PHY-AC dialogue with ulti-packet Receptio arc Realp 1 ad Aa I. Pérez-Neira 1 CTTC-Cetre Tecològic de Telecomuicacios de Cataluya Edifici Nexus C/Gra Capità, - 0803-Barceloa (Cataluya-Spai) marc.realp@cttc.es Departmet of Sigal Theory ad Commuicatios Politechic Uiversity of Cataloia (UPC) Campus Nord-mòdul D C/Jordi Giroa,1-3 0803-Barceloa (Cataluya-Spai) auska@gps.tsc.upc.es Abstract.- Cross-layer desig has bee cosidered recetly as a ew approach whe desigig AC protocols i systems with diversity such as CDA. This paper goes oe step further i the cross layer desig by proposig a PHY-AC dialogue ivolvig the exchage of parameters such as BER ad active users. By meas of this PHY-AC dialogue, system performace ca be improved. A two-stage receiver is used at PHY level. The first stage tracks active users while the secod stage is a data demodulator. The odified Dyamic Queue Protocol (DQP) is proposed as the AC protocol of our system. Whe the kowledge of active users is possible, it is demostrated by simulatios that DQP outperforms DQP. I. Itroductio I wireless radom access chaels, a commo chael is shared by may users. The covetioal assumptio o the receptio capability of the commo chael is that whe two or more are trasmitted simultaeously a collisio occurs ad cosequetly, the iformatio is lost. To recover the iformatio, the collidig have to be retrasmitted ivolvig udesired effects o the throughput ad packet delay of the etwork. ay curret sigal processig techiques itroduce multi-packet receptio capability at physical layer by meas of spatial, time, frequecy or code diversity. The improvemet i throughput performace whe spatial or code diversity is itroduced is demostrated i [1],[],[3]. However, oe of them cosider cross-layer desig, i.e., the AC techiques applied are still workig uder the covetioal assumptio of collisio. The idea of cross-layer desig is based o the iteractio betwee layers i order to improve system performace. ay articles i the literature make referece to the physical layer packet receptio capability by usig the so called multi packet receptio (PR) matrix. Each elemet of this matrix is the probability of successfully receive k whe have bee set. Basically, these probabilities ca be obtaied from bit error rate ad biomial distributios. Some AC algorithms are developed based o this PR matrix ad hece, PHY-AC dialogue reduces to a BER exchage. The work i [] is perhaps the first to itroduce the cocept of PR matrix. I this article, modificatios of the retrasmissio probability of the Aloha protocol are preseted. I [] ad [6] ew AC proposals are show. I [], the Dyamic Queue Protocol (DQP) is described. Assumig that each user has a probability q to have a packet waitig for trasmissio ad cosiderig the PR matrix, a optimal user access set is obtaied which miimises packet delay ad maximises etwork throughput. Besides, QoS costraits are icluded i [6]. A improved zero forcig estimator for CDA is developed i [7]. That is a two-stage multi user detector based o traffic burstiess theory: i)i the first stage, active users are detected by meas of both power detectio ad traffic iformatio. ii)i the secod stage, a zero forcig estimator is implemeted usig the active users sigature vectors oly. Our goal is to go oe step further o the cross-layer desig i order to achieve eve better performaces. Basically, by meas of PHY-AC dialogue, system performace ca be improved. Sice the problem of detectig active users i a dyamic CDA system is ot ew [8],[9],[10], we propose to use the kowledge of active users as a iformatio parameter to improve AC efficiecy. I our work, the first stage of the trafficaided multi user detector for CDA preseted i [7] is cosidered. Chages from CDA to spatial diversity systems are straightforward. O the other had, the DQP i [] has bee modified ad used as the referece AC protocol of our system to demostrate the improvemets achieved usig PHY-AC iformatio. The orgaisatio of this paper is as follows. I the ext sectio, the cocept of the PR matrix is described thoroughly ad a PHY-AC dialogue is proposed. I sectio III the modified
