A Framework for Mobile Data Gathering with Load BalancedClustering and MIMO Uploading
Miao Zhao and Yuanyuan Yang
Department of Electrical and Computer Engineering, Stony Brook University, Stony Brook, NY 11794, USA
Abstract— In this paper, a three-layer framework is proposed for mobiledata collection in wireless sensor networks, which includes the sensor layer,cluster head layer, and mobile collector (called SenCar) layer. The frame-work employs distributed load balanced clustering and MIMO uploadingtechniques, which is referred to as LBC-MU. The objective is to achieve goodscalability, long network lifetime and low data collection latency. At the sen-sor layer, a distributed load balanced clustering (LBC) algorithm is proposedfor sensors to self-organize themselves into clusters. In contrast to existingclustering methods, our scheme generates multiple cluster heads in each clus-ter to balance the work load and facilitate MIMO data uploading. At thecluster head layer, the inter-cluster transmission range is carefully chosen toguarantee the connectivity among the clusters. Multiple cluster heads withina cluster cooperate with each other to perform energy-saving inter-clustercommunications. Through inter-cluster transmissions, cluster head informa-tion is forwarded to the SenCar for its moving trajectory planning. At themobile collector layer, the SenCar is equipped with two antennas, which en-ables multiple cluster heads to simultaneously upload data to the SenCar.The trajectory planning for the SenCar is optimized to fully utilize MIMOuploading capability by properly selecting polling points in each cluster. Byvisiting each selected polling point, the SenCar can efficiently gather datafrom cluster heads and transport the data to the static data sink. Extensivesimulations are conducted to evaluate the effectiveness of the proposed LBC-MU scheme. The results show that when each cluster has at most two clusterheads, LBC-MU can reduce the maximum number of transmissions a sensorperforms by 90% and the average number of transmissions by 88% com-pared with the enhanced relay routing scheme. It also results in 25% shorteraverage data latency compared with the mobile collection scheme with single-head clustering.
I. INTRODUCTION
The proliferation of the implementation for low-cost, low-power, multifunctional sensors has made wireless sensor net-works (WSNs) a prominent data collection paradigm for extract-ing local measures of interests. In such applications, sensors aregenerally densely deployed and randomly scattered over a sens-ing field and require an autonomous organization among themfor scalability. Also, sensors are usually battery powered and leftunattended after being deployed, which makes it difficult or infea-sible to re-charge or replace their batteries. Moreover, the energyof sensors near the data sink is typically depleted much soonerthan others since they relay more packets for sensors far awayfrom the data sink. Thus, in case of failure or malfunctioning ofsensors around the data sink, network connectivity and coveragemay not be guaranteed. Due to such stringent constraint, it is cru-cial to design an energy-efficient data collection scheme that con-sumes energy uniformly across the sensing field to achieve longnetwork lifetime. Furthermore, as sensing data in some appli-cations are time-sensitive, data collection may be required to beperformed within a specified time frame. Therefore, an efficient,large-scale data collection scheme should aim at good scalability,long network lifetime and low data latency.
Several approaches have been proposed for efficient data col-lection, see, for example, [1]-[12]. Based on the focus of thework, we can roughly divide them into three categories. Thefirst category is the enhanced relay routing [1]-[3], in which data
Research supported by NSF grant number ECCS-0801438 and ARO grantnumber W911NF-09-1-0154.
are relayed among sensors. Besides relaying, some other fac-tors, such as load balance, schedule pattern and data redundancy,are also jointly considered. The second category of data collec-tion schemes introduces a hierarchical infrastructure to improvethe scalability. In [4]-[8], sensors are organized into clusters andcluster heads take the responsibility of forwarding data to the out-side data sink. Clustering can be very effective in local data ag-gregation since it can dampen collisions and support load balanceamong sensors. The third category of data collection schemesadopts mobile collectors [9]-[12], which take the burden of datarouting away from sensors. Shah, et al. [9] and Jea, et al. [10] ex-ploited the mobile entities (called data mules) with random walkmobility or moving along parallel straight lines in the field. Datamules pick up data and drop them off to a wired access point,which leads to substantial energy saving at sensors. To achieve amore flexible data gathering tour for the mobile collector, Ma andYang [11] proposed a moving path planning algorithm by find-ing some turning points on the straight lines, which is adaptiveto the sensor distribution and can effectively avoid obstacles onthe path. In [12], an alternative single-hop data gathering schemewas proposed to pursue the uniformity of energy consumption, inwhich a mobile collector is optimized to stop at certain locationsto gather data from nearby sensors via single-hop transmissions.
However, in relay routing schemes, minimizing energy con-sumption on the forwarding path does not necessarily prolongnetwork lifetime, since some critical sensors on the path may runout of energy faster than others. In cluster-based schemes, clus-ter heads will inevitably consume much more energy than othersensors due to the handling of intra-cluster aggregation and inter-cluster data forwarding. In contrast, using mobile collectors caneffectively alleviate the non-uniform energy consumption by con-fining packet relays, however, it may result in an unsatisfactorydata collection latency. Based on these observations, in this pa-per, we propose a three-layer mobile data collection framework,named Load Balanced Clustering and MIMO Uploading (LBC-MU). The main motivation is to utilize distributed clustering forscalability, to employ mobility for energy saving and uniform en-ergy consumption, and to exploit MIMO technique for concurrentdata uploading to lower data latency.
Compared to previous work in the literature, the main contri-butions of this work can be summarized as follows. First, we pro-pose a distributed algorithm LBC to organize sensors into clus-ters, where each cluster has multiple cluster heads. The key moti-vation of such clustering is to balance the load of intra-cluster ag-gregation and facilitate MIMO uploading between multiple clus-ter heads in a cluster and the mobile collector. Previous studies[4]-[6] are generally limited to single-head clustering. Second,multiple cluster heads within a cluster can collaborate with eachother, which enables energy-efficient inter-cluster transmissions.Different from other hierarchical schemes [7][8], in LBC-MU,cluster heads within a cluster do not relay data packets from other
This paper was presented as part of the main technical program at IEEE INFOCOM 2011
clusters, which effectively alleviates the burden of each clusterhead. Instead, forwarding paths among clusters are only usedto route the identification (ID) information of cluster heads to themobile collector for optimizing the data collection tour. Third, wedeploy a mobile collector with multiple antennas, which is calledSenCar in this paper, over the sensing field. It collects data fromthe cluster heads by visiting each cluster. The SenCar optimallychooses the stop positions inside each cluster and determines thesequence to visit them, such that data collection can be done inminimum time. Our work mainly distinguishes itself from othermobile collection schemes [10]-[12] in the utilization of MIMOtechnique, which enables multiple cluster heads to upload datasimultaneously. We coordinate the mobility of SenCar to fullyutilize the MIMO uploading, which leads to a data collection tourwith both short moving trajectory and short data uploading time.
