IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATONS, VOL. 18, NO. 9, SEPTEMBER 2000 1701
A Nea -Op imum MAC P o ocol Based on
he Dis ibu ed Queueing Random Access
P o ocol (DQRAP) o a CDMA Mobile
Communica ion Sys em
Luis Alonso, Membe , IEEE, Ramón Agus í, Membe , IEEE, and O iol Sallen , Membe , IEEE
Abs ac —This pape p esen s and analyzes a new nea -op-
imum medium access con ol (MAC) p o ocol. The p oposed
access scheme is sui able o a CDMA mobile communica ion
en i onmen , and keeps unde con ol and uppe bounded he
numbe o simul aneous ansmissions. I has a delay pe o mance
app oaching ha o an ideal op imum M/M/ sys em, whe e is
he numbe o sp eading codes being used (maximum numbe o
simul aneous ansmissions). The p o ocol is a ee andom access
p o ocol when he a ic load is ligh , and swi ches smoo hly and
au oma ically o a ese a ion p o ocol when a ic load becomes
hea ie . I is based on dis ibu ed queues and a collision esolu ion
algo i hm. Mo eo e , a physical ecei e s uc u e is p oposed
and analyzed in o de o p ese e he obus ness o he p o ocol
in a wi eless link. The esul s ob ained show ha he p o ocol
ou pe o ms o he well known medium access p o ocols in e ms
o s abili y and delay, e en when aking in o accoun he loss
caused by channel p opaga ion condi ions.
Index Te ms—Code di ision mul iaccess, mobile communica-
ions, mul iaccess communica ion, p o ocols.
I. INTRODUCTION
IN THE LAST ew yea s, many esea ch e o s ha e ocused
on he design o medium access con ol (MAC) p o ocols.
In he u u e hi d-gene a ion communica ion sys ems, mixed
se ices and di e en a ic pa e ns will ha e o sha e he same
channel s uc u e and esou ces. MAC echniques mus p o ide
lexibili y and e iciency o allow he exis ence o hese ypes o
sys ems wi h easonable complexi y and eliabili y.
ALOHA and slo ed-ALOHA echniques ha e been widely
used in he pas as andom access p o ocols. Howe e , hei
low h oughpu (0.18 and 0.36 maximum) and po en ial ins a-
bili y a hea y a ic load ha e led o he appea ance o colli-
sion esolu ion algo i hms (CRA), also called ee algo i hms
[1], which ha e a highe pe o mance (up o 0.568 based on
e na y channel eedback [2]). Some p o ocols achie e highe
h oughpu by using con ol minislo s o ese a ion pu poses.
O all hese, he announced a i al andom access p o ocols
Manusc ip ecei ed July 1, 1999; e ised Feb ua y 25, 2000. This wo k was
suppo ed by CYCIT P ojec TIC 98-684. Pa o his wo k was p esen ed a
PIMRC’99, Osaka, Sep . 1999; and a VTC’99 Fall, Ams e dam, Sep . 1999.
The au ho s a e wi h he Depa men o Signal Theo y and Communica ions,
Uni e si a Poli ècnica de Ca alunya (UPC), Ba celona 08034, Spain (e-mail:
[email p o ec ed]; [email p o ec ed]; [email p o ec ed]).
Publishe I em Iden i ie S 0733-8716(00)07135-3.
(AARA) [3] achie e he bes delay and h oughpu pe o mance
(0.853 wi h only h ee con ol minislo s). Howe e , o each
h oughpu s app oaching uni y, he AARA p o ocols need a he-
o e ically in ini e numbe o minislo s, and his is ob iously im-
p ac ical and ine icien because o he o e head in oduced by
each minislo .
One widely s udied medium access p o ocol based on con-
ol minislo s is DQRUMA (dis ibu ed queue eques upda e
mul iple access) [15]. This p o ocol uses a ce ain numbe o
access minislo s o ese a ion pu poses. Te minals wi h da a
o ansmi send an access eques in one o hese minislo s
applying a slo ed-ALOHA s a egy. This eques con ains he
iden i ica ion numbe o he e minal and he ype and quali y
o he demanded se ice. The main ad an age o using his cen-
alized s a egy is ha i allows he designe o o ally con-
ol he beha io o he sys em. I is possible o gi e p io i y
o e minals wi h s ic quali y equi emen s, such as igh delay
bounds, ins ead o simply maximizing he o e all h oughpu .
Howe e , high complexi y algo i hms, a g ea amoun o sig-
naling and eedback in o ma ion, and accu a e admission con-
ol policies a e equi ed o he sys em o wo kco ec ly. Mo e-
o e , slo ed-ALOHA s a egy is used o accessing pu poses,
and hus he po en ial ins abili y p oblem is s ill p esen when
a ic load is high.
