Alternating Opportunistic Large Arrays in Broadcasting for Network Lifetime Extension

Transcription

1 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL 8, NO 6, JUNE Alternating Opportunitic Large Array in Broadcating for Network Lifetime Extenion Aravind Kaila and Mary Ann Ingram Abtract We propoe a protocol for broadcating in wirele multihop network that i baed on a form of cooperative tranmiion called the Opportunitic Large Array (OLA) An SNR ( tranmiion ) threhold i ued to define two mutually excluive et of OLA, uch that the union of the et include all the node in the network The broadcat protocol then alternate between the et for each broadcat and i called Alternating OLA with Tranmiion Threhold (A-OLA-T) Under A-OLA- T, all participating node tranmit with the ame low power, therefore the energie of the node in the network drain efficiently and uniformly, extending the network life relative to broadcat that ue imple OLA or non-alternating OLA with a tranmiion threhold In thi paper, we optimize the A-OLA-T protocol under the continuum aumption (very high node denity) Index Term Broadcat, cooperative tranmiion, opportunitic large array, wirele enor network I INTRODUCTION COOPERATIVE Tranmiion (CT) i an effective way to achieve the benefit of an array tranmitter (diverity and/or array gain) by having two or more node cooperate to tranmit the ame meage to enhance the energy-efficiency of the wirele ytem [1], [] There are a few work that preent the benefit of multi-node cooperation [3]-[6], and a few other that pecifically addre the energy-efficiency of cooperative broadcat in wirele multi-hop network [7]-[11] In thi paper, we preent a new alternating et broadcat trategy that ue a imple form of cooperative tranmiion called the Opportunitic Large Array (OLA) [7] The Alternating OLA with a Tranmiion Threhold (A- OLA-T) algorithm introduced in thi paper i an extenion of a previou non-alternating OLA with a Tranmiion Threhold (OLA-T) algorithm [8] A-OLA-T enure that all node in a network contribute efficiently and equally to broadcat, thereby increaing the network longevity for multihop wirele network An OLA i a group of node that behave without coordination between each other, but naturally fire at approximately the ame time in repone to energy received from a ingle ource or another OLA [7] So in OLA-baed cheme, each node receive a uperpoition of ignal tranmitted by multiple node Thi i in tark contrat to non-cooperative cheme where ideally each node receive a meage from jut one Manucript received June 3, 008; revied Augut 18, 008 and February 7, 009; accepted March 10, 009 The aociate editor coordinating the review of thi letter and approving it for publication wa H Shin The author are with the School of Electrical and Computer Engineering, Georgia Intitute of Technology, Altanta, GA , USA ( aravindk@ieeeorg, mai@ecegatechedu) The author gratefully acknowledge upport for thi reearch from the National Science Foundation under grant CNS Digital Object Identifier /TWC /09$500 c 009 IEEE tranmitter All the tranmiion within an OLA are repeat of the ame waveform; therefore the ignal received from an OLA ha the ame model a a multipath channel A long a the receiver, uch a a RAKE receiver, can tolerate the effective delay and Doppler pread of the received ignal and extract the diverity, decoding can proceed normally [11] Even though many node may participate in an OLA tranmiion, energy can till be aved becaue all node can reduce their tranmit power dramatically and large fade margin are not needed In the original OLA-baed broadcating cheme [7], or Baic OLA, the firt OLA comprie all the node that can decode the tranmiion from the originating node; then the firt OLA tranmit and all node that can decode that tranmiion and that haven t decoded that meage before, form the econd OLA, and o forth In [10], the author compared the power efficiency of OLA-baed cooperative broadcating relative to non-cooperative broadcating, both with optimal power allocation, and howed that the former aved at leat 60% of the radiated power One can control the node participation in each hop or OLA by uing an explicit power tranmiion threhold in the receiver, and thi i the OLA-T algorithm [8] We note that the OLA-T concept wa propoed a the Dual Threhold Cooperative Broadcat (DTBC), but not analyzed in [10] Compared to Baic OLA, OLA-T wa hown in [8] to ave up to a maximum of 3% of the tranmitted energy by limiting the number of node in each OLA Unlike the OLA-baed cheme above, A-OLA-T optimize group of broadcat intead of a ingle broadcat The tranmiion threhold i ued to minimize the OLA ize while maintaining mutually excluive et of OLA on conecutive broadcat An important feature that all the OLAbaed cheme hare i that no individual node are addreed Thi make thi protocol calable with node denity II SYSTEM MODEL For our analyi, we adopt the notation and aumption of [8], mot of which were ued earlier in [11] Half-duplex node are aumed to be ditributed uniformly and randomly over a continuou area with average node denity ρ The originating node i aumed to be a point ource at the center of the given network area We aume a node can decode and forward (DF) a meage without error when it received ignal-to-noie ratio (SNR) i greater than or equal to a modulation-dependent threhold [11] Aumption of unit noie variance tranform the SNR threhold to a received power criterion, which i denoted a the decoding or lower threhold, We note that the decoding threhold i not

2 83 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL 8, NO 6, JUNE 009 explicitly ued in real receiver operation A real receiver alway jut trie to decode a meage If the meage wa decoded properly, then it i aumed that the receiver power mut have exceeded In contrat, the Tranmiion or upper threhold, i ued explicitly in the receiver to compare againt the received SNR Thi additional criterion for relaying limit the number of node in each hop becaue a node would relay only if it received SNR i le than So the threhold, and,define a range of received power that correpond to the ignificant boundary node, which form the OLA While each boundary node in OLA-T mut tranmit a omewhat higher power, compared to Baic OLA, there i till an overall tranmit energy aving with OLA-T becaue of the favorable location of the boundary node We define the Relative Tranmiion Threhold (RTT) a R = τu For implicity, the determinitic model [11] i aumed, which mean that the power received at a node i the um of the power from each of the node tranmiion Thi implie that ignal received from different node are orthogonal The orthogonality can be approximated, for example, with Direct Sequence Spread Spectrum (DSSS) modulation, RAKE receiver and by allowing tranmitting node to delay their tranmiion by a random number of chip [1] Continuing to follow [11], we aume a non-fading environment and a path-lo exponent of The path lo function in Carteian coordinate i given by l(x, y) =(x + y ) 1, where (x, y) are the normalized coordinate at the receiver A in [11], ditance d i normalized by a reference ditance, d 0 LetpowerP 0 be the received power at d 0 Ain[11], the aggregate path-lo from a circular dic of radiu r 0 at an arbitrary ditance p>1 from the ource i given by f(r 0,p)= r0 0 0 p l(p r co θ, r in θ)rdrdθ = ln p r0 (1) Let the normalized ource and relay tranmit power be denoted by and, repectively, and the relay tranmit power per unit area be denoted by = ρ The normalization i uch that and are actually the SNR at a receiver d 0 away from the tranmitter [8] We aume a continuum of node in the network, which mean that we let the node denity ρ become very large (ρ ) while i kept fixed Uing (1), the received power at a ditance p from the p ource, P p i given by P p = ln p r0 We note that nonorthogonal tranmiion in fading channel produce imilarly haped OLA [11], therefore the A-OLA-T concept hould work for them a well, although the theoretical reult would have to be modified Latly, we define Decoding Ratio (DR) a D = /, named a uch becaue it can be hown to be the ratio of the receiver enitivity (ie minimum power for decoding at a given data rate) to the power received from a ingle relay at the ditance to the nearet neighbor, d nn =1/ ρifρ i a perfect quare, then the d nn would be the ditance between the nearet neighbor if the node were arranged in a uniform quare grid We note that D relate to node degree, K, [13] according to K = /D Fig 1 The grey trip repreent the tranmitting node (that form the OLA) which alternate during each broadcat III ALTERNATING OLA-T (A-OLA-T) FOR TWO SETS For a fixed ource and a tatic