Collaborative broadcasting and compressi

Collaborative Broadcasting and Compression in Cluster-based Wireless Sensor Networks Anh Tuan Hoang and Mehul Motani Department of Electrical and Computer Engineering National University of Singapore Institute for Infocoinm Research, Singapore {engp 1629, mot ani} @nus.edu.sg Abstract- Achieving energy efficiency to prolong the network lifetime iS an impOFtaIIt design criterion for wireless Sensor In this paper>we propose a approach to energy by allowing sensors to exploit the inherent broadcast nature ofthe wireless to carry out joint data compressionm We illustrate this idea in a cluster-based wireless sensor network The key idea is that when a particular sensor broadcasts its data to the cluster head, other sensors can receive and utilize that d a h to compress their own data We formulate an optimization problem in which sensors in each cluster collaborate their to maximize transmitting, receiving, and compressing their lifetime, and solve for the ,,pima! control scheme B~ optimal, we mean that any other policy cannot increase the lifetime of the node which dies first We aIso propose a heuristic scheme with lower complexity and near Optimal Performance Numericai results show that by exploiting the broadcast nature of wirciess media, our control schemes can achieve significant imorovement in the sensors’ lifetime I INTRODUCTION In wireless s s s o r networks, sensor nodes are usually equipped with small batteries In addition, as the number of nodes in a sensor network can be large and the environment in which they are deployed can be difficult to access, battery rechargingkeplacing is not desirable This poses a major challenge in designing a wireless sensor network, i.e., how to let nodes fulfill their sensing, processing, and communicating responsibilities while prolonging their lifetime [ 11, [ 121 An important characteristic of sensor networks, which can be exploited in order to conserve energy and increase lifetime, is that data collected by different sensors are likely to be correlated This is especially true for data collected by sensors located close to one another This type of correlation is termed spafial correlation Note that in sensing applications, another source of correlation exists, i.e., temparul carrelarion among data collected in subsequent time instances This paper deals with removing the redundancy due to spatial correlation when nodcs are carrying out joint data compression Unlike other related works [ ] , [3], 1131, [16], we so by exploiting the inherent broadcast nature of the wireless medium By joint data compression, we mean that sensor nodes that have correlated data collaborate in compressing their data to reduce redundancy, and therefore, conserve transmission energy [21, 131, [13], [16] Even though the existing works 0-7803-880 1-1/05/$20.00 ( ~ ) 0IEEE 197 in joint data compression for wireless sensor networks follow a wide range of approaches, to the best of our howledge, most of them adopt a model for the wireless medium, i.e., II wireless channel is abstructed as U single painr-to-point link between a pair of nodes [ ] , [8-10], [13], [16] We believe that the point-to-point link model removes an important inherent advantage of the wireless media Due to the broadcast nature of wireless transmission, when a node transmits, multiple nodes can simultaneously receive its data When correlation exists, the receivers can compress their own data based on the data they receive As a result, the broadcast property offers nodes in wireless Sensor networks much freedom ipzca,-ryi,fg Out joint data compression and achieving energy eflciencs To illustrate our point, let us consider a simple system of four wireless sensor nodes (A), (B), (C), and (D), which are depicted in Figs and Note that both Figs I and represent the same network The difference is that in Fig 1, the broadcast nature of wireless media is not considered, while this is taken into account in Fig In Fig 1, nodes (A) and (E) send their data to (C) who then relays the received data to (D) In this point-to-point link model, (A) and (B) not decode the data transmitted by the other The only way (A) or (B) can compress their data is to follow the approach of distributed source coding [2], [ 131, V81, Wl In Fig 2, we suppose that all nodes transmit using omnidirectional antennas with the free-space path loss model being applied Let (A) transmit its data to (C) tint before (E) does Funhermore, assume that the distance between (A) and (C) is not less than that between (A) and (E), then when (A) transmits to (C), its data can be received by (B) Now, if (B) chooses to decode the data of (A), it can use these data in carrying out data compression In particular, node (B) can compress its data based on the explicir knowledge of the data of (A), and therefore, avoid the complexity associated with implementing distributed source coding [2], [13], 1181, [20] From the above example, we have shown that the broadcast nature of wireless media gives sensor nodes much more freedom in carrying out joint data compression In this paper, we focus on exploiting this broadcasting advantagc in a clusterbased wireless sensor network In this network, wireless sensor \ ! ', \-/ Signal of node A Fig System of four wireless sensor nodes Each wireless channel is Fig All nodes transmit using omni-directional antennas Assuming that the abstracted as a single point-to-point kink Transmission from (A) to (C) does distance behveen (A) and (C) is not less than the disrance between (A) and (E), not reach (B) (A) and (B) can only carry out data compression by following then (Et) is able to capture data sent from (A) to (C) and then uses that data to the complex distributed source coding approach compress its own data nodes are organized into clusters, with each