EXPLOITING GEOMETRICAL NODE LOCATION FOR IMPROVING SPATIAL REUSE IN SINR-BASED STDMA MULTI-HOP LINK SCHEDULING ALGORITHM

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1 Inernaonal Journal of Technology (2015) 1: ISSN IJTech 2015 EXLOITING GEOMETRICAL NODE LOCATION FOR IMROVING SATIAL REUSE IN SINR-BASED STDMA MULTI-HO LINK SCHEDULING ALGORITHM Nachwan Adransyah 1*, Muhamad Asval 1, Bago Budarjo 1 1 Deparmen of Elecral Engneerng, Faculy of Engneerng, Unversas Indonesa, Kampus UI Depo, 16424, Indonesa (Receved: July 2014 / Revsed: December 2014 / Acceped: December 2014) ABSTRACT Ths paper proposes a novel approxmaon for a Spaal Tme Dvson Mulple Access (STDMA) ln-schedulng algorhm based on geomercal node exploaon o mprove spaal reuse performance. The geomercal locaon of nodes was exploed n order o reduce compuaonal complexy and o acheve hgher accuracy n ransmsson o sasfy he Sgnal o Inerference and Nose Rao (SINR) requremen. The process of SINR global checng s a man consran n he SINR based nerference model bu s reduced hrough geomercal paron and nerference approxmaons based on geomercal node locaons. Smulaon resuls show ha he proposed algorhm ncreases he spaal reuse performance n comparson o he greedy physcal nerference model n smlar scenaros. The model ulzng geomercal paron exhbs lower complexy compared o he pure physcal nerference model ha ncludes SINR global checng. Keywords: Approxmaon algorhm; Geomercal node locaon exploaon; Ln schedulng; Mesh newor; STDMA 1. INTRODUCTION Varous developmens regardng resource allocaon algorhms have been wdely revewed by researchers n effors o ulze he nformaon o mprove he performance of wreless communcaon newors (Shara e al., 2009). Of specal neres are mesh or mul-hop opologes whch are mporan canddaes for use n realzng ubquous newors n he fuure era (Ayldz e al., 2005) and as poenal newors for varous applcaons (Bruno e al., 2005). There s a resource allocaon opporuny for achevng hgher effcency of mesh newor capacy hrough explong he possbly of usng he same meslo for dfferen communcaon lns. Ths could be acheved as long as hose ransmssons do no degrade he overall qualy of he mnmum hreshold, or so-called Spaal Tme Dvson Mulple Access or STDMA (Nelson & Klenroc, 1985). STDMA ln schedulng algorhms under he SINRbased nerference model (Gupa & Kumar, 2000) are consdered o be opporunes for mprovng wreless mesh newor performances and have been shown o have a beer spaal reuse and hroughpu performance han he graph-based model (Grönvs & Hansson, 2001). However, because SINR checng processes mus be done eravely for every acve ln and for every meslo, hs performance s more compuaonally complex and s harder o resolve. In prevous wor on SINR-based ln schedulng algorhm developmen, a SINR Graph Ln Schedule (SGLS) algorhm was proposed (Gore & Karandar, 2011) and consequenly * Correspondng auhor s emal: nachwan.muf@u.ac.d, Tel , Fax ermaln/doi: hp://dx.do.org/ /ech.v61.781