network, OLA-T caue the ame ubet of node to participate in all broadcat Let network lifetime be defined to be the length of time before the firt node die ( death happen when the batterie die) If we aume that broadcat are the only tranmiion, then we oberve that OLA-T ha no advantage over Baic OLA in term of network lifetime, even though OLA-T conume le total energy in a ingle broadcat In the next ection, we how how Alternating OLA-T (A-OLA-T) improve the network lifetime compared to Baic OLA and OLA-T The idea of A-OLA-T i that the node that do not participate in one broadcat make up the OLA in the next broadcat Fig 1 illutrate the concept The grey area on the left of Fig 1, are the OLA in Broadcat 1, which i an OLA- T broadcat, while the grey area on the right are the OLA in Broadcat Ideally thee two et of OLA have no node in common and their union include all node A-OLA- T extend the network life becaue each node participate only in every other broadcat Broadcat 1 fixe the radii for Broadcat From [8], it i learned that a neceary and ufficient condition for Broadcat 1 ucce with a contant tranmiion threhold i the inequality, D DR exp +exp () We oberve that when R, () become the condition for ucceful Baic OLA broadcat [11]: D exp (3) Inequality () can be re-written a a lower bound on R: { ln [ exp ] D } R lower bound =( 1) (4) D We note that the A-OLA-T extenion of OLA-T will not work for all R atifying (4) Next, we will how that a neceary and ufficient condition for Broadcat to alo be ucceful i an upper bound on R

3 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL 8, NO 6, JUNE Uing the initial condition r o,1 = and r i,1 = recuriveformulaeforthek-th OLA are given by [8], ro,k = β()ro,k 1 r i,k 1, ri,k β 1 = β()ro,k 1 r i,k 1 β 1 (6) After ubtituting (6) into (5), and implifying, we can rewrite the condition in (5) to how the explicit dependence on the Broadcat 1 radii: 0 β()ri,k r o,k 1 (β() 1) ri,k+1 (7) β 1 In [8], the cloed-form expreion for (6) were found to be Fig Illutration of the A-OLA-T Algorithm with (a) admiible R, (b) inadmiible R A Neceary and Sufficient Condition for Broadcat Succe Fig (a) and (b) contain illutration of ucceful and unucceful A-OLA-T broadcat, repectively Thee figure how how to enure that both broadcat are utaining The upper part of both drawing correpond to Broadcat 1, and the outer and inner OLA radii for the k-th OLA ring are labeled r o,k and r i,k, repectively The lower part of both drawing correpond to Broadcat, and the outer and inner OLA radii for the k-th OLA ring are relabeled v o,k and v i,k, repectively The initial condition for the econd broadcat are P v i,1 =0,andv o,1 =,wherev o,1 wa fixed in Broadcat 1 In Fig (a), the firt OLA during Broadcat 1 i denoted by OLA 1,1 and i defined by the radii pair, r i,1 and r o,1 Onthe other hand, the firt OLA during Broadcat i denoted by by OLA 1, and i the circular dik of radiu v o,1 Letṽ o, be the decoding range of OLA 1, during Broadcat The key idea i that ṽ o, mut be greater than r i, In Fig (a), thi inequality i atified, while in Fig (b), it i not More generally, the network deigner jut need to check that the decoding range, ṽ o,k+1,ofthek-th OLA in Broadcat i alway greater than r i,k+1, for all k Alternatively, we can compute the received power at r i,k+1 and confirm that it i greater than the minimum Uing v o,k = r i,k and v i,k = r o,k 1, we expre thi a [f(r i,k,r i,k+1 ) f(r o,k 1,r i,k+1 )] (5) Intuitively, we oberve that a R become very large, the OLA during Broadcat 1 become larger and the OLA of Broadcat become relatively maller, a hown in Fig (b) A a reult, the et of node that did not tranmit during Broadcat 1 (or the OLA during Broadcat ), eventually become o mall that their decoding range (for OLA 1,, thi i indicated by the dahed line in Fig (b)) cannot reach the next Broadcat OLA to utain propagation, ie, ṽ o, <v i, In other word, for a very high value of R, thek-th OLA in Broadcat may be o weak that no node between v i,k+1 and v o,k+1 can decode the ignal When thi happen, OLA formation die off during Broadcat and A-OLA-T fail to achieve network broadcat Thu, it make ene for R to have an upper bound ro,k = η 1A k 1 1 η A k 1, ri,k = ζ 1A k 1 1 ζ A k 1, (8) A 1 A A 1 A where A 1 = α α, A =1, A 1 A 0, (9) η i = { [A i + α] α P }, (10) { ζ i = [1 + α] +[A i α 1] P }, i {1, }, (11) α(τ) =[β(τ) 1] 1, β(τ) =exp [ τ/( ) ] (1) Subtituting the expreion for r o,k and r i,k from (8)-(11) into (7), and collecting the A 1 and A term, we get where Ω= A k 1 1 Ω A k 1 Π 0 (13) α+1 ζ 1 αη 1 A 1 1 ζ 1 A 1, and (14) Π= α+1 ζ αη A 1 ζ A Uing A = 1 and the expreion for η and ζ,weget Π=ζ η =0, which, when applied to (13) along with A 1 > 0, the inequality in (13) may be implified to Ω 0 While not obviou from Ω 0, thi inequality implie an upper bound on R The cloed-form expreion for the upper bound on R i derived in the Appendix, and i given by [ (β(τl R upper bound = β(τl D ln )+1+ )+1 ) ] 4, (15) where β i defined in (1) We oberve that (15) depend excluively on and D, and not on the ource power We remark that it i not neceary to aume the ame R for both broadcat or even for different level within a ingle broadcat [8] With the flexibility of level-dependent tranmiion threhold (τu k or R k ), a deigner may be able to make the decoding range in Broadcat match up exactly with the boundarie in Broadcat 1, and thereby ave more tranmit energy

4 834 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL 8, NO 6, JUNE 009 Fig 3 Relative Tranmiion Threhold (R), in db, Veru Decoding Ratio (D) for A-OLA-T The D correponding to the interection of the two curve i the D max B Dicuion Fig 3 i a plot of the upper and lower bound for relative tranmiion threhold, R, in db for A-OLA-T, a a function of the decoding ratio, D Firt, we oberve that a D decreae, the difference between the upper and lower bound increae A an example, for a mall decreae in D from 1 to 1, the range of R increae from [1, 4] to [17, 8] Thiha two reaon Decreaing D could be done by increaing the, which enable Broadcat 1 to be ucceful with more lender OLA Thi correpond to a decreae of the lower bound Fatter Broadcat OLA more eaily reach acro the next pair of boundarie and o thi increae the upper bound Next, decreaing alo decreae D Decreaing decreae the lower bound, becaue a lower value of correpond to a lower SNR requirement at the receiving node, and o in order to meet thi power requirement, the OLA can afford to have fewer node during Broadcat 1 OLA during Broadcat 1 become thinner but more powerful, and the OLA during Broadcat grow thicker Thi i implied by an increae in the upper bound We alo oberve from Fig 3 that the upper and lower bound converge a D increae Thi alo implie an upper bound on D for A-OLA-T, D max = τ l,where min i min the minimum value of for a given We were not able to obtain an exact value of D max, however, uing numerical analyi we found D max 17 We note from (3) that D ha a higher upper bound for Baic OLA, D max = ln() 18 For D > D max, network broadcat fail for A-OLA-T becaue the OLA die out during Broadcat For A-OLA-T, we have from D max that min 078 From (3), the minimum for Baic OLA, denoted by min, i min =046 We oberve that A-OLA-T require le than double the power of Baic OLA, becaue it ue border node Next, we compute the broadcat life extenion of A-OLA- T compared to Baic OLA By broadcat life, we mean the lifetime of the network if only broadcat were tranmitted If A-OLA-T and Baic OLA ue the ame, then A- OLA-T double the network life compared to Baic OLA However, thi i not a fair comparion ince Baic OLA can achieve ucceful broadcat at a lower Sincefora given protocol, all node ue the ame amount of power in broadcat, we aume the broadcat life of the network i inverely proportional to the time-averaged power tranmitted by each node For Baic OLA, the time-averaged power i For A-OLA-T, the time-averaged power i,ince each node tranmit only every other broadcat The ratio of broadcat live of Baic OLA to A-OLA-T i therefore Pr, and the Fraction of Life Extenion (FLE), may be defined a FLE = P r 1 (16) FLE can be evaluated for any power that atify 078 and 046τl However, when the the minimum power are ubtituted, then (16) become FLE = P rmin min 1= D max (17) D max Thi mean that A-OLA-T can offer a 17% life extenion when both protocol are optimized IV CONCLUSIONS In thi paper, we propoed and analyzed a novel ameource broadcat trategy that extend the life of a wirele ad hoc or enor network by alternating between mutually excluive et of opportunitic large array (OLA) in two conecutive broadcat In thi trategy, all participating