In gene al, me ely using con ol minislo s makes he sys em
mo e complex as i is necessa y o ha e ime slo s wi h di e en
ime sizes. Ne e heless, we obse e ha all exis ing ee p o-
ocols ha do no ha e minislo s use da a slo s o esol e colli-
sions, and hus lose he channel capaci y o all he emp y slo s
o collided packe s. The sugges ed imp o emen s o ee p o o-
cols seek o educe he numbe o collisions and emp y slo s,
bu hey do no elimina e his ype o e iciency loss. Keeping
all hese ideas in mind, Xu and Campbell p oposed he dis-
ibu ed queueing andom access p o ocol (DQRAP) [4], [5],
[19], which seems o be one o he bes -pe o ming MAC p o-
ocols p oposed o da e. This p o ocol uses h ee con ol minis-
lo s and is based on a ee- ype collision esolu ion algo i hm. I
wasini iallydesigned o aTDMAen i onmen ,pa icula ly o
he dis ibu ion o CATV (cable TV) signal. Inspi ed by DQDB
(dis ibu ed queueing dual bus, now he IEEE 802.6 s anda d o
me opoli an a ea ne wo ks), i s pe o mance app oaches ha o
an ideal M/D/1 queue, eaching maximum s able h oughpu s
close o one, and main aining i s s abili y o a ic loads up o
0733–8716/00$10.00 © 2000 IEEE
1702 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATONS, VOL. 18, NO. 9, SEPTEMBER 2000
channel capaci y. These nea -op imum cha ac e is ics add o he
appeal o using he a ionale o his p o ocol in o he ansmis-
sion en i onmen s such as packe adio sys ems.
On he o he hand, di ec -sequence code di ision mul iple
access (DS-CDMA) is going o be adop ed o hi d-gene a-
ion mobile elecommunica ion sys ems. Schemes based on
wide-band CDMA (WCDMA) [6] ha e been chosen as adio
in e aces by he s anda diza ion body in Japan (ARIB), and
also in Eu ope by he ETSI o he UMTS Te es ial Radio
Access (UTRA) [7]. This access scheme is also being con-
side ed in he In e na ional Mobile Telecommunica ion 2000
(IMT-2000) [8] by he ITU. In his pape , we p opose a andom
nea -op imum medium access p o ocol ha modi ies and
ex ends DQRAP echniques o use in a CDMA en i onmen
such as hose men ioned abo e. The ope a ion mode o he
p o ocol may allow he use o andom access channels (RACH)
o o he packe ansmission sys ems, in uplinks ( e e se links),
no only o accessing pu poses bu also o e icien ly ansmi
da a.
Fo his pu pose, he idea o using a DQRAP engine o each
oneo he sp eadingcodesisin oduced. Then,as hep o ocol is
based on wo logical dis ibu ed queues ( he collision esolu ion
queue and he ansmission queue), he queues co esponding
o each sp eading code a e joined in only one queue o each
g oup ( esolu ion and ansmission). We will show in his pape
ha he DQRAP/CDMA p o ocol can be modeled as wo con-
ca ena ed M/M/ sys ems, whe e is he numbe o a ailable
sp eading codes. Mo eo e , DQRAP/CDMA is p o ided wi h
a mechanism ha educes o a minimum he ji e in he delay
o he packe s co esponding o one message, and also becomes
a new ad an age o managing messages o mo e han one slo
leng h.
The p o ocol is a ee andom access p o ocol when he
a ic load is ligh , hus educing he ansmission delay, and
swi ches smoo hly and au oma ically o a ese a ion p o ocol
when a ic load becomes hea ie , blocking he ansmission o
newly a i ed packe s by pu ing hem in o a da a ansmission
queue. Then, gi en ce ain CDMA channel cha ac e is ics (i.e.,
sp eading ac o , bi s pe slo , ading and in e e ence model,
di e si y, coding, ARQ s a egy, e c.), DQRAP/CDMA allows
an op imum numbe o simul aneous ansmissions o be kep
in he sys em, a oiding collisions o a g ea ex en ( hey only
could appea o ligh a ic condi ions) and p e en ing he use
o mo e ecei e esou ces han s ic ly needed. This beha io
is he key o i s good delay and h oughpu pe o mance.
In o de o assess he DQRAP/CDMA scheme unde eal-
is ic condi ions, a ecei e scheme o he con ol minislo de-
ec ion was p oposedand analyzed. Exp essions o he minislo
s a emisde ec ionp obabili ieswe ede i ed,and a ious mech-
anisms we e in oduced o keep he obus ness o he p o ocol in
a Rayleigh ading channel si ua ion. Finally, a compa ison was
made o o he MAC schemes ex ensi ely s udied in he open li -
e a u e such as slo ed-ALOHA/CDMA [9] and ISMA/CDMA
[14].The esul sob ainedshowasigni ican imp o emen in he
sys em delay and h oughpu pe o mance.
The pape is o ganized as ollows. The p o ocol desc ip ion
is de ailed in Sec ion II. In Sec ion III, he analy ical model is
p esen edands udied. Exp essions o he o alsys emdelaya e
alsode i ed in hissec ion. Sec ionIV explainsand analyzes he
p oposed scheme o he con ol minislo s a e de ec ion. In his
sec ion, p o ocol algo i hm modi ica ions a e also in oduced o
eco e om e o s in he minislo de ec ion. Sec ion V shows
compu e simula ion esul sandcompa isons oo he p o ocols.
