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Energy-Efficient Communication Protocol for Wireless Microsensor Networks Wendi Rabiner Heinzelman, Anantha Chandrakasan, and Hari Balakrishnan Massachusetts Institute of Technology Cambridge, MA 02139 fwendi, anantha, harig@mit.edu Abstract Wireless distributed microsensor systems will enable the reliable monitoring of a variety of environments for both civil and military applications. In this paper, we look at communication protocols, which can have significant im- pact on the overall energy dissipation of these networks. Based on our findings that the conventional protocols of direct transmission, minimum-transmission-energy, multi- hop routing, and static clustering may not be optimal for sensor networks, we propose LEACH (Low-Energy Adap- tive Clustering Hierarchy), a clustering-based protocol that utilizes randomized rotation of local cluster base stations (cluster-heads) to evenly distribute the energy load among the sensors in the network. LEACH uses localized coordi- nation to enable scalability and robustness for dynamic net- works, and incorporates data fusion into the routing proto- col to reduce the amount of information that must be trans- mitted to the base station. Simulations show that LEACH can achieve as much as a factor of 8 reduction in energy dissipation compared with conventional routing protocols. In addition, LEACH is able to distribute energy dissipation evenly throughout the sensors, doubling the useful system lifetime for the networks we simulated. 1. Introduction Recent advances in MEMS-based sensor technology, low-power analog and digital electronics, and low-power RF design have enabled the development of relatively in- expensive and low-power wireless microsensors [2, 3, 4]. These sensors are not as reliable or as accurate as their ex- pensive macrosensor counterparts, but their size and cost enable applications to network hundreds or thousands of these microsensors in order to achieve high quality, fault- tolerant sensing networks. Reliable environment monitor- ing is important in a variety of commercial and military applications. For example, for a security system, acoustic, seismic, and video sensors can be used to form an ad hoc network to detect intrusions. Microsensors can also be used to monitor machines for fault detection and diagnosis. Microsensor networks can contain hundreds or thou- sands of sensing nodes. It is desirable to make these nodes as cheap and energy-efficient as possible and rely on their large numbers to obtain high quality results. Network pro- tocols must be designed to achieve fault tolerance in the presence of individual node failure while minimizing en- ergy consumption. In addition, since the limited wireless channel bandwidth must be shared among all the sensors in the network, routing protocols for these networks should be able to perform local collaboration to reduce bandwidth requirements. Eventually, the data being sensed by the nodes in the net- work must be transmitted to a control center or base station, where the end-user can access the data. There are many pos- sible models for these microsensor networks. In this work, we consider microsensor networks where: The base station is fixed and located far from the sen- sors. All nodes in the network are homogeneous and energy- constrained. Thus, communication between the sensor nodes and the base station is expensive, and there are no “high-energy” nodes through which communication can proceed. This is the framework for MIT’s -AMPS project, which focuses on innovative energy-optimized solutions at all levels of the system hierarchy, from the physical layer and communica- tion protocols up to the application layer and efficient DSP design for microsensor nodes. Sensor networks contain too much data for an end-user to process. Therefore, automated methods of combining or aggregating the data into a small set of meaningful informa- tion is required [7, 8]. In addition to helping avoid informa- tion overload, data aggregation, also known as data fusion, can combine several unreliable data measurements to pro- duce a more accurate signal by enhancing the common sig- nal and reducing the uncorrelated noise. The classification
performed on the aggregated data might be performed by a human operator or automatically. Both the method of per- forming data aggregation and the classification algorithm are application-specific. For example, acoustic signals are often combined using a beamforming algorithm [5, 17] to reduce several signals into a single signal that contains the relevant information of all the individual signals. Large en- ergy gains can be achieved by performing the data fusion or classification algorithm locally, thereby requiring much less data to be transmitted to the base station. By analyzing the advantages and disadvantages of con- ventional routing protocols using our model of sensor net- works, we have developed LEACH (Low-Energy Adaptive Clustering Hierarchy), a clustering-based