cluster being responsible for monitoring a certain geographical area Data captured by each sensor are forwarded to the corresponding cluster head using direct transmission The cluster heads in tum route data collected in their clusters toward a command center which can be accessed by the end users This network is depicted in Fig Note that in our network models, sensor nodes and cluster heads are treated as two different type of nodes Sensor nodes are responsible for collecting data about the surrounding environment while cluster heads perform the data-gathering and relaying functions Our focus here i s to achieve energy saving and lifetime improvement for sensor nodes in each cluster Furthermore, we will achieve this objective with almost no effect on the operation of the cluster heads and the rulaying network Therefore, our results can be combined with any rt)uiing/aggregation schemes designed for wireless sensor nutworks to achieve the final goal of energy efficiency Thc main contributions of our paper are: IVe propose the colluborufive broadcasting and compression (CBC) approach which allows sensor nodes in eltch cliister to cooperate in transmitting, receiving, and compressing data in order ro conserve energy {Section lYj We formulate an optimization problem of which the objective is to $nd a CBC scheme that jointi) optimizes the lifetime of all sensors in each cluster, with respect 10 some optimal criteria (Section v) We structure the above optimization problem as a lineur programming problem When the number of sensors in each cliister is not too iarge, the linear programming problem can be solved t o j n d an oprimal CBC scheme (Section VI) To deal with ihe case when the number of sensors in each cluster is large we propose a heuristic CBC scheme thar achieves near optimal performance or a lower complexity (Section Vll, Finally, we obtain numerical results which show that by applying the CBC approach, sign$canr increase in sensor liferime can be achieved (Section ViJlJ 198 Two works that are most closely related to the problem considered in this paper are by Chou et al [2] and by Scaglione et al [ 161 In [2], Chou, Petrovis, and Ramchandran propose an approach that combines adaptive signal processing and distributed source coding for sensor nodes in cluster-based wireless sensor networks to conserve energy The main idea of [ Z j is to let sensors in each cluster blindly compress their data with respect to one another, but without the need of explicit inter-sensor communication The processing burden in this case is shifted to the cluster heads, who need to perform decoding with side information and adaptive filtering to estimate relevant correlation For more details on distributed source coding, please refer to /13], [IXj, [20] In [16], Scaglione and Servetto propose an approach which is opposite to that of [2] In particular, they promote the idea of source coding based on explicit data of other nodes in the network, which are made available through routing They argue that, as a routing scheme is already implemented in a sensor network, nodes in each routing path actually have explicit information of some other nodes, and therefore, they can carry out classical source coding and avoid the complexity of distributed source coding Our work combines the advantages of both [2] and I161 while avoiding their disadvantages On one hand, like [Z],we allow nodes in each cluster to carry out data compression with respect to one another, and without any extra intersensor transmissions The core idea here is the realization that as one node transmits its data to the cluster head, due to the broadcast nature of the media, its transmission reaches multiple other sensor nodes In addition, as sensor nodes carry out compression based on the explicit information that they receive when other nodes broadcast, classical source codings can be employed as in [16] 111 A CLUSTER-BASED WIRELESS SENSORNETWORK A Network Architecture We consider the cluster-based wireless sensor network shown in Fig Sensor nodes are organized into clusters and each cluster is responsible for monitoring a geographical area We adopt a heterogeneous model in which there ate two types C A _ic Sensor ADC Processor Memory - Transceiver Power Unit Fig A typical wireless sensor node comprises o f four main units: sensing and analog-to-digital converter (ADC) unit, processing and storage unit, transceiver unit, and power supply unit outputs a data packet The data are then forwarded toward the command center using the following mechanisni Within each cluster, sensors send data directly to the cluster head using time division multiple access (TDMA) V V In particular, the duration of each round is divided into slots and each sensor is assigned one slot to transmit data Cluster head/ We assume that the inter-cluster interference is negligible Command Center Sensor Relayncde One way to achieve this is by assigning non-overlapping ftequency bands to adjacent clusters Fig Model of a cluster-based wireless sensor network There are two Upon receiving data collected in their clusters, cluster types o f nodes i.e sensing nodes [type I) and data-@athering/relayingnodes (type 11) Sensing nodes transmit collected data directly to the corresponding heads carry out necessary data hsion/aggregation tasks cluster heads, who then route the data toward a command center After that, the processed data is routed toward the command center over the relay network formed by all type It nodes ofnodes Type nodes are normal sensors whose responsibility We note that TDMA has been chosen in a number of is to sense the surrounding environment and then transmitting wireless sensor network implementations [ ] , [ 171, [19] due collected data directly to cluster heads who are type I1 nodes to its simplicity, low overhead, and no