA/CA network node. When i=-1, it means that the node buffer is empty and there are no data packets waiting to be transmitted; when i≥0, it means that the node buffer is not empty and there are data packets waiting to be transmitted; the second state parameter j of the two-dimensional Markov chain represents the remaining value of the current backoff timer of the node, that is, when j=-1, it means that the node buffer is empty and there are no data packets waiting to be transmitted. When j≥0, it means that the node buffer is not empty and there are data packets waiting to be transmitted.

Furthermore, the single-step transition probability of the two-dimensional Markov chain is:

Among them, Pr{-1,-1|-1,-1} represents the probability that the node is currently idle and the node state will still be idle in the next time slot;

Pr{0,j|-1,-1} represents the state transition probability of the node being idle in the next time slot and entering the initial backoff state i=0 with the backoff timer value set to j. This process indicates that a new data packet arrives and enters the initial backoff state i=0.

represents the state transition probability of the process of returning to state j from the current state j in the next time slot in the same backoff level i. This process means that the node detects that the current channel environment is busy and freezes the remaining backoff timer value;

represents the state transition probability of the process of transitioning from the current state j to the state j-1 in the next time slot in the same backoff level i. This process means that the node detects that the current channel environment is idle, and thus subtracts 1 from the remaining backoff timer value;

Pr{i+1,j|i,0} represents the state transition probability of the node's backoff level i in the current time slot being transferred to i+1 in the next time slot, and the backoff timer value is set from 0 in the current time slot to j in the next time slot. This process represents the process of the node transferring to a higher backoff level due to the failure of the current data transmission attempt due to data collision or finite code length data packet decoding error;

Pr{m,j|m,0} represents the state transition probability of the process in which the backoff level of the node in the current time slot is the highest backoff level m, and the backoff timer value is set from 0 in the current time slot to j in the next time slot. This process means that when the node reaches the maximum backoff level m, the node will no longer move to a higher backoff level, but stay at the current highest backoff level m until the transmission of the current data packet is finally completed;

Pr{-1,-1|i,0} indicates the state transition probability of the node in the current time slot being in backoff class i and the backoff timer value being 0, and the node state transitioning to the idle state in the next time slot. This process indicates that the node has successfully completed the transmission of the current data packet, and since no new data packets have arrived, the node falls back to the idle state;

Pr{0,j|i,0} represents the state transition probability of the node in the current time slot being in backoff class i and the backoff timer value being 0, and the node entering the initial backoff state i=0 and the backoff timer value being set to j in the next time slot. This process represents the process in which the node successfully completes the transmission of the current data packet and returns to the idle state due to the arrival of no new data packets. This process represents the process in which the node successfully completes the transmission of the current data packet and initializes the backoff due to the arrival of new data packets.

q represents the probability that the node buffer is still not empty after the node completes the transmission service of the current data packet, p _cl,k is the probability of collision in the transmission of the node data packet;

Among them, for any station in the CSMA/CA network The probability of detecting that the current channel state is busy is The data packet is sent to the central network access point AP with the maximum single transmission power P _max . The decoding error probability of a single data packet transmission under the finite code length theory is ε _k .

Furthermore, the closed-form solution of the steady-state probability distribution of the equivalent two-dimensional Markov model of the CSMA/CA network node described in step 1 in step 2 is:

b _i,j is the probability that for any node, when the system time tends to infinity, the state of its Markov chain node is in state (i,j).

Furthermore, based on the single-step transition probability expression obtained in step 1 above, the following steady-state probability distribution relationship is obtained:

in, It represents the closed-form solution of the steady-state probability distribution under the condition that the state variable i takes values in the range i∈[0,m) and the state variable j takes values in the range j∈(0,wi _- 1); It represents the closed-form solution of the steady-state probability distribution when the state variable i takes the value i=m and the state variable j takes the value range j∈(0,w _m -1]); represents the error transmission probability of node k in the CSMA/CA network, and p _tx,k represents the probability of transmitting a data packet when the node is in a steady state, which is expressed as:

Normalized expression based on node steady-state probability distribution And the expression of the steady-state transmission probability of node data packets is Given the total number of nodes k in the network, the probability of packet generation q and the single maximum transmission power P _max , the probability of a node transmitting a packet when in a steady state is obtained.

Furthermore, in the step 3, the boundary condition _P1 of the channel listening busy probability in the industrial Internet of Things field communication system scenario with respect to the maximum transmission power P _max of a single transmission of a CSMA/CA network node is set as two types of nonlinear equations,

Among them, the first kind of nonlinear equations:

The first type of nonlinear equations represents the expression of the probability of node k being related in the CSMA/CA network when a sufficiently large single transmission transmission power P _max ≥ P ₁ is allocated;

Nonlinear equations of the second kind:

The second type of nonlinear equations represents the expression of the probability of node k being related in the CSMA/CA network when a lower single transmission power P _max <P ₁ is assigned;

