Hindawi Publishing Cooation EURASIP Jounal on Wieless Communications and Netwoking Volume 27, Aticle ID 677, 9 ages doi:.55/27/677 Reseach Aticle On Enegy-Efficient Hieachical Coss-Laye Design: Joint Powe Contol and Routing fo Ad Hoc Netwoks Cistina Comaniciu and H. Vincent Poo 2 Deatment of Electical and Comute Engineeing, Chales V. Schaefe J., School of Engineeing, Stevens Institute of Technology, Hoboken, NJ 73, USA 2 Deatment of Electical Engineeing, School of Engineeing and Alied Science, Pinceton Univesity, Pinceton, NJ 8544, USA Received 29 Januay 26; Revised 2 Octobe 26; Acceted 3 Decembe 26 Recommended by Anantham Swami A hieachical coss-laye design aoach is oosed to incease enegy efficiency in ad hoc netwoks though joint adatation of nodes tansmitting owes and oute selection. The design maintains the advantages of the classic OSI model, while accounting fo the coss-couling between layes, though infomation shaing. The oosed joint owe contol and outing algoithm is shown to incease significantly the oveall enegy efficiency of the netwok, at the exense of a modeate incease in comlexity. Pefomance enhancement of the joint design using multiuse detection is also investigated, and it is shown that the use of multiuse detection can incease the caacity of the ad hoc netwok significantly fo a given level of enegy consumtion. Coyight 27 C. Comaniciu and H. V. Poo. This is an oen access aticle distibuted unde the Ceative Commons Attibution License, which emits unesticted use, distibution, and eoduction in any medium, ovided the oiginal wok is oely cited.. INTRODUCTION A mobile ad hoc netwok consists of a gou of mobile nodes that sontaneously fom temoay netwoks without the aid of a fixed infastuctue o centalized management. Ad-hoc netwoks ely on ee-to-ee communication, whee any souce-destination ai of nodes can eithe communicate diectly o by using intemediate nodes to elay the taffic. The communication outes ae detemined by the outing otocol, which finds the best ossible outes accoding to some secified cost citeion. Since, in geneal, many ad hoc netwoks will consist of small teminals with limited battey lifetime, outing otocols using enegy-elated cost citeia have ecently been investigated in the liteatue (e.g., [ 4]). Aside fom enegy-awae outing, othe intefeence management techniques have the otential of imoving the system efomance, with a diect effect on inceasing the netwok lifetime. Fo examle, joint owe contol and scheduling have been oosed in [5], and owe-awae outing fo netwoks using blind multiuse eceives has been analyzed in []. The benefits of owe contol fo wieless netwoks have been shown in numeous woks (see, e.g., [6 9]), but only ecently have its inteaction with enegy-awae outing begun to be addessed [ 3]. A owe-awae outing otocol design elies on the cuent owe assignments at the teminals, and in tun, otimal owe assignment deends on the cuent netwok toology, which is detemined by outing. It is aaent that thee is a stong coss-couling between owe contol and outing, due to the fact that they ae both affected by, and act uon, the intefeence level and the intefeence distibution in the netwok. Given this stong couling between layes, we exect that coss-laye intefeence management algoithms will outefom indeendently designed algoithms associated with vaious layes of the otocol stack [4]. On the othe hand, a concen associated with cossing the boundaies between layes is that many of the coe advantages of the OSI model, such as easy debugging and flexibility, easy ugading, and hieachical time-scale adatation, may be lost [5]. As a tadeoff between the os and cons of coss-laye design, we oose a hieachical coss-laye design famewok, in which the adatation otocols at diffeent layes of the otocol stack ae indeendently designed (e.g., owe contol at the hysical laye, and outing at the netwok laye), while shaing couling infomation acoss layes. Based on this famewok, we oose and analyze a joint owe contol and outing algoithm fo code-division multile-access (CDMA) ad hoc netwoks. We then extend this algoithm to