2 54 Explong Geomercal Node Locaon for Improvng Spaal Reuse n SINR based STDMA Mul hop Ln Schedulng Algorhm provded he bes spaal reuse resul o dae alhough he compuaonal complexy was hgh. On he oher hand, algorhms wh boh greedy (Brar e al., 2006) and geomerc approaches (Blough e al. 2010; Lu e al., 2012) showed lower complexy when compared wh he SGLS algorhm, bu connued o resul n lower spaal reuse. New modfed greedy-based algorhm have been proposed n our prevous wor (Adransyah e al.) n order o ncrease wreless mesh newor hroughpu capacy and lengh of schedulng. In hs paper, we exend he proposed algorhm by usng exploaon of he geomerc node locaon parameers n order o opmze spaal reuse performance. In oher words he sum of he ln s degree and schedulng wegh as a new parameers are exploed o provde hgher spaal reuse and a less complex algorhm. Addonally, he sum of he ln s degree and schedulng wegh are used as a bass of deermnng ln schedulng prores. The combnaon of hese parameers orderng are assessed as a means o oban he bes performance of he proposed algorhm. The percenage of he overall ln ha has been scheduled s proposed as a conrol varable o adjus he schedule wegh orderng, wheher he order s ascendng or descendng. Ths paper s organzed as follows: secon 2 descrbes he mul-hop ln schedulng problem formulaon and he smulaon model. Secon 3 descrbes he proposed algorhm. Secon 4 presens he smulaon resuls and analyss, and secon 5 presens he algorhm s complexy analyss. Fnally, he concluson and acnowledgmens are presened n secons 6 and 7, respecvely. 2. ROBLEM FORMULATION AND SIMULATION MODEL 2.1. Mul-hop Ln Schedulng roblem Formulaon A wreless mesh or mul-hop newor can be modeled as a connecvy graph, expressed mahemacally as (.) GV (, E ), conssng of a number of nodes (or verces) ha are conneced by lns (edges) whch ndcae a communcaon ln beween he nodes. Se of nodes (verces) saed asv v1, v2,..., v n, where v j represens he node j n mesh newor v v E, and se of lns (edge) expressed as (.), so ha, j E (, j),, j 1, 2,..., L, j so ha e (, j) E. N and L are respecvely he number of nodes and lns n he mesh newor. The capacy of arbrary wreless newors s lmed o nerference and can be assessed usng one of wo models; he proocol (graph-based) model or he physcal (SINR-based) nerference model (Gupa & Kumar 2000). To beer gauge he capacy performance, hs sudy employed he SINR-based nerference model raher han he graph-based model. In he SINR based nerference model, mulple lns can be allocaed o a parcular meslo as long as hose ransmssons do no degrade he communcaon hreshold ha s measured n he SINR parameer. For arbrary ln, for example e ha s nfluenced by oher lns e l ha are allocaed o he same meslo, he requremen of he SINR-based nerference model s expressed n Equaon 1. d c No V dj (1) where s ransmsson power, d s an eucldan dsance of ln.e. ransmsson ln from

3 Adransyah e al. 55 ransmer n node v o recever n node v j. The s exponen pahloss, N 0 s nose densy n recever, and c s a communcaon hreshold. STDMA proocol access deermnes he ransmsson ha s rgh for each meslo. Hence, he oupu of he ln schedulng algorhms s he funcon of STDMA ln schedulng, noaed as SS ( 1, S2,..., S C ), where C s he number of meslos needed o schedule all of he acve lns. The STDMA ln schedulng problem formulaon model s depced n Fgure 1. S(.) e S 11 S 21 S C1 S 12 S 22 S C 2 S 1M 1 S 2M 2 S CM C Fgure 1 The STDMA ln schedulng problem In wreless mesh newor ln schedulng opmzaon problems, an objecve funcon and consrans as Ineger Lnear rogrammng (IL) s formulaed n Equaon 2. Objecve: Subjec o: C maxu r e C1: x 1 e E 1 C2: x xj 1 V, jv ee eje C3: x R 1 v V, R v V C4: x 1 T v V, R vjv j v ( ) x d C5: e c E, (2) v ( ) N0 eje\ e dj where Ur e s he objecve of opmzaon n mesh ln schedulng problem as a funcon of user daa rae, r e. Consran C1 guaranees ha each acve ln scheduled a leas once along