II. SYSTEM OVERVIEW
In this section, we give an overview of LBC-MU framework.As depicted in Fig.1, LBC-MU consists of three layers: sensorlayer, cluster head layer and SenCar layer.
The sensor layer is the bottom and basic layer, which is formedby a set of sensors. For generality, we do not make any assump-tions on sensor distribution or node capability, such as location-awareness. Each sensor is assumed to be able to communicateonly with its neighbors, i.e., the nodes within its proximity. Forscalable data collection, scattered sensors are self-organized intoclusters before the data collection begins. Each sensor determinesits status as either a cluster head (denoted by Fnl−CH) or a clustermember (denoted by Fnl−CM) in a distributed manner. As a re-sult, the sensors with higher residual energy would become clus-ter heads and each cluster has at most M cluster heads, where Mis a system parameter. For convenience, the multiple cluster headswithin a cluster are called a cluster head group (CHG), with eachcluster head being the cluster head peer of the others. Each sen-sor is 1-hop away from at least one cluster head in its associatedcluster. The benefit of such organization is that the intra-clusteraggregation is constrained to a single hop. In the case that a sen-sor may be covered by multiple cluster heads in a CHG, it can beoptionally affiliated with a cluster head for load balancing insidea cluster. The cluster heads in a CHG collaboratively coordinatethe associated sensors in their cluster and aggregate data locallyvia time-division-multiple-access (TDMA) based transmissions.Each CHG performs local data gathering, buffers the data anduploads the data to the SenCar upon its arriving.
The cluster head layer consists of all the cluster heads, i.e., theCHGs. As aforementioned, inter-cluster forwarding is only used
to send the CHG information of each cluster to the SenCar, whichcontains an identification list of the multiple cluster heads in aCHG. Such information must be sent before the SenCar departsfor its data collection tour. Upon receiving this information, theSenCar utilizes it to determine where to stop within each clusterto collect data from its CHG. To guarantee the connectivity forinter-cluster communication, the cluster heads in a CHG can co-operatively send out duplicated information to achieve spatial di-versity, which provides reliable transmissions and energy saving[13]. Moreover, cluster heads can also adjust their output powerfor a desirable transmission range to ensure a certain degree ofconnectivity among clusters.
The topmost layer is the SenCar layer, which mainly managesthe mobility of the SenCar. There are two issues to be addressedat this layer. First, we need to determine the positions where theSenCar would stop to communicate with cluster heads when itarrives at a cluster. In LBC-MU, the SenCar communicates withthe cluster heads via single-hop transmissions. The SenCar isequipped with multiple antennas while each sensor has a singleantenna and is kept as simple as possible. The traffic patternof data uploading in a cluster is many-to-one, where data frommultiple cluster heads converge to the SenCar. Being a receiverwith multiple receiving antennas, the SenCar makes it possiblefor multiple cluster heads to concurrently upload data to it. Byprocessing received signals with filters based on the channel stateinformation (CSI), the SenCar can successfully separate and de-code the information from distinct cluster heads. To collect dataas fast as possible, the SenCar should stop at the positions insidea cluster that can achieve maximum capacity of MIMO uplink(cluster heads-to-SenCar). In theory, since the SenCar is mobile,it has the freedom to choose any preferred position in a cluster.However, this is infeasible in practice, because it is very hard toestimate the CSI for all possible positions. Thus, we only con-sider a finite set of locations. Given such possible locations ofthe SenCar, the CSI between each location and the sensors in itsneighborhood can be measured during the initial setup phase ofthe network. We call such locations the SenCar can stop pollingpoints, where the SenCar could poll the cluster heads nearby tocollect data. The SenCar does not have to visit all the pollingpoints. Instead, it optimally chooses some polling points to stopat each cluster and we call such polling points selected pollingpoints. Second, we need to determine the sequence for the Sen-Car to visit these selected polling points. Since the SenCar has thepre-knowledge about the locations of polling points, it can find agood trajectory by finding the lowest-cost round-trip route thatvisits each selected polling point exactly once and then returns tothe data sink.
III. SENSOR LAYER: LOAD BALANCED CLUSTERING (LBC)
In this section, we present the distributed load balanced clus-tering (LBC) algorithm at the sensor layer.
The essential operation of clustering is the selection of clus-ter heads. To prolong network lifetime, we naturally expect theselected cluster heads are the ones with higher residual energy.Hence, we use the percentage of current residual energy of eachsensor as the initial clustering priority. Assume that a set of sen-sors, denoted by S = {s1, s2, . . . , sn}, are homogeneous andeach of them independently makes the decision on its status basedon local information. After running the LBC algorithm, each
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(a) Network configuration. (b) Initialization.
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(c) Status claim. (d) Cluster forming.
Fig. 2. A simple example of the LBC algorithm with M = 2.
cluster will have at most M (≥ 1) cluster heads, which meansthat the size of CHG of each cluster is no more than M . Eachsensor is covered by at least one cluster head inside a cluster. TheLBC algorithm can be roughly divided into three phases: (1) Ini-tialization; (2) Status claim; and (3) Cluster forming. In the fol-lowing, we will discuss these three phases through the examplein Fig.2, where a total of 10 sensors (plotted as numbered circlesin Fig.2(a)) are labeled with their initial priorities and the con-nectivity among them is shown by the links between neighboringnodes.
In the initialization phase, each sensor acquaints itself with allthe neighbors in its proximity. If a sensor is an isolated node (i.e.,no neighbor exists), it claims itself to be a cluster head and thecluster only contains itself since no others can reach it in a singlehop. Otherwise, a sensor, say, si, first sets its status as “tenta-tive” and sets its initial priority by the percentage of its currentresidual energy. Then, si sorts its neighbors by their initial prior-ities and picks M −1 neighbors with the highest initial priorities,which are temporarily treated as its candidate cluster head peers(Can−CH−Peers). We denote the set of all the Can−CH−Peersof a sensor by A. It implies that once si successfully claims tobe a cluster head, its up-to-date Can−CH−Peers would also au-tomatically become the cluster heads, and all of them form theCHG of their cluster. Accordingly, si sets its priority by sum-ming up its initial priority with those of its Can−CH−Peers. Inthis way, a sensor can choose its favorable peers along with itsstatus decision. Fig.2(b) depicts the initialization phase of theexample, where M is set to 2, which means that each sensorwould pick a single neighbor with the highest initial priority asits Can−CH−Peer. We use the out-going arrow to indicate theCan−CH−Peer choice of each sensor. For instance, s8 is chosento be the Can−CH−Peer of s7 since it is the one with the high-est initial priority among all the neighbors of s7. Accordingly, s7
sets its priority to the sum of the initial priorities of s7 and s8.The pseudo-code describing the initialization phase of a sensor isgiven in Algorithm 1, and the notations used in the pseudo-codesare listed in Table 1 for reference.
In the second phase, each sensor determines its status by it-eratively updating its local information, refraining from promptclaim to be a cluster head. We use the node degree to controlthe maximum number of iterations for each sensor. Whether a
Algorithm 1: Phase I: InitializationMy.N ←− {v|v lies in my transmission range, v ∈ S};1if My.N = Φ then2
Notation MeaningS Set of sensors, where S[i] represents sensor si;Can−CH−Peers Candidate cluster head peers of a sensor;NBR−Can−CHs Possible neighboring cluster heads;My.N Set of neighbors in my proximity;My.A Set of my Can−CH−Peers;My.B Set of my NBR−Can−CHs;My.C Set of my cluster members;My.init−prio My initial priority;My.prio My current priority;My.status My current status (Fnl−CH, Fnl−CM, or Tentative);M Maximum number of cluster heads in a cluster;Eres, Etot Current residual and maximum energy of a sensor;CH−TH Priority threshold for claiming to be a clusterCM−TH head or cluster member;Can−Peers() Function of finding M − 1 elements with the highest
priorities among the input set as Can−CH−Peers;Highest−Prio() Function of finding the element with highest or lowestLowest−Prio() priority among the input set;Fnl−N() Function of finding the subset of the input set, in which
all the elements are Fnl−CHs;Rand−one() Function of randomly choosing an element from the
input set.
sensor can finally become a cluster head primarily depends on itspriority. Specifically, we partition the priority into three zonesby two thresholds, CH−TH and CM−TH, which enable a sen-sor to declare itself to be a Fnl−CH or Fnl−CM, respectively,before reaching its maximum number of iterations. During theiterations, in some cases, if the priority of a sensor is high (aboveCH−TH) or low (equal to or below CM−TH) enough comparedwith its neighbors, they can instantly decide its final status andquit from the iteration. We use NBR−Can−CHs to represent po-tential cluster heads in the neighborhood of a sensor. Each sensorlocally maintains a set B which contains all its NBR−Can−CHs.In each iteration, a senor, say, si, first tries to probabilistically in-clude itself into si.B as a tentative cluster head (Tent−CH) if it isnot in already (Algorithm 2, lines 2-4). Once successful, a packetincludes its node ID and priority will be sent out and the sensorsin the proximity will add si as their NBR−Can−CH upon receiv-ing the packet. Then, si checks its current NBR−Can−CHs. Ifthey do exist, there are two cases for si to make the final sta-tus decision, otherwise, si would stay in the tentative status forthe next round of iteration. The first case (Algorithm 2, lines6-10) is that si has reached its maximum number of iterationsand it prevails over others in si.B with the highest priority. Thensi will claim to be a Fnl−CH in this case. We call such a pro-cess the self-driven status transition. Also, si will announce allof its current Can−CH−Peers to be Fnl−CHs by broadcasting a
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packet including the ID list of its Can−CH−Peers, which is re-ferred to as the peer-driven status transition. Once a sensor in theneighborhood receives a status packet, it may need to update itsstatus, NBR−Can−CHs and Can−CH−Peers, accordingly. Thedetailed description of handling received packets in each sensorcan be found in Function recv−pkt. The second case (Algorithm2, lines 11-12) is that si is the one with the lowest priority andthere exist some Fnl−CHs in si.B. In this case, if the priorityof si is equal to or below CM−TH, it is clearly not qualified tobe a Fnl−CH. Accordingly, it will quit the iteration and claim tobe a Fnl−CM. It is safe for such “retirement,” since there are al-ready some Fnl−CHs in its neighborhood and it can optionallyaffiliate with one of them at a later time. Moreover, when si doesnot have any NBR−Can−CH in the current iteration and its pri-ority is already high enough (above CH−TH), it can immediatelyclaim to be a Fnl−CH (Algorithm 2, lines 13-16). Fig.2(c) showsthe result of phase II for the example with CH−TH and CM−THset to 1.8 and 0.6, respectively. (s1, s3) and (s8, s9) become theFnl−CHs while s2 is a Fnl−CM with the lowest priority. It is alsoshown that the Can−CH−Peer of each sensor has been updated,different from that in the initialization phase. For example, sensors5 is still tentative at the end of phase II, which initially consid-ered s9 as its Can−CH−Peer, and now alternatively chooses s10
as its new Can−CH−Peer when s9 reaches its final status.
The third phase is cluster forming that decides which clusterhead a sensor should be associated with. The criteria can be de-scribed as follows: for a sensor with tentative status or being aFnl−CM, it would randomly affiliate itself with a Fnl−CH amongits NBR−Can−CHs for load balance purpose. For the rare casethat there is no Fnl−CH among the NBR−Can−CHs of a sensorwith tentative status, the sensor would claim itself and its cur-rent Can−CH−Peers as the cluster heads. The details are givenin Algorithm 3. Fig.2(d) shows the finally formed clusters in theexample, where each cluster has two cluster heads and sensorsare affiliated with different cluster heads in the two clusters.
We have following properties about LBC.Property 1: Among all the cluster heads in a CHG, there is
only one self-driven cluster head, and all others are peer-drivencluster heads.
