Analysis of Energy Efficiency of Compressive Sensing in Wireless Sensor Networks

IEEE SENSORS JOURNAL, VOL. 13, NO. 5, MAY 2013 1999

Analysis of Energy Efficiency of CompressiveSensing in Wireless Sensor Networks

Celalettin Karakus, Ali Cafer Gurbuz, and Bulent Tavli

Abstract— Improving the lifetime of wireless sensor networks(WSNs) is directly related to the energy efficiency of computationand communication operations in the sensor nodes. Compressivesensing (CS) theory suggests a new way of sensing the signalwith a much lower number of linear measurements as com-pared to the conventional case provided that the underlyingsignal is sparse. This result has implications on WSN energyefficiency and prolonging network lifetime. In this paper, theeffects of acquiring, processing, and communicating CS-basedmeasurements on WSN lifetime are analyzed in comparison toconventional approaches. Energy dissipation models for both CSand conventional approaches are built and used to construct amixed integer programming framework that jointly captures theenergy costs for computation and communication for both CSand conventional approaches. Numerical analysis is performedby systematically sampling the parameter space (i.e., sparsitylevels, network radius, and number of nodes). Our results showthat CS prolongs network lifetime for sparse signals and is moreadvantageous for WSNs with a smaller coverage area.

Index Terms— Compressive sensing (CS), energy efficiency,mixed integer programming, network lifetime, wireless sensornetworks (WSN).

I. INTRODUCTION

W IRELESS Sensor Networks (WSNs) are comprised ofspatially distributed sensor nodes, where each node

contains units for sensing, processing, and communicatingdata [1]. In general, sensor nodes are assumed to have limitedprocessing power and highly constrained energy resources [2].A typical WSN topology includes a base station - a powerfulentity more capable than the ordinary sensor nodes with asignificantly higher energy budget [3]. Ordinary sensor nodestransfer processed or raw sensed data to the base station, whichperforms the final information aggregation and extractiontasks [4].

In conventional signal processing techniques for true recon-struction at the base station, ordinary sensor nodes sampledata at the Nyquist rate, generating raw measurements ofthe signal. Depending on the sophistication of the sensor,the signal can be transformed to a new domain where most

Manuscript received December 2, 2012; accepted January 24, 2013. Dateof publication February 4, 2013; date of current version April 10, 2013. Thiswork was supported in part by the TUBITAK Grant with Project 109E280 andby the FP7 Marie Curie IRG Grant with Project PIRG04-GA-2008-239506.The associate editor coordinating the review of this paper and approving itfor publication was Prof. Okyay Kaynak.

The authors are with the TOBB University of Economics and Technology,Ankara 06560, Turkey (e-mail: [email protected]; [email protected];[email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSEN.2013.2244036

of the signal energy can be represented by a small numberof coefficients (i.e., the signal is compressible or sparse).Later these coefficients and their locations are encoded andthen transmitted to the base station. Alternatively, each sensornode can also transmit its raw measurements to the basestation without any processing. For example, in an imageacquisition operation, the sensor first acquires raw data, whichcorresponds to measuring each pixel value. If the imageis compressible in discrete cosine transform (DCT) space,the raw image can be transformed to the DCT domain [5].In this way only a small number of DCT coefficients andtheir locations are saved. These coefficients constitute mostof the energy in the image. The rest of the coefficients arediscarded without deteriorating the perceived quality of theimage significantly. Either the raw image pixels or the DCTcoefficients may be transmitted depending on the selectedtechnique.

Apart from these conventional techniques, the theory ofCompressive Sensing (CS) [6], [7] proposes a novel signalacquisition and recovery method. Briefly, CS theory statesthat if a signal is sparse or compressible in a certain basis,then it can be reconstructed from a smaller number of linearmeasurements in comparison to the conventional case by solv-ing an �1 based convex optimization problem. The requirednumber of measurements are linearly related to the underlyingsignal sparsity level. An example image reconstruction resultis presented in [5]. Using CS for WSN applications, the sensornodes can directly acquire a small number of measurementsas linear projections of the raw signal and directly transmitthese CS measurements to the base station without any furtherprocessing in the sensor node [8]–[12]. In this way, the signalcan be acquired at its information rate and data is compressedwhile being sensed. This technique also eliminates the need toacquire data that is discarded after doing the transform coding.Although CS needs to transmit much less data compared totransmitting the whole raw data, it actually transmits moremeasurements as compared to the transform coding case.Hence, using a fair energy dissipation model (including bothcommunication and computation energy costs), a compari-son between conventional and CS based techniques can beperformed to understand the conditions under which CS canimprove energy efficiency, and enable longer lifetimes forWSNs.

Mixed Integer Programming (MIP) based analysis of com-munication networks is extremely useful for uncovering thefundamental performance limits [13]. Choosing an MIP basedanalysis method has a number of advantages. One of themis the abstraction from a specific protocol which enables us

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2000 IEEE SENSORS JOURNAL, VOL. 13, NO. 5, MAY 2013

to investigate energy cost in ideal conditions with optimalrouting decisions. Secondly, due to global knowledge in theoptimization problem solver, the results can be obtained in anefficient and consistent manner.

The novel contribution of our study is to characterize thetradeoffs in employing CS instead of conventional signalprocessing techniques in WSNs from energy efficiency andnetwork lifetime perspectives. We developed a unified com-putation and communication energy model based on experi-mental characterizations of mica motes to account for differentaspects of data acquisition, processing, and communicationin sensor nodes that is capable of differentiating the energydissipation of different sensing techniques. Based on thismodel, a novel MIP framework that jointly models the energydissipation of both computation and communication operationsin WSNs for varying sensing techniques is constructed.