node tranmit with the ame power We howed that A-OLA-T extend the network life by a maximum of 17% relative to Baic OLA when both protocol operate in their minimum energy configuration Further, when A-OLA-T i compared to OLA-T, the battery-life of the node i doubled The key parameter wa the tranmiion threhold, which wa aumed contant for the whole network Potential extenion of thi work include an analyi of A-OLA-T for more than two OLA et, finite denitie of node, other path-lo exponent, fading environment, radiated veru non-radiated energy, and for practical ynchronization and SNR etimation ACKNOWLEDGMENT The author are thankful for the reviewer thoughtful comment APPENDIX The condition for Broadcat OLA formation to propagate throughout the network i given by Ω 0 and (14) To determine the value that make Ω=0, ubtitute the expreion for η 1 and ζ 1 from (10) and (11), repectively, and get [ 0= α+1 1+α P ] τ [ u P αα P ] [ A α P ] A 1 We aume > 0, and 0; therefore, we can divide out the quare ( bracketed term Further implification [α(τu reult in 0 = A 1 ) ] +1 )A 1 + [ α ] Thi

5 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL 8, NO 6, JUNE equation i quadratic in A 1, and the root are A 1 = [ α ] and A 1 =1 Recall that A 1 A i a factor in the denominator of the cloed-form expreion for the OLA-T radii a given in (8) So, during the derivation for Ω, we had aumed that A 1 A 0SinceA =1, we mut take the root A 1 = [ α ] We re-ubtitute the expreion for A 1 in (9) to get [ β ] β+1 β+1 = 0, which i quadratic in β, with [ ] root r 1, =(05) β+1± β+1 4 Without lo of generality, we aume the larger root i r 1 Each root implie a different relationhip between and, which lead to two value of R where Ω=0 The greater of the two value i the upper bound on R So,β=r 1 = ln(r 1 ), and the upper bound i given by R upper bound = ln(r1) D REFERENCES [1] A Sendonari, E Erkip, and B Aazhang, Uer cooperation part I: ytem decription; part II: implmentation apect and performance analyi, IEEE Tran Commun, vol 51, no 11, pp , Nov 003 [] J N Laneman, D Te, and G W Wornell, Cooperative diveritry in wirele network: efficient protocol and outage behaviour, IEEE Tran Inform Theory, vol 50, no 1, pp , Dec 004 [3] S -H Chen, U Mitra, and B Krihnamachari, Cooperative communication and routing over fading channel in wirele enor network, in Proc International Conf on Wirele Network Communication and Mobile Computing, vol, pp , June 005 [4] T S Quek, D Dardari, and M Z Win, Energy efficiency of dene wirele enor network: to cooperate or not to cooperate, IEEE J Select Area Commun, vol 5, no, pp , Feb 007 [5] A Bleta, A Khiti, D P Reed, A Lippman, A imple cooperative diverity method baed on network path election, IEEE J Select Area Commun, vol 4, no 3, pp 659 7, Mar 006 [6] M C Valenti and N Correal, Exploiting macrodiverity in dene multihop network and relay channel, in Proc 38th Ailomar Conf on Signal, Sytem and Computer, Nov 003 [7] Y W Hong and A Scaglione, Energy-efficient broadcating with cooperative tranmiion in wirele enor network, IEEE Tran Wirele Commun, vol 5, no 10, pp , Oct 006 [8] A Kaila, L Thanayankizil, and M A Ingram, A imple cooperative tranmiion protocol for energy-efficient broadcating over multi-hop wirele network, KICS/IEEE J Commun and Network (pecial iue on wirele cooperative tranmiion and it application), vol 10, no, pp 13-0, June 008 [9] I Maric and R D Yate, Cooperative multihop broadcat for wirele network, IEEE J Select Area Commun, vol 3, no 1, pp , Aug 004 [10] B Sirkeci-Mergen and A Scaglione, On the power efficiency of cooperative broadcat in dene wirele network, IEEE J Select Area Commun, vol 5, no, pp , Feb 007 [11] B Sirkeci-Mergen, A Scaglione, G Mergen, Aymptotic analyi of multi-tage cooperative broadcat in wirele network, joint pecial iue of IEEE Tran Inform Theory and IEEE/ACM Tran Networking, vol 5, no 6, pp , June 006 [1] R Mudumbai, G Barriac, and U Madhow, Spread-pectrum technique for ditributed pace-time communication in enor network, in Proc 38th Ailomar Conference Signal, Sytem and Computer, pp , Nov 004 [13] L Thanayankizil, A Kaila, and M A Ingram, Routing protocol for wirele enor network that have an opportunitic large array (OLA) phyical layer, accepted for publication in Ad-Hoc & Senor Wirele Network: An International Journal, Dec 008