Finally, Appendix I and Appendix II a e de o ed o he conclu-
sion.
II. PROTOCOL DESCRIPTION
Le us conside da a e minals which sha e a CDMA
channel wi h a ailable sp eading codes o communica e wi h
a base s a ion. The ime axis is di ided in o slo s, and each slo
has wo ields. The i s ield is he access ield, which is u he
di ided in o con ol minislo s. The second ield is he da a
pa , whe e e minals will ansmi hei packe s. We assume
ha e e y s a ion has pe ec slo and minislo synch oniza ion.
The sp eading codes a e pu in o de , and we will deno e
o he h code. We conside ha he e minals a e able o
change he sp eading code o da a and eques ansmission on
a slo -by-slo basis. The messages gene a ed by one e minal
a e spli in o slo -du a ion packe s and pu in o a bu e . Each
packe will be sen wi h he same sp eading code, bu no all
he packe s pe aining o one message will necessa ily be sen
wi h he same sp eading code.
The p o ocol uses wo conca ena ed dis ibu ed queues: he
collision esolu ion queue and he da a ansmission queue.
When a message a i es a he sys em, he co esponding e -
minal, ollowing a ce ain se o ules desc ibed below, selec s
a sp eading code and sends a eques in one o he con ol
minislo s pe aining o his code. I i ails (i.e., he eques col-
lides wi h one o mo e eques s om o he messages), i en e s
he collision esolu ion queue. Collisions a e hen esol ed in
he o de ixed by he queue discipline. In addi ion, he da a
ansmission queue con ains he messages ha ha e succeeded
in hei eques and a e wai ing o be ansmi ed o he base
s a ion also ollowing he o de ixed by he co esponding
queue discipline. Collision esolu ion and da a ansmission
p ocesses wo k in pa allel.
All he e minals mus ha e ou in ege coun e s, which ep-
esen he wologicaldis ibu edqueues.Wewilldeno e hemas
TQ, RQ, pTQ, and pRQ. TQ is he numbe o messages wai ing
o ansmission in he dis ibu ed ansmission queue. RQ is he
numbe o collisionswai ing o esolu ionin hedis ibu edcol-
lision esolu ion queue. pTQ is he posi ion o a gi en e minal
in he da a ansmission queue, and pRQ is he posi ion o ha
e minal in he collision esolu ion queue. These alues ange
om 0, meaning ha he e minal does no ha e any posi ion in
he co esponding queue, o TQ o RQ ( espec i ely), 1 being
he i s posi ion o he queue. TQ and RQ ha e he same alue
o all he e minalsin hesys em(i.e., hey ep esen dis ibu ed
queues), while pTQ and pRQ ha e a speci ic alue o each e -
minal. We assume bo h queues o be FIFO. All ou alues a e
ini ially se o ze o and mus be kep upda ed using he eedback
in o ma ion sen by he base s a ion, each slo , using a b oadcas
channel, and ollowing a se o ules desc ibed below. I consis s
o e na y s a e da a o each con ol minislo o e e y sp eading
code, and also has o include a inal-message-bi o each code.
ALONSO e al.: NEAR-OPTIMUM MAC PROTOCOL BASED ON DQRAP 1703
The h ee di e en s a es ha he base s a ion mus be able o
dis inguish a e: emp y, success, and collision. A collision will
occu when mo e han one s a ion ansmi s in he same min-
islo o he same sp eading code. The inal-message-bi is he
ma k ha all he da a e minals mus send when hey a e ans-
mi ing he las packe om one message. This lag bi mus
be ON in he las packe o each message, and mus be OFF in
all he o he packe s. This mechanism allows all packe s om a
message o be ansmi ed wi h a single eques and minimizes
he delay ji e be ween hese packe s. Ne e heless, i p opaga-
ion delay in he sys em p e en s he e minals om ecei ing
he eedback in o ma ionabou his inal-message-bi be o e he
nex da a slo begins, anemp y slo loss is p oduced a he endo
each message. I messages a e known o be sho ( o example,
ATM cells), i should be possible and con enien o swi ch o
his mechanism and conside all messages o med by a single
packe .
Thep o ocolalgo i hmconsis so h eese so ules ha each
da a e minal has o ollow a he end o each slo . They a e, in
o de o execu ion, hequeueingdiscipline ules(QDR), heda a
ansmission ules (DTR), and he eques ansmission ules
(RTR).
A. Algo i hm Rules
We will now desc ibe he algo i hm ules ha each da a e -
minal has o execu e a he end o each slo , assuming ha , a
his ime, he eedback in o ma ion om he base s a ion abou
he s a e o he con ol minislo s o he p e ious slo has al eady
been ecei ed by he e minal. They mus be execu ed in he
o de p esen ed below. Some ules ha e ini ial condi ions ha
mus be ue o execu e he co esponding ac ions. I he asse -
ion is no e i ied, hen he algo i hm simply jumps o he nex
ule. When all he ules ha e been checked, he slo inishes and
a new one s a s.
