ENABLING DELAY-SENSITIVE APPLICATIONS OVER SENSOR NETWORKSUSING A TWO-TIER ARCHITECTURE AND MULTI-ANTENNA CLUSTER HEADS

L. Liu, J.-F Chamberland K. Qaraqe

ECE Department ECE DepartmentTexas A&M University Texas A&M University at Qatar

College Station, TX 77843-3128, USA Doha, 23874, Qatar

ABSTRACT devices with one antenna each, whereas the cluster heads aremore powerful units that can be equipped with multiple an-The timely processing and dissemination of information overtennas.wireless sensor networks is a key aspect of their future suc- Wirelss

cess. This is especially important for delay-sensitive applica- fere les, aretsubjec to stringtde contrainttions such as detection and estimation. This paper assumes a tference problems are subject to stringent delay constraints.

two-tier architecture for wireless sensor networks where sen- thati taddt th k Isor nodes are simple devices equipped with one antenna, and reduce congesion an eay in e networ. n particu-cluster heads are more powerful units endowed with multiple lar delay restrictions imposed on a sensor network may pre-antennas each. The cluster heads collect information from the dude the use of long error-correcting codes, thereby forcingsensor nodes, process data locally, and then relay pertinent in- the system to operate away from its Shannon limit. Sev-formation across the network. This article studies the poten- eral notable contributions on the delay/throughput tradeoff in

wireless systems have improved our understanding of delay-sensitive communications [1, 2, 3]. Still, the literature on thison the data collection and dissemination operations. The fo-'

cus ishondelaylentivetafcandperfeminopermanc is.measre topic is not fully developed; some aspects of delay-sensitiveCUS iS on delay-sensitive traffic, and performance iS measured comncain dean futenesiainin terms ofeffective nalysis shows that, fr Gas communications demand further investigation.intermsofeffectivecapacity. AnalysisshowsthHerein, we study the interplay between the physical layersian channels, having multiple antennas at the receiver results infrastructure and the queueing behavior of a wireless sensor

in a power gain, while having multiple antennas at the trans- network. Due to the time-varying nature of wireless chan-mitter provides a statistical gain. In both scenarios, the data nels, .rate that a wireless channel can support is increased signif- iguarantees for specific links. Accordingly, we use a popu-icantly through the use of multiple antennas at the cluster garantees for ic lns accoringy,me useapouhead. Numerical results confirm that the gains of a multiple- careueing metricf erforane assessmenth r

captures the asymptotic decay-rate of buffer occupancyantenna configuration over a single-antenna link are substan-tial for delay-sensitive applications. This provides support for log Pr {L >4(the two-tier architecture studied in this paper and for cluster 0 =- mxrheads having multiple antennas. where L denotes the queue-length distribution of the buffer

present at the transmitter. The parameter 0 reflects the per-1. INTRODUCTION ceived quality of a communication link. A larger 0 represents

a better connection for delay-sensitive applications. This per-Our work is inspired by the vision that future wireless sensor formance metric is closely related to the concepts of effectivenetworks may feature a two-tier architecture. The envisioned bandwidth [4] and effective capacity [5].networks consist of a more capable wireless core coupled to a It is well-known that the use of antenna arrays can signifi-wide array of wireless sensors that gather information locally. cantly increase the diversity [6] or the Shannon capacity [7] ofSensor nodes form small-scale clusters where data packets are wireless connections. We seek to identify the potential ben-transferred between nodes and, ultimately, to a nearby cluster efits of a multiple-antenna configuration for delay-sensitivehead. The cluster heads are then responsible for processing traffic over sensor networks. Specifically, we are interested inthe data and for further disseminating relevant information the situation where only one of the wireless agents (namelyacross the network. In our model, sensor nodes are simple the cluster head) is equipped with an antenna array. To in-

This work was supported in part by the Qatar Foundation for Education, srththeenifominisecvdcretlathee-Science, and Community Development, and by Qatar Telecom (Qtel), Qatar. tination, we assume that a feedback mechanism between theThis paper is dedicated to the memory of Sergio Servetto. sensors and their respective cluster heads provides support for

978-1-4244-1714-8/07/$25.OO ©007 IEEE 301

acknowledgments. Expressions for the effective capacities of can be designed if the receiver has the ability to acknowledgesingle-antenna and vector Gaussian channels are derived un- reception of the data to ensure that the erroneous data is re-der a block fading model. Our results suggest that there are transmitted [9, 10].substantial benefits in using multiple antennas at the cluster We denote the number of transmit antennas by nT and theheads for delay-sensitive applications. At low SNRs, just as number of receive antennas by nR. In the case where a sensorthere is a power gain associated with using multiple receive node is transmitting to its cluster head, nT = 1. Conversely,antennas in terms of ergodic capacity [8], there is a statisti- when the cluster head sends data to a sensor node, nR = 1.cal gain associated with using multiple transmit antennas in Let x denote the nT X 1 vector of transmitted symbols, and yterms of effective capacity. This suggests that antenna arrays be the nR X 1 vector of received signals. Then,are especially suitable for delay constrained communicationand hence wireless sensor networks. y = Hx + n,

where H is an nR X nT complex matrix, and n is an nR X 12. SYSTEM AND PERFORMANCE vector of additive white Gaussian noise. The element hij of