The rest of this paper is organized as follows. In Section II,a brief overview of the literature on the use of CS theory inWSNs and on mathematical programming based analysis ofWSNs is presented. Section III briefly outlines the mathemat-ical background on compressive sensing that is used to developthe system model. In Section IV, a unified energy model thatjointly captures the energy dissipation characteristics of WSNnodes for sensing, computation, and communication usingavailable data on WSN hardware platforms. In Section V, wepresent our network model formulated as an MIP framework.Section VI presents the results of numerical analysis per-formed using the MIP framework by systematically exploringthe parameter space. Conclusions are drawn in Section VII.

II. RELATED WORK

There are many studies on applications of CS theory onWSNs. In [14], novel models for joint sparsity in WSNapplications is introduced and the benefits of distributedcompressed sensing (e.g., signal recovery with fewer mea-surements, robustness, low complexity at sensor nodes) isdemonstrated. In [9], several random routing methods forWSNs exploiting CS based measurement techniques are pro-posed. Analysis of the proposed methods in comparison toexisting data gathering schemes is performed. In [10], thepotential of CS based signal acquisition for low-complexityenergy-efficient ECG compression on a wireless body sensornetwork mote (Shimmer) is investigated. The results of thisstudy reveal that CS represents a competitive alternative todigital wavelet transform based ECG compression solutions.In [11], a CS based approach for monitoring environmentalinformation using WSNs is presented. The proposed methodsexploits the compressibility of the signal to reduce the amountof acquired data. In [12], a CS based data collection algorithmfor WSNs is proposed. Theoretical analysis of the proposedalgorithm shows that it can accurately recover data from asmall amount of compressed data. In [15], a decentralizednetworking scheme that combines the concepts of randomchannel access and CS to achieve energy and bandwidthefficiency for underwater sensor networks is proposed. Theconcept of sufficient sensing probability is introduced tocompensate for the random packet loss caused by collisions.

In [16], an algorithm employing compressive sensing inconjunction with particle swarm optimization to decrease thecommunication rate and to build up the data aggregationtrees is proposed. It is shown through simulations that theproposed algorithm outperforms LEACH and Shortest-pathrouting in extending WSN lifetime. In [17], an optimiza-tion model for minimizing the network energy consumptionthrough joint routing and compressed aggregation is devel-oped. Both MIP-based and heuristic solutions are proposed.In [18], an approach utilizing the concepts of compressivesensing to minimize the number of packets to transmit inWSNs is proposed. Performance analysis using data sets gath-ered by a real-life deployment demonstrate that the approachhelps finding an optimal tradeoff between the energy spentin transmission and data compression. In [19], an algorithmfor compressive sensing in WSNs using rateless coding isproposed to keep the energy cost of inter-communicationsfor generating projections. The algorithm is independent ofrouting algorithms or network topologies and provides theadvantage of using non-uniform and unequal error protectioncodes. In [20], a modification of the canonical compressivesensing recovery is introduced to reduce the energy cost ofevent detection applications in WSNs. A practical imple-mentation of the proposed scheme with energy constrainedWSN nodes quantify the gains accrued through simulation andexperimentation.

The literature on MIP based modeling and analysis ofWSNs is extensive and has grown rapidly in recent years.Providing a comprehensive overview of the published researchon modeling WSNs through MIP is beyond the scope of ourwork. We refer interested readers to the recent review paperson this topic [21], [22].

III. COMPRESSIVE SENSING THEORY

In conventional signal processing, a sensor acquires thesignal at least at its Nyquist rate for proper reconstruction.Lets represent this acquired discrete signal as one dimensionalvector x ∈ RN . Any vector in RN can be represented as alinear combination of basis vectors {ψi }N

i as

x =N∑

i=1

siψ i x = �s (1)

where � is the basis matrix with i th column ψ i . The signal xis called K -sparse if only K of the coefficients in transformdomain vector s is nonzero. The compressibility of mostpractical signals is the basic point for transform coding. Awireless sensor node, depending on its sophistication, caneither transmit all N measurements without any processingor it can transform the signal to a new domain where it canbe represented with K � N coefficients. In transform coding,the full signal x ∈ RN is acquired; all transform coefficientsare calculated by s = �T x; the largest K coefficients arelocated and the rest are discarded. Finally, only the largest Kcoefficients and their locations are encoded and transmitted.

Although transform coding decreases the amount of datacommunicated, several fundamental points should be men-tioned.

KARAKUS et al.: ANALYSIS OF ENERGY EFFICIENCY OF COMPRESSIVE SENSING IN WSNs 2001

1) Although only K � N coefficients are sought, all Nmeasurements, which may be large, are needed to beacquired.

2) All the transform coding coefficients are computed eventhough only K of them will be used and the rest arediscarded.

3) Locations of the coefficients must also be encodedintroducing an extra overhead.

The compressive sensing (CS) theory [6], [7] addressesthese inefficiencies by compressing while acquiring data atits information rate. CS takes nontraditional linear measure-ments, y = �x, in the form of randomized projections.A signal x, which is K sparse in � can be reconstructedfrom M = O(K log N) compressive measurements, where Mis the number of required compressive measurements. Thisreconstruction requires solving a convex optimization problemof the following form

arg min ‖s‖1 s.t . y = ��s (2)

It is also shown in [23] and [24] that stable recoveryof s can be done by relaxing the optimization problem inEquation 2 for noisy measurements. In CS, much less numberof measurements M compared to the data acquisition numberN is taken, however M is larger than the sparsity level K asM = O(K log N) and no transform coding should be done atthe wireless sensor. Instead, M compressed measurements canbe transmitted to the base station and the reconstruction canbe done there. The reconstruction in CS is done by solving anoptimization problem, such as in Equation 2. This optimizationproblem is convex and can be solved using linear program-ming and the global optimal solutions can be achieved. Thecomputational complexity of this solution is gretaer than thatof transform coding, but it is done at the base station, whichwe assume to have a significantly higher energy budget thanthe ordinary sensor nodes. The base station must know themeasurement matrix � of the wireless sensor to solve theoptimization problem in Equation 2. The measurement matrix� does not change through the lifetime of the wireless sensors,hence, the sensor nodes can be preloaded with this data beforedeployment.1 Alternatively, the measurement matrix can betransmitted to the sensor nodes by the base station; however,such data dissemination is not frequent, and thus, does notlead to any significant energy consumption.