2 EURASIP Jounal on Wieless Communications and Netwoking Physical laye Netwok laye i MAC laye Figue : Hieachical coss-laye design model: inteactions among hysical, MAC, and netwok layes. include multiuse detection, fo a futhe incease in netwok efomance. The ae is oganized as follows: we fist esent the hieachical coss-laye design famewok in Section 2. We then oose a joint owe contol and outing algoithm in Section 3, and we add multiuse detection caabilities fo the hysical laye in Section 4. Finally, Section 5 esents the conclusions. 2. HIERARCHICAL CROSS-LAYER DESIGN FRAMEWORK As we have aleady mentioned, a tight couling exists between diffeent intefeence management algoithms imlemented at vaious layes of the otocol stack. In this ae we concentate mainly on inteactions between the hysical and the netwok layes, namely, we conside owe contol and eceive adatation algoithms at the hysical laye, and enegy-awae outing at the netwok laye. While owe contol and multiuse detection ae taditional intefeence management techniques, enegy-awae outing can also be seen as an effective intefeence management tool, as seeking low-enegy outes may lead to a bette intefeence distibution in the netwok. Given the tight coss-couling among these techniques, it becomes aaent that a coss-laye solution that jointly otimizes intefeence management algoithms acoss layes is desiable. On the othe hand, the OSI classical layeed achitectue has a numbe of advantages such as deloyment flexibility and ugadeability, easy debugging, and last but not least, an inheent educed netwok ovehead by imlementing adatability at diffeent time scales. Moe secifically, fast adatation can be done locally by the hysical laye, while lage-scale events can be handled by changes in outing, which imlies at least local neighbohood infomation udates. Ou oosed hieachical coss-laye design famewok seeks to maintain the advantages of the OSI model, by indeendently otimizing the intefeence management algoithms based on infomation shaing among layes. Figue illustates this hieachical model fo the fist thee layes of the otocol stack: hysical laye, MAC (data link) laye, and netwok laye. As otocols at diffeent layes act indeendently to incease the enegy efficiency in the netwok, the infomation exchange between layes leads to an iteative adatation ocedue, in which layes take tuns to adjust and minimize the enegy consumtion in the netwok based on the new intefeence level and distibution. We note that this hieachical stuctue aises convegence issues on a vetical lane, and a key issue that should be addessed is how to aoiately define the infomation shaed between layes, as well as how to incooate this infomation such that the iteative coss-laye adatation conveges, and does not lead to oscillatoy behavio. In what follows, we oose an enegy-awae hieachical joint owe contol and outing design, which we show is guaanteed to convege acoss layes. We then study how futhe enhancements at the hysical laye (i.e., multiuse detection eceives in CDMA netwoks) imove the oveall netwok efomance. 3. JOINT POWER CONTROL AND ROUTING 3.. Netwok model We conside an ad hoc netwok consisting of N mobile nodes. Fo simulation uoses, the nodes ae assumed to have a unifom stationay distibution ove a squae aea of dimension D D, but this is not a necessay assumtion fo the analysis. The multiaccess scheme is synchonous diect-sequence CDMA (DS-CDMA) and all nodes use indeendent, andomly geneated, and nomalized seading sequences of length L. The tansmitted symbols (assumed to be binay fo the uose of exosition) ae detected using eithe a matched filte eceive o a linea minimum squae eoeceive(lmmse).eachteminalj has a tansmission owe P j which will be iteatively and distibutively adated accoding to the cuent netwok configuation. The taffic can be tansmitted diectly between any two nodes, o it can be elayed though intemediate nodes. It is assumed that each node geneates taffic to be tansmitted towads a andomly chosen destination node. If taffic is elayed by a aticula node, the tansmissions fo diffeent sessions at that node ae time-multilexed. Also, it is assumed that a scheduling scheme is available at the MAC laye to schedule tansmission and ecetion minislots fo each node. This has the ole of avoiding exccesive intefeence between the eceived and tansmitted signals at any aticula node. The details of the scheduling allocation ae beyond the scoe of this ae. Fo ou design, we will use a simlifying wost-case assumtion that will conside that each node ceates intefeence at all times, while in eality, some of the time is dedicated only to eceiving. This simlifying assumtion suots ou hieachical stuctue, by avoiding intefeence tacking (outes modification) at the MAC laye time scale. We addess the oblem of meeting quality of sevice (QoS) equiements fo data, that is, BER (bit eo ate) and minimum enegy exenditue fo the infomation bits tansmitted, to conseve battey owe. We note that fo data