4 56 Explong Geomercal Node Locaon for Improvng Spaal Reuse n SINR based STDMA Mul hop Ln Schedulng Algorhm C meslos, where x s he bnary varable o ndcae ha ln e s scheduled o be ransm n meslo or no, and x 0,1. Consran C2 guaranees ha each node can no send and receve a he same me. Consrans C3 and C4 guaranee ha durng a meslo, a node can ransm o, or receve from, only one node. Consran C5 expresses he SINR-based nerference model evaluaon Smulaon Model Smulaon was conduced usng he Mone-Carlo mehod of generang a random opology npu ha s dsrbued over square-meer areas and hen performs he processes of evaluang he mesh opology from communcaon graphs and schedulng all of he acve lns of he proposed algorhm. Smulaon was repeaed 1000 mes, each me wh dfferen random posons of he nodes usng dfferen newor opologes. The smulaon model s depced n Fgure 2. Fgure 2 Smulaon model Average spaal reuse s a common parameer for measurng he wreless mesh newor performance. Ths parameer descrbes he newor capacy and effcency of he mul-hop mesh wreless newor. If I (.) s he ndcaor funcon, hen spaal reuse s defned as he average number of lns ha have SINR c normalzed wh he number of used meslos, as follows (Gore & Karandar, 2011). 1 j1 3. THE GEOMETRIC NODE LOCATION EXLOITATION AROACH In he geomerc node locaon exploaon approach, he locaon of each node s assumed o be nown from he Global osonng Sysem (GS) or Ad-hoc osonng Sysem (AS) (Nculescu & Nah, 2003). Geomercal paron s used o deermne he canddae ln o be scheduled concurrenly for parcular meslos. In Fgure 3(a), can normavely be saed ha mulple lns can be allocaed o he same meslo f hese requremens are sasfed: - node v s n dfferen bloc paron wh node v and node v l - node v s n dfferen bloc paron wh node v and node v j These normaves also sasfy he consrans n C2, C3, and C4 n Equaon (2). C M I SINR C r c (3)

5 Adransyah e al. 57 v j e v e l v v l (a) (b) Fgure 3 Ln: (a) n (22) paron sze; (b) nerference analyss Inerference quanfcaon can be represened by he nerference wegh, w l, as a funcon of he consdered ln dsance and ransmer, of oher ln recever dsances, and of he pah loss exponen as follows: d d l wl max, (4) dl dj Furhermore, schedulng wegh, w ' l, s defned as follows : w' 1 w l For havng SINR guaranee, equaon (6) can be derved from Equaon (1) below. d c I N (6) N I d o For each allocaon, he requremen n equaon (6) for SINR guaranee should be sasfed. l c (5) In Fgure 3(b), he oal number of nerferer blocs experenced n he cener bloc s 8, where = 1 f he nerference s observed from he frs chan, and = 2 f he nerference s observed from he second chan. If he number of parons s n 2, hen he accumulaed nerference experenced n he cener bloc, I, shown n Fgure 3(b) above, can be derved as follows: I m1 m2... = m m s (2 s) s s frs er second er where m s he number of nerferer from -er and s s paron wde. For generaly, Equaon (7) can be derved as follows: I n 1 d j (7) (8)

6 58 Explong Geomercal Node Locaon for Improvng Spaal Reuse n SINR based STDMA Mul hop Ln Schedulng Algorhm Consran 5 n Equaon (2) s sasfed by subsung Equaons (6) o (8) yelds, n 1 dj cd N (9) Equaon (9) defnes he requremen for he acve lns allocaon o parcular meslos based on SINR-based nerference model. The degree of verex ( ) s an mporan node parameer ha can be exploed n ln schedulng algorhms. In hs paper, he sum of a ln s degree ( ) s defned, where. The algorhm prorzes o schedule lns wh maxmum j ha s mean o prorze dense opology n he evaluaed area. The pseudo code of he proposed algorhm s as follow: The roposed Algorhm: Inpu: Sored ln se based on he sum ln s degree : GV (, E) EG ( ) e, e,..., e Oupu: Transmsson schedule S S, S,..., S 1 2 Seps of algorhm: 1. Mesh newor coverage dvded no 2. Inalzaon: 1; E ( G) E( G ) 3. S uc 2 n paron blocs; 1 2 l 4. Selec one acve ln from Euc ( G ) based on he sum ln s degree of communcaon ln ( ),.e. e ; hen allocae n S ; S e ; 5. Creae a ls of canddae lns ha can be allocaed o slo- concurenly wh e,.e e wh crera : l - v and v l n dfferen paron wh v - v and v j n dfferen paron wh v 6. Sor canddae lns based on schedulng wegh, d dl w' l 1max, dl dj 7. Selec one canddae, e.g. e l o be evaluaed. If S, hen S S e l I d l N, allocae e l o 8. Reurn for oher canddaes 9. = +1, repea sep 3 o 9 unl all lns are desgnaed o be scheduled ; Euc( G) S 10. Compue ln schedulng performance 4. RESULTS AND DISCUSSION Smulaon parameer sengs are shown n Table 1. In hs paper, we analyze he performance of he average spaal reuse parameer ha s proporonally nfluenced by he newor