Where Q represents the Q function, which is expressed as V(γ _k ) represents the channel dispersion and is expressed as C(γ _k ) represents the normalized channel capacity, expressed as C(γ _k )=log(1+γ _k ); γ _k represents the received signal-to-noise ratio of the kth network node at the network access point; M represents the code length; represents the network access point; G ₀ is the channel reference gain at the reference distance; Represents the kth node in the CSMA/CA network At the access point _Pt represents the transmission power allocated to all k nodes in the CSMA/CA network; _N0 represents the noise power; represents the Euclidean distance between the kth node and the access point in the CSMA/CA network; P ₁ represents the boundary condition of the allocated power, that is, when the allocated power satisfies the condition P _t ＝P _max ≥P ₁ , there will be no hidden station effect in the CSMA/CA network, and there is When the allocated power satisfies the condition P _t = P _max < P ₁ , there is a hidden station effect in the CSMA/CA network, and there is

Furthermore, the expression of P ₁ is as follows.

in, Represents any two CSMA/CA network nodes The maximum Euclidean distance between _Pth represents the receiving power threshold at which the node senses the carrier and determines that the current channel state is idle.

Furthermore, in step 4, the normalized network throughput model of the CSMA/CA network in the industrial Internet of Things scenario is:

Where _ps,k represents the probability of the kth node successfully transmitting a data packet in the CSMA/CA network, and its expression is: S _k represents the throughput of the kth node, and its expression is ε _k represents the decoding error probability of the kth node in the CSMA/CA network under the given maximum single transmission power, code length and data packet size; D represents the size of a single transmission data packet of each node in the CSMA/CA network, in bits; In the two-dimensional Markov chain equivalent model, the expected value of the actual running time of the CSMA/CA communication protocol equivalent to the state transition time consumption time is expressed as follows:

Where p _tr represents the probability that there is at least one ongoing data packet transmission event in any system time slot in the CSMA/CA network, and its expression is σ represents the length of a single backoff slot specified in the CSMA/CA protocol; T _col represents the time the wireless channel is occupied when a packet collision occurs; T _suc represents the time the wireless channel is occupied when a packet is successfully transmitted; _Terr represents the time the wireless channel is occupied when a packet decoding error occurs;

The average energy consumption model of CSMA/CA network in the industrial Internet of Things scenario is:

Wherein, P _ave represents the average energy consumption of the CSMA/CA network, P _idle , P _cs , and P _max represent the power consumed by any network node in the idle state, backoff state, and sending state, respectively; It represents the expected time that a node spends in idle state during a data packet transmission cycle, and its expression is: It represents the expected time that a node spends in the carrier sensing state during a data packet transmission cycle, and its expression is: It represents the expected time that node k spends in the data sending state during a data packet transmission cycle, and its expression is:

On the other hand, the present invention provides a network energy efficiency modeling system in an industrial Internet of Things scenario, comprising:

Module 1 is used to abstract the node state into a two-dimensional Markov chain based on the CSMA/CA control protocol to construct a CSMA/CA network equivalent Markov chain model and obtain the single-step transition probability of the two-dimensional Markov chain;

Module 2 is used to obtain the closed-form solution of the steady-state probability distribution of the equivalent two-dimensional Markov model of the described CSMA/CA network node based on the obtained single-step transition probability of the two-dimensional Markov chain and the solution method of the closed-form solution of the steady-state probability distribution in discrete queuing theory; at the same time, based on the closed-form solution of the steady-state probability distribution, the steady-state transmission probability of any CSMA/CA network node in any system time slot is obtained;

Module three is used to derive the boundary conditions of the maximum transmission power of a single transmission of a CSMA/CA network node based on the closed-form solution of the steady-state probability distribution and the steady-state transmission probability of the CSMA/CA network node obtained in step 2 and the channel listening busy probability in the industrial Internet of Things field communication system scenario based on probability theory;

Module 4 is used to derive the normalized network throughput model and network average energy efficiency model of the CSMA/CA network in the industrial Internet of Things scenario based on the two types of nonlinear equations obtained about the boundary conditions of the node transmission power allocation strategy based on probability theory.

Compared with the prior art, the present invention has the following beneficial effects:

The present invention provides a joint design method for drone trajectory and user scheduling for secure communication under limited code length transmission, which maximizes the maximum achievable confidentiality rate of ground users with the worst channel conditions under the constraints of drone mobility, mission time and user scheduling coefficient. This scheme constructs the optimal trajectory of drones in this scenario, significantly improving system security while reducing algorithm complexity.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an equivalent two-dimensional Markov chain node model of a non-saturated CSMA/CA network considered in the present invention.

FIG. 2 is a two-dimensional schematic diagram of the boundary conditions of power allocation for the hidden station effect considered in the present invention.

DETAILED DESCRIPTION

In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians of the present invention without making creative work are within the scope of protection of the present invention.

Example 1

Aiming at the application scenario of industrial Internet of Things field communication system based on CSMA/CA protocol, the present invention provides a CSMA/CA network performance analysis model for industrial Internet of Things field communication scenario in accordance with the performance analysis of CSMA/CA protocol and the design requirements of node power and code length joint allocation strategy for industrial Internet of Things scenario.

The present invention will be further described below with reference to the accompanying drawings:

Step 1: Based on the CSMA/CA control protocol, we abstract the node state into a two-dimensional Markov chain as shown in Figure 1, and obtain the corresponding single-step transition probability expression. Among them, the node service is non-saturated, that is, the cache area of any node in the network is not always in a non-empty state. This step realizes the construction of the equivalent Markov chain model of the CSMA/CA network.