C. Comaniciu and H. V. Poo 3 sevices, delay is not of imay concen. The taget BER equiement can be maed into a taget SIR equiement. We note that an otimal taget SIR can be detemined (as in [6]) to minimize the enegy e bit equiement, unde the assumtion that data is etansmitted until coectly eceived. At a link level, fo a given taget SIR equiement, the numbe of etansmissions necessay fo coect acket ecetion is chaacteized by a geometic distibution, which deends on the coesonding BER-SIR maing. If the tansmission ate is fixed fo all links, then the enegy can be minimized by minimizing the tansmitted owes on each link. At the hysical laye level, this is achieved by owe contol. Howeve, the achievable minimum owes will deend on the distibution of the intefeence in the netwok, and thus ae influenced by outing. In tun, outing may use owe-awae metics to minimize the enegy consumtion. The oveall coss-laye otimization oblem can be fomulated as follows: N minimize P i subject to SIR (i,j) () γ, () i= (i, j) S a, P i, Υ, whee () is the vecto of all nodes owes, S a is the set of active links fo the cuent outing configuation, obtained using the outing otocol, and Υ is the set of all ossible outes. Fom (), we can see that otimal owe allocation deends on the cuent oute selection. On the othe hand, fo a given owe allocation, efficient outing may educe the intefeence, thus futhe deceasing the equied enegy e bit. We begin ou discussion of the joint otimization of these two effects by fist consideing distibuted owe contol design fo a given oute assignment, which is a classic distibuted owe contol oblem fo ad hoc netwoks. 3.2. Distibuted owe contol In the cellula setting, a minimal owe tansmission solution is achieved when all links achieve thei taget SIRs with equality. Fo an ad hoc netwok, imlementation comlexity constaints may estict the owe contol to adat owe levels fo each node, as oosed to otimizing it fo each active outgoing link fo the node. If multile active tansmission links stat at node i (Figue 2), then the wost link must meet the taget SIR with equality. In ou model, these outgoing links coesond to destinations fo vaious flows elayed by the node, and ae used in a time-multilexed fashion. If we denote the set of all outgoing links fom node i as S i, then the minimal owe tansmission conditions become min SIR k = γ, i =, 2,..., N. (2) k S i We now exess the achievable SIR fo an abitay active link (i, j) S a: SIR (i,j) = h (i,j) P i (/L) N k=, k i, k j h (k,j) P k + σ 2, (3) i j Figue 2: Multile tansmissions fom node i. whee h (i,j) is the link gain fo link (i, j), and σ 2 is the backgound noise owe. Condition (2) can then be exessed as min (i,j) S i. h (i,j) P i (/L) N k=, k i, k j h (k,j) P k + σ 2 = γ. (4) Fom (4), the owes canbe selected as P i = max (i,j) S i γ [ h (i,j) L = max (i,j) I (i,j)(), N k=, k i, k j l m h (k,j) P k + σ 2 ] whee T = [P, P 2,..., P N ]. It can easily be shown that I (i,j) () is a standad intefeence function, that is, it satisfies the thee oeties of a standad intefeence function: ositivity, monotonicity, and scalability [7]. It was also oved in [7] that T i () = max (i,j) I (i,j) () is also a standad intefeence function. Since T i () is a standad intefeence function, fo a feasible system, an iteative owe contol algoithm based on (5) P i (n +)= T i ( (n) ), i =, 2,..., N, (6) is convegent to a minimal owe solution [7], fo both synchonous and asynchonous owe udates. Since all the infomation equied fo the owe udates can be estimated locally, the owe contol algoithm can be imlemented distibutively. In aticula, a samle aveage of the squae oot oututs of the matched filte eceive fo link (i, j) will detemine the quantity E{y 2 (i,j) }= (/L) N k=, k i, k j h (k,j) P k + h (i,j) P i + σ 2. Futhe, if the link gain h (i,j) is also estimated, all infomation equied fo owe udates atnode i is available locally. 3.3. Joint owe contol and outing The evious section has oosed an otimal owe contol algoithm, which minimizes the total tansmitted owe given SIR constaints fo all active links, fo a given netwok configuation. Howeve, the efomance can be futhe imoved by otimally choosing the outes as well. Finding the