7 Adransyah e al. 59 hroughpu capacy. Smulaon was conduced o observe he effec of he sum of ln s degree and schedulng wegh orderng combnaon, and o observe he effec of he number of canddae ln lmaons. Table 1 Smulaon parameer sengs arameers Symbol Value Bandwdh W 10 MHz Transmsson power 10 mw ah loss exponen β 4 Nose power specral densy N 0-90 dbm Communcaon hreshold c 20 db Inerference hreshold 10 db Area covered R R m 2 In frs expermen, he effec of he sum ln s degree and schedulng wegh orderng were examned. Ths process occurs n seps 4 and 6 n he pseudo-code program. There were four scenaros o explong geomercal node locaon, as follows: - Scenaro 1; Descendng degree, and descendng schedulng wegh w ' - Scenaro 2; Descendng degree, and ascendng schedulng wegh w ' - Scenaro 3; Ascendng degree, and descendng schedulng wegh w ' - Scenaro 4; Ascendng degree, and ascendng schedulng wegh w ' The smulaon resuls of he effecs of he scenaros appear n Fgure Average of Spaal Reuse Scenaro Scenaro 3 Scenaro 2 Scenaro Number of nodes (a) Average of Spaal Reuse Number of nodes Fgure 4 The effec of schedulng wegh and degree of nodes combnaons o spaal reuse performance Fgure 4(a) shows ha scenaro 2 provded he bes spaal reuse performance and scenaro 4 provded he wors performance. In scenaro 2, he ln wh he maxmum sum of he lns degree was allocaed o a parcular meslo. The canddae lns wh mnmum wegh were (b) x = 0% x = 25% x = 50% x = 75%

8 60 Explong Geomercal Node Locaon for Improvng Spaal Reuse n SINR based STDMA Mul hop Ln Schedulng Algorhm seleced o be allocaed o he same meslo. I can be concluded ha scenaro 2 prorzed he lns n he dense areas o be allocaed earler and prorzed he near lns o be allocaed o he same meslo o ncrease effcency. The maxmum value acheved by scenaro 2 n hs expermen was (110 nodes) and he mnmum value of spaal reuse was 2.09 (30 nodes). In he nex expermens, we dffered he canddae lns sor order based on he percenage of he overall ln ha was scheduled n seps 6 and 7. If he lns ha had been scheduled dd no exceed x%, hen he subsequen schedulng was sared from he lowes wegh. Conversely, f he lns ha had been scheduled exceeded x%, he schedulng was sared from he hghes wegh. Ths process was nended o mprove he effcency of schedulng when he newor was sll n a dense condon and he majory of he ln had no ye been scheduled. Therefore, schedulng sarng from he hghes wegh ndcaed ha schedulng was naed from nearby lns. Smulaon resuls shown n Fgure 4(b) shows ha he seng of x = 50% provdes he bes performance, bu a slgh dscrepancy occurs wh a resul of x = 75%. The maxmum value of he average spaal reuse s and he mnmum value s The comparson references used were he basc Greedy hyscal (G) (Brar e al., 2006), he Arborcal Ln Schedule algorhm (ALS) (Ramanahan & Lloyd, 1993) whch s based on graph-based nerference model, and he SINR Graph Ln Schedule (SGLS) whch s based on SINR-based nerference model (Gore & Karandar, 2011). The number of nodes vared from 30 o 110. In general, for nodes lower han 30 n number, mesh opology has no been esablshed. The smulaon resuls of performance compared o ha of mesh ln schedulng algorhms are presened n Fgure Average of Spaal Reuse ALS (Ramanahan e al) 1.5 G (Brar e al) SGLS (Gore e al) roposed algorhm Number of nodes (a) Number of nodes Fgure 5 The performance comparson of mesh ln schedulng algorhms Inerference Margn (db) (b) Fgure 5(a) depcs he comparson of he proposed algorhm wh he ohers. The proposed algorhm performed beer han boh he G algorhm (Brar e al., 2006) and he ALS algorhm bu performed below he spaal reuse algorhm (Gore & Karandar, 2011). Based on our smulaon resuls, he average spaal reuse performance of he proposed algorhm was 5.05% beer han he G algorhm and 7.14% worse han he SGLS algorhm performance. The proposed algorhm guaranees ha he acual SINR for all scheduled lns wll be above he communcaon hreshold, c. The average dfference beween he acual SINR from he communcaon hreshold, also called he nerference margn, s depced n Fgure 5(b). From hese fgures, can be concluded ha here s an opporuny o ncrease he mesh newor capacy.

