Performance optimization of a MAC protocol with multiple. contention slots in MIMO ad hoc networks

Transcription

1 Performance opimizaion of a MAC proocol wih muliple conenion lo in MIMO ad hoc nework Qiang Gao *, Li Fei, Jun Zhang, Xiao-Hong Peng 2 School of Elecronic and Informaion Engineering Beihang Univeriy, Beijing 009, P.R.China 2 Elecronic Engineering, School of Engineering & Applied Science Aon Univeriy, Birmingham B4 7ET, Unied Kingdom * Correponding auhor. Tel.: gaoqiang@buaa.edu.cn Abrac The Muliple-Inpu Muliple-Oupu (MIMO) echnique can be ued o improve he performance of ad hoc nework. Variou medium acce conrol (MAC) proocol wih muliple conenion lo have been propoed o exploi paial muliplexing for increaing he ranpor hroughpu of MIMO ad hoc nework. However, he exience of muliple reque-o-end/clear-o-end (RTS/CTS) conenion lo repreen a evere overhead ha limi he improvemen on ranpor hroughpu achieved by paial muliplexing. In addiion, when he number of conenion lo i fixed, he efficiency of RTS/CTS conenion i affeced by he ranmiing power of nework node. In hi paper a join opimizaion cheme on boh ranmiing power and conenion lo number for maximizing he ranpor hroughpu i preened. Thi include he eablihmen of an analyical model of a implified MAC proocol wih muliple conenion lo, he derivaion of ranpor hroughpu a a funcion of boh ranmiing power and he number of conenion lo, and he opimizaion proce baed on he ranpor hroughpu formula derived. The analyical reul obained, verified by imulaion, how ha much higher ranpor hroughpu can be achieved uing he join opimizaion cheme propoed,

2 compared o he non-opimized cae and he reul previouly repored. Key word: ad hoc nework, MIMO, performance opimizaion, MAC proocol wih muliple conenion lo, ranpor hroughpu Inroducion Wirele ad hoc nework have araced a grea deal of aenion in variou applicaion for heir flexibiliy o operae wihou any infrarucure. The Muliple-Inpu Muliple-Oupu (MIMO) echnique ha alo been widely applied in wirele nework for miigae fading effec and conequenly enhance performance of he nework [-3]. Recen reearch on MIMO ad hoc nework ha mainly focued on eiher miigaing fading of wirele link by exploiing paial diveriy [4-6] or improving he efficiency of nework by exploiing paial muliplexing [7-2]. To employ he MIMO echnique in ad hoc nework he medium acce conrol (MAC) proocol need o be properly deigned. The convenional MAC proocol deigned for Single-Inpu Single-Oupu (SISO) yem have been exended o exploi he paial diveriy in MIMO yem [3, 6] in ad hoc nework. In paricular, ome new MAC proocol have alo been propoed o creae paial muliplexing of MIMO ranmiion [8-2]. Spaial muliplexing in a MIMO ad hoc nework form muliple link in a neighborhood for imulaneou daa ranmiion o improve he ranmiion efficiency of he nework [7]. In [8] a muliple conenion lo MAC proocol named Miigaing Inerference uing Muliple Anenna MAC (MIMA-MAC) ha been propoed. The ranmier ue a ingle anenna from he available muliple anenna for daa ranmiion and he receiver ue all he muliple anenna equipped for ignal recepion and inerference uppreion. The medium acce conenion in muliple reque-o-end/clear-o-end (RTS/CTS) conenion lo i inroduced for 2

3 muliple ranmier in a neighborhood before imulaneou daa ranmiion ake palce. An enhanced verion of hi MAC proocol wih muliple conenion lo called Miigaing Inerference uing Muliple Anenna wih Anenna Selecion MAC (MIMA/AS-MAC) i preened in [9]. Similar approache are alo repored, uch a he Parallel RTS Proceing MAC proocol for conrolling he maximum number of coexiing daa ream in a neighborhood [0], he Muliple Anenna Receiver-Iniiaed Buy-Tone MAC proocol [], and a MAC proocol ha ake ino accoun of he rengh of inerference and he paial correlaion beween inerference and he deired ignal in order o exploi he inerference cancellaion capaciy of he MIMO yem [2]. However, o he be of our knowledge, in he MAC proocol ha employ muliple conenion lo for muliple ranmier in a neighborhood, he effec of he conenion lo number and ranmiing power on ranpor hroughpu have no been inveigaed and conequenly he work on join opimizaion of hee wo facor for improving ranpor hroughpu ha no been repored. In he MAC proocol ha employ muliple RTS/CTS conenion lo, muliple ranmier in a neighborhood conend for medium acce before ranmiing heir daa imulaneouly. The muliple RTS/CTS conenion lo impoe a evere overhead ha limi he performance improvemen by exploiing paial muliplexing in ad hoc nework. Therefore, here i a need o opimize he number of conenion lo in order o have he be rade-off beween he paial muliplexing gain and he overhead caued by muliple RTS/CTS conenion lo. For a given number of conenion lo, he efficiency of RTS/CTS conenion in a MAC proocol will alo be affeced by he ranmiing power ha deermine he number of neighboring node. Therefore, o maximize ranpor hroughpu he number of conenion lo and ranmiing power hould be opimized joinly. In hi paper, we 3