dyamic queue protocol is preseted. Sectio IV gives some simulatios to show the improvemets achieved by meas of PHY-AC dialogue. Coclusios are give i sectio V. BER AC Active Users N i II. ulti-packet Receptio The PR matrix is the tool used to describe the capability of the receiver to detect more tha oe packet simultaeously. Cosiderig a system with users ad that the chael is such that the probability of receivig k successfully whe there are trasmissios depeds oly o the trasmitted, the followig probability ca be defied, C k, P[ k are correctly received are trasmitted] (1) 1 (um. of users) ; 0 k If the packet success probability (Ps()) of oe packet is idepedet of the others, C,k ca be computed aalytically as, Ck, B( k,, Ps( )) () Where B(k,,Ps()) deote de biomial distributio with probability Ps(), i.e, k BkPs (,, ( )) Ps ( ) (1 Ps ( )) k The, the PR matrix ca be defied as, C1,0 C1,1 0 0 C,0 C,1 C, 0 C 0 C C k,0, (3) If the expected umber of correctly received whe are set is defied as, C kc () k 1, k The, the capacity of the chael is ad cosequetly, 1,.., max C () PHY Figure 1. PHY-AC dialogue arg( max C ) (6) 0 1,.., gives the umber of that should be trasmitted simultaeously to achieve chael capacity. Sice the PR matrix etries deped o the packet success probability ad cosequetly o the bit error rate (BER), the BER exchage betwee PHY ad AC is implicit whe a AC algorithm uses the PR matrix. O the other had, by meas of the first stage of the receiver preseted i [7], it is possible to detect the active users i a slot. Assumig o error i the kowledge of the active users, this additioal iformatio is used at AC level to improve system performace. The Iformatio flows betwee PHY ad AC layers of our system are described i figure 1. Parameter N i refers to the optimal size of the users access set as described by the DQP i sectio III. The kowledge of the N i at the physical layer could be used to focus the active users search o the N i polled users. I essece, it could be used to simplify UD user codes selectio i the secod stage of the receiver i [7]. However, we focused our work i the desig of a more efficiet AC protocol by meas of the iformatio obtaied from the physical layer. III. odified Dyamic Queue Protocol III.a DQP Vs DQP We cosider the DQP as the basis for the odified DQP (DQP). The DQP is described i []. It is desiged for a system with users (or odes) who trasmit data to a cetral cotroller. The DQP divides the time axis i trasmissio periods (TP). I each TP, the geerated i the previous TP are trasmitted. A TP eds whe all the users of the system have bee polled ad the geerated i the previous TP have bee successfully received. A example is give i figure. P is defied as the probability of a ode to geerate a packet i a slot ad q i is the probability of a ode to have a packet waitig for trasmissio at the begiig of the ith TP. The,
Trasmit geerated before 0 Trasmit geerated i (0,] Trasmit geerated i (,] First TP Secod TP Third TP L1= L=3 L3= Figure. DQP Trasmissio Period q P 1 1 (1 ) L i i (7) where L i-1 is the legth of the previous TP. The basic structure of this protocol is a waitig queue where all users are processed i groups of access set size (N i ). Based o q i ad the PR matrix, the value of N i is chose so that the expected legth for the ith TP is miimised. Whe processig the received, the DQP assumes that the cetral cotroller is capable to distiguish betwee empty slots ad o-empty slots. I the case of a o-empty slot, the cetral cotroller is oly capable to determie the users of the access set who have successfully trasmitted their packet i the curret slot. O the cotrary, i a o-empty slot, the cetral cotroller is icapable to determie whether the remaiig users i the access set have trasmitted a packet with a collisio or have ot trasmitted ay packet. O the other had, with the additioal iformatio about users activity give by the physical layer of our system, the cetral cotroller is capable to distiguish users whose have bee trasmitted successfully, users whose have collided ad users who have ot trasmitted. Hece, the assumptios made about the cetral cotroller i DQP are o loger correct ad must be modified. This is show i figure 3. I that figure, the cetral cotroller sets Nopt to 3. I cosequece, the users of the system are polled i groups of