9 Adransyah e al COMUTATIONAL TIME COMLEXITY Due o me consran, he analyss of he proposed algorhm me complexy was deermned by usng asympoc me complexy analyss. In he npu process, he paron evaluaon was performed for each ransmng node n he acve lns n order o creae he node s geomercal parameer and he canddae lns ha could be ransmed concurrenly wh he evaluaed ln, so ha hs processes requres O(e) operaons. The se of acve lns s sored based on he sum ln s degree requres O(e log e) operaons. The calculaon of he nerln co-schedule-ably wegh aes O(e 2 ) operaons. So ha, he npu generaor requres O(e + e log e + e 2 ) O(e 2 ). In he proposed algorhm, he frs sep s o selec a ln wh a larges sum of ln s degree o allocae o he frs meslo and read s canddae lns. Furhermore, sorng he canddae lns and selec one ln wh hghes (or lowes) schedulng wegh o be SINR evaluaed requres O(ec logec) me, where ec<eand n he wors case ec= e. SINR checng for m canddae lns requres O(m) complexy where m s he number of lns ha s allocaed o he same meslo and. Ths process s repeaed unl all lns have been allocaed. The oal me complexy of he proposed algorhm s O(e(ec log ec + m)). Furhermore, n he wors case he oal compuaonal complexy s approxmaed o O(e(e log e + m)) O(e 2 log e). The comparson of he compuaonal me complexy wh oher algorhms s shown n Table 2. Table 2 Compuaonal me complexy comparson Inerference model Algorhm Compuaonal me complexy SINR-based SINR graph ln schedule (SGLS) algorhm O(e 3 ) SINR-based Greedy hyscal (G) algorhm O(ve 2 ) Graph-based Arborcal Ln Schedule (ALS) algorhm O(ev log v + v 2 ) SINR-based roposed algorhm O(e 2 log e) For he able above, e s he number of acve lns, v s he number of nodes, s he hcness of graph, and s he maxmum node degree. 6. CONCLUSION The research shows ha geomercal node locaon parameers, such as he sum of a ln s degree and dsance, derved hrough nerference and schedulng wegh parameers, can be exploed o mprove he spaal reuse n a SINR-based STDMA wreless mesh newor. Ths mprovemen proporonally ncreases he newor hroughpu. The smulaon resuls show ha he proposed approxmaon algorhm can ncrease he spaal reuse performance wh smlar complexy wh he convenonal greedy physcal algorhm. 7. ACKNOWLEDGEMENT The frs auhor would le o acnowledge he suppor of D s BDN gran number 908/D/T/2010 for pursung a docoral degree a he Unversas Indonesa.

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