IV. ENERGY MODEL

In this section, we develop an energy dissipation model forthree approaches2:

1) Data Acquisition and No Processing (DANP) approach2) Data Acquisition and Transform Coding (DATC)

approach3) Data Acquisition and Compressive Sensing (DACS)

approach

1In our analysis, we adopted this approach.2In the rest of the paper, DANP and DATC are referred to as conventional

approaches and DATC is referred to as the CS-based approach.

TABLE I

THIS TABLE PRESENTS TRANSMISSION ENERGY DISSIPATION (μJ/BIT)

AND RANGE (M) VALUES FOR MICA2 MOTES EQUIPPED WITH CC1000

RADIOS AS A FUNCTION OF POWER LEVEL (l). CHANNEL BANDWIDTH,

ς , IS 38.4 Kb/s [27]. ENERGY DISSIPATION FOR RECEPTION (Erx ) IS

0.923 μJ/BIT. VALUES ARE COMPUTED USING THE DATA PROVIDED

IN [25]

Power Level (l) Transmission Energy (Elt x ) Range (Rl

max )l-1 0.672 19.30l-2 0.688 20.46l-3 0.703 21.69l-4 0.706 22.69l-5 0.711 24.38l-6 0.724 25.84l-7 0.727 27.39l-8 0.742 29.03l-9 0.758 30.78l-10 0.773 32.62l-11 0.789 34.58l-12 0.813 36.66l-13 0.828 38.86l-14 0.844 41.19l-15 0.867 43.67l-16 1.078 46.29l-17 1.133 49.07l-18 1.135 52.01l-19 1.180 55.13l-20 1.234 58.44l-21 1.313 61.95l-22 1.344 65.67l-23 1.445 69.61l-24 1.500 73.79l-25 1.664 78.22l-26 1.984 82.92l-27 2.538 100.00

Energy dissipation in a typical WSN node can be catego-rized into two groups: (i) energy dissipation due to computa-tion – EC M P and (ii) energy dissipation due to communica-tion – EC O M . We used the energy dissipation characteristicsof the Mica2 platform to determine the energy dissipationmodel. Mica2 platform consists of an Atmel Atmega 128Lprocessor and Chipcon CC1000 radio. Both of them havevery well characterized energy dissipation properties. We usethe communication energy dissipation model for Mica2 motesequipped with CC1000 radios presented in [25]. Transmissionranges and corresponding energy dissipations for this modelare presented in Table I. Energy dissipation for transmittingone bit of data at power level l is denoted as El

t x and themaximum transmission range at power level l is denoted asRl

max. If the distance between node-i and node- j is larger thanRl

max (i.e., di j > Rlmax) then they cannot communicate using

power level l. Energy dissipation for receiving one bit of datais constant and denoted as Erx . Each data packet has a headerlength of 168 bits and the maximum packet size is 2040 bits,thus, the maximum data payload per packet is 1872 bits [26].Acknowledgement packet length is 160 bits (L A = 160).

Energy dissipation for computation is comprised of threemain components:

1) data acquisition energy dissipation – E AC Q

2) background energy dissipation – EBC K

3) energy dissipation for processing – ES P


Therefore, computation energy dissipation can be expressed asa sum

EC M P = E AC Q + EBC K + ES P (3)

Power consumption for sensing (including the power con-sumption of both the CPU and the sensor board) in the Mica2motes is measured as PAC Q = 15.01 mW [28]. Acquisitionof an N-byte raw signal requires N CPU operations. Atan operation frequency of 7.4 MHz the Atmega 128L canexecute 7.4 Machine Instructions Per Second (MIPS) 3. [27].Hence, the energy dissipation for acquiring an N-byte signalis obtained as follows:

E AC Q = N PAC Q DO P (4)

Note that most of the instruction set of Atmega 128L areexecuted in a single CPU clock cycle [27]. Furthermore,measurements presented in [29] show that CPU access tovarious peripherals does not draw more current than any otherCPU instruction.

If the raw data is to be communicated without any signalprocessing operation (e.g., the sensors might not be able todo the transform coding operations by themselves) then theenergy dissipation for computation is for signal acquisitiononly as expressed in Equation 5.

EC M P−D AN P = E AC Q (5)

Background energy dissipation does not vary for differentsignal processing techniques. The energy dissipation of varioussources necessary to operate the platform is obtained bymultiplying the power for running the CPU in the idle modePBC K = 9.6 mW [28] by the total CPU utilization time forsignal processing (DS P), as shown in Equation 6

EBC K = PBC K DS P . (6)

The number of operations for a particular signal processingtask determines the amount of CPU time utilized. In otherwords, the background energy dissipation is scaled with theduration of the signal processing operations.

In DATC, a transformation using a transform basis isobtained for signal decomposition, yielding N transform coef-ficients. To obtain a K -sparse approximation of the signal, theK largest values with corresponding locations should be found.Locations and values of the K largest coefficients represent thesignal. In the transform coding process, multiplication with atransform basis requires N2 additions and N2 multiplications.Sorting and selecting large coefficients requires Nlog(N)comparisons. Thus, the computation energy dissipation in thesensor CPU for DATC is expressed as

ES P−D AT C = Nεmrd + N2(εadd + εmul)+NlogN(εcmp + εs f t )+ 2K εmwr , (7)

where εadd (3.30 nJ), εmul (9.90 nJ), εcmp (3.30 nJ), εs f t

(3.30 nJ), εmrd (0.26 nJ), and εmwr (4.30 nJ) are the energydissipation values for addition, multiplication, comparison,shift, read, and write operations (per byte) in the CPU, respec-tively [26], [30]. The total number of operations involved in