1) QDR (Queueing Discipline Rules):
a) Each s a ion inc emen s he alue o TQ by one uni o
each con ol minislo in he success s a e, aking in o ac-
coun he eedback in o ma ion om all he con ol min-
islo s om any o he sp eading codes.
b) Each s a ion educes he alue o TQ by one uni o
each packe co ec ly ecei ed by he base s a ion wi h
he inal-message-bi se o ON om any o he sp eading
codes.
c) I RQ , each s a ion educes he alue o RQ by
RQ uni s.
d) Each s a ion inc emen s he alue o RQ by one uni
o each con ol minislo in he collision s a e, aking
in o accoun all he con ol minislo s om any o he
sp eading codes.
e) Dependingoni ss a e,and he esul s o hecon olminis-
lo s, each s a ion calcula es he alues o pTQ and pRQ.
Tha is, i i has sen a eques and his eques has suc-
ceeded, i calcula es i s posi ion among all he succeeding
minislo s and se s pTQ o he co esponding alue a he
end o TQ. Fo his pu pose, all he successes a e so ed
using he o de o he sp eading code o which hey be-
long, and wi hin he same sp eading code, using a ime
a i al c i e ion. On he o he hand, i he eques has
collided, he e minal calcula es i s posi ion among all
he p esen collisions and se s pRQ o he co esponding
alue a he end o RQ. I i has no sen any eques , hen
pTQ and pRQ ollow he same upda e ules as TQ and
RQ, espec i ely, bu only i he ini ial alues a e o he
han ze o.
2) DTR (Da a T ansmission Rules):
a) I TQ , each s a ion ha has pTQ , pRQ and
da a packe s eady o be sen ansmi s he i s packe o
i s bu e using he sp eading code . This ule is
also called he ee access ule, as i allows newly a i ed
packe s o be ansmi ed immedia ely when a ic load
is ligh . Howe e , using his ule may cause a collision in
he da a pa o a slo .
b) I a s a ion has pTQ and pTQ , he s a ion
ansmi s he i s packe o i s bu e using he sp eading
code . I his packe is he las one o he cu en
message, he s a ion se s he inal-message-bi o ON.
3) RTR (Reques T ansmission Rules):
a) I RQ , each s a ion ha has pRQ and pTQ
and da a packe s eady o be sen andomly selec s one o
he con ol minislo s o he sp eading code and
ansmi s a eques in i .
b) I a s a ion has pRQ and pRQ , he s a ion an-
domlyselec soneo hecon olminislo so hesp eading
code and ansmi s a eques in i .
B. Example
The example shown in Fig. 1 illus a es he ope a ion o he
p o ocol wi h , , and s a ing om an idle
sys em (all alues a e ini ially ze o). All he messages gene a ed
by he e minals a e assumed o be o leng h one, so each da a
slo has he inal-message-bi se o ON.
In slo , h ee messages a i e a he sys em. In ,
hey y o send a eques and also o ansmi he da a in he
i s sp eading code (using ules RTR-1 and DTR-1). Only he
eques om succeeds and enables o en e he ansmis-
sion queue. As he eques s o and collide, hey en e he
collision esolu ion queue. All packe s use he ee access ule
(DTR-1), and hen he da a pa also collides. In his slo , a mes-
sage om a i es a he sys em.
In , is he only packe in he ansmission queue and
i is hus ansmi ed using he i s sp eading code (DTR-2).
Packe s and esol e hei collision (RTR-2) and en e he
ansmission queue ( in he i s posi ion, as i s eques used
a p io con ol minislo ) (QDR-5). Howe e , ansmi s i s
eques and da a using he second sp eading code (RTR-1 and
DTR-1). As is he only new packe a i ing a he sys em,
i s da a ansmission succeeds, and he e o e i does no need o
en e any queue. Two mo e packe s a i e a his slo .
In , and a e ansmi ed using he i s and second
sp eading codes (DTR-2). The new packe s and send hei
eques s and collide. They en e he collision esolu ion queue.
In , eques s om and collide and he packe s again
en e he collision esolu ion queue. The eques s om and
1704 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATONS, VOL. 18, NO. 9, SEPTEMBER 2000
Fig. 1. Example o DQRAP/CDMA p o ocol ope a ion.
also collide and en e his la e queue in he nex posi ion, as
hey ha e used a highe -in-o de sp eading code. In , all
he packe s a emp o esol e hei collisions and succeed, en-
e ing he ansmission queue. This p ocess con inues endlessly.
C. P ac ical Conside a ions
A his poin , we a e going o ou line some p ac ical consid-
e a ions o eal implemen a ion pu poses. Fi s o all, we a e
conside ing ha he eedback in o ma ion abou he s a es o
he con ol minislo s is b oadcas ed o he e minals and a i es
be o e he nex ime slo begins. This is a easible ea u e as he
sys em has he da a slo du a ion o pe o ming his ansmis-
sion.