H denotes the channel gain from transmit antenna j to re-The effective capacity denotes the maximum constant arrival ceive antenna i. We assume that the {hij} 's are independentrate a system can support subject to a buffer-occupancy re- and identically distributed (i.i.d.) zero-mean complex Gaus-quirement specified by 00. Consider the situation where the sian random variables with unit variance. For a fixed H, thewireless channel is subject to block fading. That is, the chan- mutual information between x and y is given by [7]nel coefficients stay invariant within a block of duration T,but vary independently from block to block. Let r be a ran- I (H, P) = WT log (1 + H 2P/InTNoW)dom variable that represents the system throughput duringone block, the effective capacity of the service process is de- where H 2 denotes the 12 norm of the channel vector H.fined by

a (0) -(1/OT) log E [e-r] (2) 2.1. Single-Antenna System

If the arrival rate a satisfies a < a (0o) then the exponent In the situation where the service process is governed by a0 defined in (1) satisfies 0 > Oo [4]. This characterization single-input single-output (SISO) channel, the channel vectoris tight; the decay requirement Oo is satisfied if and only if H reduces to a scalar h for every block. The channel capacitya < a (Oo). r during each block can be expressed as

Fact 1. Thefunction a(0) is monotonically decreasing. r = WTlog (I + Ih 2P/NoW) nats per second, (3)

Fact 1 implies that the maximum admissible arrival rate where No/2 denotes the power spectral density of the noisedecreases as the service requirement Oo becomes more strin- process. The moment generating function of the service pro-gent. This reveals a fundamental tradeoff between system cess E [e-Or] can be written as follows,throughput and queueing performance.

Fact 2. The effective capacity is upper bounded by E[r]/T. e r (P/NoW)-OWT F (1 - OWT, NoW/P)Also, if r > ,T almost surely for some constant ', then where F (z, x) is the upper incomplete gamma function. The(0) . K. effective capacity for the SISO system can be obtained as

Fact 2 provides two nontrivial bounds for the effective a (0) W log (P/NoW)capacity of a wireless system. Specifically, the effective ca-pacity is upper bounded by the ergodic capacity and lower (1/OT) (log (F (1 -WT, N0W/P)) + N0W/P)bounded by the minimum instantaneous service rate of the In the low SNR regime, as is the case with sensor networks,underlying wireless channel. the nature of the effective capacity for the SISO system can be

We now study the effective capacities of single-antenna seen more clearly. At low SNRs, the approximation log(1 +and multiple-antenna channels under Rayleigh block fading. s s holds and the effective capacity can be expressed asSuppose that the wireless sensor node (or cluster head) has amean power constraint P and a total spectral bandwidth al- a (0) = (I/ST) log (I + OTPINo) . (4)location W. Also, a large buffer is available at each wire-less agent, where outgoing packets are stored before being When the mean received power P is small, the system istransmitted to their destination. We assume that a transmitter operating in the power-limited regime and this first-order ap-sends uncorrelated circularly symmetric zero-mean complex proximation is very accurate. To further our understanding ofGaussian signals of equal power across all the transmit an- the SISO system, we analyze (4) in both the delay-insensitivetennas [7]. Practical implementations with near optimal rates regime and the delay-intolerant asymptotics. In the low SNR

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regime, the effective capacity converges to the ergodic capac- Comparing (6) with (4), we find that the use of multiple re-ity of the wireless system as 0 { 0, ceive antenna results in a power gain of nR.

The effective capacity and the low SNR approximation oflima(0 ) P/No F [Wlog (1 + h 2P/NoW)]. this SIMO system appear in Fig. 1 for P = 10 mW, W = 1

As 0 T oc, the effective capacity of the SISO system vanishes, MHz, T 5 is, and No 10-6 W/Hz. We note that the

limOTO a(O) = 0. Thus, this sensor network cannot support 102delay-intolerant traffic. For any arrival rate e > 0, there exits .....i.....i...i ..i...i...i- SISO systema non-negligible probability that e exceeds the instantaneous -f-Low SNR approximationsystem capacity r in (3). These findings are hardly surprising =.2 SIMO systemin the light of Fact 2. cap.acit Low SNR approximation

Define the first-order derivative of the effective capacity =3 M systemas the decay function of the wireless link, .Low SN approxima

a' (0) 1g(+N ..~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.......

The magnitude of this function indicates the decay speed of 100a(0) as 0 increases. Let p--lmrn10 ag' (0), denote the ini- 0 0.2 0.4 0.6 0.8 1tial decay-rate of the effective capacity for the correspondingwireless system. We note that the initial decay-rate for the Exoeta eqieet0SIS0 system (which will soon be useful) is equal to Fig. 1. Effective capacity for SIMO systems.