three. For the DQP, the cetral cotroller ca ot distiguish whether ode 1 ad have empty buffers or their are lost due to collisio. The AC protocol polls odes 1 ad agai eve though they have empty buffers. Whe all the odes polled i a slot have empty buffers the, the cetral cotroller determies that o of the polled odes have a packet waitig to be trasmitted. Opposite to that, by meas of the user activity detector i the DQP, the cetral cotroller is able to determie that odes 1 ad have ot trasmitted a packet i the first slot ad cosequetly they are processed ad ot polled agai. Sice the time take to trasmit all the with the DQP is shorter, throughput ad packet delay are improved. III.b The optimal size of the access set The procedure to determie the optimal size of the access set (N i ) is the same as i the DQP. The N i for the ith TP is chose so that the expected legth of that TP is miimised. N i is the, N arg mi E[ L q, N] (8) i i i N1,.., where E[L i N] is the expected legth of the ith TP whe the size of the access is N. It ca be show that a fiite state discrete arkov chai ca be formed with states (j,k). Where j ( j 0) determies the umber of uprocessed users at the begiig of oe slot ad k (N k 0) determies the umber of to be trasmitted i that slot. The trasitio probability from state (j,k) to state (l,m) is differet depedig if we are dealig with the DQP protocol or with the DQP. For the DQP protocol that probability is give at the bottom of this page. Cosequetly, the trasitio probability matrix ca be writte as I R A 0 N r ( jk, ),( lm, ) Bm (,mi Nl,, qi ) ( if k 0, l max j N,0,0m mi N, l) Ck, j l NkB( m, mi jl, max jn,0, qi) if k N j l j N N l j m N l Ck, j l NkB( m jln, mi jl, max jn,0, qi) ( 1 mi,,, mi, ) ( if 1 k mi N, j, l j N, N l j m mi N, l,max j N,0 l mi( N, l)) 0 ( otherwise)
where I deotes the trasitio probability from a absorbig state to a absorbig state, i.e., the idetity matrix (i our system the absorbig state is the state (0,0)), 0 is a ull matrix represetig the trasitio probability matrix from a absorbig state to a o-absorbig state, A is the trasitio probability matrix with etries represetig the trasitio probability from a o-absorbig state to a absorbig state ad fially, the trasitio probabilities from o-absorbig states to o absorbig states are the etries of N. With that represetatio, the expected time util absorptio for the ith state is the sum of the ith row of the (I- N) -1 matrix. Hece, we ca defie a vector e with compoets e(j,k) represetig the expected time util absorptio of the state j,k. Besides, the iitial state of this arkov chai is always with j= ( uprocessed users). Hece, the iitial coditio of this arkov chai is give by P[X0=(,k)]=B(k,N,q i) for k=0,..,n (9) Sice E[L i N] ca be viewed as the expected time util absorptio, E[L i N] is computed as N i (10) k=0 E[Li N] = B( kn,, q) e (, k) Computig E[L i N] for all possible N, the N i which accomplishes (8) is chose as the optimum oe. IV. Simulatios This sectio presets some umerical results aimed to demostrate the advatages i terms of throughput ad packet delay give by the kowledge of the active users at AC layer. For these simulatios, throughput is defied as the umber of correctly received i oe slot ad packet delay is the average time (i slots) for a packet to be successfully trasmitted i a TP. I the examples show, the SNR at the receiver is always 10dB, data modulatio is BPSK. CDA diversity is used ad the user spreadig codes are obtaied from differet phases of a m- sequece with legth m 1. The user activity detector is assumed to detect active users without error ad hece, oly the active user codes are used for data demodulatio. For the secod stage of the receiver, a bak of matched filters (F) have bee used. Dyamic Queue Protocol odified Dyamic Queue Protocol No-empty slot. Node 3 packet successfully received. Node packet lost. No-empty slot. Nodes ad successfully received. empty slot No-empty slot. Node packet lost. Node 3 packet successfully received. Node 1 empty No-empty slot. Nodes ad successfully received. Node empty. Success. received packet Nopt=3 3 1 3 1 1 3 1 3 Packet Lost Packet waitig for trasmissio Empty buffer Cetral cotroller does ot kow whether from odes 1 ad have collided or the buffers of these odes were empty. Cetral cotroller determies that odes 1 ad have empty buffers. Figure 3. DQP Vs. DQP