protocol that min- imizes energy dissipation in sensor networks. The key fea- tures of LEACH are: Localized coordination and control for cluster set-up and operation. Randomized rotation of the cluster “base stations” or “cluster-heads” and the corresponding clusters. Local compression to reduce global communication. The use of clusters for transmitting data to the base sta- tion leverages the advantages of small transmit distances for most nodes, requiring only a few nodes to transmit far distances to the base station. However, LEACH out- performs classical clustering algorithms by using adaptive clusters and rotating cluster-heads, allowing the energy re- quirements of the system to be distributed among all the sensors. In addition, LEACH is able to perform local com- putation in each cluster to reduce the amount of data that must be transmitted to the base station. This achieves a large reduction in the energy dissipation, as computation is much cheaper than communication. 2. First Order Radio Model k bit packet ETx(d) Transmit Electronics Eelec* k Tx Amplifier amp* k * d2 d k bit packet ERx Receive Electronics Eelec* k Figure 1. First order radio model. Table 1. Radio characteristics. Operation Transmitter Electronics (ET xelec) Receiver Electronics (ERxelec) (ET xelec = ERxelec = Eelec) Transmit Amplifier (amp) Energy Dissipated 50 nJ/bit 100 pJ/bit/m radio expends: ET xk; d = ET xeleck + ET xampk; d ET xk; d = Eelec  k + amp  k  d and to receive this message, the radio expends: ERxk = ERxeleck ERxk = Eelec  k (1) (2) Currently, there is a great deal of research in the area of low-energy radios. Different assumptions about the radio characteristics, including energy dissipation in the transmit and receive modes, will change the advantages of different protocols. In our work, we assume a simple model where the radio dissipates Eelec =  nJ/bit to run the transmit- ter or receiver circuitry and amp =  pJ/bit/m for the transmit amplifier to achieve an acceptable Eb (see Figure 1 No and Table 1). These parameters are slightly better than the current state-of-the-art in radio design. We also assume an r energy loss due to channel transmission. Thus, to trans- mit a k-bit message a distance d using our radio model, the For example, the Bluetooth initiative [1] specifies 700 Kbps radios that operate at 2.7 V and 30 mA, or 115 nJ/bit. For these parameter values, receiving a message is not a low cost operation; the protocols should thus try to minimize not only the transmit distances but also the number of transmit and receive operations for each message. We make the assumption that the radio channel is sym- metric such that the energy required to transmit a message from node A to node B is the same as the energy required to transmit a message from node B to node A for a given SNR. For our experiments, we also assume that all sensors are sensing the environment at a fixed rate and thus always have data to send to the end-user. For future versions of our protocol, we will implement an ”event-driven” simulation, where sensors only transmit data if some event occurs in the environment. e
3. Energy Analysis of Routing Protocols There have been several network routing protocols pro- posed for wireless networks that can be examined in the context of wireless sensor networks. We examine two such protocols, namely direct communication with the base sta- tion and minimum-energy multi-hop routing using our sen- sor network and radio models. In addition, we discuss a conventional clustering approach to routing and the draw- backs of using such an approach when the nodes are all energy-constrained. Using a direct communication protocol, each sensor sends its data directly to the base station. If the base sta- tion is far away from the nodes, direct communication will require a large amount of transmit power from each node (since d in Equation 1 is large). This will quickly drain the battery of the nodes and reduce the system lifetime. How- ever, the only receptions in this protocol occur at the base station, so if either the base station is close to the nodes, or the energy required to receive data is large, this may be an acceptable (and possibly optimal) method of communica- tion. The second conventional approach we consider is a “minimum-energy” routing protocol. There are several power-aware routing protocols discussed in the literature [6, 9, 10, 14, 15]. In these protocols, nodes route data des- tined ultimately for the base station through intermediate nodes. Thus nodes act as routers for other nodes’ data in addition to sensing the environment. These protocols dif- fer in the way the routes are chosen. Some of these proto- cols [6, 10, 14], only consider the energy of the transmitter and neglect the energy dissipation of the receivers in de- termining the routes. In this case, the intermediate nodes are chosen such that the transmit amplifier energy (e.g., ET xampk; d = amp  k  d) is minimized; thus node A would transmit to node C through node B if and only if: ET xampk; d = dAB + ET xampk; d = dBC  ET xampk; d = dAC (3) or BC  d AC AB + d d (4) However, for this minimum-transmission-energy (MTE) routing protocol, rather than just one (high-energy) trans- mit of the data, each data message must go through n (low- energy) transmits and n receives. Depending on the rela- tive costs of the transmit amplifier and the radio electronics, the total energy expended in the system might actually be greater using MTE routing than direct transmission to the base station. To illustrate this point, consider the linear network shown in Figure 2, where the distance between the nodes is r. If we consider the energy expended transmitting a sin- gle k-bit message from a node located a distance nr from n nodes r Base Station Figure 2. Simple linear network. the base station using the direct communication approach and Equations 1 and 2, we have: Edirect = ET xk; d = n  r = Eelec  k + amp  k  nr = kEelec + ampnr (5) In MTE routing, each node sends a message to the closest node on the way to the base station. Thus the node located a distance nr from the base station would require n transmits a distance r and n  receives. EM T E = n  ET xk; d = r + n   ERxk = nEelec  k + amp  k  r + n   Eelec  k = kn Eelec + ampnr (6) Therefore, direct communication requires less energy than MTE routing if: Edirect  EM T E Eelec + ampnr  n Eelec + ampnr rn  Eelec amp  (7) Using Equations 1 - 6 and the random 100-node network shown in Figure 3, we simulated transmission of data from every node to the base station (located 100 m from the clos- est sensor node, at (x=0, y=-100)) using MATLAB. Figure 4 shows the total energy expended in the system as the net- work diameter increases from 10 m  10 m to 100 m  100 m and the energy expended in the radio electronics (i.e., Eelec) increases from 10 nJ/bit to 100 nJ/bit, for the sce- nario where each node has a 2000-bit data packet to send to the base station. This shows that, as predicted by our anal- ysis above, when transmission energy is on the same order as receive energy, which occurs when transmission distance is short and/or the radio electronics energy is high, direct transmission is more energy-efficient on a global scale than MTE routing. Thus the most energy-efficient protocol to use depends on the network topology and radio parameters of the system.
50 45 40 35 30 25 20 15 10 5 0 −25 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 1 x 10−7 −20 −15 −10 −5 0 5 10 15 20 25 Figure 3. 100-node random network. MTE −> Direct |v 0.8 0.6 0.4 0.2 40 20 100 80 60 l ) s e u o J ( i m e t s y s n i d e t a p s s d y g r e n e l a t o T i Electronics energy (Joules/bit) 0 0 Network diameter (m) Figure 4. Total energy dissipated in the 100- node random network using direct commu- nication and MTE routing (i.e., Edirect and EM T E). amp =  pJ/bit/m, and the mes- sages are 2000 bits. e v i l a l l i t s s r o s n e s f o r e b m u N 100 90 80 70 60 50 40 30 20 10 0 0 Direct MTE 50 100 150 200 250 300 350 400 450 500 Time steps (rounds) Figure 5. System lifetime using direct trans- mission and MTE routing with 0.5 J/node. It is clear that in MTE routing, the nodes closest to the base station will be used to route a large number of data messages to the base station. Thus these nodes will die out quickly, causing the energy required to get the remaining data to the base station to increase and more nodes to die. This will create a cascading effect that will shorten system lifetime. In addition, as nodes close to the base station die, that area of the environment is no longer being monitored. To prove this point, we ran simulations using the random 100-node network shown in Figure 3 and had each sensor send a 2000-bit data packet to the base station during each time step or “round” of the simulation. After the energy dissipated in a given node reached a set threshold, that node was considered dead for the remainder of the simulation. Figure 5 shows the number of sensors that remain alive after each round for direct transmission and MTE routing with each node initially given 0.5 J of energy. This plot shows that nodes die out quicker using MTE routing than direct transmission. Figure 6 shows that nodes closest to the base station are the ones to die out first for MTE routing, whereas nodes furthest from the base station are the ones to die out first for direct transmission. This is as expected, since the nodes close to the base station are the ones most used as “routers” for other sensors’ data in MTE routing, and the nodes furthest from the base station have the largest transmit energy in direct communication. A final conventional protocol for wireless networks is clustering, where nodes are organized into clusters that communicate with a local base station, and these local base stations transmit the data to the global base station, where it is accessed by the end-user. This greatly reduces the dis- tance nodes need to transmit their data, as typically the local base station is close to all the nodes in the cluster.