Mo eo e , i is assumed ha he base s a ion also b oadcas s
he alues o TQ and RQ pe iodically in he con ol downlink,
in o de o allow new use s o join he sys em and eco e om
possiblelosseso hecoun e s.Thisin o ma ionconsis so only
wo in ege alues ha occupy a ewbi s. Ano he p ac ical pos-
sibili y is o ansmi his numbe o he mobile e minals only
when needed o join he sys em o eco e om e o s.
III. PROTOCOL MODEL AND ANALYSIS
The DQRAP/CDMA p o ocol can be modeled as shown in
Fig. 2. We ha e wo queue subsys ems: he collision esolu ion
subsys em and he ansmission subsys em. The enable ans-
mission in e al (ETI) se ice ime ep esen s he ime each
message has o wai om when i a i es a he sys em un il he
nex ime slo s a s. No malizing he ime axis in slo uni s, his
Fig. 2. Model o DQRAP/CDMA p o ocol.
se ice ime will hus be a uni o mly dis ibu ed andom a i-
able in he in e al (0, 1). Bo h subsys ems ha e as many se e s
as a ailable sp eading codes (i.e., ).
The elemen s in he sys em a e he messages gene a ed by he
use s, al hough hey only use he con ol minislo s o accessing
pu poses in he collision esolu ion subsys em. The eedback
line in his subsys em ep esen s ha he messages ha collide
in hei eques s mus en e he queue again un il hey succeed.
A. Delay Analysis
The o al delay o a message can be b oken down in o
ou e ms: he se ice ime o he ETI , he o al delay
o he collision esolu ion subsys em , he o al delay o
he da a ansmission subsys em , and he delay caused by
he collision o a da a packe in a da a slo . This la e e m
appea s when mo e han one e minal ansmi s i s packe using
ALONSO e al.: NEAR-OPTIMUM MAC PROTOCOL BASED ON DQRAP 1705
ule 1 o he DTR ( he ee access ule) in he same slo . Thus,
he expec ed alue o he o al delay o he sys em is
EE E E E (1)
We will now desc ibe he exp ession o he e ms in (1). Fi s
o all, E equals 0.5 because he a i al o messages is in-
dependen o he slo iming and, as no ed abo e, is a uni-
o mly dis ibu ed andom a iable in he in e al (0, 1).
1) To al Delay o he Collision Resolu ion Subsys em: Le
be he p obabili y ha a message will ind a ee con ol
minislo o access when i a i es a he sys em, whe e is he
o al message inpu a e o he sys em (wi h Poisson dis ibu-
ion). We may no e ha , acco ding o RTR, all newly a i ed
messages use he same sp eading code o send hei eques .
In addi ion, he a i al p ocess is memo yless, and he p o ocol
uses a ee algo i hm o collision esolu ion, ha is, all packe s
ha ha e collided in a ce ain minislo use an exclusi e code o
esol e hei con en ion. Then, i we ha e con ol minislo s
pe code, i esul s in
(2)
whe e is he p obabili y o andomly
choosing an emp y minislo when packe s ha e a i ed a he
sys em in a gi en slo , and is he p obabili y ha
packe s a i e a he sys em in ha slo . The e o e, i can be
w i en ha
(3)
All he messages in he collision esolu ion subsys em (in-
cluding bo h he messages wai ing in he queue and he newly
a i ed ones) ha e a p obabili y o succeeding in hei
eques . Thus, he se ice ime o he collision esolu ion
subsys em will be a geome ically dis ibu ed disc e e andom
a iable (whe e deno es he in ege pa ), wi h p obabili y
dis ibu ion unc ion (PDF):
(4)
A his poin , i we use he exac disc e e se ice ime dis i-
bu ion, he sys em is an M/G/ and, as poin ed ou in [10],
his ype o sys em is analy ically unmanageable and only loose
bound exp essions exis o hem. Howe e , in ou case, we can
app oxima e he geome ical dis ibu ion by he co esponding
exponen ial dis ibu ion o a con inuous se ice ime as, in
ac , he geome ical dis ibu ion alues a e only he sampling
o he exponen ial one. Compu e simula ion esul s, as will be
shown in Sec ion IV, will con i m ha his app oxima ion is ea-
sible, as hey i his model e y well. Then, wi h his assump-
ion, we can w i e i s p obabili y densi y unc ion as
(5)
We can hus see ha he se ice ime o he collision esolu ion
subsys em is a Poisson-dis ibu ed andom a iable wi h mean
(6)
We can he e o e model he sys em as an M/M/ . Following
he analysis in [10], adding he wai ing ime in he queue plus
he se ice ime, we can w i e he o al delay o he collision
esolu ion subsys em
(7)
whe e
(8)
and
(9)
This las exp ession is he E lang C o mula o he delay p ob-
abili y.
