Efficient Powe Contol fo Boadcast in Wieless Communication Systems A. T. Chonopoulos Compute Science Depatment Univesity of Texas at San Antonio San Antonio, TX Email:atc@cs.utsa.edu P. Cotae Depatment of Electical Engineeing, Univesity of Texas at San Antonio, San Antonio, TX Email:pcotae@utsa.edu S. Ponipieddy Compute Science Depatment Univesity of Texas at San Antonio San Antonio, TX Email:sponipi@cs.utsa.edu Abstact Enegy efficiency is a measue of pefomance in wieless netwoks. Theefoe, contolling the tansmitte powe at a given node inceases not only the opeating life of the battey but also the oveall system capacity by successfully admitting new nodes between a souce and a destination. It is essential to find effective means of powe contol of point-to-point, boadcasting and multicasting scenaios. In past wok [], we pesented a new scheme State Space-based Contol Design (SSCD) using both the state space and optimal contol methodology in discete-time fo powe contol in wieless systems. Futhe, we poved the convegence of the oveall netwok with ou algoithm using Lyapunov stability analysis. We made a compaison with a well known Distibuted Powe contol (DPC) scheme in [,]. Hee we pesent simulation esults and compaisons fo point-to-point communication with andom node placement. We also combined the schemes SSCD and DPC with a tee based boadcast algoithm BIP to obtain boadcast tee in ad-hoc netwoks with powe contol. We show the effectiveness of the new algoithm though simulations. Key wods and Phases: Enegy efficiency, Wieless Netwok, Distibuted Powe Contol. I. INTRODUCTION In any wieless multiple-access system, the need fo powe contol is evident. The poblems of boadcast access in allwieless netwoks ae being cuently studied. Seveal aticles study point-to-point and multicast/boadcast communication fo example see [], [],[],[],[],[],[],[]. In [] we consideed the poblem of deiving a new distibuted powe contol scheme (SSCD) using state space and optimal contol in discete time. We poved the convegence of the oveall netwok and compaed the effectiveness of ou method to the DPC method [], [] fo unifomly placed nodes. Hee we implement DPC and SSCD and make compaisons fo andomly placed nodes. The wieless netwoking envionment pesents fomidable challenges to the above study. Among the most difficult issues elated to mobile wieless applications is that of opeation in limited-enegy envionments. In this pape we popose to use distibuted powe contol scheme with one of the main Quality of Sevice featue that consides SIR fo the addition of each node in boadcast tee method. The schemes developed in [], [] addess the issues of tansmitte powe levels (and hence netwok connectivity), and the fomation of a link (outing). This appoach elies on the node-based natue of wieless communication. To assess each complex tade-off sepaately, we assume the following: No mobility. The availability of a lage numbe of bandwidth esouces. (So that contention fo channel is not an issue) Sufficient tansceive esouces ae available at each node. (So calls ae neve blocked) The channel conditions ae unchanged. Unde these assumptions we focus on the detemination of minimum-enegy boadcast tee constuction taking into consideation the SIR. In the following sections we study the Wieless communication model (Section ), Powe contol appoaches (Section ), Minimum enegy boadcast tee (Section ), Boadcast incemental powe (BIP) with SIR (Section ), Simulations (Section ) and conclusions (Section ). II. A WIRELESS COMMUNICATIONS MODEL In wieless netwoks it is possible to establish a node between any pai of nodes, povided that each has a tansceive available fo this pupose and that the SIR at the eceive node is sufficiently high, (i.e above the equied theshold). The nodes in the wieless netwoks ae detemined depending on factos such as distance between nodes, tansmitte powe, eo-contol schemes, othe-use intefeence, and backgound noise. Futhemoe, in wieless netwoks no distinction can be made between up-node and down-node taffic. This complicates the intefeence envionment. The connectivity of the netwok depends on the tansmission powe and the intefeence at the eceive node. Assuming that each node can set its own powe level, which is not to exceed a maximum value P max. We assume that the eceive signal powe vaies as α, whee is the ange and α is a paamete that typically takes on a value between and depending on the chaacteistics of the communication medium. III. POWER CONTROL APPROACHES Ou goal is to maintain a equied SIR theshold fo each netwok node while the tansmitte powe is adjusted so that the least possible enegy is consumed. Suppose thee ae n nodes in the netwok. Let G ij be the powe loss(gain) fom the tansmitte of the ith node to the eceive of the jth node. It involves the fee space loss, multi-path fading, WCNC / IEEE Communications Society ---//$. 