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University of Twente, Faculty of Electrical Engineering, Mathematics and Computer Science, Telecommunication Engineering Group, P.O. Box 217, 7500 AE, Enschede, The Netherlands R. T. Rajan1, S. Engelen2, A. Meijerink3, C. J. M. Verhoeven2 and M. J. Bentum4 Abstract—Low-frequency space observation is one of the de-
veloping directions in radio astronomy, as scientists try to reveal
more of the universe. The Orbiting Low Frequency Array for
Radio Astronomy project is aimed at developing a distributed
radio telescope sensitive to ultra-long waves, by placing an array
of antennas, far away from any terrestrial interference. It will
consist of over 50 small satellites grouped in a swarm capable of
collecting and processing astronomical data. The system will use
its resources to the limit and will need an efficient communication
topology in order to guarantee functionality. In this paper we
present a clustering scheme that reduces data distribution efforts
at the cost of decreasing imaging redundancy.

The Ultra Low Frequency band below 30 MHz is one of the last unexplored frequency band in radio astronomy, dueto ionospheric distortion, man-made interference and evensolar flares. An unequivocal solution to the problem is toplace antennas far away from Earth to observe at these longwavelengths. The Orbiting Low Frequency Antennas for Radioastronomy (OLFAR) [1] project is aimed at designing anddeveloping a detailed system concept for an array of scalable Satellite swarm orbiting around the Moon. Eccentric orbiting causes autonomous nano satellites in space (not more than 100 km the satellite cloud to vary its distribution with position.
apart), to be used as a scientific instrument for ultra-low-frequency observations. The OLFAR swarm could either orbitthe moon, whilst sampling during the Earth-radio eclipse each other, both for radio astronomy observations and com- phase, or orbit the sun, Earth-trailing or -leading, sampling munications. The swarm will employ distributed correlation almost continuously. To avoid single point of failure, OLFAR [2], with inter-satellite data rates in excess of 6 Mbits/sec for will be a distributed system with satellites cooperating with an instantaneous observation bandwidth of larger than 1 MHz and a data resolution higher than 1 bit. At the system level, R. T. Rajan is with Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands and ASTRON, P.O. Box 2, 7900 AA Dwingeloo, each nano satellite [3] is by definition power constrained. In The Netherlands (e-mail: [email protected]).
addition, the satellites are mobile and thus the topographical 2S. Engelen and C. J. M. Verhoeven are with the Delft University distribution keeps changing with time. All these requirements of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands (e-mail:[email protected]; [email protected]).
make data distribution within the swarm very complex.
3A. Meijerink is with the Telecommunication Engineering Group, As already described, the OLFAR project will consist of a Faculty of Electrical Engineering, Mathematics and Computer Science,University of Twente, 7500 AE Enschede, The Netherlands (e-mail: large number (50 to 1,000) [4] of small satellites, that will gather data individually and process it in a collective manner, 4M. J. Bentum is with the Telecommunication Engineering Group, Faculty ensuring this way the functionality of a low-frequency radio of Electrical Engineering, Mathematics and Computer Science, University ofTwente, 7500 AE Enschede, The Netherlands and with ASTRON, P.O. Box telescope. On the whole, the system will act as a large wireless 2, 7900 AA Dwingeloo, The Netherlands (e-mail: [email protected]).
sensor network, with a few peculiar requirements.
First of all, the network of satellites will be positioned for low latency and high data rates makes it an inappropriate in space, orbiting either the sun or the moon [3]. Little is solution for the OLFAR network, at least for the permanent known about the environment from the communication point regime. Although it cannot guarantee the correct functioning of view, and, thus, the behavior of the satellites will have a of the swarm as a radio telescope, gossiping remains a high degree of uncertainty. Added to this, offline debugging good solution for the initialization of the system—network and component replacement is practically impossible. Hence, discovery and synchronization.
the system designer has to consider the harshest conditions For large-scale mobile ad-hoc networks (MANETs), a clus- that may appear.