3The duration of instruction execution is DO P = 17.4×106

the process is denoted by OS P−D AT C , which has a valueof 2N2 + 2Nlog(N) + N + 2K for this process. Hence,the total time required for this operation is DS P−D AT C =OS P−D AT C DO P

4.The main idea behind compressive sensing is to compres-

sively sense and acquire the signal at its information rate.Hence, the goal is to acquire M random projections of theanalog signal, instead of measuring N � M measurements.Although there is a considerable amount of work on thedevelopment of CS-based sensing hardware, which acquiresmeasurements as linear projections [31]–[33], these effortsare mainly at experimental stage. Moreover, complete energymodels for such hardware platforms are not available. Hence,the CS energy model assumes an N dimensional signalacquired as in the conventional case but the M compressivemeasurements are generated using a multiplication processwith a random M × N Bernoulli (random ± 1) matrix withinour comparison platform. Since the matrix contains onlythe values of ± 1, it requires M N additions in terms ofcomputation cost in addition to the read and write operations.The computation cost for DACS is

ES P−D AC S = Nεmrd + M Nεadd + Mεmwr . (8)

The total number of operations for DACS is OS P−D AC S

= M N + N + M and the time required for DACS isDS P−D AC S = OS P−D AC S DO P .

V. NETWORK MODEL

In this section, we formulate data processing and routingin the network as an MIP framework using the energy modelpresented in Section IV. We apply our models to conventionaland compressive sensing based processing techniques.

In the MIP framework, we assume that there is a singlebase station and multiple sensor nodes (total number of nodesin the network is ζ ). The network topology is represented bya connected graph G = (V , A). V is the set of all nodes,including the base station (node-0). We also define set W ,which includes all nodes except the base station (i.e., W =V \ {0}). A = {(i, j) : i ∈ V , j ∈ V − i, di j ≤ Rl−27

max }is the ordered set of arcs. The total number of data packetstransmitted by node-i to node-j is represented as fi j . The totalnumber of acknowledgement packets transmitted in responseto data packets are represented as gi j . Note that the definitionof A implies that no node sends data to itself or to a node thatis separated from it beyond the maximum transmission rangeRl−27

max .Although there is no data flow from the base station to

any sensor node5, the base station transmit acknowledgementpackets, and, hence the arcs from the base station to the sensornodes are included in the set of arcs. We assume that allnodes are roughly time synchronized and time is organized

4Symbols and acronyms used in the paper and their descriptions arepresented in the appendix (Table II).

5It is possible to use a CSMA/CA type MAC protocol like IEEE 802.15.4in beacon enabled mode for low energy dissipation, where, beacon packetsare periodically transmitted by the base station to synchronize sensor nodes.Such an approach necessitates flow of beacon packets from the base stationto the sensor nodes.


Fig. 1. MIP framework.

into rounds. We also assume that a TDMA-based MAC layeris in operation and a time-slot assignment algorithm outputsa conflict-free transmission schedule. In [34], it is shown thatsuch an algorithm is possible hence collision free commu-nication is achieved if sufficient bandwidth requirements aresatisfied. Each sensor node generates a constant amount ofdata and all generated data is conveyed to the base station ateach round [17].

The optimization problem is formulated as an MIP problem,presented in Figure 1. Since the objective is to maximizenetwork lifetime (H ), our problem is the maximization of theminimum lifetime in the network by finding the flows thatsatisfy the constraints. Note that variable H gives the networklifetime in terms of number of rounds and the actual networklifetime can be expressed by the product H ×Trnd , where Trnd

is the duration of a round. The number of rounds the networksurvives (H ) is a unitless quantity.

Equation 9 and Equation 10 state that all flows are non-negative. Equation 11 is used for flow balancing at the sensornodes and the base station. The sum of data flows relayed tonode-i plus the data generated at node-i is equal to the sumof data flows relayed out to the rest of the network (i.e., toother sensor nodes acting as relays or directly to the basestation). Note that H × si gives the total amount of datagenerated at node-i (si is the number of data packets generatedin each round at node-i ). All data generated by the sensornodes terminate at the base station (the total amount of data

generated in the network is H ×∑i∈W si ). Equation 12 states

that the number of acknowledgement packets on arc ( j, i) isequal to the number of data packets on arc (i, j). Equation 13is used to guarantee that there are no data packets flowingout of the base station. Equation 14 states that for all nodesexcept the base station energy dissipation for communicationand computation is bounded by the energy stored in batteries(�). In the analysis, we use � = 25 KJ (energy provided bytwo AA batteries) [29]. The optimal transmission energy valueis found using Equation 16. For instance, for di j = 20 m,since 19.30 m < di j ≤ 20.46 m, node-i uses power level 2 totransmit data on its link to node- j (i.e., Eopt

t x,i j = 0.688 μJ).Both the number of data bytes generated at each round andcomputation energy dissipation at each round are determinedby the data representation approach selected. Lifetime of anetwork ends when the first node exhausts its energy. However,this definition should not be misinterpreted – when we exam-ine the framework carefully it can be seen that to maximizethe minimum lifetime, all nodes are forced to dissipate theirenergies in a balanced fashion, hence, sensor nodes in thenetwork deplete their battery energies simultaneously.

Eoptt x,i j =

⎧⎨

⎩

El−1t x if di j ≤ Rl−1

max∞ else if di j > Rl−27

maxEl+1

t x else if Rlmax < di j ≤ Rl+1

max

(9)

To take channel bandwidth limitations into consideration ina broadcast medium, we need to make sure that the bandwidthrequired to transmit and receive at each node is limited by thechannel bandwidth. Such a constraint should take the sharedcapacity into consideration. We refer to the flows around node-i (both data and acknowledgement), which are not flowing intoor flowing out of node-i and affect the available bandwidthto node-i , as interfering flows. Equation 15 guarantees thatfor all nodes including the base station the aggregate rateof incoming flows, outgoing flows, and interfering flows isupper bounded by the channel bandwidth. This constraint isa modified version of the sufficient condition given in [34].The interference function (I i

j l) is presented in Equation 17. Ifnode-i is in the interference region of the transmission fromnode- j to node-l, then the value of interference function fornode-i (I i

j l) is unity, otherwise it is zero. Generally speaking,interference range is equal to or greater than transmissionrange (i.e., γ ≥ 1). This means depending on the value ofγ , node- j ’s transmission to node-l can interfere with node-ieven if the distance between node- j and node-l is less thanthe distance between node- j and node-i .