The first state parameter i of the two-dimensional Markov chain represents the current backoff stage of the CSMA/CA network node (i=-1 means the node buffer is empty and there are no data packets waiting to be transmitted; i≥0 means the node buffer is not empty and there are data packets waiting to be transmitted). The second state parameter j of the two-dimensional Markov chain represents the remaining value of the node's current backoff timer (j=-1 means the node buffer is empty and there are no data packets waiting to be transmitted; j≥0 means the node buffer is not empty and there are data packets waiting to be transmitted).

At the same time, the parameter w _i in Figure 1 represents the maximum contention window length of any CSMA/CA network node when it is in the current backoff class i. According to the CSMA/CA control protocol, w _i = 2 ⁱ w ₀ . The one-way arrow in Figure 1 represents the single-step transition probability of the node from state (i, j) _t to the next state (i, j) _t+1 . Among them, the process of the CSMA/CA network node parameter i in the equivalent two-dimensional Markov chain transferring from state i to state i+1 (backoff failure) represents the process of the node transferring to a higher backoff class due to the failure of the current data transmission attempt due to data collision or finite code length data packet decoding error. The state transition probability of this process is In this process, the maximum backoff window of the node will become twice the current window (exponential backoff mechanism). At the same time, in the same backoff level i, the process of node parameter j transferring from state j to state j-1 indicates that the node detects that the current channel environment is idle (no data transmission from other nodes is heard), and thus the remaining backoff timer value is reduced by 1. The state transition probability of this process is On the contrary, the process of returning from state j to state j indicates that the node detects that the current channel environment is busy (hears data transmission from other nodes), thereby freezing the remaining backoff timer value. The state transition probability of this process is In addition, the probability q represents the probability that the node buffer is still not empty after the node completes the transmission service of the current data packet. Whenever the node completes the transmission of the current data packet, if there is a data packet waiting to be transmitted in the buffer at this time, the node will initialize the backoff process. The state transition probability of the initialization process is If the cache is empty at this time, the node will return to the idle state, and the state transition probability of returning to the idle state is (1-q)(1-ε _k )(1-p _cl,k ).

In addition, it is worth noting that when a node reaches the maximum backoff level m, it will no longer move to a higher backoff level, but will stay at the current highest backoff level m until the transmission of the current data packet is finally completed. In summary, we can obtain the single-step transition probability based on the above state transition probability expression.

Among them, Pr{-1,-1|-1,-1} represents the probability that the node is currently idle and the node state will still be idle in the next time slot;

Pr{0,j|-1,-1} represents the state transition probability of the node being idle in the next time slot and entering the initial backoff state i=0 with the backoff timer value set to j. This process indicates that a new data packet arrives and enters the initial backoff state i=0.

represents the state transition probability of the process of returning to state j from the current state j in the next time slot in the same backoff level i. This process means that the node detects that the current channel environment is busy and freezes the remaining backoff timer value;

represents the state transition probability of the process of transitioning from the current state j to the state j-1 in the next time slot in the same backoff level i. This process means that the node detects that the current channel environment is idle, and thus subtracts 1 from the remaining backoff timer value;

Pr{i+1,j|i,0} represents the state transition probability of the node's backoff level i in the current time slot being transferred to i+1 in the next time slot, and the backoff timer value is set from 0 in the current time slot to j in the next time slot. This process represents the process of the node transferring to a higher backoff level due to the failure of the current data transmission attempt due to data collision or finite code length data packet decoding error;

Pr{m,j|m,0} represents the state transition probability of the process in which the backoff level of the node in the current time slot is the highest backoff level m, and the backoff timer value is set from 0 in the current time slot to j in the next time slot. This process means that when the node reaches the maximum backoff level m, the node will no longer move to a higher backoff level, but stay at the current highest backoff level m until the transmission of the current data packet is finally completed;

Pr{-1,-1|i,0} indicates the state transition probability of the node in the current time slot being in backoff class i and the backoff timer value being 0, and the node state transitioning to the idle state in the next time slot. This process indicates that the node has successfully completed the transmission of the current data packet, and since no new data packets have arrived, the node falls back to the idle state;

Pr{0,j|i,0} represents the state transition probability of the node in the current time slot being in backoff class i and the backoff timer value being 0, and the node entering the initial backoff state i=0 and the backoff timer value being set to j in the next time slot. This process represents the process in which the node successfully completes the transmission of the current data packet and returns to the idle state due to the arrival of no new data packets. This process represents the process in which the node successfully completes the transmission of the current data packet and initializes the backoff due to the arrival of new data packets.

For any station in the CSMA/CA network The probability of detecting that the current channel state is busy is The maximum single transmission power P _max is used to send a data packet to the central network access point AP (Access Point, AP). The decoding error probability of a single data packet transmission under the finite code length theory is ε _k , and we get the node equivalent two-dimensional Markov chain single-step transition probability. Among them, the first and second probability transition expressions illustrate the impact of the data packet generation process on the node state under the non-saturated model; the third and fourth probability transition expressions represent the impact of the signal coverage problem on the node channel listening process under the consideration of hidden station interference; the fifth and sixth probability transition expressions represent the impact of failed transmission attempts on node state transition; finally, the seventh and eighth probability transition expressions indicate the probability that the data transmission attempt is successful and the node enters the idle state or restarts the next channel listening process.