i t e a n d r o o c − Y 50 45 40 35 30 25 20 15 10 5 0 −25 −20 −15 −10 −5 0 X−coordinate 5 10 15 20 25 50 45 40 35 e t i a n d r o o c − Y 30 25 20 15 10 5 0 −25 −20 −15 −10 −5 0 X−coordinate 5 10 15 20 25 Figure 6. Sensors that remain alive (circles) and those that are dead (dots) after 180 rounds with 0.5 J/node for (a) direct trans- mission and (b) MTE routing. Thus, clustering appears to be an energy-efficient commu- nication protocol. However, the local base station is as- sumed to be a high-energy node; if the base station is an energy-constrained node, it would die quickly, as it is be- ing heavily utilized. Thus, conventional clustering would perform poorly for our model of microsensor networks. The Near Term Digital Radio (NTDR) project [12, 16], an army-sponsored program, employs an adaptive clustering approach, similar to our work discussed here. In this work, cluster-heads change as nodes move in order to keep the network fully connected. However, the NTDR protocol is designed for long-range communication, on the order of 10s of kilometers, and consumes large amounts of power, on the order of 10s of Watts. Therefore, this protocol also does not fit our model of sensor networks. 4. LEACH: Low-Energy Adaptive Clustering Hierarchy LEACH is a self-organizing, adaptive clustering protocol that uses randomization to distribute the energy load evenly among the sensors in the network. In LEACH, the nodes organize themselves into local clusters, with one node act- ing as the local base station or cluster-head. If the cluster- heads were chosen a priori and fixed throughout the system lifetime, as in conventional clustering algorithms, it is easy to see that the unlucky sensors chosen to be cluster-heads would die quickly, ending the useful lifetime of all nodes belonging to those clusters. Thus LEACH includes random- ized rotation of the high-energy cluster-head position such that it rotates among the various sensors in order to not drain the battery of a single sensor. In addition, LEACH performs local data fusion to “compress” the amount of data being sent from the clusters to the base station, further reducing energy dissipation and enhancing system lifetime. Sensors elect themselves to be local cluster-heads at any given time with a certain probability. These cluster- head nodes broadcast their status to the other sensors in the network. Each sensor node determines to which clus- ter it wants to belong by choosing the cluster-head that re- quires the minimum communication energy. Once all the nodes are organized into clusters, each cluster-head creates a schedule for the nodes in its cluster. This allows the radio components of each non-cluster-head node to be turned off at all times except during its transmit time, thus minimizing the energy dissipated in the individual sensors. Once the cluster-head has all the data from the nodes in its cluster, the cluster-head node aggregates the data and then transmits the compressed data to the base station. Since the base station is far away in the scenario we are examining, this is a high energy transmission. However, since there are only a few cluster-heads, this only affects a small number of nodes. As discussed previously, being a cluster-head drains the battery of that node. In order to spread this energy usage over multiple nodes, the cluster-head nodes are not fixed; rather, this position is self-elected at different time intervals. Thus a set C of nodes might elect themselves cluster-heads at time t, but at time t + d a new set C of nodes elect themselves as cluster-heads, as shown in Figure 7. The de- cision to become a cluster-head depends on the amount of energy left at the node. In this way, nodes with more en- ergy remaining will perform the energy-intensive functions of the network. Each node makes its decision about whether to be a cluster-head independently of the other nodes in the Note that typically this will be the cluster-head closest to the sensor. However, if there is some obstacle impeding the communication between two physically close nodes (e.g., a building, a tree, etc.) such that commu- nication with another cluster-head, located further away, is easier, the sen- sor will choose the cluster-head that is spatially further away but “closer” in a communication sense.