I ij l =

{1 if γ d jl ≥ d j i ∀ j ∈ V \ {i},∀l ∈ V \ {i, j}0 otherwise

(10)

WSNs are assumed to be consisting of stationary sensornodes, thus, topology discovery, route creation, and otherinitialization operations (e.g., measurement matrix dissemi-nation) are one-time operations – for a substantial amountof time these functions are not repeated. If the networkreorganization period is long enough, the energy costs of theseoperations constitute a small fraction (less than 1%) of the totalnetwork energy dissipation [35]. Hence, routing overhead canbe neglected in stationary WSNs without leading to significant


underestimation of total energy dissipation. We opt to keepour model as simple as possible to eliminate the shadowingeffects of implementation details not specifically related to theconcept under investigation, per se.

VI. ANALYSIS

In this section, we first perform numerical analysis withvarious sparsity levels to determine the required number ofmeasurements for CS to reconstruct the acquired signal. Thel1-magic packet [36] is used to solve the signal recovery prob-lem. It is a collection of MATLAB routines for solving the con-vex optimization programs central to compressive sampling.We first use these results together the developed computationand communication energy dissipation models to investigatethe effects of DANP, DATC, and DACS on network lifetimewithout considering data routing (i.e., communication andcomputation energy dissipation characteristics for a single sen-sor node is investigated). Later, we systematically explore andcompare the aforementioned processing approaches’ effects onWSN lifetime by sampling the parameter space through theconstructed MIP model, which can model both computationand communication energy dissipation terms within a unifiedframework.

We use the General Algebraic Modeling System (GAMS)[37] for numerical analysis of MIP models. GAMS is a high-level modeling system for mathematical programming andoptimization. It consists of a language compiler and integratedhigh-performance solvers. GAMS is used widely for complex,large scale modeling applications.

To determine the energy consumption of a wireless nodeemploying CS for a given signal of dimension N and sparsitylevel K , the required number of measurements M for correctreconstruction is needed. CS theory defines this measurementnumber M as in the order of K log N [7]. In the literature, therequired number of measurements for correct reconstructionwith CS is a studied topic and phase transition curves explain-ing these relations are obtained [38]. For the sake of com-pleteness, we perform numerical analysis to determine M as afunction of K and N . A signal of length N = 512 is taken withsparsity levels K varying between 20 to 200. For each sparsitylevel K , M compressive measurements are produced usinga random Bernoulli/Rademacher (random ±1) measurementmatrix of dimension M × N . Measurement numbers between20 and 512 are tested and the signals are reconstructed usingthe �1 minimization problem defined in Equation 2. Thesenumerical experiments are run 500 times with independentrandom sparse signal and measurement matrix selections andthe number of correct reconstructions are counted. Figure 2shows the correct reconstruction ratio as a function of numberof measurements for different sparsity levels.

The required number of measurements for each spar-sity level is estimated from the numerical experiments asM ≈ 1.5K log N which is consistent with results in theliterature. This relation is also tested with different signaldimensions N and successful recoveries for all cases areobserved. This level of M is sufficient to recover a K sparsesignal perfectly for all sparsity levels K used with CS. Hence,

50 100 150 200 250 300 350 400 450 5000

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Tru

e re

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truc

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K=20K=30K=40K=50K=60K=80K=100K=120K=140K=160K=180K=200

Fig. 2. True reconstruction ratio as a function of number of measurementsfor different sparsity levels.

0.05 0.1 0.15 0.2 0.25

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Ene

rgy

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(J)

DACS (50 m)DACS (100 m)DATC (50 m)DATC (100 m)DANP (50 m)DANP (100 m)

Fig. 3. Total energy consumption of a wireless sensor node using DANP,DATC, and DACS approaches for transmitting to ranges (1) 50 and (2) 100 m.

in the rest of our analysis, M = 1.5K log N is used for theCS energy model computations.

To have a basic understanding of the tradeoffs involvedin communication and computation without the shadowingeffects of routing, first, the energy dissipation of a singlewireless sensor node for acquisition, processing, and commu-nication of N = 1024 bytes of data as a function of level ofsparsity is analyzed. The DANP, DATC, and DACS approachesas detailed in Section IV are compared. Two transmissionranges of 50 m and 100 m are utilized, where the sensornode transmits data by using l-18 and l-27, respectively.Communication energy dissipation is due to data transmissionand acknowledgement reception. Figure 3 presents energyconsumption as a function of sparsity ratio K/N .

We observe that the energy consumption levels for DACSand DATC increases with the sparsity level of the signal, while


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(c) (d)

Fig. 4. Normalized network lifetime as a function of ζ with Rnet = 100 m. (a) K/N = 0.05. (b) K/N = 0.10. (c) K/N = 0.15. (d) K/N = 0.20.

the energy consumption level of DANP stays constant sinceit transmits all the acquired N data samples independent ofthe signal sparsity. Another observation is that the energyconsumption for DACS is lower as compared to both DATCand DANP, provided that the signal is sparse enough (i.e.,K/N < 0.15) for both ranges. On the other hand, for non-sparse signals, using CS is not advantageous. The energyconsumption level of DATC is higher when compared toDACS due to the transform coding operations needed to becompleted before transmitting. However, due to the highercommunication energy dissipation of DACS, for transmissionsover longer distances, DATC has better energy efficiency. Toinvestigate the effects of different approaches on networklifetime, we use the MIP model introduced in Section V.We use a disk topology with radius Rnet . Sensor nodes arerandomly deployed and uniformly distributed on the networkarea. The base station is at the center of the disc. Each problemis solved for 200 random topologies and the average networklifetimes are obtained. Normalized network lifetime resultsfor varying levels of sensor node number and network radius

for sparsity levels of K/N = 0.05, 0.10, 0.15, and 0.20 aregiven. Normalization is achieved by dividing all data points ina figure by the largest value.