4 eablih an analyical model for a implified MAC proocol wih muliple conenion lo in MIMO ad hoc nework. Baed on hi model, ranpor hroughpu, a a funcion of he number of conenion lo and ranmiing power, i derived and maximized hrough he join opimizaion of he wo facor. Boh numerical and imulaion reul are produced o how he benefi of he cheme propoed hrough comparion wih oher MAC proocol and he implified proocol wihou opimizaion. The paper i organized a follow. In Secion 2, a implified MAC proocol wih muliple RTS/CTS conenion lo i inroduced. In Secion 3, an analyical model of he MAC proocol i eablihed. Numerical and imulaion reul are preened wih dicuion in Secion 4. In Secion 5 he effec of channel error on he performance i analyzed. Finally, we conclude he paper in Secion 6. 2 The MAC proocol wih muliple RTS/CTS conenion lo We aume ha each node in an ad hoc nework i equipped wih muliple anenna. To exploi paial muliplexing, a ranmiing node ranmi independen daa ream from one of he muliple anenna o one receiving node, while a he receiving node all he anenna are ued o receive he daa and uppre inerference [8-0]. The number of receiver anenna deermine he degree of freedom (DOF), which i equal o he maximum number of coexiing link in a neighborhood [9]. The channel i aumed quai-aic and hu unchanged during he ranmiion of a packe. When he number of independen daa ream i le han or equal o DOF, he receiver can differeniae he daa ream received imulaneouly and uppre inerference hrough ome algorihm uch a zero-forcing or maximum likelihood deecion baed on he eimaed channel ae informaion [9]. Therefore, 4

5 muliple ranmier-receiver pair can coexi in a neighborhood when paial muliplexing i creaed in an ad hoc nework. To allow muliple ranmier in a neighborhood o ranmi daa o heir arge receiver imulaneouly, ome MAC proocol wih muliple conenion lo have been propoed, i.e. MIMA-MAC [8] and i enhanced verion [9-2] which have more delicae funcion uch a anenna elecion, parallel RTS proceing and buy one medium acce. In [2] he paial correlaion beween he ignal and inerference i aken ino accoun o exploi he paial dimenion of freedom offered by MIMO in deigning he MAC proocol. In hi paper we will inveigae he effec of he conenion lo number and ranmiing power on ranpor hroughpu, aiming o improve he ranpor hroughpu by joinly opimizing hee wo facor. In our inveigaion, in order o keep he model from being over-complicaed, a implified MAC proocol i inroduced and udied, where only he eenial funcion for node o conend for medium acce and ranmi daa packe imulaneouly are included in he proocol. The mehodology ued here can be exended o embrace more complex funcion uch a carrier ene and back-off procedure in fuure work. The MAC proocol aume ha he node in he nework are ynchronized, which can be achieved by employing a cheme uch a he global poiioning yem (GPS). The ranmiion ime i divided ino fixed-ize frame. The frame rucure of he implified MAC proocol wih muliple conenion lo i hown in Fig.. A MAC frame conain four period: conenion period, raining period, daa period, and Acknowledgemen (ACK) period. The conenion period for medium acce coni of muliple RTS/CTS conenion lo. The raining period for raining equence ranmiion o eimae channel ae coni of muliple raining lo. The daa period i for imulaneou daa packe ranmiion by he ranmier which have acquired a channel during he conenion period. The ACK period for 5

6 he receiver ranmiing ACK packe o confirm ha hey have received he daa packe wihou error coni of muliple ACK lo. The number of conenion lo, raining lo and ACK lo are e o be he ame [9], and i denoed a m c. The adjacen frame are eparaed by Diribued Iner-frame Space (DIFS), and any wo adjacen period or lo wihin a frame are eparaed by Shor Iner-frame Space (SIFS). DIFS and SIFS are adoped from he IEEE 802. MAC andard. According o he frame rucure, he duraion of a frame f i given by = m ( + + ) + + DIFS () f c c r ACK D where c i he duraion of a conenion lo, r i he duraion of a raining lo, ACK i he duraion of an ACK lo, and D i he duraion of daa period. Compared wih oher lo he duraion of a raining lo i very hor [8-0]. Oher duraion are given repecively by LRTS + LCTS = + 2 SIFS (2) r c b ACK D L r ACK = + (3) L r b SIFS D = + (4) b SIFS where packe, r b i he ranmiion bi rae; RTS L D i he ize of a daa packe, and L i he ize of a RTS packe, L CTS i he ize of a CTS L ACK i he ize of an ACK packe, all in bi. To beer explain he MAC proocol, we preen an exemplary proce of he proocol in Fig. 2. Four node wih wo anenna each are locaed wihin he ranmiion range of each oher, a hown in Fig. 2 (a). Node wan o end a daa packe o node 2; likewie node 3 inend o end a daa packe o node 4. The ranmier randomly elec a conenion lo o ranmi he RTS packe o i arge receiver for medium acce conenion. If he receiver ha no daa o ranmi and ha no received any 6