tering approach is essential to guarantee basic levels of system Secondly, the distances between the nodes of the network performance, such as throughput or delay. In most cases, will be up to 100 km. This is imposed by the low-frequency network division offers important benefits. A cluster structure telescope functionality. In order to achieve sufficient spatial eases spatial reuse of resources and can increase the system's resolution, the telescope needs to have an aperture diameter capacity. Same frequencies or codes can be deployed in of 10–100 km [1]. All the satellites will then be distributed disjoint clusters. Added to this, routing is more facile to do in over a very large cloud, making the network a low-density one.
a hierarchical approach. Cluster heads or gateways can form This also adds complexity to the communication problem.
a back-bone for the system, simplifying the data distribution Finally, space observation in low frequencies requires gath- task. Nonetheless, one of the most important advantages of ering and processing large amounts of data. What is more, the clustering is that it makes the network more stable and smaller satellites need to transmit their observed astronomical data to from the members' point of view. Local changes in one domain all the other members of the swarm. The necessary throughput will not cause disturbances in the entire system [7].
of every node will be very high. The observed data Dobs Therefore, clustering might be a good solution for many rate will exceed 6 Mbit/second/satellite [2], while the required WSNs, but, in order to be suitable for the OLFAR satellite inter-satellite reception rate Din will be swarm, it should also be power-efficient. Our goal is to reducethe complexity of the communication task and minimize theenergy consumed for transmitting and receiving information.
Din = Nsat − 1 D In this way, the system's resources will be used more effi- ciently to achieve the science objective, namely, exploring the where Nsat is the number of satellites.
universe in the low-frequency band.
Apart from the up-mentioned requirements, the swarm will also have constraints that most sensor networks encounter. The power of each satellite will be limited and should be used To prove the power efficiency of a clustering scheme, the mainly to serve the purpose of the system—space observation.
following test scenario has been considered: a random sensor Mobility is another characteristic that has to be taken into network with N nodes was generated. A full-mesh topology consideration. Nodes will drift away from the ideal trajectory and a clustered topology were employed to the system and then and will move relative to each other [5]. The topographical the total necessary power for communication was calculated.
distribution of the satellites will not be constant in time.
By necessary power we refer to the sum of power needed for All these requirements make the communication task very transmitting the data to all members of the network and the difficult to fulfill.
power needed for receiving and processing the data.
The rest of this paper is organized as follows: in Sections II, The following assumptions have been made: III and IV, we motivate our clustering approach. In Section V, 1) The network terminals are uniformly distributed on a L a new dynamic clustering algorithm is described. Simulation by L square surface.
results are presented in Section VI, and concluding remarks 2) The communication environment is contention-free and are drawn out in Section VII.
error-free, hence, there is no need for data retransmis-sion.
II. PROBLEM FORMULATION 3) In the full-mesh topology, each sensor transmits and The most straightforward way to solve the communication receives data from all the other sensors layer problem would be to employ a full-mesh topology for the 4) Clusters are attained by dividing the initial surface into network. This copes well with the fact that all the satellites are M equal squares, M taking only the values 4 and 16.
identical and also provides robustness to the system. However, This is illustrated in Fig. 2. As the clusters are formed it comes with high demands of communication resources. It considering a geometric criterion, the number of nodes is certainly not feasible for a large network distributed over may vary from cluster to cluster.
a vast area in space, because the necessary power will tend 5) For each cluster, the the node closest to the center of to increase exponentially with the number of nodes and the gravity rG of the cluster is elected as the cluster head, distances between them.
One may suggest that a Gossip protocol would be a better solution [6]. It is successfully used in some ad-hoc networks that implement distributed algorithms. Unfortunately, the need Fig. 3. Power-efficiency of clustering: the ratio between the necessary powerfor a full-mesh network and the necessary power for a clustered network asa function of dmin/L.
Fig. 2. Clustering example. The area over which the sensor network is spread was divided into four equal subareas, each one corresponding to a different cluster. The master nodes are represented by pentagon shapes, whereas the slaves are represented by circles.
Index k denotes a particular cluster, Nk is the number
of nodes in cluster k, and r
i corresponds to node i in 6) A node that is not a cluster head is considered to be a slave node. All slave nodes send and receive data only Average Node Power Consumption [dB] to and from their corresponding cluster head. In other words, each cluster employs a star topology.