Step 2: Based on the single-step transition probability of the two-dimensional Markov chain obtained in step 1, and based on the closed-form solution of the steady-state probability distribution in discrete queuing theory, we obtain the closed-form solution of the steady-state probability distribution of the equivalent two-dimensional Markov model of the CSMA/CA network node described in step 1; at the same time, based on the closed-form solution of the steady-state probability distribution, we obtain the steady-state transmission probability of any CSMA/CA network node in any system time slot: This can improve the model accuracy in heterogeneous CSMA/CA networks.

Based on the closed-form solution of steady-state probability distribution in discrete queuing theory, for any node, when the system time tends to infinity (steady state), the probability that its Markov chain node state is in state (i, j) is b _i,j , that is, Based on the single-step transition probability expression obtained in step 1 above, we can obtain the steady-state probability distribution relationship as shown below:

Among them, the first steady-state probability distribution relationship represents the transition relationship from any node state of the two-dimensional Markov chain to the idle node state b _-1,-1 . According to the CSMA/CA control protocol, the idle state can only be obtained from the idle state itself and the transmission state that has undergone successful transmission. The second curly bracket contains the steady-state probability distribution relation that represents the transition from any node state of the two-dimensional Markov chain to the first-level backoff state steady-state distribution b _0,j ,j∈[0,w ₀ ]. For the first-level backoff state distribution b _0,j , it may be transferred from the idle state b _-1,-1 through the packet generation process, that is, the backoff initialization process; through the transmission state that has experienced successful transmission and the node buffer is not empty Transition to state b _{0,j; the current channel is detected as occupied through the CCA (Clear Channel Assessment, CCA) function of the network node, and the current state b 0,j} is returned to; it is also possible to detect that the channel is idle through CCA and transition from state b _0,j+1 ,j∈[0,w ₀ -1). For the i-th layer backoff state distribution b _i,j , it may transition to state b _i-1,0 through a successful transmission and a non-empty node buffer; the current channel is detected as occupied through the CCA function of the node, and the current state b _i,j is returned to; it is also possible to detect that the channel is idle through CCA and transition from state b _i,j+1 ,j∈[0,w _i -1). Finally, for the backoff state distribution bm _,j at the mth layer, it may enter the state bm _-1,0 , bm _,0 after experiencing successful transmission and the node buffer is not empty; it may return to the current state _bm,j by detecting that the current channel is occupied through the node's CCA function; it may also enter the state _bm,j+1 , j∈[0, _wm -1) by detecting that the channel is idle through CCA.

After sorting out and rewriting the above steady-state probability distribution relationship, we can further obtain the following probability distribution expression.

in, It represents the error transmission probability of node k in the CSMA/CA network. This transmission error is caused by decoding error under the finite code length transmission strategy or node data packet transmission collision.

Finally, the normalized expression based on the node steady-state probability distribution is And the expression of the steady-state transmission probability of node data packets is Given the total number of nodes k in the network, the probability of packet generation q, and the maximum single transmission power P _max , we can obtain the closed-form solution of the node's steady-state transmission probability expression as follows.

Step 3: Based on the closed-form solution of the steady-state probability distribution obtained in step 1 The steady-state transmission probability of CSMA/CA network nodes obtained in step 2 Based on probability theory, the channel listening busy probability for the industrial Internet of Things field communication system scenario is derived Regarding the boundary conditions of the maximum single transmission power P _max of CSMA/CA network nodes, in order to analyze the boundary conditions of the maximum single transmission power P _max of CSMA/CA network nodes under the condition of hidden station effect (wireless signal coverage problem).

We consider a wireless channel model with logarithmic path fading effect, where the channel gain _Gtx can be calculated by the sending node With receiving node The Euclidean distance between The channel gain reference distance _d0 and the path fading factor a are jointly expressed as follows.

Wherein, G _tx (d ₀ ) represents the channel gain at the reference distance d _0. Here, the reference distance d ₀ =1 is taken, and the channel reference gain at the reference distance is expressed as G ₀ , and we obtain the following expression.

In a CSMA/CA network, when any network node obtains the right to use the wireless channel, the network node will immediately start sending a data packet with the maximum single transmission power P _max . Considering that all nodes use a single omnidirectional antenna, the single data packet transmission process will approximately generate a circular signal coverage area on a two-dimensional plane. The radius of this circular signal coverage area is determined by the carrier sense receiving power threshold P _th specified in the 802.11 protocol, that is, when the receiving power is greater than the threshold value P _th , the current channel state is determined to be busy, and when it is less than the threshold value P _th , the current channel state is determined to be idle. Given the carrier sense receiving power threshold P _th and the maximum single transmission power P _max of the network node, we can get the carrier sensing range CSR (Carrier-Sensing Range, CSR) of the CSMA/CA network node, which is represented as R _s here, and its expression is as follows.