PoSISO= TP2/2NO2 (5)approximation of the effective capacity for the SIMO system

2.2. Multiple-Antenna Systems in the low SNR regime is quite accurate. Furthermore, the

Next, we explore the more general situation where the ser- effective capacity of the SIMO system scales linearly with thevice process of a wireless system is governed by a multiple- number of receive antennas for all service constraint 0o. Thisantenna channel. The effective capacity for such channels is result can be viewed as an extension of the statement that theobtained based on the moment generating function of its mu- ergodic capacity of the SIMO system scales linearly with nhRtual information. The performance gains of the vector Gaus- in the low SNR regime [8].sian systems over the SIS0 configuration are evaluated in the In the situation where the service process is governed bylow SNR regime. Our results suggest that, at low SNRs, a a multiple-input single-output (MISO) channel (ThT transmitmultiple receive antenna configuration provides a power gain antennas and one receive antenna), the channel matrix H=of nhR and a multiple transmit antenna configuration provides [h,1, . .., hi,nTJ becomes a 1 x ThT vector of i.i.d. complexa statistical gain of nhT over a single-antenna system. Gaussian random variables. The realized system throughput

Consider the situation where the wireless link has one of the MISO channel during each block can be expressed astransmit antenna and nhR receive antennas. The channel ma- -/ Ttrix of this single-input multiple-output (SIMO) system H=.r=.WT.log (i + E h..k.2..[h11,, . . ., hR,il]T becomes an nhR Xl vector of i.i.d. complex k...' NoW.T)Gaussian random variables. During each block, the realizedsystem throughput can be expressed as Using the low SNR approximation and the independence as-

fnc i t ssumption between the components of H, F [e-r] simplifiesr =WTlog ( l+Z htk,l2NPW) nats per second. to

Using the low SNR approximation and the fact that the com- [ 6e < e0.h2d h 2] 0.(1 0+TP/No ITTponents of the channel vector H are independent, F[epor]can be expressed as The effective capacity of the service process for the MISO

[JOsystem (which 2llsoon be useful) is equal to Fig. Effsystem can then be expressed asFJ e N,, e-lh~ dh 21 =(1 + 0TP/No) n'.

psLs = a2(0) N(2T/OT)log(1 + OTP/NOT) (7)Accordingly, the effective capacity of the SIMO system in thelow SNR regime iS found t o be

antenna case is not entirely obvious by looking at (4) and (7).(0) =(mR/OT) log (1 +sTP/Nw)e (6) As such, we compare the values of the effective capacity in

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two asymptotic regimes for the service requirements. We 102know that, without power allocation, having multiple trans- -............ SISO system lmit antennas does not increase the ergodic capacity at low Low MSN approximatiSNRs [8]. This can also be seen by evaluating the effective T = 2 MISO systemcapacityas 0 { 0, Low SNR approximationcapacity as C; 0,

t l_ _ n =3MISO system

o~~~oN0 NOWThT/J~~n 1p n p 1c) 1 0 Low SNR approximation

i a 0( ) - (4E+Wog 1T0P+ (i + capacityZ fr S

01 (0) N0Wn .N....+.0TP.

However, there is a statistical gai nof nTdassociated with a - -multiple transmit antenna configuration. Th(8) SNR ri htsistgaint a n

is seen more clearly from the decay function of the effective 0 0.2 0.4 0.6 0.8 1capacity. The decay function of the MISO system is given by Eepeialhelulrelen steo

nTOTP ~ ~~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~xonna -eurmn (Nn2+nOP0lgI T

t n tennasy TTi imple tha hNang t Fig. 2. Erffctive capacity for MISO systems.02T (NonT + OTP)

and the initial decay-rate of the corresponding effectiveca-pacit

as ~ ~ ~~ ~ ~ ~ ~ ~ ~ ~~ytmaerfunctionzedofr0.sltThisstatiseseillleeicaeoadlysns-4rEFRNE

tivetric.nes be tradeoff between throughput and service quality. In the low

PMhSo = Tp2/2nTNhlow SNR regime, having multiple transmit antennas can provide againoftheMSOsystemoverthestatistical gain of nT, while multiple receive antennas result in

Comparing (5) and (8), we find that the decay-rate of the ef- a power gain of nR. This result suggests that multiple-antennafective capacity for the MISO system is n-1 times that of configurations are especially helpful for delay-sensitive com-the single-antenna system. This implies that having multiple munication over wireless sensor networks.transmit antennas reduces the decay of the effective capacityas a function of 0. This is especially beneficial for delay sensi- 4. REFERENCEStive traffic. Since both the SIMO system and the SISO systemhave the same ergodic capacity in the low SNR regime, we [1] A. Ephremides and B. Hajek, "Information theory andecommu-define the statistical gain of the MISO system over the single- nication networks: An unconsummated union," IEEE Trans.Intenisalsoyteresting to note that asT ,Inf: TheoryM vol.446 no.6- pp. 2416 - 2434n October 1998.

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effective capacities of the single-antenna and vector-GaussiansimoInratnThry204

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