7) Each cluster head sends and receives data to all slaves in its cluster and to all the other cluster heads.
8) Each sensor consumes energy E for receiving and processing one unit of data.
Power requirements: average node power consumption as a function 9) Each sensor has a minimum transmission power that corresponds to a transmission distance dmin. If thedistance dij between the sending sensor i and receivingsensor j is smaller than d For the scenario described above, we also calculated the min, energy E is consumed for transmitting one unit of data. Otherwise, the con- average power consumed by every type of node: slave and sumed energy for transmitting one unit of data increases master for clustered network, and peer node for the full-mesh quadratically, by the following rule: case. In Fig. 4, the values are plotted on a logarithmic scale, as a function of dmin/L. Clustering a network will make most of the members consume less power for communication, at the cost of overloading the relay nodes. There is a trade-off, yet,for low values of dmin/L the advantage is clearly in favor of Considering all the assumptions, we calculate the total The average power consumed by a slave node is very necessary power for communication duty for both cases: full- low compared to a peer node or a master node. Thus, in a mesh topology and clustered network. In Fig. 3, the ratio clustered network the slaves could save their resources for between the two is plotted as a function of dmin/L. The fulfilling other tasks than data distribution. Master nodes, on value is higher than one proving that a clustered network is the other hand, will tend to consume their energy mostly more power efficient. For low values of dmin/L (low-density for communication duty. For that reason, masters will not networks), the required power for a full-mesh topology tends contribute to the observation task.
to be one magnitude order higher than for the clustered case.
Despite the basic clustering scheme we used, the results show that dividing a network into multiple clusters increases nodes that receive only one paging signal are allocated with its efficiency.
communication channels, and, afterwards, other slaves areallocated channels in the decreasing order of their received V. A DYNAMIC CLUSTERING SCHEME FOR THE power level. By giving priority to slaves that receive only one paging signal and employing power control, this scheme Clustering is a step forward in achieving a functional can achieve nearly optimum performance. However Ryu's distributed radio telescope in space. By dividing the OLFAR algorithm uses pre-defined masters and has no method for swarm into small groups of satellites, and electing certain gate- mobility scenarios.
way satellites to route the astronomical data, energy resources The global k-means algorithm [10] describes a deterministic of the system will be used more efficiently. This hierarchical global optimization method that minimizes the clustering error approach, though an effective tool for the communication (sum of the squared distances between nodes and cluster layer, comes with one major drawback. Some of the satellites centers). The algorithm is a fast iterative one that solves the that will act as group leaders, will not be able to actively clustering problem with M clusters by solving all intermediate participate in the scientific task of the swarm. However, as long problems with 1, 2, . . , M − 1 clusters. The basic idea is that as this trade-off only impacts the redundancy of the system, an optimal solution for the M clusters problem can be obtained the improvements are uncontestable.
using a series of local searches with the k-means algorithm.
At each local search, M − 1 cluster centers have their initial A. Existing algorithms optimal position according to the M − 1 clusters problem. In There are many proposed clustering schemes in the litera- [10] the method is proposed for a pattern recognition scenario ture suitable for dynamic wireless sensor networks. Most of but can be extended for the networking case.
them have the same objective, and that is to optimize the Both ACE [11] and ASH [12] are emergent cluster forma- resource usage of the network. Nevertheless, for achieving tion algorithms. In their approaches there is no use of central this goal, different criteria are used. Dominant-Set-based [7] control or visibility over all the network. Added to this, all the protocols aim to reduce the routing cost by finding a Dominant nodes communicate with only a limited number of immediate Set in the network. Other clustering schemes [7] try to provide neighbors. In ACE, the objective to create highly uniform stable cluster architectures so that re-clustering situations are clusters is achieved using two processes. The first controls the avoided. In this way, the maintenance cost of the network is spawning of new clusters by having nodes elected as leaders, minimized. Mobility-aware clustering [8] tries to group nodes and the second controls how clusters migrate dynamically to by their dynamics as movement is usually the main cause reduce overlap. For instance, a node can decide by itself to for changes in the topology. Other used algorithms try to become a cluster head. It will broadcast a "Recruit" message to maximize the life time of mobile devices in a network or to its neighbors that will become the followers of the new cluster.