2) To al Delay o he Da a T ansmission Subsys em: As
bo h a i al and se ice ime p ocesses a e Poisson-dis ibu ed,
he collision esolu ion subsys em ou pu a ic pa e n will
also be Poisson-dis ibu ed and, as shown in [11], wi h he
same a e as he inpu a ic . This ou pu a ic is di ec ly
he inpu a ic o he da a ansmission subsys em.
All he e minals gene a e messages o exponen ially dis-
ibu ed leng h wi h mean . Then, assuming ha he
sys em uses a S op & Wai ARQ s a egy o e ansmi each
packe con aining one o mo e e o bi s, he se ice ime o
he da a ansmission subsys em will also be exponen ially
dis ibu ed. The mean alue o his se ice ime will be he
mean leng h o he messages, , mul iplied by he mean
ansmission ime o each packe o he message, . Calling
he p obabili y ha a packe has a leas one e o bi , we can
w i e he alue o as
(10)
I we disca d and e ansmi any packe ha ing a leas one e -
oneous bi , is he block e o a io, BLER, so we can inally
1706 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATONS, VOL. 18, NO. 9, SEPTEMBER 2000
w i e he mean se ice ime o he da a ansmission subsys em
as
BLER (11)
Again, bo h he inpu a ic and he se ice ime o he da a
ansmission subsys em a e exponen ially dis ibu ed, and we
can hus model his subsys em as an M/M/ queue sys em. I s
o al delay exp ession hus has he same e ms as he one o
he collision esolu ion subsys em bu changing he se ice ime
a e by he new alue , ha is,
BLER BLER (12)
whe e he exp ession o is also he same as o bu
subs i u ing he alue o wi h he new alue . Tha is,
(13)
No e ha is he E lang C o mula wi h se e s and
wi h his new alue .
3) Da a Collision Delay: Acco ding o he algo i hm ules
o he p o ocol, he only possible si ua ion whe e a da a colli-
sion can occu is when he sys em has ewe han messages
wai ing in he da a ansmission subsys em, and mo e han one
packe a i es a he sys em in he same slo . The mean delay
caused by his e en will be i s p obabili y, since i a da a colli-
sion occu s, he message will en e any o he wo subsys ems o
he model (depending on whe he i s eques has succeeded o
collided) and will no longe collide. We can e alua e his p ob-
abili y as
(14)
whe e is he p obabili y ha he sys em has uni s, aking
in o accoun he ones in he queue and he ones being se ed.
4) To al Sys em Delay: The a e age o al delay o a mes-
sage will be
BLER BLER
To e alua e his exp ession, we need o know he alue o he
BLER. I we assume a pe ec powe con ol o a s eady s a e
andneglec he e ec o he mal noise,we mayuse heGaussian
hypo hesis o he in e e ences. Then, as we disca d and e-
ansmi all he packe s con aining one o mo e e o s, we can
w i e [12]
BLER e c (15)
whe e sp eading ac o ;
numbe o simul aneous da a ansmissions;
numbe o bi s con ained in he packe s sen du ing a
ime slo .
No e ha is no cons an wi h ime. Fo analy ical e alua ion
pu poses, we will use , as his is he wo s case alue.
Howe e , his pe ec powe con ol is no a ailable in he ini-
ial ansien s a e when minislo s a e used o access he media.
The e o e, a Rayleigh ading model can app oach he commu-
nica ion channel be e , as is shown in he ollowing.
B. De ec ion o Access Reques s in Con ol Minislo s
One o he main p oblems o he p ac ical implemen a ion
o p o ocols using minislo s o accessing pu poses is he com-
plexi y hey en ail in he physical laye . In no mal condi ions,
he only di e ence be ween hese con ol minislo s and he da a
slo s is hei leng h, measu ed in bi s o in ime uni s. Un o -
una ely, ega dless o he ac ual leng h o a slo , special sym-
bols such as bi aining pa e ns mus be ansmi ed a he be-
ginning o each slo o channel synch oniza ion, equaliza ion,
and powe con ol. The numbe o hese symbols equi ed de-
pends on he cha ac e is ics o he adio link. The pe o mance
imp o emen o he minislo s is hus impai ed when aking in o
accoun hisphysicallaye o e head.Mo eo e ,mixedslo sizes
complica e he ha dwa e design o he adio in e ace.
Howe e , DQRAP/CDMA has a c i ical ad an age o ack-
ling his p oblem. Con ol minislo s a e simply a bu s o chips
ha a e minal has o send inside a ce ain window o ime o
he base s a ion o de ec i s access demand. The only equi e-
men is ha i mus be possible o he base s a ion o dis inguish
be ween h ee di e en s a es: 1) emp y, ha is, no ene gy is e-
cei ed; 2) success, ha is, a single bu s om any e minal has
been de ec ed; and 3) collision, when wo o mo e bu s s ha e
been de ec ed.
The ecei e s uc u e o his access scheme could be as ol-
lows: each s a ion has wo di e en assigned access sequences,
and no o he e minal will ha e he same pai o sequences.