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shadowing, and othe adio wave popagation effects, as well as the speading/pocessing gain of CDMA tansmissions []. The powe attenuation is taken to follow the invese fouth powe law i P ij j G ii = g ij α, () Calculation of SIR R i at ith node, [] R i = G ii P i (Σ j =i G ij P j + η i ), () whee i, j ɛ {,,,..., n}, P i is the i th node s tansmitte powe and η i > is the themal noise at its eceive node. Fo each node i thee is a lowe SIR theshold γ. Wetake the theshold to be the same as γ fo all nodes, eflecting a cetain QoS the node has to maintain in ode to opeate popely. Theefoe, we equie fo evey i =,,,.., n. R i γ () A. Distibuted Powe Contol(DPC): The above condition is used to minimize the tansmitte powe but it is not mandatoy. If the equation () fails (i.e R i <γ) then the tansmitte powe of the tansmitte has to be updated using equation (). Theefoe each node independently inceases its powe when its cuent SIR is below its taget γ, and deceases it othewise. The associated powe update can be obtained fom [] as P i (k +)= γp i(k) R i (k) whee k =(,,,..) (see [] - []). If P i (k +)>P max, the new node is not added. If the powe slips unde the minimum theshold powe P i (k +)<P min (the minimum powe needed to fom a link), then we keep P i (k+) = P min. SIR potection of an active node Fo any active node i, that we have R i (k) γ => R i (k +) γ. This implies that a new node is added if and only if the new state of the system is stable, i.e. none of the existing nodes ae boken. The final state contains all the feasible nodes added out of n nodes maintaining a stable state. Though the wok of [] can be expessed in the above algoithm, but thee is stong evidence that the powe update can cause convegence poblems. We poposed a state space scheme fo updating the tansmitte powe [] which addesses the limitations of DPC. B. State Space-based Contol Design (SSCD): Using state space theoy [] ou goal is to maintain a equied SIR theshold fo each netwok node while the tansmitte powe is adjusted so that the least possible enegy is consumed. Using () the SIR denoted hee as, R i, at the (k +)th iteation can be witten as () Pik Fig.. The wieless boadcast advantage. P i,(j,k) = max{p ij,p ik } R i (k + l) =R i (k)+v i (k), () whee by definition R i = P i /I i, and intefeence I i (k) = (Σ n j =i P j Gij G ii + ηi G ii ), with n is the numbe of active nodes. The v i in each system should only depend on the total intefeence poduced by the othe uses. To maintain the SIR of each node above a desied taget its new powe is computed as follows, P i (k +)=R i (k +) I i (k). () Using this new tansmitte powe, the ae calculated and checked till the stable state of all the nodes is achieved. IV. MINIMUM ENERGY BROADCAST TREE The Boadcast Incemental powe algoithm (BIP) in [] detemines the minimum- powe tee outed at the souce node, that eaches all the othe nodes in the netwok. Fo wieless netwoks, this is a difficult poblem fo which no scalable solutions appea to be available. Theefoe, this heuistic based algoithm is explained in []. This is a node-based (athe than link-based) appoach because it enables to exploit the wieless multicast advantage. Wieless boadcast advantage P ij =powe needed fo link between Node i and Node j = α whee is the distance between node Node i and Node j. An example of boadcasting to destination nodes which includes wieless boadcast advantage is shown hee. In this simple example, thee ae two altenative stategies:. S tansmits using P s : both D and D ane eached.. S tansmits using P s : only D is eached. D then tansmits to D with powe P, esulting in a total powe of P s + P. Hee, souce-initiated, cicuit-switched, boadcast sessions have been consideed. The netwok consists of N nodes, andomly distibuted ove a specific egion. Any node is pemitted to initiate boadcast sessions. Each boadcast goup consists of a souce node. Some of the nodes may act as elays also, eithe to povide connectivity to all membes of the boadcast goup o to educe oveall enegy consumption o both. These set of nodes that suppot a boadcast session (the souce node, all othe nodes with in the ange) is efeed to as a boadcast tee. The connectivity of the netwok depends on the tansmission powe. Assuming that each node can choose its own powe k WCNC / IEEE Communications Society ---//$. IEEE Authoized licensed use limited to: Univesity of Texas at San Antonio. Downloaded on May, at :: UTC fom IEEE Xploe. Restictions apply.