balance the energy consumption amongst all the nodes. Added Migration of a cluster is controlled by the leader. Each cluster to these, combined metrics can also be employed to attain a head will poll its followers to determine the best candidate for desired clustering scheme.
the leader of the cluster. Once the best candidate is determined, When dealing with a swarm of satellites, it is difficult to find it will be promoted as the new leader. Thus, the position of the a clustering algorithm that matches all the requirements: power cluster will appear to migrate in the direction of the new cluster efficiency, mobility and high data rates. However, there are a head as some of the former followers of the old cluster-head few algorithms that are partially fit for the OLFAR project, will be no longer part of the cluster, while some new nodes and, out of these, worth mentioning are Ryu's algorithm near the new cluster head will become new followers of the for energy-efficient clustering, the global k-means algorithm, cluster [11].
the Algorithm for Cluster Establishment (ACE) for uniform Based also on emergent behavior, ASH [12] tackles the cluster formation, the so-called ASH algorithm for highly problem of node grouping in networks that exhibit high dynamic networks, or MOBIlity-aware Clustering (MOBIC) mobility. Node movement usually introduces a lot of problems for networks that have group mobility behavior.
in a wireless network, such as routing failure, information loss, In his paper [9] Ryu proposes two distributed heuristic and others. The mechanism described in [12] handles mobility clustering schemes that minimize the required transmission in large-scale networks by employing a diffusion process that energy in two-tiered MANETs. It assumes that the network tends to equalize the pressure in the created groups. By using has only two types of nodes: masters (cluster heads) and slaves only local interactions, it creates domains whose centers of (members). A slave node can be connected only to one master, gravity move around slowly, providing a quasi-static overlay.
and links between slaves are not allowed. Master nodes are The MOBIC clustering scheme [8] takes mobility into selected in advance, and each master node establishes a cluster consideration for cluster formation, and, especially, for leader based on its connection to the slaves. The clustering process election. It uses the premise that cluster head election is a starts with a paging phase in which every master pages the local process and should only be determined by the neighbors slave nodes with the maximum allowed power. A slave that and itself. The algorithm calculates the variance of a node's receives this messages replies with an acknowledgement to speed relative to its neighbors, and increases its probability of the master corresponding to the strongest signal. First, the becoming a master based on that. This is suitable for MANETs in which groups of nodes tend to move with similar speeds anddirections. However, if the network is characterized by randommovement, MOBIC might not show good performance.
All the algorithms described above have good results in terms of efficiency for different scenarios. Yet, applying themon a complex system such as the OLFAR satellite swarm, will,most probably, cause the system to overload and fail. For in-stance, Ryu's algorithm and the global k-means algorithm bothoptimize the energy consumption for a static network. Thepresence of mobile terminals will cause the cluster structure tobe re-built when events take place, and, thus, the performancewill be degraded. Mobility-aware schemes generate eitherlarge numbers of clusters or multi-hop topologies. For a high-speed network, it is best to avoid these scenarios as much aspossible, because of their need for data aggregation.
The algorithm that we propose combines the aforemen- tioned advantages, fitting to the necessities of a satellite swarm.
It starts with electing the cluster heads and creating theircorresponding clusters, depending on the distribution of nodes.
Afterwards, it uses two procedures for node migration and forleader election that keep the system stable and minimize therisk of re-clustering. All the decision-making is done usingpower metrics, so that, in the permanent regime, the networktends to evolve to minimum power consumption.
B. Assumptions The following assumptions were made when designing the clustering scheme: 1) The clustering process starts after a gossiping round takes place in the swarm. Hence, every node is awareof the spatial distribution of the swarm.
2) The initialization is done very fast compared to the Initial cluster formation. (NACK is the number of acknowledgment mobility of the nodes. For the initial cluster formation, messages that an elected cluster head receives after paging, NK is the number we assume that the network is static.
of formed clusters, and M is the desired number of clusters) 3) All the nodes are either masters or slaves.