7 RTS packe before, i replie wih he CTS packe in he correponding CTS ub-lo. The node ha have uccefully exchanged RTS/CTS acquire a ranmiion channel. In hi example, he RTS/CTS exchange beween node and node 2 i conduced in conenion lo and he RTS/CTS exchange beween node 3 and node 4 i conduced in conenion lo 2, a hown in Fig. 2 (b). The ranmier and he receiver deermine which raining lo and ACK lo o ue baed on he conenion lo in which hey have uccefully exchanged RTS and CTS. Therefore, in hi example, node and node 3 ue raining lo and raining lo 2, repecively, and node 2 and node 4 ue ACK lo and ACK lo 2, repecively. During he daa period, he ranmier ha acquire a channel during he conenion period will ranmi daa packe imulaneouly. Receiver are reponible for proceing he received daa and uppreing inerference uing he eimaed channel ae informaion. 3 Syem model of he MAC proocol We conider a MIMO ad hoc nework coniing of N node ha are uniformly diribued in an a a quare area. Each node in he nework i equipped wih D anenna, i.e., he degree of freedom i D. We define he neighborhood of a node a a group of node ha are wihin he ranmiion range of he node. The average node number in he neighborhood of an arbirary node x including ielf, M, i given by M = ( N ) P n + (5) where z denoe he large ineger ha doe no exceed real z and n P i he probabiliy ha an arbirary node i wihin he neighborhood of node x, and i given by Pn R = f ( r) dr (6) 0 where R i he maximum ranmiion diance of node x. A in [3], he probabiliy deniy 7

8 funcion characerizing he diance r beween wo node in he quare area, f ( r ), i given by and 4r f ( r) = f 4 0( r) (7) a π 2 2 a 2 ar + r, 0 r a a a 2 f0( r) = a arcin( ) + 2a r a a a arcco( ) r, a r 2a r r 2 0, oherwie (8) We aume ha he free pace propagaion model i applied wih quare-law pah lo, hence R i given by c P R = (9) 4π f P c rh where f c i he carrier frequency, c i he peed of ligh, P i he ranmiing power, and P rh i he minimum required ignal power received by he receiver or receiver eniiviy. We aume ha a node generae a new packe deined o i neighbor afer a random idle period ha i exponenially diribued wih an average of λ econd, where λ i he average number of packe generaed in a node per econd. The probabiliy ha a node ha daa o ranmi a he beginning of a MAC frame, p, i given by f e λ p = (0) Suppoe ha an arbirary node x ha a newly generaed packe deined o a randomly eleced node y in i neighborhood. In he implified MAC proocol he ranmiion from node x o node y i ucceful if and only if he following condiion are aified: 8

9 (i) during he conenion period he RTS/CTS exchange beween node x and node y i ucceful; (ii) node y receive all he raining equence from neighboring ranmier uccefully in order o eimae channel ae; (iii) he number of ranmier, k, ha have acquired a channel wihin y neighborhood i le han he degree of freedom (DOF), D, and hereby node y can receive daa packe from node x correcly and uppre he inerference produced by neighboring ranmier; and (iv) node x can uccefully receive he confirmed ACK packe from node y. There i no more han one ACK packe ranmied in one lo a he index of ACK lo i deermined by ha of conenion lo where he ranmier and he receiver have uccefully exchanged RTS and CTS packe. Therefore, here i no colliion in ranmiion of ACK packe. The probabiliy of ucceful daa packe ranmiion from node x o node y can be expreed a P = P{ RTS / CTS exchange beween x and y i ucceful} P{ y receive all he raining quence from neighboring ranmier uccefully} D k = 0 P{ k ranmier beide x wihin y ' neigborhood acquire channel} () Since node x randomly elec a conenion lo o exchange RTS/CTS packe wih node y, he fir probabiliy erm in Eq.() i given by P{ RTS / CTS exchange beween x and y i ucceful} m c = [ P{ x elec he ih conenion lo} i= P{ RTS / CTS exchange beween x and y in he ih conenion lo i ucceful}] = m c m c i= P{ RTS / CTS exchange beween x and y in he ih conenion lo i ucceful} (2) 9