packet collisions Type I I nodes gatherlaggregate the data collected in their corresponding clusters and relay them toward a command center Direct communication between sensor nodes and correspondWe assume that type 11 nodes are less energy-constrained than ing cluster heads is feasible as the distances involved are type nodes Note that in Fig 3, broadcast communications usually short Moreover, in wireless sensor networks where the always takes place and the transmission of one node can be receiving energy is comparable to transmitting energy, direct received by every node in the coverage area The arrows are communication can be more energy-efficient than multi-hop routing used to indicate intended destinations There are several advantages to adopting a cluster-based architecture for wireless sensor ne’works Firstly, as a wire- C Energy Model for Wireless Sensor Nodes less sensor networks can consist of a very large number Most of the currently existing sensor platforms can be of nodes, organizing them into clusters makes control and abstracted into a generic model as depicted in Fig (see management more scalable [l I] Secondly, a cluster-based also [I], [14]) A typical sensor node consists of four main architecture makes it easier to implement data compression components, i.e., a sensing and analog-to-digital converter and aggregation Data collected by nodes in the same cluster (ADC) unit, a processing and storage unit, a transceiver unit, are likely to be highly correlated Therefore, it is natural for and finally a power supply unit Useful information about nodes in the same cluster to jointly compress their data, and for the surrounding environment is first captured by the sensing cluster heads to carry out data fusiodaggregation [I 11 Finally, devices and then converted to digital signal by the ADC by organizing nodes into clusters and allowing direct commu- The digital signal is then processed by the processor unit nications between sensor nodes and their corresponding cluster and stored The transceiver unit is responsible for transmitting heads, the total number of hops needed to forward information collected data to other nodes in the network The transceiver toward the command center i s reduced, hence reducing the and processor units are also responsible for receiving data sent information-gathering latency by other nodes We assume that all nodes transmit using omni- a B Sensing and Communication We consider a periodic sensing scenario in which time is divided into intervals of equal duration called dam-gathering round In each data-gathering round, cach sensor collects useful information about the surrounding environment and I99 directional antennas As the focus of this papa is only on the energy consumption for communication, we simply assume that the sensing/ADC unit operates in a periodic manner and consumes a fixed amount o f energy during each data-gathering round For the energy consumption at the transceiver unit, we adopt the firstorder energy model used in I61 and [ ] In particular: i) The energy consumed to receive T B Incentives for Joint Data Compression bits is where E, (in Jouleslbtt) is the energy consumed in the electronic circuits of the transceiver when receiving or transmitting one bit of information Typical value for E, is from lOnJibit to lOOnJlbit [5] ii) The energy consumed to transmit r bits over a distance of d meters is Let $AC and dDG denote the distances (in meters) from (A) and (B) to (C) respectively and let d A B be the distance between (A) and (€3) For this section, we assume that AB d A c Let T A and T B be the amounts of uncompressed data (in bits) that (A) and (B) need to send to ( C ) during each datagathering round Furthermore, let T D ~ Abe the amount of data that E needs to transmit to (C) if it compresses based on (A) Using ( I ) , (Z), and (3), the energy (B) consumes to transmit T B bits to (C) is EB = E, x where d (in meters) is the transmission distance, and cy is the channel loss exponent which is typically in the range N For short communication distances, a free-space path loss model can be assumed and a = As the transmission distance increases, a multipath model IS more appropriate and in such cases Q = or [15].E, (in Joules/bit/m") is the energy consumed in the power amplifier to transmit one bit of information aver a distance of one meter Ea depends on the receiver sensitivity and its range is from 10pl/bit/m2 to 100pJ/bit/m2 for the frec-space path loss model [5], [6] iii) The energy consumed to compress T bits is Ecp(T)= Ec x r (3) where E, (in Jouleshit) is the energy consumed by the processor to compress one bit of information in a data packet In general, this parameter is much smaller than the electronic energy E, [51 Iv COLLABORATIVE BROADCASTTNG AND COMPRESSION: A SIMPLE CASE A A Simple Cluster-based Sensor Network Let us introduce our approach by considering a very simple cluster-based wireless sensor network depicted in Fig This network consists of only one cluster, which is composed of two sensor nodes (A) and (B) and the cluster head (C), which gathers data collected by (A) and (3)and routes them toward the command center (D) We assume that all nodes transmit using omni-directional antennas with the free-space path loss model being applied ( a = 2) By studying this simple network, we will illustrate the main concepts of our approach, We consider a more general network in Sections V, VI, and' VJI If the distance between (A) and (C) is not less than that between (A) and (B), then when (A) transmits to (C), its transmission can also be received by (B) Node (B) therefore has the option of first receiving the data of (A) and then using these data to compress its own data If (B) does so, for the sake of brevity, we simply say (B) compresses based on (A) We refer ro the upproad1 in which