4) Every cluster has a star topology. Master nodes are connected in a full-mesh. A slave node can only be will suffer a power penalty. This will be detailed in the connected to one master.
5) A slave node can migrate to another cluster. A master node cannot migrate, unless it changes its role to a slave.
C. Initial cluster formation 6) For the transmission power, we use the same assumption In order to choose the nodes that are most suited for the as in Section III.
leader role, the influence that a node has on all the other nodes of the network is quantized into a density parameter which is defined below. Using this value, the clusters are formed as described in the flowchart in Fig. 5.
The steps of the cluster formation algorithm are as follows: ij is the distance between sensor i and sensor j.
7) The communication between every pair of nodes is 1) Calculate node densities.
2) The node with the highest density is elected as the 8) Receiving and processing power is ignored. After sim- cluster head.
ulating the scenario described in Section III, we con- 3) The cluster head pages all its neighbors in a radius cluded that receiving and processing power is a neg- dmin. Nodes that do not belong to any cluster respond ligible quantity when comparing it to the transmission with an acknowledgement signal and join the newly formed cluster. If the number of acknowledgements is 9) Each master can have, by default, up to Nch slaves.
larger than the number of channels Nch, the cluster head If the number of slaves is larger than Nch, the master chooses only the closest Nch nodes as his followers.
4) The process is repeated until an apriori chosen number channels a master can allocate. In most of the clustering M of clusters is created or all the nodes are connected.
algorithms, it is not allowed to have more slaves than the The density of a node i is a power-related parameter and is number of channels. Yet, this cannot be the case for our algorithm. We cannot afford to lose data from any satellite.
According to the Shannon-Hartley theorem: where C is the communication channel's maximum capacity, where node i is an unconnected node, and Eij is the energy B is the bandwidth, and SN R is the signal-to-noise ratio.
required for transmitting one unit of data from node i to node Taking into account that the communication between every j, if node j is unconnected, or 0 otherwise.
two nodes is ideal, we can proceed as follows. Let us assume D. Slave migration that Cn is the channel capacity for accommodating n users,requiring SN Rn. And let us assume that in order to satisfy In order to maintain the cluster structure and to keep the the requirements of an additional m users a channel capacity power consumption to a minimum, we define a slave migra- Cn+m is needed, respectively, SN Rn+m. In both of the cases tion procedure. The migration mechanism will be controlled we assume that the available bandwidth B is the same, and entirely by the cluster heads and will work as follows: also the noise power is the same.
1) Each master node will calculate a cost parameter Cij for Due to the fact that all users are supposed to have the same all the slaves in the network, where Cij approximates requirements, we also have: the necessary power for node i to be part of cluster j.
2) Nodes that do not belong to any cluster are attributed a default cost value.
3) If for a slave node i, member of cluster j, the following Using (8) and (9) we can deduce a relation between SN Rn condition is true: and SN Rn+m, which describes, in fact, the amount of addi-tional power needed for a cluster to host n + m slaves when it is designated for n slaves.
n+m = (1 + SN Rn)(1+m/n) − 1 As a result, in case a cluster will have more than N then node i cancels its membership to cluster j, and joins the necessary power will increase exponentially.
cluster k. θmig is a migration parameter and is equal to Based on (10), using a Taylor series approximation, and 1 in the ideal case. In order to avoid node migrating back and forth between two clusters, as a result of their 1 and m considerably smaller than n, we define a new cost function: random movement, the migration constant can be setlower than 1. This way, a node joins a different cluster θcost(Nj − Nch)Cij only if it finds a much better one in terms of cost.
for when the number of slaves in a cluster is larger than the As already mentioned, the cost function of a slave will number of allocated channels. In (11) θ approximate the necessary power for a slave node to be part cost is a parameter depending on SN R of a certain cluster. Initially, we defined the cost C n, Nj is the number of nodes in cluster j (including the potential node i), and C the necessary power for a node i to communicate with another ij is the cost calculated according to (7).
hypothetical node positioned in the center of gravity of clusterj.