10 The probabiliy erm of he la line in Eq. (2) can be derived a follow. The probabiliy ha here are M node beide node x in he neighborhood of node y ha have daa o ranmi a he beginning of a frame i given by P{ M node beide x wihin y ' neighborhood have daa o ranmi} M 2 M M 2 M = p ( p), M = 0,, 2, M 2. M (3) The probabiliy ha here are M 2 node among M node ha have daa deined o node y i given by P{ M node have daa deined o y M } M 2 M 2 M M2 = ( ) ( ), M 2 = 0,, 2, M. M 2 M M (4) Le A denoe he even ha M node do no ranmi RTS packe in he i h lo, and A 2 denoe he even ha node y ha no uccefully received RTS packe from M 2 node before he i h lo. The probabiliy ha boh A and A 2 occur can be expreed a P( A I A ) 2 = P( A ) P( A A ) 2 = P( A ) [ P( A A )] 2 (5) where P( A ) ( mc ) m M c M =, and (6) 0

11 M i ( 2) m P( A2 A ) = M ( mc ) 2 M c, i >, M M > 0, and m > 2 0, oherwie. 2 c (7) Suppoe ha M node beide node x in he neighborhood of node y have daa o ranmi a he beginning of a MAC ime frame, among which M 2 node have daa deined o node y. The RTS/CTS exchange beween node x and node y in he i h conenion lo i ucceful only if i) node y ha no daa packe o ranmi; ii) M node do no ranmi RTS packe in he i h lo; and iii) node y ha no uccefully received RTS packe from M 2 node before he i h lo. The correponding probabiliy can hen be formulaed a P{ RTS / CTS exchange beween x and y in he ih conenion lo i ucceful M, M } = P{ y ha no daa o ranmi} P( A I A ) = ( p) P( A I A ) (8) Combining Eq. (3)-(8), he probabiliy erm in Eq. (3) can be obained accordingly a P{ RTS / CTS exchange beween x and y in he ih conenion lo i ucceful} M 2 M = [ P{ M node beide x wihin y ' neighborhood have daa o ranmi} M= 0 M 2 = 0 P{ M node have daa deined o y M } 2 P{ RTS / CTS exchange beween x and y in he ih conenion lo i ucceful M, M }] 2 (9) Now le u conider he econd probabiliy erm in Eq. (). Node y receive all he raining equence from neighboring ranmier uccefully if and only if he raining equence from neighboring ranmier of node y are ranmied in eparae raining lo. According o he

12 implified MAC proocol preened in Secion 2, i i he ranmier and he receiver ha deermine which raining lo o ue baed on he conenion lo in which hey have uccefully exchanged RTS and CTS packe. The neighboring ranmier of node y excep node x (e.g., node T and node T 2 in Fig. 3) may conend for medium acce uccefully in he ame conenion lo (e.g., he j h lo) due o heir arge receiver (e.g., node R and node R 2 in Fig. 3) being locaed far from each oher. In hi cae, he raining equence from node T and node T 2 can no be received uccefully by node y. Thu he even ha he neighboring ranmier of node y ranmi heir raining equence in eparae raining lo i equivalen o ha here are le han wo node among he node in he nework which uccefully conend for medium acce in an arbirary conenion lo i wihin he neighborhood of node y. The econd probabiliy erm in Eq. () i given by M j P{ y can receive all he raining quence} = Pn ( Pn ) j= 0 j M j (20) where M i he average number of node in he nework excep node y ha uccefully conend for medium acce in an arbirary conenion lo, and i i given by M p Pc ( N ) = mc where [ z ] denoe he ineger ha i cloe o real z, (2) P c denoe he probabiliy ha an arbirary node in he nework conend for medium acce uccefully, which i probabiliy ha node x and one of i neighboring node y exchange RTS/CTS uccefully and i expreed by Eq.(2). The hird probabiliy erm in Eq. () i given by P{ k ranmier wihin y ' neigborhood acquire channel} M = = k 2 ( ) k ( ) M 2 k p Pc p Pc, k 0,,2, M 2. (22) 2

13 Combining Eq. ()-(22), he probabiliy of ucceful daa packe ranmiion from node x o node y, P, can be calculaed accordingly. Given he ize of a daa packe, L D, he ime duraion of he MAC frame, f, he number of node in he nework, N, and he probabiliy ha a node ha daa o ranmi a he beginning of a MAC frame, p, we define he nework carried load, G, in bi per econd a G L N p D = (23) f We alo define he produc of hroughpu (in bi per econd) and average diance beween ranmier and receiver in he nework a he ranpor hroughpu. Thi bi-diance produc ha can be ranpored by he nework ha been ued a an indicaor of a nework capabiliy of ranporing daa from one end o he oher [3, 4]. The ranpor hroughpu S i given by S = P G E[ l] (24) where l i he random variable of diance beween ranmier and receiver. The probabiliy deniy funcion of l i given by [3] f ( l) 2 l, 0 l R R 0, oherwie. 2 = (25) 3