sensor nodes coordinate rheir transmission and reception activities in carrying out joint dura compression us collaborative broadcasting and compression (CBC) 200 TB + E, x d;C x (4) rg On the other hand, the total energy that (B) will spend if i t receives from (A), compresses based on (A), and finally transmits T B ~ Abits to (C) is + E BI A E E, X T A +J%X T A E, X T B I +EaX d& X T g IA (5) To make it easier to identify the incentives in letting (B) compress based on (A), let us assume that rA = r g = R while T B ~ A= r'! T R, then from (4)and (3,node (B) will gain positive energy saving by compressing based on (A) when -T < E, x d i e - E, R E, x d& E,' We term the compression ratio as it is the ratio of the compressed and uncompressed amounts of data that (B) sends to (C) As can be seen from (6), there is more incentive for (B) to compresses based on (A) when d o c is large, i.e., node ( B ) locates far fmm the cluster head (C) is smull, i.e., a significant reduction in the size of the dura of ( B ) cun be achieved by compressing based on (A) So it can be concluded that our CBC approach will be most effective for nodes that are far away from the cluster head and when the correlation among data collected by nodes in t h e same cluster is high How far and how correlated depend on the actual parameters of the energy model of sensor nodes Let us illustrate this by assigning a set of values to the parameters E,: E,! E(:,as used in [ ] In particular, let E, = 100pJ/bit/m2, E, = 50nJ/bit, and E, = d m i t , Fig shows the area when it is beneficial for (B) to compress based on (A) Specifically, the area below the curve corresponds to the joint values of the compression ratio and the transmission distance d n at ~ which node (B) should compress based on (A) + C Maximizing the Lqetime of the Node Who Dies First In this section, we consider the problem of finding the control scheme that maximizes the time until one of the sensors in a cluster dies For the network in Fig 2, we have two possible CBC policies: Policy { I ] : Let (A) transmit to (C) first, (B) chooses either to transmit uncompressed data to (C) or, if it is beneficial, to compress based on (A) and then transmits to (C) P o k y pz: Let (B) transmit to (C) first; (A) chooses either to transmit unconipressed data to (C) or, if it is beneficial, to compress based on (B) and then transmits to (C) I " " " " formulation, we assume that t l , t can take non-integer values If it is required hat each policy ,u1 and ,uz are employed for an integer number of data-gathering rounds, then the above linear programming problem can be modified into an integer programming problem in a straightforward manner I D Esfects on the Relaying Network Fig The incentives for node (B) to compress based on (A) (for the network in Fig 2) The parameters for h e energy model are E;, = 100pJ/bit/in2, E, = 5OnJhit and E, = SnJhit The area below the curve corresponds to the joint values of the compression ratio and the transmission distance dBC at which node (B) can save energy by compressing based on (A) For policy p1, the energy consumed by (A) will be while the energy consumed by (Bj will be (8) l ( X ) denotes the indicator function of X , which returns 1if X is true and returns otherwise Note that (B) can coiupress based on (A) only when dAB I dAc, if d > ~ ~ A then = +m and (8) gives E: = Eg Similarly, when policy p2 is applied, we can write the energy consumptions of (A) and (B) as: In lJdA2$Ac) We note that our CBC approach, which controls the transmission and compression of nodes within each cluster, has very little effect on the relay network formed by type 11 nodes Therefore, it can be used in conjunction with other routinglaggregation schemes proposed for the relaying network For example, in the simple network in Fig 2, the application of the CBC approach on nodes (A) and (B) affects the relaying network consisting of nodes (C) and (D) in the following ways: i ) Node (C) will receive less data if either node (A) or (B) compresses based on the other before transmitting As a result, ( C ) will spend less receiving energy This can be regarded as a positive effect ii) Node (C) will need to some extra processing when one of the nodes (A) and (E) compresses based on the other However, we believe that this increase in the processing energy in node (Cj can be well-compensated for by the reduction in the receiving energy discussed above i i i ) Finally, there is no effect on the amount o f data being transmitted from (C) to (D) Therefore, other parts of the relaying network are not affected by the data compression C carried out within each cluster (9) and E g =En v COLLABORATIVE BROADCASTING A N D COMPRESSION: A GENERAL NETWORK We now apply the CBC approach for a general cluster-based sensor network as depicted in Fig Note that our control will still be carried out with'in each cluster However, unlike the simple case considered in Section IV, now in each cluster there can be more than two sensor nodes Note that in (9) ~ A I B = ~ ~ ~ X T ~ + ~ ~ ~ X T ~ ~ E , X T (1 1) with r."1lB is the amount of data that (A) needs to transmit if it compresses based on (€3) Now let en and eo be the initial energies of (A) and (B) respectively, the problem of maximizing the time until at least one of the nodes (A) and (B) dies can be formulated as a linear programming problem, which can be solved efficiently with standard methods 171: subject to X tl + E;' eA, (14) EF x tl + E r x tz eB (15) E:' Xtz Here tl and t z are the number of data-gathering rounds that policies p1 and 1.r~are employed rcspectively In the above 20 A ~General A ~ S +Notations ~ ~ ~ X ~ C X T A ~ ~ We consider a cluster composed of h ' sensor nodes and a cluster head The sensor nodes are numbered from to K and the cluster head is denoted by H Let us introduce the