The network nodes deployed in the signal coverage area defined by the radius _Rs with the coordinates of a network node in two-dimensional space as the center will detect the data packet transmission event initiated by the network node at the center of the circle through the CCA function, and stay in the backoff state to avoid data packet conflicts caused by the simultaneous transmission of data packets. However, other network nodes deployed outside the circular signal coverage area will not be able to detect data packet transmission events due to path fading. At the same time, these nodes will perform channel sensing and exponential backoff processes according to the CSMA/CA protocol, and try to send data packets in the buffer when the backoff timer returns to zero, thereby causing potential data packet collisions. This channel sensing error caused by wireless propagation effects, and the resulting data packet collisions, are generally referred to as the hidden station effect in academia. We get the following expression.

in, represents the set of non-hidden sites of node k, that is, belongs to the set Network nodes within The data packet transmission event initiated by node k with the maximum single transmission power P _max can be detected; represents the hidden site set of node k, that is, belongs to the set Network nodes within The packet transmission event initiated by node k with the maximum single transmission power P _max cannot be detected. p _cl,k represents the collision probability of node k when the remaining value of the backoff timer returns to 0 and the packet transmission is started; It represents the probability that node k judges the channel status as busy during the exponential backoff process.

There is a boundary condition, that is, any CSMA/CA network node sending a data packet transmits with a sufficiently large power P ₁ , which is expressed as follows.

in, Represents any two CSMA/CA network nodes The maximum Euclidean distance between Under this power allocation strategy, in addition to the network node itself that sends the data packet, the network node set All network nodes in the network will detect the current transmission event, thereby avoiding the interference of the hidden station effect on the communication process. Correspondingly, when the CSMA/CA network node that sends the data packet transmits with a relatively small transmission power, some nodes in the network may have a hidden station collision effect due to the influence of path fading, as shown in Figure 2. In summary, we can define these two situations as two types of nonlinear equations based on the boundary condition P ₁ , as shown below.

The first type of nonlinear equations represents the expression of the correlation probability of node k in the CSMA/CA network when a sufficiently large single transmission transmit power P _max ≥ P ₁ is allocated.

The second type of nonlinear equations represents the expression of the probability of node k in the CSMA/CA network when the lower single transmission power P _max <P ₁ is assigned. Where Q represents the Q function, and the expression is V(γ _k ) represents the channel dispersion and is expressed as C(γ _k ) represents the normalized channel capacity, expressed as C(γ _k )=log(1+γ _k ); γ _k represents the received signal-to-noise ratio of the kth network node at the network access point; M represents the code length; represents the network access point; G ₀ is the channel reference gain at the reference distance; Represents the kth node in the CSMA/CA network At the access point _Pt represents the transmission power allocated to all k nodes in the CSMA/CA network; _N0 represents the noise power; represents the Euclidean distance between the kth node and the access point in the CSMA/CA network; P ₁ represents the boundary condition of the allocated power, that is, when the allocated power satisfies the condition P _t ＝P _max ≥P ₁ , there will be no hidden station effect in the CSMA/CA network, and there is When the allocated power satisfies the condition P _t = P _max < P ₁ , there is a hidden station effect in the CSMA/CA network, and there is

Step 4. Based on the two types of nonlinear equations about the boundary conditions of the node transmission power allocation strategy obtained in step 3, we derive the normalized network throughput model and network average energy efficiency model of the CSMA/CA network in the industrial Internet of Things scenario based on probability theory. On the premise of refining the analysis of wireless signal coverage conditions, we provide a set of CSMA/CA network performance analysis models for industrial Internet of Things field communication scenarios.

Based on the closed-form solution of the steady-state transmission probability of heterogeneous nodes obtained in step 2 and step 3 We can obtain the following conditional probability _ps,k , that is, any node in the network will successfully send the current data packet with probability _ps,k after completing the exponential backoff process (the remaining value of the backoff timer returns to zero), and its expression is as follows.

At the same time, considering that the residence time of a node in each state b _i,j in the two-dimensional equivalent Markov chain is not a fixed real system time, that is, each time slot in the Markov chain may be occupied by a successful packet transmission attempt, a packet collision, or a wireless channel idle event, the length of the time slot in the Markov chain is non-uniform. Therefore, in order to realize the conversion between the state residence time of the equivalent two-dimensional Markov chain and the actual time, we need to derive the expected value of the real system time corresponding to each time slot in the Markov chain.

We express the expected value of this time as Its expression is as follows.

Where p _tr represents the probability that there is at least one ongoing data packet transmission event in any system time slot in the CSMA/CA network, and its expression is σ represents the length of a single backoff slot specified in the CSMA/CA protocol; T _col represents the time the wireless channel is occupied when a packet collision occurs; T _suc represents the time the wireless channel is occupied when a packet is successfully transmitted; _Terr represents the time the wireless channel is occupied when a packet decoding error occurs. According to the 802.11 protocol, the three types of channel occupation times T _col , T _suc , _{and Terr} can be approximated as the sum of multiple CSMA/CA frame times, and their expressions are as follows.