4 EURASIP Jounal on Wieless Communications and Netwoking Udate outes Yes Initial distibution of owes and outes Powe contol Udate link costs Comute outes N P i i= lowe? No Figue 3: Joint owe contol and outing. Sto otimal outes to minimize the total tansmission owe ove all ossible configuations is an NP-had oblem. We oose a subotimal solution, based on iteative owe contol and outing, which is shown to convege aidly to a local minimum enegy solution. This solution is comatible with ou oosed hieachical coss-laye famewok, by omoting indeendent otocol udates with infomation shaing accoss layes. Moe secifically, we oose a joint algoithm that altenates between owe contol (at the hysical laye) and oute assignments (at the netwok laye), until futhe imovements in the enegy consumtion cannot be achieved. At each ste of the algoithm, the owe contol otimizes owes based on the cuent oute assignment, while afte owe assignment, new minimum enegy outes ae detemined based on the cuent owe distibution of the nodes (see Figue 3). As we have mentioned in Section 3., the otimization oblem that we ae solving can be exessed as in (), that is, we ty to minimize the sum of tansmission owes, subject to SIR constaints, by both owe contol and oute assignments. We note that the taget SIR equiement is selected such that a BER equiement is met fo a fixed escibed ate allocation, detemined by a escibed seading gain. Thus, in ou system model the tansmission ate is fixed. In the evious section, we have descibed how the tansmission owes ae chosen fo each node given a cuent oute configuation, and we have shown that fo ou system model, they ae unique e node, no matte which flow is cuently elayed by the node. Thus, the infomation that the netwok laye sees is the vecto of owes fo all the nodes, T = [P, P 2,..., P N ], which comletely chaacteizes the intefeence distibution in the system, given a cetain location fo the nodes. Fo outing, we use Dijksta s algoithm [8, 9]with associated costs fo the links. In ode to ty to minimize futhe the total tansmitted owe in the netwok, a natual choice of costs fo the outing would be based on the tansmission owe sent by a node sending on a given link. Howeve, fo convegence easons fo the coss-laye algoithm (which will be exlained shotly), the cost fo an abitay link (i, j) is detemined as P i if SIR (i,j) γ, c(i, j) = if SIR (i,j) <γ. The eason fo choosing the link costs as in (7) is that we would like to estict the ool of links available fo outing to include only links that aleady meet the taget SIR. As we will see shotly, this condition will ensue the convegence of the algoithm towads a minimum enegy solution. To detemine a bette ossible outing otion, we need to evaluate the new costs fo all links, given the cuent distibution of owes esuling fom the evious owe contol ste. In ode to detemine the outing costs fo the links that ae not cuently active, the achievable SIR fo these links must be estimated. This equies that each node i udate a outing table which should contain the estimated link gains towads all the othe nodes, h (i,j), j =, 2,..., N, j i, the tansmitted owes of all nodes, P j, j =, 2,..., N, and the extended estimated intefeence at all the othe nodes, defined as Ĩ(i, j) = N k=, k i, k j h (k,j) P k +h (i,j) P i, j =, 2,..., N, j i. Hence, the estimated SIR fo link (i, j) can be exessed as SIR (i,j) = (7) h (i,j) P i (/L) ( Ĩ(i, j) h (i,j) P i ) + σ 2. (8) We note that the achievable SIR on any otential link (cuently active o not) deends only on the cuent distibution of nodes, and on the cuent owe assignment, and does not deend on the cuent assigned outes, and consequently does not change fo new oute assignments. This oety is a esult of the fact that multile sessions ae timemultilexed at a node, and ae all tansmitted with the same owe, such that the tansmitted owe fo a node i is fixed and equal to P i. This esult can be summaized in the following oosition. Poosition. Fo a given distibution of nodes in the netwok, afte the convegence of the owe contol algoithm, the achievable SIR on any abitay link deends only on the nodes tansmitted owes and is indeendent of the cuent oute assignment. We note that if sessions ae not time-multilexed at a elaying node, the above oosition does not hold any moe (e.g., the total owe tansmitted by a node is additive ove the numbe of elayed flows fo multicode tansmission, and thus deends on the outing configuation), and the convegence of the oosed joint owe contol algoithm is not guaanteed. Howeve, as a disadvantage fo the timemultilexed scheme, the thoughut e session is limited by the numbe of sessions elayed by a node. In an extension of this wok [2], we also have oosed a cost modification fo the outing to account fo this effect, which yielded a moe unifom distibution of elayed flows e node ove the entie netwok. Also, in [2], we have comaed the efomance of a time-multilexed scheme with the case in which multi-code CDMA is used fo simultaneous tansmission of