following notations: e k ; k = , K , is the initial energy of node k dil;? i : k = 1: K , is the distance (in meters) between node i and node k d k ~ k, = 1, K , is the distance between node k and the cluster head N = { 1, K } is the set of all sensors in the cluster, Nk = {i E N! i # k I dik d i ~ } k, = ) .If, is the set of all nodes whose transmission to the cluster head can be received by k E k ( i ) ; k , i = , K , i # IC, is the total energy consumed by node IC in each round when it compresses based on i We also use &(O) to denote the energy consumed by k when it does not compress based on any other node E k ( i ) can be determined using (l), (2), (3) B Control During Each Data-gathering Round During each data-gathering round, we need to specify how nodes collaborate their data transmission and compression This involves two tasks First, a transmission order should be determined, i.e., each sensor should be assigned a time slot for transmitting its data Then, given the transmis5ion order, each node needs to know which other nodes it should compress based on As there are more than two sensor nodeb in each cluster, a node can compress based on more than one node However, allowing a node to so will make the control problem become very complex At the same time, as the energy spent when receiving is significant, if a node already compresses based on another node, it is likely to get just a little gain when trying to receive and compress based on one more node Therefore, we set the following constraint for the control in each data-gathering round: Constraint I : During each data-gathering round, each sensor node is allowed to compress bused on the datu of at most one node With the above constraint, we give the following definition for a collaborative broadcasting and compression policy that controls the transmission and compression of sensor nodes during each data-gathering round De$nition 1: Let v N be a subset of the set of all K sensors, a CBCpolicy p" specifies for each node k E v: p v ( k ) = if k is not allowed to compress based on another node p v ( k ) = i, i E v, if k is allowed to compress based on i Furthermore, in rhis case we must have p v ( i ) = Note that ;I particular CBC policy p" only controls the operation of those nodes belonging to v, which is a subset of the set of all ' h sensors This makes Definitiond applicable even if not all K sensors in the cluster are active It can be easily shown that, given a CBC policy p", a transmission order can always be determined so that each node k E v can carry out the transmission and compression activities as specified by F", prior to the application of xPV, then if and only $ *v is said to be feasible rn E&Lg(k)) x tr e y s , Q k E v (16) i=l Condition ( 6) guarantees that when *v is applied, each node in v does not consume more than its residual energy D Sensor Llfetime and System Performance Let us suppose that some feasible CBC schemes are employed to control IC sensors until all of them use up their energy and die In this case, the operation of the cluster can be divided into K separate phases, with phase k , k = 1, K , starts when k - out of K sensors die and ends when k out of K sensors die We then define a lifetime vector of the cluster (when some CBC schemes are employed) as follows Definition 3: The K-element vector L with L ( k ) being the time when phase k ends is called a lgetime vector of the cluster Furthermore, a lifetime vector L is said to be achievubk if it is rhe result of the application of some K feasible CBC schemes Now, let us examine some options for characterizing the cluster data-gathering performance based on the lifetime vector L For the most stringent performance, the cluster ceases functioning when one of its K sensors dies, i.e., at time L(1) For the least stringent case, we may assume that the cluster keeps on functioning until all of its sensors die, i.e., at time L ( K ) However, in reality, when sensor nodes die one by one, what will be observed is a gradual decrease in the quality of the data-gathering job The decrease here is in terms of information-fidelity andlor geographical coverage This gradual decrease in performance can not be captured by any single element of the lifetime vector L, i.e., not by L(1) or L ( K ) or any chosen L ( k ) , k = 1!, K From the above discussion, we propose to maximize elements of L in sequence, with the maximization of the L f h element being carried out conditioned on the maximization of the l s t , ( k - l ) t ' relements In a more concrete form, we adopt the following definition for the optimality of the cluster lifetime vector: I Definition 4: An achievable lfetimc vector L' is w i d to be optimal if for every other achievable lifetime vector L, L # L* there exists k : k E N, such that C Control over Multiple Data-gathering Rounds By definition, each CBC policy pv specifies how those sensors in the set v, v N, operate during a particuIar datagathering round To control the sensors in v over multiple data-gathering rounds, we employ a CBC scheme defined as follows N be a subset of rhe set of all K qefinition 2: Let v sensors, a CBC scheme is U policy-time set (&",ti),1 i m, indicates that CBC policy p r is employed for tr datu-gathering rounds Furthermore, let e?' be the residual energy thar node k has in which the pair 202 L*(i) qi),vz E (1; I k}, (17) with at least one strict inequality There are two main advantages of adopting the optimality criteria introduced in Definition Firstly, as the priority is on improving the lifetime of nodes who die early, WG will keep as many nodes to stay alive as possible, and therefore, assure a high-level data-gathering performance for a long period of time Secondly, the optimization objective aims to equalize the lifetime of all nodes in the cluster As a result, nodes die closer