Wherein, under a given data link layer transmission rate, H represents the time occupied by the MAC layer header specified in the 802.11 protocol; D represents the time occupied by transmitting a D-bit data packet. Under the finite code length coding strategy, D can be expressed as the product of the code length M and the code element duration _Ts , that is, D= _MTs ; δ represents the wireless signal propagation delay; ACK represents the time occupied by transmitting the ACK frame; SIFS represents the time occupied by the short inter-frame spacing SIFS (Short-Inter Frame Spacing, SIFS) specified in the CSMA/CA protocol; DIFS represents the time occupied by the distributed inter-frame spacing DIFS (Distributed Inter-Frame Spacing, DIFS) specified in the CSMA/CA protocol; ACK _timeout represents the ACK frame receiving time threshold.

In summary, we can get the normalized CSMA/CA network throughput expression as shown below.

Finally, we will derive the overall energy consumption required by CSMA/CA network nodes taking into account carrier sensing, packet collisions, decoding errors, backoff freezing mechanisms, and hidden station interference. This overall energy consumption takes into account the energy consumed by collision events, retransmission attempts (if any), and packet corruption caused by erroneous decoding at the access point. Here, we will propose an average energy consumption model for the considered CSMA/CA uplink network, which is expressed as follows.

Wherein, P _ave represents the average energy consumption of the CSMA/CA network, P _idle , P _cs , and P _max represent the power consumed by any network node in the idle state, backoff state, and sending state, respectively; It represents the expected time that a node spends in idle state during a data packet transmission cycle, and its expression is: It represents the expected time that a node spends in the carrier sensing state during a data packet transmission cycle, and its expression is: It represents the expected time that node k spends in the data sending state during a data packet transmission cycle, and its expression is:

Example 2

This embodiment provides a CSMA/CA network energy efficiency modeling system based on Markov chain in an industrial Internet of Things scenario, including:

Module 1 is used to abstract the node state into a two-dimensional Markov chain based on the CSMA/CA control protocol to construct a CSMA/CA network equivalent Markov chain model and obtain the single-step transition probability of the two-dimensional Markov chain;

Module 2 is used to obtain the closed-form solution of the steady-state probability distribution of the equivalent two-dimensional Markov model of the described CSMA/CA network node based on the obtained single-step transition probability of the two-dimensional Markov chain and the solution method of the closed-form solution of the steady-state probability distribution in discrete queuing theory; at the same time, based on the closed-form solution of the steady-state probability distribution, the steady-state transmission probability of any CSMA/CA network node in any system time slot is obtained;

Module three is used to derive the boundary conditions of the maximum transmission power of a single transmission of a CSMA/CA network node based on the closed-form solution of the steady-state probability distribution and the steady-state transmission probability of the CSMA/CA network node obtained in step 2 and the channel listening busy probability in the industrial Internet of Things field communication system scenario based on probability theory;

Module 4 is used to derive the normalized network throughput model and network average energy efficiency model of the CSMA/CA network in the industrial Internet of Things scenario based on the two types of nonlinear equations obtained about the boundary conditions of the node transmission power allocation strategy based on probability theory.

Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

Obviously, those skilled in the art can make various changes and modifications to the embodiments of the present invention without departing from the spirit and scope of the embodiments of the present invention. Thus, if these modifications and variations of the embodiments of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Other parts not described in detail are all prior art.

Claims (9)