1.1 1 0.9 n o i t 0.8 i a p s s d i y g r e n e d e z i l a m r o N 0.7 0.6 0.5 0.4 0.3 0.2 Direct Trans LEACH −20 −15 −10 −5 0 5 10 15 20 25 0.1 0 10 20 30 40 Percent of nodes that are cluster heads 50 60 70 80 90 100 50 45 40 35 30 25 20 15 10 5 0 −25 50 45 40 35 30 25 20 15 10 5 0 −25 Figure 8. Normalized total system energy dis- sipated versus the percent of nodes that are cluster-heads. Note that direct transmission is equivalent to 0 nodes being cluster-heads or all the nodes being cluster-heads. in the system to be large. If there are more than ^N cluster- heads, the distance nodes have to transmit to reach the near- est cluster-head does not reduce substantially, yet there are more cluster-heads that have to transmit data the long-haul distances to the base station, and there is less compression being performed locally. For our system parameters and topology, ^N = %. Figure 8 also shows that LEACH can achieve over a fac- tor of 7 reduction in energy dissipation compared to direct communication with the base station, when using the opti- mal number of cluster-heads. The main energy savings of the LEACH protocol is due to combining lossy compression with the data routing. There is clearly a trade-off between the quality of the output and the amount of compression achieved. In this case, some data from the individual sig- nals is lost, but this results in a substantial reduction of the overall energy dissipation of the system. We simulated LEACH (with 5% of the nodes being cluster-heads) using MATLAB with the random network shown in Figure 3. Figure 9 shows how these algorithms compare using Eelec =  nJ/bit as the diameter of the net- work is increased. This plot shows that LEACH achieves between 7x and 8x reduction in energy compared with di- rect communication and between 4x and 8x reduction in energy compared with MTE routing. Figure 10 shows the amount of energy dissipated using LEACH versus using di- rect communication and LEACH versus MTE routing as the network diameter is increased and the electronics energy varies. This figure shows the large energy savings achieved using LEACH for most of the parameter space. −20 −15 −10 −5 0 5 10 15 20 25 Figure 7. Dynamic clusters: (a) cluster-head nodes = C at time t (b) cluster-head nodes = C at time t + d. All nodes marked with a given symbol belong to the same cluster, and the cluster-head nodes are marked with a . network and thus no extra negotiation is required to deter- mine the cluster-heads. The system can determine, a priori, the optimal number of clusters to have in the system. This will depend on sev- eral parameters, such as the network topology and the rela- tive costs of computation versus communication. We sim- ulated the LEACH protocol for the random network shown in Figure 3 using the radio parameters in Table 1 and a com- putation cost of 5 nJ/bit/message to fuse 2000-bit messages while varying the percentage of total nodes that are cluster- heads. Figure 8 shows how the energy dissipation in the system varies as the percent of nodes that are cluster-heads is changed. Note that 0 cluster-heads and 100% cluster- heads is the same as direct communication. From this plot, we find that there exists an optimal percent of nodes ^N that should be cluster-heads. If there are fewer than ^N cluster- heads, some nodes in the network have to transmit their data very far to reach the cluster-head, causing the global energy
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 l ) s e u o J ( m e t s y s n i d e t i a p s s d i y g r e n e l t a o T Direct MTE LEACH l ) s e u o J ( m e t s y s n i t d e a p s s d i i y g r e n e l t a o T Direct −> 1 0.8 0.6 0.4 0.2 0 1 0.8 0.6 x 10−7 0.4 0.2 Electronics energy (Joules/bit) 0 0 140 160 180 200 LEACH |v 200 50 150 100 Network diameter (m) <− MTE 0 0 20 40 60 80 100 120 Network diameter (m) Figure 9. Total system energy dissipated us- ing direct communication, MTE routing and LEACH for the 100-node random network shown in Figure 3. Eelec =  nJ/bit, amp =  pJ/bit/m, and the messages are 2000 bits. In addition to reducing energy dissipation, LEACH suc- cessfully distributes energy-usage among the nodes in the network such that the nodes die randomly and at essentially the same rate. Figure 11 shows a comparison of system lifetime using LEACH versus direct communication, MTE routing, and a conventional static clustering protocol, where the cluster-heads and associated clusters are chosen initially and remain fixed and data fusion is performed at the cluster- heads, for the network shown in Figure 3. For this exper- iment, each node was initially given 0.5 J of energy. Fig- ure 11 shows that LEACH more than doubles the useful sys- tem lifetime compared with the alternative approaches. We ran similar experiments with different energy thresholds and found that no matter how much energy each node is given, it takes approximately 8 times longer for the first node to die and approximately 3 times longer for the last node to die in LEACH as it does in any of the other protocols. The data from these experiments is shown in Table 2. The ad- vantage of using dynamic clustering (LEACH) versus static clustering can be clearly seen in Figure 11. Using a static clustering algorithm, as soon as the cluster-head node dies, all nodes from that cluster effectively die since there is no way to get their data to the base station. While these simu- lations do not account for the setup time to configure the dynamic clusters (nor do they account for any necessary routing start-up costs or updates as nodes die), they give a good first order approximation of the lifetime extension we can achieve using LEACH. Another important advantage of LEACH, illustrated in Figure 12, is the fact that nodes die in essentially a “ran- l ) s e u o J ( m e t s y s i i n i d e t a p s s d y g r e n e l a t o T 0.6 0.5 0.4 0.3 0.2 0.1 0 1 LEACH |v 0.8 0.6 x 10−7 0.4 0.2 Electronics energy (Joules/bit) 0 0 200 50 150 100 Network diameter (m) Figure 10. Total system energy dissipated using (a) direct communication and LEACH and (b) MTE routing and LEACH for the ran- dom network shown in Figure 3. amp =  pJ/bit/m, and the messages are 2000 bits. 100 90 80 70 60 50 40 30 20 10 e v i l a l l i t s s r o s n e s f o r e b m u N Direct MTE Static Clus LEACH 0 0 200 400 600 800 Time steps (rounds) 1000 1200 1400 Figure 11. System lifetime using direct trans- mission, MTE routing, static clustering, and LEACH with 0.5 J/node.