S Fig.. D Boadcasting to two destinations level, which is not to exceed a maximum value P max.we assume that the eceiving signal powe vaies as α, whee is the ange and α is a paamete that typically takes on a value between and depending on the chaacteistics of the communication medium. Based on this model the tansmitting powe equied to suppot a link between two nodes, sepaated by ange, is popotional to α. The Boadcast Incemental Powe (BIP) Algoithm pesented in [] (based on Pim s minimum spanning tee algoithm) [] is detemined to get the minimum-enegy tee being outed at the souce node that eaches all the othe nodes in the netwok. This algoithm exploits the wieless boadcast advantage in the constuction of the boadcast tee, but the QoS issues ae not consideed in []. Hee we included one of the main QoS issue i.e. SIR at the eceiving nodes and pesent the following algoithm. V. BROADCAST INCREMENTAL POWER (BIP) WITH SIR We next pesent the distibuted algoithm [] fo constucting a boadcast tee with powe contol. We denote the local souce node by SN. Algoithm:. Each SN eceives the position (i.e. coodinates of each node) of a subset of the nodes to be diectly linked to it.. SN stats the boadcast tee fomation accoding to the BIP algoithm in []. Befoe adding a new link to the tee: a. Each futue eceive node calculates the SIR and checks against its theshold. b. The new SIR will be sent to SN. c. SN checks the SIR, if any of the conditions () o () is not satisfied then the new tansmitting powes ae calculated accoding to the equations () and() espectively.. If any new nodes ae still unlinked then, Go to step. Else tee constuction is complete. The final tee is the minimum-enegy boadcast tee, fo the given set of N nodes. D VI. SIMULATIONS The setup fo the simulation expeiments to investigate DPC schemes developed in [] and ou SSCD is as follows. The netwok egion is assumed to span a squae egion of side units. All eceiving nodes have the same SIR taget γ =dbm. The nomalized noise floo η i /g fom equation () is taken to be the same fo all eceives and equal to.e. The initial powe value fo each node is assigned as P = dbm. We have an uppe limit on the powe of each tansmitte i.e. P max =dbm. When the tansmitte powe of an active node is in dange of exceeding P max, while a new inactive node is being admitted, the new node is not added to the system. A new node is added only if it maintains the system s stable state even afte its addition. The of all the active nodes ae maintained just above the taget γ. Point to point simultaneous links In the fist scenaio, we conside point to point links Figue (with a tansmitte and a eceive) which ae placed andomly. In ode to geneate a spatially unifom statistical mixtue of links, each one is andomly constucted as follows. Fo evey new link, the link tansmitte is unifomly placed in the given squae egion. The link eceive is placed isotopically aound its tansmitte (given a efeence diection, the link angle is distibuted in [, π) unifomly) and at a andom distance fom it. In this scenaio, we can see that the speed of convegence is faste fo SSCD appoach in compaison with the DPC appoach Figue and. In the above un the DPC scheme took moe than iteations whee as SSCD took less than iteations Figues and. One moe obsevation hee is, that the fluctuation of in DPC is moe and it often goes below the theshold (γ =.). In SSCD its minimal. Fom this we can say that the active links ae potected bette in SSCD than in the DPC scheme. In tems of system capacity, the SSCD scheme admits moe new links than DPC scheme. This clealy shows the supeioity of SSCD scheme ove the DPC scheme. Also, the total enegy of the system is moe fo SSCD when compaed to DPC []. This can be explained as a tadeoff between the total enegy consumed and the speed of convegence. Boadcasting In this scenaio, a boadcast tee is constucted based on the above algoithm. Shown hee Figue is a scenaio with nodes andomly placed and node as the souce node. The above algoithm is simulated with both the DPC and SSCD appoachs. The of each node ae plotted while the tee was foming. Figue shows the DPC appoach while Figue shows the SSCD appoach. The final tee consumes minimum enegy and is stable until a new node aives. Fom the figues we can see that DPC conveges faste than SSCD appoach while the total enegy consumed by SSCD appoach is less than DPC appoach. VII. CONCLUSIONS This pape pesents an enegy efficient powe contol scheme fo boadcast in wieless netwoks. We implemented two existing Distibuted Powe Contol schemes (SSCD and DPC). At fist, we compae them fo andomly placed nodes WCNC / IEEE Communications Society ---//$. IEEE Authoized licensed use limited to: Univesity of Texas at San Antonio. Downloaded on May, at :: UTC fom IEEE Xploe. Restictions apply.