1. A CSMA/CA network energy efficiency modeling method in an industrial Internet of Things scenario, characterized by comprising the following steps: Step 1: Based on the CSMA/CA control protocol, the node state is abstracted into a two-dimensional Markov chain to construct a CSMA/CA network equivalent Markov chain model, and the single-step transition probability of the two-dimensional Markov chain is obtained; Step 2: Based on the single-step transition probability of the two-dimensional Markov chain obtained in step 1 and the closed-form solution of the steady-state probability distribution in discrete queuing theory, a closed-form solution of the steady-state probability distribution of the equivalent two-dimensional Markov model of the CSMA/CA network node described in step 1 is obtained; at the same time, based on the closed-form solution of the steady-state probability distribution, the steady-state transmission probability of any CSMA/CA network node in any system time slot is obtained; Step 3: Based on the closed-form solution of the steady-state probability distribution obtained in step 2 and the steady-state transmission probability of the CSMA/CA network node obtained in step 2, the boundary conditions of the channel listening busy probability for the industrial Internet of Things field communication system scenario and the maximum transmission power of the CSMA/CA network node for a single transmission are derived based on probability theory; Step 4: Based on the two types of nonlinear equations about the boundary conditions of the node transmission power allocation strategy obtained in step 3, the normalized network throughput model and network average energy efficiency model of the CSMA/CA network in the industrial Internet of Things scenario are derived based on probability theory. 2. According to a CSMA/CA network energy efficiency modeling method in an industrial Internet of Things scenario according to claim 1, it is characterized in that the two-dimensional Markov chain in step 1 constructs an equivalent Markov chain model of the CSMA/CA network as a two-dimensional Markov chain with backoff level i and backoff timer remaining value j as state variables, and each state of the Markov chain is represented by two random variables {s(t), v(t)}, wherein the random variable s(t) of the first dimension represents the backoff level i of the node at time t, and i∈[-1,m], wherein m represents the maximum backoff order of the CSMA/CA network; the random variable v(t) of the second dimension represents the backoff timer remaining value j of the node at time t, and j∈[-1,w _m -1]; wherein w _m represents the contention window size when the CSMA/CA network reaches the maximum backoff order m, and w _i =2 ⁱ ·w ₀ ,i∈[0,m]; wherein w _i represents the maximum contention window size when the backoff order is i, w ₀ represents the contention window size when the backoff order is 0; when the backoff class i and the remaining value j of the backoff timer are both -1, it means that the node is in an idle state, that is, the sending queue of the node is empty. The first state parameter i of the two-dimensional Markov chain represents the current backoff class of the CSMA/CA network node. When i=-1, it means that the node buffer is empty and there are no data packets waiting to be transmitted; when i≥0, it means that the node buffer is not empty and there are data packets waiting to be transmitted; the second state parameter j of the two-dimensional Markov chain represents the remaining value of the current backoff timer of the node, that is, when j=-1, it means that the node buffer is empty and there are no data packets waiting to be transmitted. When j≥0, it means that the node buffer is not empty and there are data packets waiting to be transmitted. 3. According to a CSMA/CA network energy efficiency modeling method in an industrial Internet of Things scenario in claim 2, it is characterized in that the single-step transition probability of the two-dimensional Markov chain is: Among them, Pr{-1,-1|-1,-1} represents the probability that the node is currently idle and the node state will still be idle in the next time slot; Pr{0,j|-1,-1} represents the state transition probability of the node being idle in the next time slot and entering the initial backoff state i=0 with the backoff timer value set to j. This process indicates that a new data packet arrives and enters the initial backoff state i=0. represents the state transition probability of the process of returning to state j from the current state j in the next time slot in the same backoff level i. This process means that the node detects that the current channel environment is busy and freezes the remaining backoff timer value; represents the state transition probability of the process of transitioning from the current state j to the state j-1 in the next time slot in the same backoff level i. This process means that the node detects that the current channel environment is idle, and thus subtracts 1 from the remaining backoff timer value; Pr{i+1,j|i,0} represents the state transition probability of the node's backoff level i in the current time slot being transferred to i+1 in the next time slot, and the backoff timer value is set from 0 in the current time slot to j in the next time slot. This process represents the process of the node transferring to a higher backoff level due to the failure of the current data transmission attempt due to data collision or finite code length data packet decoding error; Pr{m,j|m,0} represents the state transition probability of the process in which the backoff level of the node in the current time slot is the highest backoff level m, and the backoff timer value is set from 0 in the current time slot to j in the next time slot. This process means that when the node reaches the maximum backoff level m, the node will no longer move to a higher backoff level, but stay at the current highest backoff level m until the transmission of the current data packet is finally completed; Pr{-1,-1|i,0} indicates the state transition probability of the node in the current time slot being in backoff class i and the backoff timer value being 0, and the node state transitioning to the idle state in the next time slot. This process indicates that the node has successfully completed the transmission of the current data packet, and since no new data packets have arrived, the node falls back to the idle state; Pr{0,j|i,0} represents the state transition probability of the node in the current time slot being in backoff class i and the backoff timer value being 0, and the node entering the initial backoff state i=0 and the backoff timer value being set to j in the next time slot. This process represents the process in which the node successfully completes the transmission of the current data packet and returns to the idle state due to the arrival of no new data packets. This process represents the process in which the node successfully completes the transmission of the current data packet and initializes the backoff due to the arrival of new data packets. q represents the probability that the node buffer is still not empty after the node completes the transmission service of the current data packet, p _cl,k is the probability of collision in the transmission of the node data packet; Among them, for any station in the CSMA/CA network The probability of detecting that the current channel state is busy is The data packet is sent to the central network access point AP with the maximum single transmission power P _max . The decoding error probability of a single data packet transmission under the finite code length theory is ε _k . 4. According to a CSMA/CA network energy efficiency modeling method in an industrial Internet of Things scenario according to claim 3, it is characterized in that the closed-form solution of the steady-state probability distribution of the CSMA/CA network node equivalent two-dimensional Markov model described in step 1 in step 2 is: b _i,j is the probability that for any node, when the system time tends to infinity, the state of its Markov chain node is in state (i,j). 