Figure 4 presents normalized network lifetime as a func-tion of the number of nodes when the network radius isfixed to 100 meters for different sparsity levels. DACS hasthe highest network lifetime throughout the whole parameterspace. Especially for sparser signals (e.g., K/N = 0.05)network lifetimes obtained with DACS is much larger than thelifetimes obtained with other approaches (e.g., DACS approachcan result in a lifetime improvement of up to 4 times overDATC approach for ζ = 50 and K/N = 0.05). However,as the sparsity level increases the difference between thenetwork lifetimes obtained with CS and with other approachesdecreases (e.g., network lifetimes of DACS and DANP arewithin 15% neighborhood of each other for K/N = 0.20).Network lifetime increases for all approaches with increasingnumber of nodes, since increasing the number of nodes for afixed network radius Rnet increases the node density, whichcreates more paths towards the base station (i.e., number


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of neighbor nodes increase). Larger network lifetimes canbe obtained with richer routing options available in stronglyconnected networks. Furthermore, increasing the node densitydecreases the average hop distance. Note that transmissionenergy dissipation increases as the distance between thetransmitter and the receiver increases. In summary, Figure 4shows that:

1) WSN lifetime is significantly prolonged by DACS incomparison to conventional approaches (DATC andDANP) for all values of the number of nodes in thenetwork. Efficiency of compressive sensing in reducingcomputation energy dissipation is the key factor insuperior energy efficiency of DACS.

2) Lifetime gains obtained by DACS is higher for lowerK/N because, as characterized in Figure 3, energydissipation for DACS increase as the ratio K/Nincrease.

Figure 5 presents normalized network lifetime as a functionof network radius for varying sparsity levels (ζ = 50). For allvalues of K/N except K/N = 0.20, DACS network lifetime

is larger than the lifetimes obtained with other approachesprovided that Rnet ≤ 150 m (e.g., DACS approach can resultin a lifetime improvement of up to 4 times over DATC andDANP approaches for Rnet = 100 m and K/N = 0.05).DATC outperforms DACS for larger values of network radius(i.e., Rnet ≥ 250 m for K/N = 0.05, Rnet ≥ 200 mfor K/N = 0.10, Rnet ≥ 150 m for K/N = 0.15, andRnet ≥ 150 m for K/N = 0.20) with respect to networklifetime. DANP has longer network lifetime values for smallernetwork radii and high K/N (Rnet ≤ 50 m for K/N = 0.20).Network lifetime decreases as Rnet increases because theaverage hop distance increases, which results in increasedcommunication cost. Furthermore, increasing network areawhile keeping the number of nodes constant leads to a decreasein the number of neighbors per node. This limits the energybalancing capabilities of the network. In summary, Figure 5shows that DACS provides longer network lifetimes in densernetworks with lower K/N because in such circumstanceslower energy dissipation of DACS on computation can com-pensate its higher communication energy dissipation resultingin lower overall energy dissipation.


VII. CONCLUSION

In this study, the energy dissipation characteristics of WSNsutilizing the concepts of compressive sensing is investi-gated and compared to two other well known conventionalapproaches (DANP and DATC). A model to quantify theenergy dissipation in sensor nodes due to data acquisition,computation, and communication for the compared methodsis developed using the measured characteristics of the Micasensor network platform. By using the created energy dissipa-tion models an MIP framework is built. The MIP frameworkmodels both computation and communication aspects within aunified framework. A systematic exploration of the parameterspace, including sparsity level, node density, and network size,to characterize the energy dissipation and network lifetimeperformances of CS-based (DACS) and conventional (DANPand DATC) approaches is performed. Our results show thatcompressive sensing prolongs network lifetime significantlyin comparison to conventional approaches provided that theacquired signals are highly sparse (e.g., K/N ≤ 0.10) andnode density in the network is not too low (e.g., Rnet ≤ 150 mand ζ = 50).

APPENDIX

TABLE II

SYMBOLS/ACYRONYMS AND THEIR DESCRIPTIONS

Sym/acy Description

x Vector representing acquired signal

ψ i Basis vector in RN

� Basis matrix

s Transform domain vector

N Total number of unknowns

M Total number of measurements in CS

K Number of nonzero coefficients

y CS measurements in RM

� CS measurement matrix in RM×N

ECMP Computation energy dissipation

ECOM Communication energy dissipation

Elt x Transmission energy dissipation at level l

Rlmax Maximum transmission range at level l

di j Distance between node-i and node- j

Erx Reception energy dissipation (0.923 μJ/bit)

ς Channel bandwidth (38.4 Kb/s)

L P Actual data packet length

L A ACK packet length (160 b)

EACQ Data acquisition energy dissipation

EBCK Background energy dissipation

ESP Signal processing energy dissipation

PACQ Sensing power consumption (15.01 mW)

DOP Instruction execution duration (0.14 μs)

ECMP-DANP Computation energy dissipation for DANP

DSP Signal processing CPU utilization time

ESP-DATC Computation energy dissipation for DATC

εadd Energy dissipation for addition (3.30 nJ)

εmul Multiplication energy dissipation (9.90 nJ)

εcmp Comparison energy dissipation (3.30 nJ)

Sym/acy Description

εsft Shift energy dissipation (3.30 nJ)

εmrd Memory read energy dissipation (0.26 nJ)

εmwr Memory write energy dissipation (4.30 nJ)

OSP-DATC Total number of operations for DATC

DSP-DATC Total time for DATC

ESP-DACS Computation energy dissipation for DACS

OSP-DACS Total number of operations for DACS

DSP-DACS Total time for DACS

ζ Total number of nodes in network

V Set of nodes, including the base station

W Set of nodes, except the base station

A Set of arcs

fi j Data flow from node-i to node-j

gi j ACK flow from node-i to node-j

H Network lifetime

Trnd Duration of a round (500 s)

si Data generated at node-i per round

� Battery energy of each node (25 KJ)

Eopttx,i j Optimum transmission power

I ijk Interference function

γ Interference factor (1.7)

Rnet Disk radius

REFERENCES

[1] I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, “Wirelesssensor networks: A survey,” Comput. Netw., vol. 38, no. 4, pp. 393–422,Mar. 2002.