together so that the portion of time during which the system operate with low data-gathering quality, i.e., because there are few alive nodes, is reduced Let U be the set of all subsets of N that satisfies condition E Lifetime Oprirnization Problems Based on Definition 4, we introduce the following lifetime vector optimization (LVO) problem: (lX), i.e., Lifetime Vector Optimization (LVO) Problem: Given a clusrer of K sensor nodes, find K feasible CEC schemes, each controlling one phase of the cluster operarion, so that the resultant lifetime vector L is optimal Also, let t U , uE U be the number of data-gathering rounds that all nodes belonging to U transmit without compressing while all nodes not belonging to U carrying out data compression The SPLO problem can be formulated as the following linear programming problem, which can be solved by standard techniques [7],: It is clear that the LVO problem can be broken into a sequence of K optimization problems as follows In phase k , there are K - k alive sensors, with their residual energies depending on the solutions to the optimization problems in the first k - phases The objective of the optimization problem in phase k is to find a CBC scheme that maximizes the time when one of the K - k f alive nodes dies Without loss of generality, we focus on solving the optimization problem for phase The approaches to this optimization problem can then be applied to the other K - optimization problems in a straightforward manner We define the following single-phase lifetime optimization (SPLO) problem: + SingIe-Phase Lifetime Optimization (SPLO) Problem: Given a cluster of K sensor nodes, with node k having a residual energy e k , find a feasible CBC scheme U = {U maximize: N I v k f N\u, UnNk # 0) (20) c VutU subject to: tu , (22) VUEU, (1" x Ek(y'(u))) Ie k , V k E N (23) VUEU The size of the above linear programming problem depends on the cardinality of the set U , which in turn depends on the cluster topology and sensor's energy model In the most complex case, U contains all non-empty subsets of N, and therefore, has the cardinality of Z K This means it is only practical to solve the above linear programming problem when the number of nodes in the cluster, i.e., K , is not too large ~ that maximizes L ( l ) , which is the cumulative rime until one of the K sensors uses up its energy and dies To simplify the notation, we drop the superscript N so that the CBC scheme becomes ( p t l ) , (p,,,,t n ) } { VI LINEARPROGRAMMING FORMULAT~ON In this section, we follow the same approach as in Section IV-C to formulate the SPLO problem as a linear programming problem This involves identifying all possible CBC policies and doing time-sharing among them However, in this case, the number of possible CBC policies can be very large Therefore, what we will first is to narrow down the policies that should be time-shared Given a CBC policy p1 let U, denote the set of all nodes that transmit without compressing based on another node, we must have: Vk E N \ u ~ ,U, fl Nk # (18) In other words, each node belonging to N\ui should be able to receive the transmission of at least one node in ui Furthermore, each policy pi in the CBC scheme that solves the SPLO problem must satisfy: Vl1 HEURISTIC ALGORITHM In this section, we propose a heuristic CBC scheme which can be obtained at a much lower complexity compared to solving the linear programming problem in Section VI Moreover, in Section VIII, we will present numerical results which show that the heuristic CBC scheme achieves near optimal performance In the heuristic CBC scheme (PI,t l ) , , (pm,t m ) }each policy p i is employed for an interval of T data-gathering rounds, i.e., t, = T, i = , m, where T is a fixed integer During each interval, a CBC policy is selected in a greedy way, with the objective of maximizing the minimum residual energy of IC nodes after the interval { A A CEC Policy for T Data-gathering Rounds Let interval n, R = , , , denote the time from the beginning of data-gathering round ( n- 1)x T + until the end of data-gathering round n x T Let e:, e; 0, k = 1, K , be the residual energy of node k at the beginning of interval tz Also, let p n be the CBC policy being employed in interval TZ If no node uses up its energy during interval n, the residual energy of node IC at the beginning of interval n is + As a result, a policy pi in the CBC scheme that solves the SPLO problem is completely specified if the set of nodes that transmit without compressing, i.e., ui, is given 203 The lifetime of each node is directly related to its residual energy Therefore, during each interval, it is intuitive to employ a greedy CBC policy that maximizes the minimum value of the residual energy of all K nodes after the interval In other words, for interval 71, we will find the CBC policy p:, that In order to obtain pi, we start with a CBC policy p in which no node compresses based on any other node and improve p in each iteration Policy p is improved by first identifying the node i* that will have the least residual energy at the end of interval n if policy fi is applied and then Iet i* compress based on another node When there are more than one node that 'i can compress based on, i' will choose the node j * that satisfies j * = arg 1na.x { min{er* - Tx ~i-(j): jEQ (e; - 2- x E m ) l n ( j w} (26) The reason for 'i to compress based on j * selected by (26) is that if we let 'i to compress based some node j , then j is not allowed to compress based on any node, and j can become the node who has the least residual energy at the end of interval n In (26), Q is the set of nodes that i* can compress based on while U consists of nodes that are not able to compress and nodes that have already been used by other nodes for their data compression After improving e:?' by letting i' compress