Function recv−pktfor each recvd PKT with My.id �= PKT.src−id do1
if PKT.type = 1 then2Add sensor S[PKT.src−id] to My.B;3
else if PKT.type = 2 then4Add sensor S[PKT.src−id] to My.B;5if S[PKT.src−id]∈ My.A then6
Remove S[PKT.src−id] from My.A;7Find a sensor u from My.N , which is not in current My.A8and its status is tentative with the highest initial priority;if u exists then My.A←− My.AS{u};9
for i = 1 to M − 1 do10if My.id = PKT.src−peerlist[i] then11
else if S[PKT.src−peerlist[i]] ∈ My.N then16Add S[PKT.src−peerlist[i]] to My.B;17if S[PKT.src−peerlist[i]]∈ My.A then18
Remove S[PKT.src−peerlist[i]] from My.A;19Find a sensor u from My.N , which is not in20current My.A and its status is tentative with thehighest initial priority;if u exists then My.A ←− My.AS{u};21
else if My.id = PKT.cluster−head then Add S[PKT.src−id] to My.C;22Delete the PKT;
My.prio←−My.init−prio+P
v∈My.A v.init−prio;23
Property 2: Some clusters may have fewer than M clusterheads.
Based on the clustering method, it is apparent that each clus-ter in LBC typically has a total of M cluster heads. However,some of clusters may have fewer than M cluster heads. The rea-son can be explained as follows. To circumvent the situation thatthe CHGs of different clusters may share common cluster heads,sensors with tentative status always update their Can−CH−Peersonce receiving status packets. Consider sensor si. Once its neigh-bors reach their final status, if si is still tentative, it would up-date its Can−CH−Peers by examining whether they are its cur-rent Can−CH−Peers. If yes, these Can−CH−Peers will be ex-purgated from si.A. We define a set X = {v|v ∈ si.N , v /∈si.A, v.status = tentative}, which represents the possible newCan−CH−Peers of si. si would choose the sensors in X withthe highest initial priorities to fill the vacancy among its M − 1Can−CH−Peers. However, in the rare case that X = Φ, si
would have no replenishment for the vacancy. Therefore, theCan−CH−Peers of si could only become fewer and fewer as theupdating goes on. At a later time, if si happens to be a Fnl−CH
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by the self-driven status transition, the size of the CHG, which isformed by si and its update-to-date Can−CH−Peers, would be nomore than M .
Property 3: In LBC, a larger M results in fewer clusters.In LBC, once a sensor, say, si, claims to be a Fnl−CH at an
instance, its current Can−CH−Peers will also be identified tobe the Fnl−CHs immediately and their priority will be updatedto the priority of si. si and all of its Can−CH−Peers form theCHG of the corresponding cluster. Suppose sj is one of theCan−CH−Peers of si (i.e., sj ∈ si.A). Without loss of general-ity, we assume that there exists another sensor in tentative status,denoted by sk, in the neighborhood of sj , but out of the reach-able range of si (i.e., sk ∈ sj .N and sk /∈ si.N ). Based onLBC, if the priority of sk is less than that of sj , sk will stay attentative status through the end of the iterations in phase II. Thisimplies that sj essentially restrains its neighbors with lower pri-orities from claiming to be Fnl−CHs. At a later time, sk mayhave an opportunity to affiliate itself to sj as a Fnl−CM in phaseIII. If there are more Can−CH−Peers like sj , more sensors in thesimilar situation to sk will refrain from claiming to be Fnl−CHsand alternatively join the current cluster as Fnl−CMs in the clus-ter periphery. Hence, the cluster size becomes larger comparedwith that of a smaller M . In other words, when the sensing fieldand the number of sensors are given, a larger M would result infewer clusters.
IV. CLUSTER HEAD LAYER: CONNECTIVITY AMONG CHGS
In this section, we consider the cluster head layer. As afore-mentioned, the multiple cluster heads in a CHG coordinate amongcluster members and collaborate to communicate with otherCHGs. Hence, the inter-cluster communication in LBC-MU isessentially the communication among CHGs. By employing themobile collector, cluster heads in a CHG need not to forward datapackets from other clusters. Instead, the inter-cluster transmis-sions are only used to forward the information of each CHG tothe SenCar. The CHG information will be used to optimize themoving trajectory of the SenCar, which will be discussed in thenext section. For CHG information forwarding, the main issueat the cluster head layer is the inter-cluster organization to ensurethe connectivity among the CHGs.
The inter-cluster organization is determined by the relation-ship between the inter-cluster transmission range Rt and the sen-sor transmission range Rs. Clearly, Rt is much larger than Rs.It implies that in a traditional single-head cluster, each clusterhead must greatly enhance its output power to reach other clusterheads. However, in LBC-MU the multiple cluster heads of a CHGcan mitigate this rigid demand since they can cooperate for inter-cluster transmission and relax the requirement on the individualoutput power. In the following, we first find the condition on Rt
that ensures inter-cluster connectivity, and then discuss how thecooperation in a CHG achieves energy saving in output power.
We assume that an l× l sensor field is divided into square cells,each of which is of size c × c and c = 2Rs. Based on the resultin [14], Ye, et al. [15] showed that when n sensors are uniformlydistributed and c2n = kl2 ln l for some k > 0, each such a cellcontains at least one sensor. When Rt > 2(
√5 + 1)Rs, the inter-
cluster connectivity can be guaranteed with single-head cluster-ing. In a similar way, the following property gives the conditionto guarantee the inter-cluster connection in LBC-MU.
Rs
2Rs
s b
CHG b
Rs
2Rs
sa
CHG a
cc
K
Cluster a Cluster b
sk
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4 5 6
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c
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sk
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Cluster a
CHGa
ca
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cb
(a) M > 2. (b) M = 2.
Fig. 3. Maximum distance between two neighboring clusters when both of themhave M cluster heads.
Property 4: Under the assumption that each cell contains atleast one sensor, for any cluster a and its neighboring clusterb, liml→∞ Pr
(min(D(a, b)) <
(√26 + 2
)Rs
)= 1 when M >
2 and liml→∞ Pr
(min(D(a, b)) <
(√17 + 3
2
)Rs
)= 1 when
M = 2, where D(a, b) is the distance between clusters a and b,and Pr(·) represents the corresponding probability.