C. Comaniciu and H. V. Poo 5 all elayed flows (which inceases the intefeence in the system). Stating fom an initial distibution of owes and outes, and assuming that the system is feasible fo the initial configuation, the joint owe contol and outing algoithm is summaized in Figue 3. Theoem. Fo a feasible initial netwok configuation, the joint owe contol and outing algoithm conveges to a locally minimal tansmitted owe solution. Poof. As we eviously showed, fo a feasible initial netwok configuation, the owe contol minimizes the total tansmitted owe, while ensuing that all active links meet thei SIR equiements: SIR (i,j) γ,foall(i, j) S a. Afte the convegence of the owe contol algoithm, the link costs ae estimated and udated accoding to (7) and(8), and a minimal cost oute, equivalent to a minimal tansmitted owe oute, is selected fo each session. As a consequence, the new outes ae selected such that the sum of all tansmitted owes fo all active links is minimized, while the SIR constaints ae met fo all links (fom Poosition and (7)). If no owe imovements can be achieved, the algoithm stos. Othewise, the sum of tansmission owes deceases afte the oute selection. Since all the new active links satisfy SIR (i,j) γ,foall(i, j) S a, the system is feasible, and theefoe, the owe contol algoithm oduces a deceasing sequence of owe vectos conveging to a minimal owe solution [7]. Hence, each ste of the iteation (owe contol o outing) oduces an imovement in the total tansmitted owe, while meeting SIR equiements fo all active links. The algoithm stos at a locally minimal tansmitted owe solution, whee no futhe decease in tansmission owe can be achieved by the outing otocol. We note that the locally minimal tansmitted owe solution achieved by the oosed algoithm deends on the initial netwok configuation chosen. Fo initialization, we oose an algoithm simila to that which was oosed in []. We fist select an initial distibution of owes (equal owes o andom distibution) and then detemine outes by assigning link costs equal to the enegy-e-bit consumtion, which is ootional to the tansmitted owe and invese ootional to the obability of coect ecetion fo a acket[5]. This aoach also emits us to quantify the enegy equiement imovements of the joint otimization elative to the initial stating oint. We note that the total enegy equiement deends on the cuent initialization fo the owes. To imove the exanded enegy with minimal comlexity incease, the algoithm can be un seveal times with diffeent andom owe initializations, and the best enegy solution ove all uns can be detemined. 3.4. Simulations In this section, we esent some numeical examles fo ad hoc netwoks with 55 and 4 nodes, esectively, unifomly 7 4 3.5 3 2.5 2.5.5 2 3 4 5 Figue 4: Distibution of owes afte convegence. distibuted ove a squae aea of 2 2 metes. The taget SIR is selected to be γ = 2.5 (which was shown to be an otimal value that minimizes enegy-e-bit consumtion fo an FSK scheme [6]), and the noise owe is σ 2 = 3, which aoximately coesonds to the themal noise owe fo a bandwidth of MHz. We conside low-ate data uses, using a seading gain of L = 28. Fo this aticula examle, we choose equal initial tansmit owes, 7 db above the noise floo (P t = 6 W), and a ath loss model with ath loss coefficient n = 2. In Figue 4, we show the final distibution of owes afte the convegence of the joint owe contol and outing algoithm. Figues 5 and 6 illustate the efomance of the oosed joint otimization algoithm. In Figue 5, itcanbe seen that the total tansmitted owe in the netwok ogessively deceases as the oosed algoithm iteatively otimizes owe and outes. The values in Figue 5 eesent the total tansmitted owe obtained ove a sequence of iteations: (owe contol, outing, owe contol, outing, owe contol). In Figue 6, theachievedenegyebitiscomaed fo the same exeiment with the fist enegy value, which eesents the enegy e bit obtained in the initial state. It can be seen that substantial imovements ae achieved by the oosed joint otimization algoithm. Note that at the end of each iteation ai (outing, owe contol), the enegy is futhe minimized. Howeve, afte new outes ae selected, the owes ae not yet otimized, so it is ossible that evious outes might have bette enegye-bit efomance (fo the same owe allocation, highe SIRs may imove the enegy consumtion). As we have eviously mentioned, the actual enegy esults afte convegence deend on the initial stating oint fo the algoithm. In Figue 7, we illustate the vaiation in the total tansmission owe obtained with vaious initializations ( tials ae consideed) fo an ad hoc netwok with 4 nodes. We can see that significant enegy imovements can be achieved if the algoithm is un eeatedly with diffeent initializations and the best configuation is selected.