14 The average diance beween ranmier and receiver i given by R 2l 2 E [ l] = l dl = R 0 2 R 3 c = 6π f c P P rh (26) Combining Eq. (23), (24), (26) and (), ranpor hroughpu S can be obained a S [ ] = P G E l N p LD c P = P m ( + + ) + + DIFS 6 π f P c c r ACK D c rh. (27) The parameer ued for repreening c, ACK and D can be found in Eq. (2)-(4). 4 Reul and dicuion In hi ecion boh he analyical model eablihed in he la ecion and he imulaion mehod are ued o evaluae he performance of he implified MAC proocol wih muliple conenion lo in MIMO ad hoc nework. Our primary goal of hi work i o inveigae he effec of ranmiing power P and he number of conenion lo m c on he ranpor hroughpu of he nework. For hi purpoe, we e phyical and link layer parameer in relaion o Eq. (27) baed on he IEEE 802. pecificaion, a ued in [8-0]. All he yem parameer ued are ummarized in Table. Table : The ummary of parameer Parameer Value Parameer Value 4

15 N 200 L CTS (24+4) 8 bi a 000 m L D ( ) 8 bi f c 2.4 GHz L ACK (24+4) 8 bi P rh dbm r 0 µ r b Mbp DIFS 50 µ λ 5 SIFS 0 µ L RTS (24+20) 8 bi Fig. 4-8 how he reul of ranpor hroughpu in connecion wih ranmiing power and he number of conenion lo when he number of he anenna of a node (or DOF) i 4. In Fig. 4, he ranpor hroughpu i ploed again he number of conenion lo under eleced ranmiing power. The difference in ranpor hroughpu beween numerical and imulaion reul i wihin 5%, which confirm he effecivene of he analyical model derived. I can be een ha ranpor hroughpu increae raher harply wih he number of conenion lo when few conenion lo are ued in he MAC frame, ince in hi iuaion here are adequae reource available (a ufficien number of node which have daa o ranmi in a neighborhood and hence adequae DOF) for upporing imulaneou daa ranmiion in a neighborhood. A more conenion lo are ued, he overhead of muliple RTS/CTS conenion lo a a reul of he increaed number of conenion lo become everer and he number of imulaneou daa ranmiion i limied by DOF. Conequenly, ranpor hroughpu decreae a he number of conenion lo increae. Therefore, an opimal number of conenion lo can be deermined o maximize he ranpor hroughpu of he 5

16 nework, which i alo relaed o he ranmiing power, a hown in Fig. 5. In Fig. 6, he ranpor hroughpu i ploed again ranmiing power under differen number of conenion lo. Again, boh numerical and imulaion reul cloely agree wih each oher. Similar properie o hoe in Fig. 4 can be een here, i.e., wih low ranmiing power ued ranpor hroughpu increae a he ranmiing power increae. When ranmiing power i low here are few ranmiing node in a neighborhood. A he ranmiing power increae he number of neighboring node increae, and more node in a neighborhood will conend for medium acce uccefully o uppor imulaneou daa ranmiion; herefore he ranpor hroughpu i growing. When he ranmiing power i high, here are many node in a neighborhood conending for medium acce. A he ranmiing power increae he efficiency of medium acce conenion i reduced, reuling in fewer node in a neighborhood ha are able o conend for medium acce uccefully. Conequenly, he ranpor hroughpu will decreae. Again, an opimal ranmiing power can be deermined o maximize he ranpor hroughpu of he nework, which i varied wih he number of conenion lo available, a hown in Fig. 7. In Fig. 8, he ranpor hroughpu i depiced a a funcion of boh ranmiing power and he number of conenion lo. The curve marked wih circle illurae he maximum ranpor hroughpu correponding o he opimal number of conenion lo over ranmiing power. The curve marked wih quare illurae he maximum ranpor hroughpu correponding o he opimal ranmiing power over he number of conenion lo. The global maximum ranpor hroughpu, which i a reul of join opimizaion on boh ranmiing power and he number of conenion lo, i indicaed by he 6