link link link link link link link link link link Fig.. Random distibution of links fo point to point communication. Then we include these two schemes as pat of the new algoithm fo boadcast communication. We un simulations to study the feasibility of the new boadcast algoithm and compaed the contol schemes as pat of this algoithm. Fig.. DPC with Random link ACKNOWLEDGMENTS () NSF CCR- (-), () NASA NAG- (-), () State of Texas Highe Education Coodinating Boad though the Texas Advanced Reseach/Advanced Technology Pogam ATP -- REFERENCES [] A. Ephemides, J. E. Wieselthie and G. D. Nguyen, On the Constuction of Enegy-Efficient Boadcast and Multicast Tees in Wieless Netwoks. pp.-, IEEE INFOCOM. [] M. H. Amma, G. C. Polyzos and S. K. Tipathi, Special Issue on netwok suppot fo multipoint communication IEEE Jounal on Selected Aeas in Communications,, Apil. [] N. Bambos, Towads Powe-Sensitive Netwok Achitectues in Wieless Communications:concepts, issues and Design Aspects. IEEE Pesonal Communications, pp.-, June. [] N. Bambos, S. Chen and G. J. Pottie, Channel Access Algoithms with Active Link potection fo Wieless Communication Netwoks with Powe Contol. IEEE ACM Tansactions on netwoking, pp.-, Octobe. [] G. J. Foschini and Z. Miljanic, A Simple Distibuted autonomous powe contol algoithm and its convegence. IEEE Tan. Veh. Tech., vol., pp.-, Apil. [] A. El-Osey, and C. Abdallah Distibuted Powe Contol in CDMA Cellula Systems, IEEE Antennas and Popagation Magazine, Vol., No., August. [] T. S. Rappanpot, Wieless Communications, Pinciples and Pactices, book Pentice Hall,. [] F.L. Lewis, Optimal Contol, John Wiley and Sons,. [] A. T. Chonopoulos, J. Saangapani, S. Ponipieddy, Distibuted Powe Contol in Wieless Communication Systems, at the IEEE Intenational Confeence on Compute Communications and Netwoks (ICCCN ), Oct., pp -. [] N. Hescovici, C. Chistodoulou, A. El-Osey, and C. Abdallah Distibuted Powe Contol in CDMA Cellula Systems, IEEE Antennas and Popagation Magazine, Vol., No., August. [] C. Tang and C. S. Raghavenda, Enegy Efficient Adaptation of Multicast Potocol in Powe Contolled Wieless Ad Hoc Netwoks, Intenational Symposium on Paallel Achitectues, Algoithms and Netwoks (ISPAN ) May, [] K. Obaczka, G. Tsudik Multicast Routing Issues in Ad Hoc Netwoks, IEEE. link link link link link link link link link link Fig.. SSCD with Random link Fig.. Conveged Boadcast Tee WCNC / IEEE Communications Society ---//$. IEEE Authoized licensed use limited to: Univesity of Texas at San Antonio. Downloaded on May, at :: UTC fom IEEE Xploe. Restictions apply.
node node node node node node node node node node - - - - Fig.. DPC node node node node node node node node node node - - - - Fig.. SSCD WCNC / IEEE Communications Society ---//$. IEEE Authoized licensed use limited to: Univesity of Texas at San Antonio. Downloaded on May, at :: UTC fom IEEE Xploe. Restictions apply.