Table 2. Lifetimes using different amounts of initial energy for the sensors. Energy (J/node) 0.25 Protocol Direct MTE Static Clustering LEACH Direct MTE Static Clustering LEACH Direct MTE Static Clustering LEACH 0.5 1 Round first Round last node dies node dies 55 5 41 394 109 8 80 932 217 15 106 1848 117 221 67 665 234 429 110 1312 468 843 240 2608 dom” fashion. If Figure 12 is compared with Figure 6, we see that the order in which nodes die using LEACH is much more desirable than the order they die using direct commu- nication or MTE routing. With random death, there is no one section of the environment that is not being “sensed” as nodes die, as occurs in the other protocols. 5. LEACH Algorithm Details The operation of LEACH is broken up into rounds, where each round begins with a set-up phase, when the clus- ters are organized, followed by a steady-state phase, when data transfers to the base station occur. In order to mini- mize overhead, the steady-state phase is long compared to the set-up phase. 5.1 Advertisement Phase Initially, when clusters are being created, each node de- cides whether or not to become a cluster-head for the current round. This decision is based on the suggested percentage of cluster heads for the network (determined a priori) and the number of times the node has been a cluster-head so far. This decision is made by the node n choosing a random number between 0 and 1. If the number is less than a thresh- old T n, the node becomes a cluster-head for the current round. The threshold is set as: T n = P P rmod  P  if n  G otherwise where P = the desired percentage of cluster heads (e.g., P = :), r = the current round, and G is the set of nodes i t e a n d r o o c − Y 50 45 40 35 30 25 20 15 10 5 0 −25 −20 −15 −10 −5 0 5 10 15 20 25 X−coordinate Figure 12. Sensors that remain alive (circles) and those that are dead (dots) after 1200 rounds with 0.5 J/node for LEACH. Note that this shows the network 1020 rounds further along than Figure 6. that have not been cluster-heads in the last  P rounds. Us- ing this threshold, each node will be a cluster-head at some point within  P rounds. During round 0 (r = ), each node has a probability P of becoming a cluster-head. The nodes that are cluster-heads in round 0 cannot be cluster-heads for the next  P rounds. Thus the probability that the remaining nodes are cluster-heads must be increased, since there are fewer nodes that are eligible to become cluster-heads. Af- ter   rounds, T =  for any nodes that have not yet P been cluster-heads, and after  P rounds, all nodes are once again eligible to become cluster-heads. Future versions of this work will include an energy-based threshold to account for non-uniform energy nodes. In this case, we are assum- ing that all nodes begin with the same amount of energy and being a cluster-head removes approximately the same amount of energy for each node. Each node that has elected itself a cluster-head for the current round broadcasts an advertisement message to the rest of the nodes. For this “cluster-head-advertisement” phase, the cluster-heads use a CSMA MAC protocol, and all cluster-heads transmit their advertisement using the same transmit energy. The non-cluster-head nodes must keep their receivers on during this phase of set-up to hear the ad- vertisements of all the cluster-head nodes. After this phase is complete, each non-cluster-head node decides the cluster to which it will belong for this round. This decision is based on the received signal strength of the advertisement. As- suming symmetric propagation channels, the cluster-head advertisement heard with the largest signal strength is the cluster-head to whom the minimum amount of transmitted
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