17 dark olid circle and clearly ha a higher value han any of hoe produced by non-join opimizaion or non-opimizaion cheme. For example, he global maximum ranpor hroughpu can reach 49.5 Mbp*m when he opimal ranmiing power i 200 mw and he opimal number of conenion lo i 8. We have alo obained he opimal reul for DOF o be 2 and 3, repecively. The numerical and imulaion reul for he cae of DOF = 2, 3 and 4 are ummarized in Table 2. Obviouly, boh he opimal ranmiing power and opimal number of conenion lo and, conequenly, he global maximum ranpor hroughpu increae wih DOF. Thi i becaue a DOF increae, more poenial ranmier in a neighborhood can ranmi daa packe imulaneouly. Table 2: Opimizaion reul when DOF i 2, 3 and 4 DOF Opimal ranmiing power (mw) Opimal conenion lo number Global maximum ranpor hroughpu (Mbp*m) Numerical Simulaion Numerical Simulaion Numerical Simulaion In order o demonrae he improvemen of ranpor hroughpu achieved by uing join opimizaion on ranmiing power and he number of conenion lo, we imulae he implified MAC proocol wih join opimizaion, he implified MAC proocol wihou opimizaion, and MIMA-MAC propoed in [8-9]. In MIMA-MAC he carrier ene muliple acce wih colliion avoidance (CSMA/CA) mechanim i adoped o reduce colliion beween conending ranmier. Before he ranmiion of an RTS packe, here i a back-off period coniing of a mall number of mini-lo, during which he 7

18 ranmier randomly elec a mini-lo for ranmiing he RTS packe. In he implified MAC proocol (wih or wihou join opimizaion), however, he CSMA/CA mechanim doe no apply. For he implified MAC proocol wihou join opimizaion and MIMA-MAC, he ranmiing power i e o be 24.5 dbm and he number of conenion lo i choen a he ame a DOF ha i e o be 2 [9-0]. In Fig. 9, he ranpor hroughpu i ploed again he average number of packe generaed per econd λ a a node for differen MAC cheme. I can be een ha he implified MAC proocol wih join opimizaion achieve higher nework capaciy, in erm of he ranpor hroughpu, by 38% han MIMA-MAC, and 85% han he implified MAC proocol wihou join opimizaion, when λ i over 0 packe/. To how how he ranmiion bi rae affec he opimizaion reul, he ranpor hroughpu i ploed again conenion lo number under he ranmiion bi rae r b =, 5.5, Mbp, repecively, in Fig. 0 uing he numerical mehod. The ranmiing power i e o be 400 mw and DOF i 4. I can be een ha he maximum ranpor hroughpu are achieved a he differen opimal number of conenion lo when he bi rae change. The higher he bi rae he maller he number of conenion lo i required o maximize he ranpor hroughpu. The ranmiion rae for he preamble and Phyical Layer Convergence Proocol (PLCP) header a he phyical layer remain Mbp when ranmiion bi rae increae from Mbp o Mbp, hu he RTS/CTS conenion co in he MAC proocol wih muliple conenion lo will increae. The RTS/CTS conenion co can be reduced hrough he opimizaion proce ha reul in fewer conenion lo o be ued for medium acce conenion when higher ranmiion bi rae i adoped. 8

19 5 Performance analyi of he MAC proocol wih channel error In he udie above channel error i no conidered in our model. To inveigae how channel error affec he performance of he MAC proocol wih muliple conenion lo in MIMO ad hoc nework he error probabiliy i inroduced ino he model. There are five ype of packe o ranmi in he implified MAC proocol, namely RTS, CTS, raining equence, daa, and ACK packe. The RTS, CTS and ACK packe are ranmied in he SISO manner. The MIMO paial muliplexing echnique i employed o ranmi daa packe. The raining equence i ued o eimae he channel ae and normally conidered o be error free [9-2]. A Rayleigh-fading channel wih quare-law pah lo i aumed. We alo aume ha no error correcion code (ECC) block are included in he yem. For SISO ranmiion he ignal i furher aenuaed on op of he quare-law pah lo by a fading calar, which i a zero-mean circularly ymmeric complex Gauian (ZMCSCG) random variable wih uni variance. The received ignal-o-noie raio (SNR) γ SISO i a random variable and i probabiliy deniy funcion i given by [5] f ( γ ) SISO SISO _ γ SISO = e (28) _ γ SISO γ where _ γ i he average received SNR and given by SISO _ γ SISO G P P = (29) N where P N i he background noie power level a he receiver. Under he free pace propagaion model, G i given by G c 2 = ( ) 2 (30) 4π fc l where l i he diance beween he ranmier and he receiver. 9

20 Since he RTS, CTS and ACK packe are relaively hor, he ranmiion of hee packe i aumed ucceful when he received SNR a he receiver γ SISO i above a given hrehold γ 0 if here i no conenion. In hi cae, he probabiliy of ucceful ranmiion of RTS, CTS and ACK packe beween arbirary wo node i given by p SISO = P( γ > γ ) = γ 0 SISO 0 f ( γ ) dγ SISO SISO (3) The average probabiliy of ucceful RTS, CTS and ACK packe ranmiion beween a node and i neighboring node i given by R = (32) 0 SISO SISO P p f ( l) dl where f ( l ) i he probabiliy deniy funcion of he diance beween arbirary wo node, which i given by Eq. (25). For MIMO ranmiion wih paial muliplexing, he ignal i furher aenuaed on op of he quare-law pah lo by a calar fading marix, in which each enry i an independen and idenically diribued ZMCSCG random variable wih uni variance. Suppoe ha a node receive k + ( k < D ) daa ream imulaneouly from i neighboring node and he i h daa ream i deined o ielf. A hown in [6], when we ue a zero-forcing (ZF) receiver for inerference cancellaion, he SNR probabiliy deniy funcion of he i h daa ream can be calculaed a γ _ MIMO γ MIMO D ( k + ) γ _ MIMO f ( γ MIMO ) = e ( ) _ γ Γ( D k) γ MIMO MIMO (33) where Γ( ) denoe he Gamma funcion. he receiver, which i given by _ γ i he average SNR of he daa ream deined o MIMO 20