5. According to the CSMA/CA network energy efficiency modeling method in the industrial Internet of Things scenario of claim 4, it is characterized in that based on the single-step transition probability expression obtained in the above step 1, the following steady-state probability distribution relationship is obtained: in, It represents the closed-form solution of the steady-state probability distribution under the condition that the state variable i takes values in the range i∈[0,m) and the state variable j takes values in the range j∈(0,wi _- 1); It represents the closed-form solution of the steady-state probability distribution when the state variable i takes the value i=m and the state variable j takes the value range j∈(0,w _m -1]); represents the error transmission probability of node k in the CSMA/CA network, and p _tx,k represents the probability of transmitting a data packet when the node is in a steady state, which is expressed as: Normalized expression based on node steady-state probability distribution And the expression of the steady-state transmission probability of node data packets is Given the total number of nodes k in the network, the probability of packet generation q and the single maximum transmission power P _max , the probability of a node transmitting a packet when in a steady state is obtained. 6. The CSMA/CA network energy efficiency modeling method in an industrial Internet of Things scenario according to claim 5 is characterized in that the boundary condition _P1 of the channel listening busy probability in the industrial Internet of Things field communication system scenario with respect to the maximum transmission power P _max of a single transmission of a CSMA/CA network node in step 3 is set as two types of nonlinear equations, Among them, the first kind of nonlinear equations: The first type of nonlinear equations represents the expression of the probability of node k being related in the CSMA/CA network when a sufficiently large single transmission transmission power P _max ≥ P ₁ is allocated; Nonlinear equations of the second kind: The second type of nonlinear equations represents the expression of the probability of node k being related in the CSMA/CA network when a lower single transmission power P _max <P ₁ is assigned; Where Q represents the Q function, which is expressed as V(γ _k ) represents the channel dispersion and is expressed as C(γ _k ) represents the normalized channel capacity, expressed as C(γ _k )=log(1+γ _k ); γ _k represents the received signal-to-noise ratio of the kth network node at the network access point; M represents the code length; represents the network access point; G ₀ is the channel reference gain at the reference distance; Represents the kth node in the CSMA/CA network At the access point _Pt represents the transmission power allocated to all k nodes in the CSMA/CA network; _N0 represents the noise power; represents the Euclidean distance between the kth node and the access point in the CSMA/CA network; P ₁ represents the boundary condition of the allocated power, that is, when the allocated power satisfies the condition P _t ＝P _max ≥P ₁ , there will be no hidden station effect in the CSMA/CA network, and there is When the allocated power satisfies the condition P _t = P _max < P ₁ , there is a hidden station effect in the CSMA/CA network, and there is 7. According to a CSMA/CA network energy efficiency modeling method in an industrial Internet of Things scenario according to claim 6, it is characterized in that the expression of P ₁ is as follows: in, Represents any two CSMA/CA network nodes The maximum Euclidean distance between _Pth represents the receiving power threshold at which the node senses the carrier and determines that the current channel state is idle. 8. The CSMA/CA network energy efficiency modeling method in an industrial Internet of Things scenario according to claim 7, characterized in that in step 4, the normalized network throughput model of the CSMA/CA network in the industrial Internet of Things scenario is: Where _ps,k represents the probability of the kth node successfully transmitting a data packet in the CSMA/CA network, and its expression is: S _k represents the throughput of the kth node, and its expression is ε _k represents the decoding error probability of the kth node in the CSMA/CA network under the given maximum single transmission power, code length and data packet size; D represents the size of a single transmission data packet of each node in the CSMA/CA network, in bits; In the two-dimensional Markov chain equivalent model, the expected value of the actual running time of the CSMA/CA communication protocol equivalent to the state transition time consumption time is expressed as follows: Where p _tr represents the probability that there is at least one ongoing data packet transmission event in any system time slot in the CSMA/CA network, and its expression is σ represents the length of a single backoff slot specified in the CSMA/CA protocol; T _col represents the time the wireless channel is occupied when a packet collision occurs; T _suc represents the time the wireless channel is occupied when a packet is successfully transmitted; _Terr represents the time the wireless channel is occupied when a packet decoding error occurs; The average energy consumption model of CSMA/CA network in the industrial Internet of Things scenario is: Wherein, P _ave represents the average energy consumption of the CSMA/CA network, P _idle , P _cs , and P _max represent the power consumed by any network node in the idle state, backoff state, and sending state, respectively; It represents the expected time that a node spends in idle state during a data packet transmission cycle, and its expression is: It represents the expected time that a node spends in the carrier sensing state during a data packet transmission cycle, and its expression is: It represents the expected time that node k spends in the data sending state during a data packet transmission cycle, and its expression is: 9. A CSMA/CA network energy efficiency modeling system in an industrial Internet of Things scenario, characterized by comprising: Module 1 is used to abstract the node state into a two-dimensional Markov chain based on the CSMA/CA control protocol to construct a CSMA/CA network equivalent Markov chain model and obtain the single-step transition probability of the two-dimensional Markov chain; Module 2 is used to obtain the closed-form solution of the steady-state probability distribution of the equivalent two-dimensional Markov model of the described CSMA/CA network node based on the obtained single-step transition probability of the two-dimensional Markov chain and the solution method of the closed-form solution of the steady-state probability distribution in discrete queuing theory; at the same time, based on the closed-form solution of the steady-state probability distribution, the steady-state transmission probability of any CSMA/CA network node in any system time slot is obtained; Module three is used to derive the boundary conditions of the maximum transmission power of a single transmission of a CSMA/CA network node based on the closed-form solution of the steady-state probability distribution and the steady-state transmission probability of the CSMA/CA network node obtained in step 2 and the channel listening busy probability in the industrial Internet of Things field communication system scenario based on probability theory; Module 4 is used to derive the normalized network throughput model and the average network energy efficiency model of the CSMA/CA network in the industrial Internet of Things scenario based on the two types of nonlinear equations obtained about the boundary conditions of the node transmission power allocation strategy based on probability theory; The Markov chain-based CSMA/CA network energy efficiency modeling system in the industrial Internet of Things scenario is used to execute the steps in the Markov chain-based CSMA/CA network energy efficiency modeling method in the industrial Internet of Things scenario described in any one of claims 1-8.