[2] W. Heinzelman, A. Chandrakasan, and H. Balakrishnan, “An applicationspecific protocol architecture for wireless microsensor networks,” IEEETrans. Wireless Commun., vol. 1, no. 4, pp. 660–670, Oct. 2002.

[3] G. Anastasi, M. Conti, M. D. Francesco, and A. Passarella, “Energyconservation in wireless sensor networks: A survey,” Ad Hoc Netw.,vol. 7, no. 3, pp. 537–568, May 2009.

[4] K. Akkaya and M. Younis, “A survey on routing protocols for wirelesssensor networks,” Ad Hoc Netw., vol. 3, no. 3, pp. 325–349, May 2005.

[5] D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron,S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compres-sive imaging camera architecture using optical-domain compression,”in Proc. Comput. Imaging IV, SPIE Electron. Imaging, Jul. 2006,pp. 43–52.

[6] D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory, vol. 52,no. 4, pp. 1289–1306, Apr. 2006.

[7] E. J. Candes, J. Romberg, and T. Tao, “Robust uncertanity principles:Exact signal reconstruction from highly incomplete frequency informa-tion,” IEEE Trans. Inf. Theory, vol. 52, no. 2, pp. 489–509, Feb. 2006.

[8] J. Haupt, W. U. Bajwa, M. Rabbat, and R. Nowak, “Compressedsensing for networked data,” IEEE Signal Process. Mag., vol. 25, no. 2,pp. 92–101, Mar. 2008.

[9] X. Wang, Z. Zhao, Y. Xia, and H. Zhang, “Compressed sensing forefficient random routing in multi-hop wireless sensor Network,” Int. J.Commun. Netw. Distrib. Syst., vol. 7, no. 3–4, pp. 275–292, Sep. 2011.

[10] H. Mamaghanian, N. Khaled, D. Atienza, and P. Vandergheynst, “Com-pressed sensing for real-time energy-efficient ECG compression onwireless body sensor nodes,” IEEE Trans. Biomed. Eng., vol. 58, no. 9,pp. 2456–2466, Sep. 2011.

[11] W. Chen and I. J. Wassell, “Energy efficient signal acquisition viacompressive sensing in wireless sensor networks,” in Proc. Int. Symp.Wireless Pervasive Comput., Feb. 2011, pp. 1–6.

[12] G. Cao, F. Yu, and B. Zhang, “Improving network lifetime for wirelesssensor network using compressive sensing,” in Proc. IEEE Int. Conf.High Perform. Comput. Commun. (HPCC), Sep. 2011, pp. 448–454.

[13] R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows: Theory,Algorithms, and Applications. Englewood Cliffs, NJ, USA: Prentice-Hall, 1993.


[14] D. Baron, M. B. Wakin, M. F. Duarte, S. Sarvotham, and R. G. Baraniuk,“Distributed compressed sensing,” Rice Univ., Dept. Electr. Comput.Eng., Tech. Rep. TREE-0612, 2006.

[15] F. Fazel, M. Fazel, and M. Stojanovic, “Random access compressedsensing for energy-efficient underwater sensor networks,” IEEE J. Sel.Areas Commun., vol. 29, no. 8, pp. 1660–1670, Sep. 2011.

[16] S. Mehrjoo, J. Shanbehzadeh, and M. M. Pedram, “A novel intelligentenergy-efficient delay-aware routing in WSN, based on compressivesensing,” in Proc. Int. Symp. Telecommun., Dec. 2010, pp. 415–420.

[17] L. Xiang, J. Luo, and A. Vasilakos, “Compressed data aggregationfor energy efficient wireless sensor networks,” in Proc. Annu. IEEECommun. Soc. Conf. Sensor, Mesh Ad Hoc Commun. Netw., Jun. 2011,pp. 46–54.

[18] C. Caione, D. Brunelli, and L. Benini, “Distributed compressive sam-pling for lifetime optimization in dense wireless sensor networks,” IEEETrans. Industrial Informatics, vol. 8, no. 1, pp. 30–40, Feb. 2012.

[19] M. Sartipi and R. Fletcher, “Energy-efficient data acquisition in wirelesssensor networks using compressed sensing,” in Proc. Data Compress.Conf., 2011, pp. 22–232.

[20] Z. Charbiwala, Y. Kim, S. Zahedi, J. Friedman, and M. B. Srivastava,“Energy efficient sampling for event detection in wireless sensor net-works,” in Proc. 14th ACM/IEEE Int. Symp. Low Power Electron.Design, 2009, pp. 419–424.

[21] F. Ishmanov, A. S. Malik, and S. M. Kim, “Energy consumptionbalancing (ECB) issues and mechanisms in wireless sensor networks(WSNs): A comprehensive overview,” Eur. Trans. TeleCommun., vol. 22,no. 4, pp. 151–167, Feb. 2011.

[22] A. Gogu, D. Nace, A. Dilo, and N. Meratnia, “Review of optimiza-tion problems in wireless sensor networks,” in Proc. TeleCommun.Netw.–Current Status Future Trends, New York, USA: InTech, 2012,pp. 153–180.