Proof: Consider M > 2 first. In the worst case, all otherclusters are far away from cluster a. Cluster a and its neighbor-ing cluster b both have M cluster heads since if any CHG hasfewer cluster heads than M , the distance between the two clus-ters would be shorter, which can be easily deducted from Property3. Based on the principle of LBC, the self-driven cluster head sa,and all its up-to-date Can−CH−Peers form the CHG of cluster a.Since these Can−CH−Peers are all in the neighborhood of sa, allthe cluster heads in the CHG of cluster a are within an area withradius Rs and centered at sa. Since each cluster member shouldbe covered by at least one cluster head in a CHG, the maximumcoverage of cluster a is a circle area with radius 2Rs regardlessof the value of M . The same is applicable to cluster b. Withoutloss of generality, we assume that cluster a is centered at a cellas shown in Fig.3(a). Given that a sensor can be located any-where in a cell, in the worst case, sensors in cells 1 ∼ 9, thearea completely or partially covered by cluster a, are all locatedwithin the range of cluster a. Consider the sensor at the closestcell outside of cluster a, say, sk, which is located at cell k to theright of cell 6. The farthest sk can be from cluster a is at the po-sition of the right topmost corner of cell k. Then sk should bewithin the range of cluster b. In the worst case, it is located at theperiphery of the coverage area of cluster b. Hence, the maximumpossible distance between the two clusters is the length of the linesegment between sa and sb with sa, sk and sb in an alignment.This distance is equal to (
√26 + 2)Rs, which implies that within
this distance from a cluster, there must exist at least one anothercluster.
Similarly, when M = 2, the distance between two clusterheads in a CHG is no more than Rs and the maximum coveragearea of a cluster is achieved when two cluster heads are Rs apartfrom each other. Fig.3(b) depicts such two clusters a and b, wherethe shadowed area is the coverage area of each cluster. Considercluster a. No matter where it is located and how it is oriented, itcan completely or partially cover at most 6 cells. The worst caseis that all the sensors in these 6 cells are in the range of cluster a.Thus, the closest sensor sk outside of cluster a should be at theright bottommost corner of cell k, which is under cell 5. Similarto the case of M > 2, we can derive that the maximum possibledistance between two neighboring clusters is (
√17 + 3
2 )Rs.
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Property 5: If inter-cluster transmission range Rt ≥ (√
26 +2)Rs when M > 2 or Rt ≥ (
√17 + 3
2 )Rs when M = 2, LBC-MU generates a connected graph among CHGs.This can be easily proved by contradiction.
Next, we discuss how cluster heads in a CHG collaborate forenergy-efficient inter-cluster communication. We treat clusterheads in a CHG as multiple antennas both in the transmittingand receiving sides such that an equivalent MIMO system canbe constructed [13]. The self-driven cluster head in a CHG caneither coordinate the local information sharing at the transmittingside or act as the destination for the cooperative reception at thereceiving side. Each collaborative cluster head as the transmit-ter encodes the transmission sequence according to a specifiedspace-time block code (STBC) [16] to achieve spatial diversity.It has been shown [17] that a MIMO system with spatial diver-sity leads to higher reliability under the same power budget as thesingle-input single-output (SISO) system. An alternative view isthat for the same receive sensitivity, MIMO systems require lesstransmission energy than SISO systems for the same transmis-sion distance. Therefore, given two connected clusters, comparedwith the single-head structure, in which the inter-cluster trans-mission is equivalent to a SISO system, the multi-head structurein LBC-MU can save energy for inter-cluster communication. Inparticular, the maximum distance of two neighboring clusters is2(√
5 + 1)Rs [15] in single-head clustering. Thus, the requiredtransmission power of a cluster head for such inter-cluster trans-mission can be expressed as follows when the free space propa-gation model is employed.
PSHC = μ · (4π)2L
GtGrλ2·
h2(√
5 + 1)Rs
i2
α2(1)
where μ is the given receive sensitivity, α represents the small-scale fading parameter between two cluster heads, Gt and Gr arethe transmitting and receiving antenna gains, λ is the transmissionwavelength and L is a system loss factor not related to propaga-tion. In contrast, in LBC-MU, the inter-cluster communicationbetween two CHGs is equivalent to a MIMO transmission. Eachtransmitted data symbol would enjoy a diversity gain of at × ar,where at and ar are the numbers of transmitting and receiving an-tennas, respectively. In the worst case, two neighboring clustersare apart as far as possible, i.e., the size of CHGs on both sides isM , and the maximum distance between two neighboring clustersis equal to the lower bound of Rt given in Property 5. Hence,the output power of each cluster head in the transmitting CHG isgiven by
PLBC =
8>>><>>>:
μ · (4π)2LGtGrλ2 · [(
√26+2)Rs]2
Pati=1
Parj=1 α2
ij
, at = ar = M > 2
μ · (4π)2L
GtGrλ2 · [(√
17+ 32 )Rs]
2
Pati=1
Parj=1 α2
ij
, at = ar = M = 2
(2)
where αij represents the small-scale fading parameter of thechannel between the ith antenna in the transmitting CHG and thejth antenna of the receiving CHG. We assume these channels areindependent and identically distributed (i.i.d).
We further define the saving ratio ρM as follows to evaluate thedifference in the output power of a cluster head between single-head clustering and LBC.
ρM =E(PSHC)
E(PLBC)=
8>><>>:
4(√
5+1)2
(√
26+2)2/M2≈ 0.83M2, M > 2
4(√
5+1)2
(√
17+ 32 )2/4
≈ 5.3, M = 2(3)
From the above discussion, we can see that the saving ratio ofeach cluster head is 5.3 when M = 2 in LBC-MU. This ratiobecomes higher with the increase of M . Thus, for long-haul inter-cluster transmissions in LBC-MU, more cluster heads in a CHGcan balance the load and save energy at each sensor.
V. SENCAR LAYER: TRAJECTORY PLANNING
In this section, we focus on how to optimize the trajectory ofthe SenCar for the data collection tour with the CHG information,which is referred to as the mobility control at the SenCar layer. Asmentioned in Section II, the SenCar would stop at some selectedpolling points within each cluster to collect data from multiplecluster heads via single-hop transmissions. Thus, finding the op-timal trajectory for the SenCar can be reduced to finding selectedpolling points for each cluster and determining the sequence tovisit them.