Access Set Throughput Packet Delay Figure. Access Set Vs. User Packet Prob. =1 = q i q i DQP DQP =10 DQP DQP Figure. Throughput Vs. User Packet Prob. q i DQP DQP =1 =10 = Figure 6. Packet Delay Vs. User Packet chose to achieve chael capacity as described i (6). Figures ad 6 show differeces i throughput ad packet delay for a F receiver whe usig DQP ad DQP. For these simulatios, the gai factor is chose to be 6, packet legth equal to 00 bits ad a error correctig code is used capable to correct up to bits. It ca be oticed that throughput ad packet delay improvemets are achieved at low ad medium traffic. Furthermore, improvemets have are show for =, 10 ad 1. I low ad medium traffic, the user activity iformatio is used to process users with empty buffers whe they are polled for the first time. Hece, the TP legth ca be optimised. At high traffic, the user activity iformatio is less useful, i.e., almost all users are active ad there are o users with empty buffers to allow DQP reduce TP legth. As show i figure, access set is chose so that chael capacity is achieved. V. Coclusios This paper studies the possibility of usig PHY-AC dialogue for system performace improvemet. The cosidered flows of iformatio betwee PHY ad AC layers go oe step further i the cross-layer desig. The system cosidered is a CDA system with users sedig data to a cetral cotroller. O this basis, the receiver at the cetral cotroller is composed by i)a user activity detector alog with a data demodulator at the PHY level ad ii)a AC protocol which uses user activity iformatio. Particularly, the AC protocol used is a modificatio of the DQP protocol. DQP protocol already cosiders cross-layer desig by meas of the PR matrix. However, if oly the PR matrix were cosidered by the AC, the receiver capabilities i terms of multi-packet receptio would ot be ot fully exploited. Hece, a modified DQP protocol which uses the additioal kowledge of active users has bee preseted. Simulatios depicted system performace improvemet i terms of throughput ad packet delay. Figure, depicts the value of N i as a fuctio of q i for both, the DQP ad the DQP. From this figure oe ca otice that at low traffic the DQP access set size is bigger tha that for the DQP. This ca be uderstood sice at low traffic the umber of users with a packet waitig for trasmissio is low. I cosequece, for the DQP it is preferable to poll a large umber of users ad discard those of them who are ot willig to trasmit i the first slot of the TP. Cotrary, as the traffic icreases, a lower N i is preferable to avoid excessive collisios. At q i =1, the access set is Refereces [1] James Ward ad R.T. Compto, Improvig the performace of slotted ALOHA packet radio etwork with a adaptive array, IEEE tras. comm., vol. 0, NO., Feb. 199. [] _, High throughput slotted ALOHA packet radio etworks with adaptive arrays, IEEE tras. o comm., vol. 1, NO. 3, ar. 1993. [3] S. Roy ad H.Y. Wag, Performace of CDA slotted ALOHA multiple access with multiuser detectio, Wireless Commuicatios
ad Networkig Coferece 1999, vol., 1999 Page(s): 839-83. [] Sylvie Ghez, Sergio Verdú ad Stuart C. Schwartz, Optimal decetralised cotrol i the radom access multipacket chael, IEEE tras. o automatic cot., vol. 3, NO. 11, Nov. 1989. [] Qig Zhao ad Lag Tog, The Dyamic Queue Protocol for spread spectrum radom access etworks, ilitary Commuicatios Coferece 001, vol., 001, Page(s): 10 108. [6] Qig Zhao ad Lag Tog, A multi-queue service room AC protocol for wireless etworks with multipacket receptio, submitted to AC/IEEE tras. etworkig, Ja 001. [7] Biao Che ad Lag Tog, Traffic-aided multiuser detectio for radom-access CDA etworks, IEEE tras. o sigal proc., vol. 9, NO. 7, Jul 001. [8] K. W. Halford ad.bradt-pearce, Newuser idetificatio i a CDA system, IEEE tras. comm., vol. 6, Ja. 1998. [9] U. itra ad H. V. Poor, Adaptive decorrelatig detectors for CDA systems, J. wireless pers. comm., vol., Dec. 199 [10] W. WU ad K. Che, Idetificatio of active users i sychroous CDA multiuser detectio, IEEE J. select. areas comm., vol. 16, Dec. 1998.