[23] J. Haupt and R. Nowak, “Signal reconstruction from noisy randomprojections,” IEEE Trans. Inf. Theory, vol. 52, no. 9, pp. 4036–4048,Sep. 2006.

[24] E. Candès, J. Romberg, and T. Tao, “Stable signal recovery fromincomplete and inaccurate measurements,” Commun. Pure Appl. Math.,vol. 59, no. 8, pp. 1207–1223, Mar. 2006.

[25] J. Vales-Alonso, E. Egea-Lopez, A. Martínez-Sala, P. Pavon-Marino,M. V. Bueno-Delgado, and J. García-Haro, “Performance evaluation ofMAC transmission power control in wireless sensor networks,” Comput.Netw., vol. 51, no. 6, pp. 1483–1498, Apr. 2007.

[26] V. Lecuire, C. Duran-Faundez, and N. Krommenacker, “Energy-efficientimage transmission in sensor networks,” Int. J. Sensor Netw., vol. 4,no. 1–2, pp. 37–47, 2008.

[27] K. Bilinska, M. Filo, and R. Krystowski. (2007).Mica, Mica2, MicaZ [Online]. Available: www.pub.zih.tu-dresden.de/dargie/wsn/slides/students/MICA.ppt

[28] V. Shnayder, M. Hempstead, B. Chen, G. W. Allen, and M. Welsh,“Simulating the power consumption of large-scale sensor networkapplications,” in Proc. ACM Conf. Embedded Netw. Sensor Syst., 2004,pp. 188–200.

[29] O. Landsiedel, K. Wehrle, and S. Gotz, “Accurate prediction of powerconsumption in sensor networks,” in Proc. IEEE Workshop EmbeddedNetw. Sensors, May 2005, pp. 37–44.

[30] Y. Liang and W. Peng, “Minimizing energy consumptions in wirelesssensor networks via two-modal transmission,” ACM Comput. Commun.Rev., vol. 40, no. 1, pp. 12–18, Jan. 2010.

[31] R. Robucci, J. D. Gray, L. K. Chiu, J. Romberg, and P. Hasler,“Compressive sensing on a CMOS separable-transform image sensor,”Proc. IEEE, vol. 98, no. 6, pp. 1089–1101, Jun. 2010.

[32] X. Chen, Z. Yu, S. Hoyos, B. M. Sadler, and J. Silva-Martinez, “A sub-nyquist rate sampling receiver exploiting compressive sensing,” IEEETrans. Circuits Syst. I, Regular Papers, vol. 58, no. 3, pp. 507–520,Mar. 2011.

[33] F. Chen, A. P. Chandrakasan, and V. Stojanovic, “Design and analysis ofa hardware-efficient compressed sensing architecture for data compres-sion in wireless sensors,” IEEE J. Solid-State Circuits, vol. 47, no. 3,pp. 744–756, Mar. 2012.

[34] M. Cheng, X. Gong, and L. Cai, “Joint routing and link rate allocationunder bandwidth and energy constraints in sensor networks,” IEEETrans. Wireless Commun., vol. 8, no. 7, pp. 3770–3779, Jul. 2009.

[35] K. Bicakci, H. Gultekin, and B. Tavli, “The impact of one-time energycosts on network lifetime in wireless sensor networks,” IEEE Commun.Lett., vol. 13, no. 12, pp. 905–907, Dec. 2009.

[36] J. Romberg. (2005). �1magic-recovery of sparse signals [Online]. Avail-able: http://users.ece.gatech.edu/justin/l1magic/

[37] J. Kallrath, Modeling Languages in Mathematical Optimization. Boston,MA, USA: Kluwer, 2004.

[38] D. L. Donoho, “The noise-sensitivity phase transition in compressedsensing,” IEEE Trans. Inf. Theory, vol. 57, no. 10, pp. 6920–6941, Oct.2011.

Celalettin Karakus received the B.S. degree in elec-trical and electronics engineering from the TOBBUniversity of Economics and Technology, Ankara,Turkey, in 2010. He is currently pursuing the M.S.degree under the supervision of Dr. Tavli and Dr.Gurbuz.

He was a Research and Teaching Assistant with theElectrical and Electronics Engineering Departmentfrom 2010 to 2011. Since then, he has been withRoketsan Missiles Industries Inc., Ankara, where heis currently an Avionics System Design and Test

Engineer. His current research interests include signal processing, compressivesensing, and wireless sensor networks.

Ali Cafer Gurbuz received the B.S. degree inelectrical and electronics engineering from BilkentUniversity, Ankara, Turkey, in 2003, and the M.S.and Ph.D. degrees from the Georgia Institute ofTechnology (Georgia Tech), Atlanta, GA, USA, in2005 and 2008, respectively, both in electrical andcomputer engineering.

He participated in multimodal landmine detectionsystem research as a Graduate Research Assistantfrom 2003 to 2008 and from 2008 to 2009, as Post-Doctoral Fellow, with Georgia Tech. He is currently

an Assistant Professor with the Department of Electrical and ElectronicsEngineering, TOBB University of Economics and Technology, Ankara. Hiscurrent research interests include compressive sensing applications, groundpenetrating radar, array signal processing, remote sensing, and imaging.

Bulent Tavli received the B.S. degree in electri-cal and electronics engineering from Middle EastTechnical University, Ankara, Turkey, in 1996, andthe M.S. and Ph.D. degrees in electrical and com-puter engineering from the University of Rochester,Rochester, NY, USA, in 2001 and 2005.

He is currently an Associate Professor with theDepartment of Electrical and Electronics Engineer-ing, TOBB University of Economics and Technol-ogy, Ankara, Turkey. His current research inter-ests include telecommunications, networking, signal

processing, and embedded systems.

Documents

Analysis of Energy Efficiency of Compressive Sensing in Wireless Sensor Networks