We consider the case that the SenCar is equipped with two an-tennas, as it is not difficult to mount two antennas on the SenCar,while it likely becomes difficult and even infeasible to mountmore antennas due to the constraint on the distances betweenantennas to ensure independent fading. Note that each clusterhead has only one antenna. The multiple antennas of the Sen-Car, which act as the receive antennas in data uploading, make itpossible for multiple cluster heads in a CHG to transmit distinctdata simultaneously. To guarantee successful decoding when theSenCar receives the mixed streams, we need to limit the num-ber of simultaneous data streams to no more than the number ofreceive antennas. In other words, since the SenCar is equippedwith two receive antennas, at most two cluster heads in a CHGcan simultaneously send data to the SenCar in a time slot. Hence,an equivalent 2 × 2 MIMO system for an uplink transmission isformed, which achieves spatial multiplexing gain for higher datarate. With such concurrent transmissions, data uploading timecan be greatly reduced. If there are always two cluster heads thatsimultaneously upload their data to the SenCar in each time slot,data uploading time can be cut into half in the ideal case.
In fact, when the size of a CHG is larger than 2, we have mul-tiple choices to schedule cluster head pairs to communicate withthe SenCar. Each such a pair is called a scheduling pair. We useΠ to denote all the possible scheduling options in a CHG. With-out loss of generality, we assume that M is an even number. For agiven schedule π ∈ Π, there are M
2 scheduling pairs. The SenCarwill choose a selected polling point for each of them. When theSenCar arrives at a cluster, it will visit each selected polling point,where it stops to simultaneously collect data from the two clusterheads in a scheduling pair. To collect data as fast as possible in acluster, the following two requirements should be satisfied.
• The two cluster heads in a scheduling pair both should becovered by the SenCar with the same transmission range asa sensor, i.e., Rs, when the SenCar is at the selected pollingpoint specific for this scheduling pair.
• By visiting the selected polling points in a cluster, the Sen-Car should achieve maximum sum of the uplink MIMO ca-pacities in the cluster.
For each polling point, we assume that the SenCar has the knowl-edge of the ID of sensors in the proximity within range Rs andthe channel vectors between the sensors and the SenCar located atthe polling point. The information can be obtained when the Sen-Car is used to deploy sensors during the initial setup phase of the
2764
network. Upon receiving the CHG information which containsthe IDs of the cluster heads in a CHG, for each possible sched-ule π, the SenCar can choose a set of candidate polling points foreach scheduling pair in π, each of which can cover the two clusterheads in a scheduling pair at the same time. Specifically, let P ′
i
denote such a set of candidate polling points for scheduling pairi in a cluster, where i = 1, 2, . . . , M/2. Clearly, each P ′
i is asubset of set P that contains all the polling points. Based on thefirst requirement, the selected polling point for scheduling pair iin a cluster should be chosen from P ′
i . Next, we will first findthe distribution condition of the polling points to guarantee thatthere are always candidate polling points for choosing, and thenpresent the criteria for selecting the schedule and selected pollingpoints, which are addressed by the second requirement.
First, we have the following property regarding the distancebetween two cluster heads in a scheduling pair.
Property 6: In a CHG with M cluster heads, for any evennumber M , ∃π ∈ Π, for each scheduling pair (a, b) in π, suchthat da,b ≤ √
3Rs, where da,b represents the distance betweenthe two cluster heads a and b in the same scheduling pair.
Proof: We prove the property by induction on M . As men-tioned above, in a CHG, there is only one self-driven cluster headand a total of M − 1 peer-driven cluster heads, which are de-noted as CH0, CH1, . . ., CHM−1 for clarity. All of them arewithin a circle area with radius Rs and centered at the self-drivencluster head (i.e., CH0). First consider the case of M = 2.Apparently, the property holds since the distance between CH0
and CH1 is clearly no more than Rs. We can pair them di-rectly. Assume that there is a feasible schedule π for some Mwith pair (CH0, CHx) ∈ π where x ∈ [1, M − 1]. Now weprove that schedule π for M implies a valid schedule π′ forM + 2 cluster heads. Suppose we add two new cluster headsCHa and CHb. If the distance between the two new headsda,b is no longer than
√3Rs, then there exists a valid schedule
π′ = π⋃
(a, b). Otherwise, we can pair (CHx, CHy) where{dx,y ≤ √
3Rs|CHy ∈ {CHa, CHb}}, and pair CH0 with theremaining new cluster head. Based on the above discussion, wecan conclude that for any even number M there exists a validschedule satisfying da,b ≤ √
3Rs for any pair (a, b).To successfully choose the selected polling points in a cluster,
there should exist at least one possible schedule in which the setsof candidate polling points for all scheduling pairs are non-emptyat the same time, i.e., ∃π ∈ Π such that P ′
i �= Φ, for all thescheduling pair i ∈ π. This requirement imposes challenges onthe distribution of polling points. We study the case that pollingpoints are located at the intersections of grids with each pollingpoint apart from its adjacent neighbors in horizontal and verticaldirections in the same distance t, as plotted in Fig.4(a). We havethe following property on t to satisfy the above requirement.
Property 7: If polling points are uniformly distributed as de-picted in Fig.4(a), for a CHG with M cluster heads, when t ≤√
2(1 −
√3
2
)Rs, regardless of the value of M , ∃π ∈ Π, for each
scheduling pair (a, b) ∈ π,∑
p∈P Pr (da,p ≤ Rs, db,p ≤ Rs) �=0, where P denotes the set of all polling points, da,p and db,p arethe distances between cluster heads a and b in a scheduling pairand the polling point p, respectively.