6 EURASIP Jounal on Wieless Communications and Netwoking 5 9 7 2 8.5.8.6 Total tansmitted owe 8 7.5 7 6.5 6.5 2 2.5 3 3.5 4 4.5 5 Iteations Figue 5: Total tansmission owe..4.2.8.6.4.2 5 5 2 25 3 35 4 Figue 8: Distibution of owes fo the minimal enegy solution. P av 3 Initialization In Figue 8 we show the final distibution of owes fo this minimal enegy solution. 3.5. Unifom enegy consumtion E b 4 5 2 3 4 5 6 3 Iteations Figue 6: Enegy e bit. While we saw that the owe distibution in Figue 8 gives a vey low total enegy consumtion, this solution leads to unequal owe consumtion among nodes, which ultimately esults in shote life san fo cetain nodes (e.g., node 4 in Figue 8). Note that in mobile nodes, this oblem is ovecome by the fact that node locations change with time, so in the long un, the owe consumtion tends to be moe unifom. Fo fixed nodes, o slow moving ones, we ovecome this oblem by selecting a set of altenate good outes (N s outes) and thei coesonding owe distibutions. The outes (and owe vectos) ae then andomly assigned, such that the owe consumtion vaiance among nodes is minimized. A oute i and its coesonding owe vecto i ae selected fom the initial set of good outes, with obability w i. The obabilities w i, i =,..., N s, ae assigned to outes such that the following conditions hold: P t 4 min w P P av 2 2, w i, i =,..., N s, N s w j =, j= (9) 5 E min 6 2 4 6 8 Numbe of initializations Figue 7: Enegy function fo diffeent initializations. whee w = [w, w 2,..., w Ns ], P = [, 2,..., Ns ], and P av is the aveage owe consumtion acoss nodes obtained fo the minimal enegy solution. Altenatively, outes can be assigned deteministically, such that w i eesents the faction of time oute i and its coesonding owe vecto ae selected fo tansmission. In Figue 9 we illustate how the owe distibution changes in the ad hoc netwok when N s = 9 good outes ae selected. These outes (and thei coesonding owe distibution)
C. Comaniciu and H. V. Poo 7 7.4.2.8.6.4.2 Unifom distibution of owes 5 5 2 25 3 35 4 Figue 9: Enegy e bit. ae selected to be within % of the minimal enegy solution obtained with diffeent andom initializations. Comaing the esults fom Figue 9 with the ones in Figue 8, we can see a moe unifom consumtion acoss all nodes in the ad hoc netwok. 4. JOINT POWER CONTROL, ROUTING, AND MULTIUSER DETECTION To extend the above-descibed joint owe contol and outing algoithm to include eceive otimization, we build on esults on iteative, distibuted, joint owe contol, and minimum mean squae eo multiuse detection esented in [22]. In [22], an iteative two-ste integated owe contol and multiuse detection algoithm was oosed, fo which, in the fist ste, the LMMSE filte coefficients ae adjusted accoding to the cuent vecto of owes (), then in the second ste, a new owe vecto is selected fo the given filte coefficients. Ste. Otimize filte coefficients given the owe vecto T = [P, P 2,..., P n ]: Pi (n) ĉ i = +P i (n)s T i Ai ( ) A ( ) (n) i (n) si, () si whee c i and s i ae the filte coefficients vecto, and the signatue sequence vecto fo use i,esectively,n is the iteation numbe, and A i is defined as A i = j i P j h ij s j s T j. Ste 2. Otimize owes based on cuently selected filte coefficients: P i (n +)= γ i j i P j (n)h i,j (ĉi T ) 2 s j + σ2ĉ Tĉi i h ii (ĉi T ) 2. () s i Given the above algoithm, to extend ou joint owe contol and outing scheme to include eceive otimization, we simly elace the simle owe contol adatation at the P av 5.9.8.7.6.5.4.3.2. 5 5 2 25 3 5.9.8.7.6.5.4.3.2. (a) 5 5 2 25 3 (b) Figue : Joint owe contol, multiuse detection, and outing: distibution of owes vesus node numbe, (a) initially, (b) afte convegence (final distibution of owes). hysical laye by the above joint owe contol and multiuse detection algoithm. Simulation esults show a vey simila convegence behavio and enegy savings fo the joint owe contol, multiuse detection and outing algoithm, comaed to the solution with matched filtes (see Figues,, and 2). We also note a significant caacity incease when multiuse detection is emloyed. We use as a caacity measue the total thoughut that can be suoted by the netwok such that the owe contol is feasible fo a taget SIR of γ = 2.5. We note that the owe contol feasibility deends on the actual netwok toology. To detemine the maximum load fo the netwok, we andomly geneated diffeent toologies (fo the same numbe of uses) and we selected the maximum numbe of uses (fo a given seading gain) that yielded feasible toologies 95% of the time, fo a given initial owe distibution fo the nodes.