based on j " , we move to the next iteration and repeat the process We name the above algorithm Single-CBC and present its pseudo-code as follows vt0 u4-0; arg niin {e; - T x Ek(,u(k))} k E N\(UUV) { Q +k C N,*\V if Q # then p(i*) +j* U + uu {j*); else U + U U (i'} E,- (k) < Ei*(0)} v + v u {i') i f U U V = N then break return Given the residual energies of K sensors node at the beginning of interval T L , i.e., (e:, e ; ) , the Single-CBC algorithm constructs a CBC policy that controls the collaboration of these K sensors for the next T data-gathering rounds By repeatedly applying the Single-CBC algorithm until one of the sensor nodes uses up its energy and dies, we obtain a set of CBC policies, each control the collaboration of K sensors for T data-gathering rounds This gives a sub-optimal solution to the SPLO problem defined in Section V We name the algorithm that does so the Multiple-CBC The inputs for Multiple-CBC is the initial energy of K nodes, i.e., (el, e x ) Multiple-CBC outputs a sequence of CBC policies that are employed until one of the sensors dies The pseudo-code for Multiple-CBC are as follows Multiple-CBC(el, e K ) *+I1 IMP p t SingIe-CBC(el, er;) @ - P, ck + e k if PI -T X miIiI;EN{ek} Ek(p(k)), Vik E N then break return C Complexi@ of Heuristic Algorithm First, let us determine the complexity of Single-CBC algorithm From the pseudo-code of Single-CBC, it can be seen that the main tasks inside the loop is to find' i and j * Both of these involve finding the minimum value from a set of at most IC elements and therefore, the complexity is of the order U ( K ) At the same time, the main loop is repeated for no more than K times Therefore, we can conclude that the worst-case complexity of SingleXBC is O ( K ) During each iteration uf Multiple-CBC algorithm, Single-CBC algorithm is carried out The number of iterations being taken in Multiple-CBC depends on the lifetime of the node who dies first We note that the energy consumed by each node in a data-gathering round is lower-bounded by the energy consumed in the electronic circuits In particular, if in each data-gathering round, each node is required to communicate a packet of length R bits (without compression) to the cluster head, then no matter whether a node compresses based on other nodes or not, the energy consumed in each round is lower bounded by (refer to (4) and (5) for more details): S i n g l e _ C B C ( e ~ , e k ) p(k) + 0, Vk E N loop i* t- B A Heuristic CBC Scheme Eib = E , x /I Note that the inputs for algonthm Single-CBC are the residual energies of the 'h senbors at the beginning of interval n, i.e., (e?, e;) The output of Single-CBC is a CBC policy that control K sensors during interval n As has been mentioned, U denotes the set of nodes that are either used by other nodes for their data compression andor not able to compress Besides, V denotes the set of nodes who compress based on some nodes in U 204 Therefore, the lifetime o f sensor k , IC bounded by: ek Lub = - Elb t 27) R = , ~, h ' , is upper(28) As the upper-bound L I L bdoes not grow with K , the number of iterations of Multiple-CBC algorithm does not grow with h ' either As a result, the complexity of Multiple-CBC algorithm is of the same order of that of the Single-CBC algorithm, which is equal O ( K ) on the compression ratio , i.e., on the spatial correlation among data collected at different sensors When $ is low, the performance gain of both optimal and heuristic schemes are very significant The gain is largest for L(1) while there is negligible gain for L(10) This is exactly what our objective is; we want to improve the lifetime of those nodes who die earlier than others Another important observation is that the performance of the heuristic scheme is nearly the same as that of the optimal control scheme This indicates that we can use the heuristic scheme, which has much lower complexity without sacrificing performance Now we look at how the performance of the heuristic scheme depends on the number of sensors per cluster and Fig An example of nctwork of size 100 x 100m The monitoring area is divided inro four clusters In each cluster, there are K = 70 sensing nodes the cluster size In Fig we show the percentage increase for iind one cluster head Sensing nodcr and cluster heads are deployed randomly L( 1) when the heuristic scheme is applied, as compared to the and uniformly within their clusler area case when no node carries out compression for different values of K and D , i.e., K = 10, 25 and D = l o o m , 200m The percentage increase is plotted against the compression ratio VJII NUMERICAL RESULTS AND DISCUSSION As can be seen, the gain in lifetime increases in the number of In this section, we present numerical results which show nodes per cluster This can be explained by the fact that, when the performance gain, i.e., the increase in sensors' lifetime, there are more nodes in each cluster, the distance among them when sensor nodes carry out collaborative broadcasting and gets shorter, each node has more options on which node it can compression We will compare the performance of three used to compress its data At the same time, when the cluster control schemes, i.e., the optimal scheme obtained by solving size D is increased, the performance gain also increases the linear programming problem in Section VI, the heuristic Finally, we look at how the performance gain of the scheme proposed in Section VII, and finally the scheme heuristic scheme, relative to the case when no nodes carry in which all K nodes transmit to the cluster head without out compression, depends on the energy model of sensor compressing based on any other node nodes In particular, we let the value of electronic energy, The monitored field is represented by a square area of size i.e., E, vary from 10 to 100nJhit while still