Whena e minalhas o ansmi anaccessbu s in acon olmin-
islo , i will send bo h sequences simul aneously. The de ec ion
ALONSO e al.: NEAR-OPTIMUM MAC PROTOCOL BASED ON DQRAP 1707
Fig. 3. S uc u e o he minislo ecei e a he base s a ion.
o mo e han wo access sequences will allow he base s a ion
o de ec collisions wi hou any need o ha e one ma ched il e
o each use . Fig. 3 shows he s uc u e o he ecei e a he
base s a ion. This ecei e consis s o a bank o ma ched il e s,
one o each di e en sequence. A ma ched il e will ou pu
a peak whene e i de ec s ha any e minal has ansmi ed he
co esponding sequence. Then, he decision block only needs o
coun he numbe o co ela ion peaks a he ou pu o he bank
o il e s. Ideally, i wo peaks a e de ec ed, i means ha only
one e minal has sen i s eques . A g ea e numbe o peaks will
deno e he p esence o a collision. The absence o peaks simply
e eals heabsenceo access eques s.No e ha i weuseabank
o il e s, we can add ess di e en use s.
In o de o assess he pe o mance o he p oposed ecei e
scheme in e ms o he p obabili y o minislo s a e misde ec-
ion, we i s mus calcula e he de ec ion and alse ala m p ob-
abili iesa heou pu o each de ec ion il e , ha is, hema ched
il e wi h he squa e powe and h eshold decision blocks.
C. Analysis o he Minislo S a e De ec ion Scheme
Using an op imal ecei e scheme, wi h an enna and pos de-
ec ion di e si y o o de (see Appendix II), he alse ala m
p obabili y and he de ec ion p obabili y o each de ec-
ion il e a e gi en by
(16)
(17)
whe e is he decision h eshold, and
(18)
and
(19)
is he numbe o chips, is he o al in e e ence le el, is
he ene gy pe chip, and is he numbe o simul aneous access
eques ansmissions.
No e ha and depend on he numbe o simul aneous
use ansmissions ha cause in e e ence in he sys em, ha
is, on he alue o . In ou p ac ical case, he ansmi ed se-
quences a e used o access eques de ec ion (and possible col-
lisions) in he con ol minislo s. This numbe o simul aneous
ansmissions hus ma ches he numbe o access eques se-
quences sen in he same conside ed minislo , using any o he
a ailable sp eading codes. Mo eo e , his alue will depend on
he a ic load o e ed o he sys em, measu ed in e ms o he
numbe o messages ying o access he channel pe ime uni
(doubled). We mus choose a alue o ( he numbe o simul-
aneous access eques s), which we will call design , o simply
, and selec he alse ala m p obabili y we wish o his spe-
ci ic alue. Indeed, i we neglec he e ec o he he mal noise
(in e e ence limi ed sys em), and deno ing as he design
alse ala m p obabili y, he alue o he decision h eshold can
be explici ly w i en o (no di e si y)
(20)
The e o e, he de ec ion p obabili y is
(21)
Fig. 4 shows he alues o he alse ala m and de ec ion p ob-
abili ies as a unc ion o he pa ame e o a sequence o
leng h .
Howe e , he eal alse ala m and de ec ion p obabili ies in
he sys em will no be as p esen ed in his igu e. Indeed, once
he h eshold o he deciso has been chosen, hese p obabili-
ies s ill depend on he numbe o simul aneous access eques s
ansmi ed in each minislo , ha is, he o al in e e ence le el,
which will no always be he design one . In gene al, we will
ac ually ha e a ce ain alue o di e en om .
1708 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATONS, VOL. 18, NO. 9, SEPTEMBER 2000
Fig. 4. De ec ion and alse ala m p obabili ies in a Rayleigh ading en i onmen wi hou di e si y.
Gi en he h eshold alue de ined in (20), he exp essions o
he p obabili ies in he sys em will be
(22)
(23)
whe e is he ac ual numbe o access eques s. As an example,
Figs. 5 and 6 show he alse ala m and de ec ion p obabili ies as
a unc ion o o a and wi h .
We can obse e ha he a ia ion o he de ec ion p obabili y
is e y small wi h . Fu he mo e, he alse ala m p obabili y
also inc eases smoo hly o and dec eases ab up ly
when . These p ope ies ma ch ou p ac ical applica ion
well: when a ic load is highe han he design a e, he p ob-
abili ies a e only sligh ly wo se han decided; and when a ic
load becomes ligh e , he alse ala m p obabili y dec eases d a-
ma ically, imp o ing he sys em pe o mance.
Using an enna di e si y , i is no possible o w i e
he explici exp ession o he h eshold as a unc ion o he alse
ala mp obabili y. Le us use o he ela ion ha ul ills
(24)
whe e, again,
design alse ala m p obabili y;
numbe o simul aneous access eques s used o de-
sign;
numbe o ac ual simul aneous access eques s.