21 _ γ MIMO G P P = (34) N The receiver can receive he deined daa ream uccefully if he SNR γ MIMO of he daa ream exceed he given hrehold γ 0. Thu if he number of daa ream i no more han DOF he probabiliy of ucceful daa packe ranmiion beween arbirary wo node i given by p MIMO = P( γ > γ ) = γ 0 MIMO 0 f ( γ ) dγ MIMO MIMO (35) The average probabiliy of ucceful daa packe ranmiion beween a node and i neighboring node i given by R = (36) 0 MIMO MIMO P p f ( l) dl If channel error i conidered Eq. () will be changed o Eq. ( ), a hown below, for calculaing he probabiliy ha a ucceful ranmiion from an arbirary node x o one of i neighboring node in he implified MAC proocol. In hi expreion four condiion mu be aified, which are decribed in Secion 3. P = P{ RTS / CTS exchange beween x and y i ucceful} P{ y receive all he raining quence from neighboring ranmier uccefully} D MIMO [ P P{ k ranmier beide x wihin y ' neigborhood acquire channel}] k = 0 P SISO ( ) where SISO P repreen he impac of channel error on ACK packe ranmiion, and MIMO P repreen he impac of channel error on daa packe ranmiion. In addiion, he impac of channel error on he exchange beween RTS and CTS packe along wih he effec of conenion mu be included in he calculaion of he probabiliy of ucceful RTS/CTS exchange, hu Eq. (2) i changed o 2

22 P{ RTS / CTS exchange beween x and y i ucceful} m c SISO 2 ( P ) [ P{ x elec he ih conenion lo} i= = P{ RTS / CTS exchange beween x and y in he ih conenion lo i ucceful}] (2 ) In Fig., he effec of channel error on ranpor hroughpu i demonraed hrough a comparion beween he cenario wih channel error conidered, where Eq. ( ) and (2 ) are ued, and he cenario wihou conidering channel error, where Eq. () and (2) are ued. I can be ee ha he exience of channel error will caue reducion in ranpor hroughpu a any number of conenion lo; however, he opimal number of conenion lo for obaining he maximum hroughpu remain unchanged. For he reul in Fig., he SNR hrehold i e o be 0 db and he background noie power i -90dBm. 6 Concluion In hi paper, we have inveigaed he impac of ranmiing power and he number of conenion lo on he ranpor hroughpu of MIMO ad hoc nework where he MAC proocol wih muliple conenion lo i employed. Baed on he inveigaion, we have preened a cheme o maximize he ranpor hroughpu of he nework by joinly opimizing he number of conenion lo and ranmiing power of nework node. We have hown wih boh analyical and imulaion reul ha ignifican improvemen in ranpor hroughpu can be achieved hrough he join opimizaion, in comparion wih non-opimizaion approache. For example, when DOF i 2 he implified MAC proocol wih join opimizaion ouperform boh MIMA-MAC and he implified MAC proocol wihou join opimizaion in ranpor hroughpu by 38% and 85%, repecively, when λ i over 0 packe/. We have alo examined he effec of DOF, he ranmiion bi rae and channel error on he opimized reul. In paricular, i i hown ha increaing he bi rae will lead o he reduced opimal 22

23 number of conenion lo, while he inroducion of channel error doe no affec he opimal number of conenion lo alhough he maximum achievable hroughpu i reduced. Our reul can be ued a a guideline in elecing proper ranmiing power and he number of conenion lo for he deign of fuure MAC proocol in MIMO ad hoc nework. Acknowledgemen Thi work wa uppored by he Naional Naural Science Foundaion of China (Key Program) under Gran No , Naional Fund for Diinguihed Young Scholar under Gran No , Naional High Technology Reearch and Developmen Program of China (863) under Gran No. 2008AA0Z29, and Aviaion Fund under Gran No. 2007ZD5049. The auhor would like o expre heir graiude o he Edior and all reviewer for heir inighful commen and uggeion ha have grealy improved he paper. Reference [] Chen, B., and Gan, M.J.: MIMO communicaion in ad hoc nework, IEEE Tran. Signal Proce., 2006, 54, (7), pp [2] Chu, L., Yuan, J., and Chen, Z.: A coded beamforming cheme for frequency-fla MIMO fading channel, IET Commun., 2007,, (5), pp [3] Roeo, F., and Zorzi, M.: A low-delay MAC oluion for MIMO ad hoc nework, IEEE Tran. Wirel. Commun., 2009, 8, (), pp [4] Gelal, E., Jakllari, G., and Krihnamurhy, S.V.: Exploiing diveriy gain in MIMO equipped ad hoc nework. Proc Forieh Ailomar Conf. Signal, Syem and Compuer, Pacific 23