Proof: Under the above specified distribution of pollingpoints, regardless of the orientation of grids, there is at least one
t
t
t
ta b
sR
sR3
sR
(a) (b)
Fig. 4. (a) Distribution of polling points. (b) Candidate polling points for thescheduling pair (a,b) in a CHG should be within the shadowed area.
polling point located in a circle area with radius√
22 t. For ex-
ample, in Fig.4(a), there are 4 polling points distributed in suchan area, which is highlighted in shadow. Moreover, it is knownfrom Property 6 that there exist some schedules, in which thedistance between two cluster heads in any scheduling pair is up-per bounded by
√3Rs. Consider the worst case that there is
a scheduling pair (a, b) with da,b =√
3Rs (see Fig.4(b)). Acandidate polling point p for (a, b) should be within the trans-mission range of cluster heads a and b simultaneously. The lineshadowed area in Fig.4(b), which is the intersection of transmis-sion areas of a and b, indicates the possible distribution regionof candidate polling points for (a, b). It is clear that when da,b
is shorter, the area of the region would be larger, which corre-sponds to the lower distribution density requirement on pollingpoints. Hence, considering the case with da,b =
√3Rs is suf-
ficient for the proof of the property. It is shown in Fig.4(b) that
there exists an inscribed circle with radius(1 −
√3
2
)Rs inside
the line shadowed area. If t =√
2(1 −
√3
2
)Rs, substituting
Rs with the expression of t, the radius of the inscribed circle inthe line shadowed area is equal to
√2
2 t. As mentioned earlier,there is at least one polling point located in such an area. Thusthere always exist some candidate polling points for schedulingpair (a, b), i.e.,
∑p∈P Pr (da,p ≤ Rs, db,p ≤ Rs) �= 0. In other
words, when t ≤ √2
(1 −
√3
2
)Rs, there exist some schedules
in which the set of candidate polling points for each schedulingpair is always non-empty.
We jointly consider the selections of the schedule pattern andselected polling points for the corresponding scheduling pairs,aiming at achieving the maximum sum of MIMO uplink capac-ity in a cluster. We assume that the SenCar utilizes the minimummean square error receiver with successive interference cancella-tion (MMSE-SIC) as the receiving structure for each MIMO datauploading. Based on this receiver, the capacity of a 2 × 2 MIMOuplink between a scheduling pair (a, b) and the SenCar located ata selected polling point can be expressed as follows.
C�(a,b)
= log
„1 +
Pt‖ha‖2N0I2 + Pt‖hb‖2
«+ log
„1 +
Pt‖hb‖2N0
«, (4)
where ha and hb are two 2 × 1 channel vectors between clusterheads a and b and the SenCar at , respectively, Pt is the out-put power of a sensor for transmission range Rs, and N0 is thevariance of the back-ground Gaussian noise. The MMSE-SIC re-ceiver first decodes the information from a, treating the signals ofb as the interference. Then, it cancels the signal part of a fromthe received signals. The remaining signal part of b only has tocontend with the background Gaussian noise.
Accordingly, the criteria for the schedule and the selectedpolling point for each corresponding scheduling pair in a clusteris given by
2765
[π,1,2, . . . ,M2
] = argmaxπ∈Π,�i∈P′
i
0@ X
(a,b)∈π
C�i(a,b)
1A (5)
where π is a specified schedule, scheduling pair i ∈ π consistsof cluster heads a and b, i and P ′
i are the selected polling pointand the set of candidate polling points for scheduling pair i, re-spectively, and C�i
(a,b) is the achieved 2×2 MIMO uplink capacityfor scheduling pair i when the SenCar is positioned at i.
Once the selected polling points for each cluster are chosen,the SenCar can finally determine its trajectory. The moving timeon the trajectory can be reduced by a proper visiting sequence ofselected polling points. Since the SenCar departs from the datasink and also needs to return the collected data to it, the trajectoryof the SenCar is a round-trip route that visits each selected pollingpoint once. This is the well-known traveling salesman problem(TSP). Since the SenCar has the knowledge about the locations ofpolling points, it can utilize an approximate or heuristic algorithmfor the TSP problem to find the shortest moving trajectory amongselected polling points.
VI. PERFORMANCE EVALUATIONS
In this section, we evaluate the performance of LBC-MU andcompare it with other two schemes. The first scheme to com-pare is the enhanced relay routing, denoted by ERR, in whichdynamic routing is used for load balance and packets are for-warded to the sensor in the next hop with the highest residualenergy. The second scheme used for comparison is the mobiledata collection scheme with single head clustering, or MDG-SHCfor short. In this scheme, sensors are also organized into clusters,however, each with a single cluster head, and a mobile collectorvisits each cluster head to collect data. The main performancemetrics adopted are network lifetime, energy efficiency and datalatency. For simplicity and clarity, we evaluate network lifetimeby the maximum number of transmissions that a sensor performsin the network. Such measure is reasonable since energy expen-diture in WSNs is primarily due to the radio transmissions. Ingeneral, the larger the maximum number of transmissions is, theshorter network lifetime would be. Similarly, we use the aver-age number of transmissions among sensors to indicate networkenergy efficiency since a larger average number of transmissionsimplies higher energy cost for a given number of sensors. Fi-nally, the data latency is defined as the time duration for the datasink to gather all the sensing data in the field. For all the mobilecollection schemes under investigation, the data latency is equiv-alent to the time cost of a data collection tour, which comprisesdata aggregation time, data uploading time and moving time ofthe mobile collector.
The parameters used in the simulations are set as follows. Atotal of n sensors are randomly scattered in an l × l field. Thedata sink is located at (0, 0). There are a total of np polling pointsuniformly distributed in the field. The sensor transmission rangeRs is 40m. Each sensor holds 512Kbytes sensing data and eachpacket has the size of 100bytes. The transmission bandwidth is200Kbps and the moving velocity of the SenCar is 1m/s. Eachperformance point is the average of the results in 200 simulationexperiments.