E. Cluster head re-election Similar to the slave migration process, we define a mecha- nism for changing the leader of a certain cluster. As the nodes move, a master can turn up to be inefficient as a cluster head,so that another member of the cluster should take its role. The dij is the distance between node i and the center of master node should always be the node closest to the center of gravity of cluster j. The coordinates for the centers of gravity the group, moving in similar direction and at a similar speed are calculated according to (2).
as its members.
Calculating the cost relative to the center of gravity instead The re-election process is a local activity, in which all the of relating to the position of the master node makes the system members of a certain domain are involved. Let there be a more stable. The movement or re-election of the cluster head cluster j with master node i. Let G be the center of gravity has less influence on the behavior of the slave nodes. The of the cluster with its position vector rG and its speed vector
migration process will be controlled by the entire cluster.
vG, calculated according to (2), respectively:
The cost function described by (7) is valid only if the number of slaves in a cluster is less than the number of Power Ratio: transmission power needed for a full-mesh topology divided by the transmission power necessary when applying the dynamicclustering scheme.
The movement pattern was chosen to be a random walk pattern: each node was given a speed of L/200 per time stepand could change its movement direction at every simulationstep with a probability of 0.1. Finally, we set the parametersθcost, θmig, θCH and α with the values 2, 0.6, 0.6 and 0, thelast one corresponding to a random movement scenario.
Master Node Task.
The results of the numerical simulations are statistic results, which are the mean values of 1,000 random configurationsof the network. As performance metrics, we use the total consumed power for transmission and the average cluster size.
i are the speed vectors of nodes i in the cluster j.
With these definitions, the decision to attribute the role of We ignored the receiving and processing consumed energy as the leader to a new node is made based on the following it is very low comparing it to the transmitting energy [13].
The total consumed power consists of the power necessary forall the existing links in the considered network: slave-master, − α) kri − rGk + α i − vGk 6 θ
master-slave, and master-master links. We compare this value rj − rGk
kvj − vGk
with the total necessary power in case a full-mesh structurewould be used. In Fig. 7, we plotted the ratio between the two where i denotes the slave node that candidates for a leader values, i.e. the power needed for a full-mesh topology divided position, and j is the actual master node. α is a tunable by the power needed when we apply our clustering scheme.
parameter for strengthening one of the two terms, and θCH After the initial cluster formation, the value of the ratio will be is a parameter that has the same role as θmig defined in the very high because some of the nodes will be unconnected. In previous section.
time, the coverage of the clusters grows to 100% and the value In Fig. 6 a flowchart of the entire process of a master node tends to stabilize. As anticipated in Section IV, the clustered network is more power-efficient.
The average number of nodes in a cluster and the standard deviation are plotted in Fig. 8. The proposed clustering scheme We simulated the algorithm using a Netlogo environment generates quasi-equal-sized domains in term of number of and Matlab. The test scenario consisted of a network of 100 nodes. The mean value will remain constant once every node is nodes uniformly distributed on square plane. The number assigned to a cluster. However, the standard deviation indicates of clusters was selected to be 6, and for every cluster 16 that cluster sizes will vary slightly, in order to keep the cost channels were allocated without any penalty. For all the nodes, functions to a minimum.
a minimum transmission range of L/4 was chosen. The default The proposed algorithm comes with a few drawbacks, some cost value for unconnected nodes was set to four. According of which are shown in Fig. 9 and Fig. 10. Node mobility will to this value, it is possible for unconnected terminals to join a generate node transitions from one cluster to the other, and cluster only when the distance to the center of gravity is less role-transitions from master to slave and vice-versa. Changes in the node distribution will not generate re-clustering, but Cluster Size: average number of nodes per cluster and standard Power Requirements: maximum transmission power for master nodes (clustering approach) and peer nodes (full-mesh topology).
Power consumption for communication will mainly be con- centrated in only a few satellites, leaving the other members of the swarm with enough resources to fulfill the low-frequencyobservation task.
Although we designed the presented mechanisms for a particular application, they can be used for most WSNs with similar characteristics. By simply tuning the parameters, the scheme may be a solution for many distributed systems that exhibit mobility.
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