8 EURASIP Jounal on Wieless Communications and Netwoking Total tansmitted owe 5 8.8 +MUD 8.6 8.4 8.2 8 7.8 7.6 7.4 7.2 7 +MUD 6.8 2 3 Iteations Figue : Total tansmission owe: joint owe contol, multiuse detection, and outing. E b 3 4 Initialization +MUD +MUD 5.5 2 2.5 3 3.5 4 Iteations Figue 2: Total enegy consumtion: joint owe contol, multiuse detection, and outing. Fo the matched filte case, we selected L = 28 and the maximum numbe of uses that met the feasibility condition was detemined to be N = 55. Fo the LMMSE case, since the caacity inceases significantly, to educe the comlexity of the simulation (the numbe of nodes), we have selected L = 32, with a esulting caacity of N = 3. This yielded a total nomalized thoughut gain fo the LMMSE case of T g(lmmse) = N LMMSE L MF = 2.8. (2) L LMMSE N MF To illustate the efomance of the joint owe contol, multiuse detection and outing otocol, we have consideed simila netwok aametes as befoe, with the sole diffeence of selecting N = 3 and L = 32. Random initial tansmission owes wee selected, aoximately 7 db above the noise floo. Figue shows the initial distibution of owes, as well as the otimal owe contol distibution afte convegence. Figues and 2 illustate the efomance of the oosed joint otimization algoithm with multiuse detection. In Figue, it can be seen that the total tansmitted owe in the netwok ogessively deceases as the oosed algoithm iteatively otimizes owe, filte coefficients, and outes. The values in Figue eesent the total tansmitted owe obtained ove a sequence of iteations: (owe contol + MUD, outing, owe contol + MUD, outing, owe contol + MUD). In Figue 2, the achieved enegy e bit is comaed fo the same exeiment with the initial enegy value (with andomly selected owes). It can be seen that substantial imovements ae achieved by the oosed joint otimization algoithm (aoximately one ode of magnitude). 5. CONCLUSIONS In this ae, we have oosed joint owe contol and outing otimization fo wieless ad hoc data netwoks with enegy constaints. Both enegy minimization and netwok lifetime maximization have been consideed as otimization citeia. We have shown that enegy savings of an ode of magnitude can be obtained, comaed with a fixed tansmission owe, enegy-awae outing scheme. Ou oosed algoithm is based on a hieachical coss-laye famewok which maintains the advantages of the OSI layeed achitectue, while allowing fo otocol otimization based on infomation shaing between layes. The netwok caacity has been futhe enhanced by emloying multiuse detection, with a simila obtained enegy efomance. Ou simulation esults show that ou distibutive joint otimization algoithm conveges aidly towads a local minimum enegy. The aid convegence of the owe-outing otocol makes it suitable fo imlementation in mobile ad hoc netwoks. ACKNOWLEDGMENTS This wok was esented in at at the 42nd IEEE Confeence on Decision and Contol, Maui, Hawaii, Decembe 23. This eseach was suoted by the National Science Foundation unde Gants ANI-33887 and CCR-2-524, by the New Jesey Cente fo Pevasive Infomation Technology, and by inets Cente at Stevens Institute of Technology. REFERENCES [] Z. Cai, M. Lu, and X. Wang, Minimum aveage tansmission owe outing in CDMA ad hoc netwoks utilizing the blind multiuse detection, in Poceedings of the 6th Intenational Paallel and Distibuted Pocessing Symosium (IPDPS 2),. 428 433, Fot Laudedale, Fla, USA, Ail 22. [2]D.Kim,J.J.Gacia-Luna-Aceves,K.Obaczka,J.Cano,and P. Manzoni, Powe-awae outing based on the enegy dain ate fo mobile ad hoc netwoks, in Poceedings of the th IEEE Intenational Confeence on Comute Communications and Netwoks (ICCCN 2),. 565 569, Miami, Fla, USA, Octobe 22.
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