keeping the D meters This area is further divided into C2disjoint clusters, amplifier and processing energy unchanged In Fig 9, we each of them is a square of size $ meters In each cluster, plot the percentage increase for the lifetime of the node who there are IC sensor nodes and one cluster head We assume that dies first, i.e., L ( ) ,versus the compression ratio $ for two the sensor nodes, together with the cluster head, are deployed E, = 10: 50 and 100nJbit As can be seen, the gain decrease randomly within each cluster, with their coordinates uniformly in E, However, even when E= = 100nJlbit, the gain is still distributed In Fig 6, a sample network of size D = 100 about 30% for the compression ratio of 0.5 meters, being divided into four clusters and with K = 10 sensors per cluster, i s shown The energy model of each sensor node is as described IX CONCLUSION in Section 111-C with the following parameters: E, = In this paper, we propose an approach in which the inherent 100pJ/bit/m2,Ee = SOnJhit, and E, = 5nJhit Each sensor node has an initial energy storage of 5J In each round, without broadcast nature of the wireless medium is used by sensor compression, each sensor needs to send a packet of length nodes to carry out joint data compression and conserve energy R = 400 bits to the cluster head For the sake of simplicity, This is different from the usual abstraction of a communication we ignore the bits used in the packet header This assumption network by a communication graph, in which nodes interact is justified when the size of the packet header is much smaller in a point-to-point fashion Our results show the importance of than that o f the data payload We also assume that, if a exploiting the opportunity to collaborate in wireless settings Our metric of interest is sensor network lifetime We first particular node k compresses based on another node, then the compression ratio, i.e., 5, is fixed Note that L ( k ) , k = present algorithms which optimize the lifetime vector of the 1, , K , denotes the time when k out of the K sensors in a network, meaning that any other algorithm will not increase the lifetime of the node which dies first We then propose cluster die when some control scheme is employed In Fig 7, we show the percentage increases in sensors' life- a heuristic algorithm which has significantly lower computatime when the optimal control scheme and the heuristic control tional complexity with near optimal performance We present scheme are applied, relative to when no node compresses extensive simulations to support these claims its data The percentage increases in the lifetime of nodes We are currently looking at extending our approach to who die first, second, fifth, and tenth are plotted versus the non-cluster based networks and designing scalable efficient compression ratio Thesc values are obtained by generating heuristic algorithms Moreover, we are implementing these 500 instances of the nctwork, and averaging the performance algorithms in hardware and software to see haw they perform As can be seen, the lifetime improvements strongly depend in real-world situations 14r m Sensing node 5~ 205 '01 02 03 Compression Ratio dR 04 OS 06 07 08 09 Compression Ratio rlR Fig Percentage increases (relative lo no compression) in sensors' lifetime versus compression ratio when the optimal CBC and heuristic CBC bchemes are applied L(1), L ( ) , L(5), L(10) arc the lifetime of nodes who die first, third fifth and tenth, respectively There are K = 10 nodes in each cluster and the energy model is: E, 100pJ/bidmZ,Ee = 50nJibit and Fig Percentage increase (relative to no compression) in the lifetime of the node who dies first versus compression ratio when the heuristic CBC scheme is applied There are K = 10 nodes in each clustcr and the energy model is: E, = 100pJ/bit/m2 E, = SnJhit and E, takes (he values { 10,50,100nJhit} Ec = SnVbit [9] C Intanagonwiwat, R Govindan, D Estrin, J Heidemann, and E 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Conference on Mobile Computing and k !f O0.1 02 04 11.3 05 01 07 0.8 0.9 Compression Ratio r/R Fig Percentage increase (relative to no compression) in the lifefime of the node who dies first versus compression ratio when the heuristic CBC scheme is applied The cluster size is D = {100,200 m } and the number of scnsors/cluater i s K = {10,25} The cncrgy model is: Ea = 100pJ/blLfm2,Ee = 5(mJ/bit and Ec = 5nJhit REFERENCES I Akyildiz, W Su, Y Sankariisubramaniam, and E Cayirci A survey on sensor networks lEEE Comm Magazine, pages 102- 1171 %?%ii,% ?!?Of' o N Ickes, R Min, A Sinha, A Wang, and A Chandrakasan Physical layer driven protocol and algorithm design for energy-efficient wireless sensor networks In PmM 200 [ 181 %%&i$%##%?? k'lnisehs encoding of correlated information sources IEEE Trans on Inform Theory, pages Aug 200 f.14Chou, D Jetrovis, and L19] %?.1dE%b!,93.3Gao, V Ailawadhi, and G Pottie Protocols for self-organization of a wireless sensor network IEEE Personal s 1201 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Mc raw-Hill Igc 19 C (intanagonwi&l, Govindan, and D Estrin Directed diffusion: A scalable and robust communication paradigm for sensor networks In Pruc ACM MobiConi'00, 2000 @gyp %: 206 ... rheir transmission and reception activities in carrying out joint dura compression us collaborative broadcasting and compression (CBC) 200 TB + E, x d;C x (4) rg On the other hand, the total energy... above constraint, we give the following definition for a collaborative broadcasting and compression policy that controls the transmission and compression of sensor nodes during each data-gathering... Let $AC and dDG denote the distances (in meters) from (A) and (B) to (C) respectively and let d A B be the distance between (A) and (€3) For this section, we assume that AB d A c Let T A and T