Fig.5 plots the performance of different schemes when thenumber of sensors n varies from 50 to 800, where l = 250m,np = 400, and M = 2 in LBC-MU, which means that each
cluster has at most 2 cluster heads. Note that when n is small,network connectivity, which is crucial in ERR, cannot be guar-anteed all the time. The results of ERR shown here are onlythe average results of the connected networks in the experiments.In contrast, LBC-MU and MDG-SHC can work well not onlyin connected networks but also in disconnected networks, sincethe mobile collector acts as virtual links to connect the separatedsubnetworks. From Fig.5(a), we can see that the maximum num-ber of transmissions increases with n in all the schemes. Thisis because that the volume of data packets in the network cor-respondingly increases. We can also observe that LBC-MU al-ways outperforms other schemes. Specifically, it achieves up to90% reduction in the maximum number of transmissions with re-spect to ERR. The underlying reason for such improvement ismainly due to the fact that sensors are organized into clusters inLBC-MU, thus, the burden of data aggregation and uploading aredecomposed into smaller tasks in different clusters. In contrast,sensors close to the data sink in ERR need to forward data for sen-sors far away from the data sink. If certain “popular”sensors areon many forwarding paths, network lifetime would be severelyshortened. LBC-MU also lowers the maximum number of trans-missions by about 36% on average compared with MDG-SHC.This is because that in LBC-MU, the multiple cluster heads ineach cluster would share the data uploading tasks among them toalleviate each other’s workload. LBC-MU also achieves the min-imum average number of transmissions among the three schemesas shown in Fig.5(b), which implies that LBC-MU is the mostenergy-efficient scheme. For instance, LBC-MU saves up to 88%in the average number of transmissions with respect to ERR. Itis also noticed that the difference in the average number of trans-missions between LBC-MU and MDG-SHC becomes indistin-guishable as n increases. This is because that LBC-MU typ-ically results in fewer clusters than MDG-SHC (see Fig.5(d)),however, LBC-MU has more cluster heads in each cluster thanthat of MDG-SHC. Thus, the total number of cluster heads inthe two schemes turns to be comparable, which actually is thedominant factor that determines the average number of transmis-sions. Fig.5(c) compares the data latency for LBC-MU, ERR andMDG-SHC. ERR results in the lowest latency most of the timesince LBC-MU and MDG-SHC spend extra time on the movingtrajectory. However, the difference between the latency of ERRand LBC-MU is quite small with ERR achieving only about 10%lower latency on average compared with LBC-MU. This is be-cause that though LBC-MU has to incur extra moving time, thesingle-hop transmissions for both data aggregation and upload-ing save time in packet routing significantly. It is also shown inFig.5(c) that LBC-MU surpasses MDG-SHC with an average of25% reduction in data latency due to the concurrent data upload-ing between cluster heads and the SenCar.
Fig.6 plots the performance of LBC-MU obtained with differ-ent M when l varies from 50m to 400m, where n is set to 200.We fix the interval distance t between a polling point and its adja-cent neighbors in horizontal and vertical directions at about 20m,which means that np varies from 16 to 441 with different set-tings of l. It is shown in Fig.6(a) that the maximum number oftransmissions drops as l increases in all the cases. This is be-cause that more clusters would be formed when sensors becomesparsely distributed as indicated in Fig.6(d). It is also noticed that
2766
200 400 600 8000
1
2
3
4x 10
5
n
l = 250m, n
p = 400, R
s = 40m
Max
imum
tran
smis
sion
s ERRLBC−MUMDG−SHC
200 400 600 800
104
105
n
Ave
. tra
nsm
issi
ons
l = 250m, n
p = 400, R
s = 40m
ERRLBC−MUMDG−SHC
200 400 600 8000
1
2
3
4x 104
n
Dat
a la
tenc
y (s
)
l = 250m, n
p = 400, R
s = 40m
ERRLBC−MUMDG−SHC
50 150 250 350 450 550 650 7500
10
20
30
40
Num
of c
lust
ers
n
l = 250m, n
p = 400, R
s = 40m
LBC−MUMDG−SHC
(a) Max. no. of transmissions vs n. (b) Ave. no. of transmissions vs n. (c) Data latency vs n. (d) Number of clusters vs n.
Fig. 5. Performance comparison among LBC-MU, ERR and MDG-SHC when M = 2.
100 200 300 400
0.5
1
1.5
2
2.5
3
3.5
4x 105
l (m)
Max
imum
tran
smis
sion
s
M = 2M = 4M = 6
n = 200, t = 20m, Rs = 40m
100 200 300 4006
6.5
7
7.5
8
l (m)
Ave
. tra
nsm
issi
ons
( × 1
03 )
M = 2M = 4M = 6
n = 200, t = 20m, Rs = 40m
100 200 300 4006
6.5
7
7.5
8
l (m)
Dat
a la
tenc
y (
× 10
3 s )
M = 2M = 4M = 6
n = 200, t = 20m, Rs = 40m
50 100 150 200 250 300 350 4000
10
20
30
40
Num
of c
lust
ers
l (m)
M = 2M = 4M = 6
n = 200, t = 20m, Rs = 40m
(a) Max. no. of transmissions vs l. (b) Ave. no. of transmissions vs l. (c) Data latency vs l. Number of clusters vs l.
Fig. 6. Performance of LBC-MU with different settings of M .
a larger M results in a fewer maximum number of transmissions.For instance, when l is set to 200m, the maximum number oftransmissions in the case of M = 4 is 35% less than the caseof M = 2. This result is intuitive since cluster heads are al-ways the ones that perform more transmissions than other nodes.When M increases, there are more cluster heads in a cluster toshare the workload. Fig.6(b) shows the average number of trans-missions among sensors. Since more cluster heads can directlyupload their data to the SenCar without any relay, the case witha larger M results in a slightly less average number of transmis-sions. For example, when l = 300m, the average number oftransmissions of the case with M = 6 is 15% less than the casewith M = 2. In Fig.6(c), it is demonstrated that the case with alarger M also leads to higher data latency. The reason is that moreselected polling points need to be visited in a cluster, which leadsto a longer moving trajectory in the case with a larger M . Forinstance, when l = 400m, the data latency in the case of M = 6and M = 4 are 14% and 7% higher than the case of M = 2,respectively. Fig.6(d) shows the number of clusters formed withdifferent M . It further validates that a larger M typically leads toa fewer number of clusters. However, it is also noticed that thedifference becomes less evident when l becomes larger. This isbecause that many clusters formed under this condition actuallyhave less than M cluster heads since sensors become sparsely dis-tributed such that the controlling impact of M on the cluster sizeis not fully extracted.
VII. CONCLUSIONS
In this paper, we have introduced the LBC-MU framework formobile data collection in a WSN. LBC-MU consists of sensorlayer, cluster head layer and SenCar layer. It employs distributedload balanced clustering, collaborative inter-cluster communica-tion and mobility control of the SenCar to fully utilize MIMO up-loading. Our performance study fully demonstrates the effective-ness of LBC-MU. In a large-scale WSN, LBC-MU greatly damp-ens the number of transmissions in the network by limiting packetrelays and balancing workload among multiple cluster heads in acluster, which results in up to 90% reduction in the maximum
number of transmissions and 88% reduction in the average num-ber of transmissions compared to ERR. It also effectively shortensdata latency for about 25% compared to MDG-SHC.
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