24 Grove, CA, USA, Oc.-Nov. 2006, pp. 7-2 [5] Fakih, K., Diouri, J.F., and Andrieux, G.: On he capaciy opimizaion for MIMO ad hoc nework. Proc IEEE Vehicular Technology Conf., Singapore, -4 May 2008, pp [6] Khojaepour, M.A., Wang, X., and Madihian, M.: MIMO hroughpu opimiaion via quanied rae conrol, IET Commun., 2007,, (3), pp [7] Sundarean, K., Sivakumar, R., Ingram, M.A., and Chang, T.Y.: Medium acce conrol in ad hoc nework wih MIMO link: opimizaion conideraion and algorihm, IEEE Tran. Mob. Compu., 2004, 3, (4), pp [8] Tang, T., Park, M., Heah, Jr. R.W., and Nele, S.M.: A join MIMO-OFDM ranceiver and MAC deign for mobile ad hoc neworking. Proc In. Workhop on Wirele Ad-Hoc Nework, 3 May-3 Jun. 2004, pp [9] Park, M., Heah, Jr. R.W., and Nele, S.M.: Improving hroughpu and fairne for MIMO ad hoc nework uing anenna elecion diveriy. Proc. IEEE 2004 Global Telecommunicaion Conf., 29 Nov.-3 Dec. 2004, pp [0] Shirau, M., and Saae, I.: A MAC proocol for maximum ream allocaion depending on he number of anenna and received RTS packe in MIMO ad hoc nework. Proc. IEEE 2007 In. Conf. Communicaion, Glagow, Scoland, Jun. 2007, pp [] Wang, D., and Tureli, U.: Cooperaive MIMO-OFDM and MAC deign for broadband ad hoc nework. Proc. IEEE 2005 Miliary Communicaion Conf., 7-20 Oc. 2005, pp [2] Ke, B.W., Zhang, Y.J., and Liew, S.C.: Media acce conrol wih paial correlaion for MIMO ad hoc nework. Proc. IEEE 2007 In. Conf. Communicaion, Glagow, Scoland, Jun. 24

25 2007, pp [3] Hu, J.L., and Rubin, I.: Performance analyi of muli-rae capable random acce MAC proocol in wirele muli-hop nework. IEEE h In. Symp. Peronal, Indoor and Mobile Radio Communicaion, Helinki, Sep. 2006, pp. -5 [4] Gupa, P., and Kumar, P.R.: The capaciy of wirele nework, IEEE Tran. Inform. Theory, 2000, 46, (2), pp [5] Simon, M.K., and Alouini, M.S.: Digial communicaion over fading channel: a unified approach o performance analyi (WILEY-INTERSCIENCE Pre, 2000) [6] Paulraj, A., Nabar, R., and Gore, D.: Inroducion o pace-ime wirele communicaion (CAMBRIDGE UNIVERSITY Pre, 2003) 25

26 Figure Fig. The frame rucure of he implified MAC proocol wih muliple conenion lo Fig. 2 Exemplary proce of he MAC proocol Fig. 3 An example of neighboring node of y conending for medium acce Fig. 4 Tranpor hroughpu over he number of conenion lo under eleced ranmiing power level, DOF = 4 Fig. 5 Opimal number of conenion lo over ranmiing power, DOF = 4 Fig. 6 Tranpor hroughpu over ranmiing power under differen number of conenion lo, DOF = 4 Fig. 7 Opimal ranmiing power over he number of conenion lo, DOF = 4 Fig. 8 Tranpor hroughpu a a funcion of ranmiing power and he number of conenion lo, DOF = 4 Fig. 9 Tranpor hroughpu over he average number of packe generaed per econd λ a a node for differen MAC cheme Fig. 0 Tranpor hroughpu over he number of conenion lo under differen ranmiion bi rae, DOF = 4 Fig. Tranpor hroughpu over he number of conenion lo wih and wihou channel error, P = 20 mw, DOF = 4 26

27 Fig. Fig. 2 27

28 Fig. 3 Fig. 4 28

29 Fig. 5 Fig. 6 29

30 Fig. 7 Fig. 8 30

31 Fig. 9 Fig. 0 3

32 Fig. 32