The alse ala m and de ec ion p obabili ies a e hus
(25)
(26)
No e ha all he exp essions p esen ed assume a pe ec min-
islo synch oniza ion, ha is, all he access eques s a i e a he
base s a ion simul aneously. In ac , his si ua ion is a wo s case
scena io, as all he access eques s su e he maximum possible
in e e ence le el. Howe e , his si ua ion keeps he size o he
minislo s o a minimum and, as hey ep esen an access o e -
head ha is no use ul o da a ansmission, maximizes he da a
h oughpu e iciency. I would be possible o ul ill his condi-
ion using mobile loca ion echniques [13]. I hey a e no a ail-
able, he minislo size is lowe bounded by he maximum p op-
aga ion delay in he sys em. In a mac ocell en i onmen , his
alue may be signi ican ly g ea e han he access eques size,
and he de ec ion p obabili y will be en o ced, as no all he e-
cei ed eques s will be simul aneous in ime. Fo his case, he
exp ession p esen ed in (26) will ep esen a lowe bound o
he de ec ion p obabili y.
No e also ha he alues p esen ed in Fig. 6 o he de ec ion
p obabili y o he ecei e il e seem o be low, bu hey ep e-
sen a wo s -case si ua ion. We a e sending a chip sequence in
a Rayleigh ading channel using no di e si y and only a e age
open loop powe con ol. Fo example, using an enna di e si y
o o de , and o and we ha e
.
I is p o ed in [4], [5], and [19] ha wi h only h ee con ol
minislo s, he a e age numbe o slo s in which packe s
ALONSO e al.: NEAR-OPTIMUM MAC PROTOCOL BASED ON DQRAP 1709
Fig. 5. False ala m p obabili y as a unc ion o he numbe o access eques s.
Fig. 6. De ec ion p obabili y as a unc ion o he numbe o access eques s.
esol e hei con en ion is lowe han , and hus he sys em
h oughpu is only limi ed by he da a ansmission channel
a e. The e o e, using only h ee con ol minislo s, he p o ocol
achie es i s bes pe o mance, keeping he access o e head
loss e y small. Hence o h we will always use o all
analy ical and simula ion pu poses. E en mo e, i messages a e
long ( hey consis in mo e han one ansmission packe ), i can
be seen ha wi h only minislo s, i could be enough o
each he maximum h oughpu pe o mance [18]. We will also
show his ea u e in Sec ion IV.
D. P obabili y o Minislo S a e Misde ec ion
Acco ding o he alse ala m and de ec ion p obabili ies de-
sc ibed abo e, he e will be a ce ain p obabili y o he base s a-
ion ailing o de ec he s a e o each con ol minislo . We will
now desc ibe he exp essions o his p obabili y, o all six di -
e en e o si ua ions possible. We will use o ep esen he
pos de ec ion emp y s a e, o he pos de ec ion success s a e,
and o hepos de ec ioncollisions a e. Fig.7showsall hese
e o si ua ions.
Fi s o all, he p obabili y o de ec ing one o wo co ela ion
peaks ( he base s a ion de ec s a success ul access), when in ac
no use has ansmi ed i s access sequence, is
(27)
Fig. 7. Possible misde ec ion si ua ions.
whe e is he alse ala m p obabili y o each de ec ion il e
and is he o al numbe o de ec ion il e s. This exp ession
implici ly assumes ha he sys em decides ha he e has been
a single access eques ansmission when only one co ela-
ion peak is de ec ed. This assump ion is made supposing ha
he alse ala m p obabili y is much lowe han he no-de ec ion
p obabili y, which is a easonable assump ion as he alse ala m
p obabili y is a design pa ame e .
1716 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATONS, VOL. 18, NO. 9, SEPTEMBER 2000
Fig. 17. IP message delay wi h mixed IP- oice a ic sou ces.
Finally, we may no e ha e en he concep ual complexi y o
DQRAP/CDMA seems o be a he conside able, he p o ocol
algo i hm is qui e simple o implemen , and he compu a ional
load added is minimum (only in ege simple ope a ions a e e-
qui ed). Mo eo e , i would simpli y, o some ex en , he base
s a ion complexi y, as i educes he numbe o o al ecei e s
needed o manage a ce ain numbe o mobile e minals.
V. CONCLUSION
A p oposal o a nea -op imum andom access p o ocol o
a CDMA en i onmen sui able o he u u e hi d gene a ion
mobile communica ion sys ems has been p esen ed. An analy -
ical model has been in oduced, and he esul s ob ained ma ch
he ones ob ained by compu e simula ions well. I has been
shown ha he p o ocol has good delay and s abili y cha ac-
e is ics, main aining he s anda d de ia ion o he message’s
delay bounded by i s mean alue and achie ing a nea ly op-
imum maximum s able h oughpu , o gi en channel cha ac-
e is ics. I is he e o e a sui able p oposal o imp o ing he use
o he capaci ies o andom access channels in a e e se link.
A ecei e scheme o he de ec ion o access eques s has
been p oposed and analyzed, and he misde ec ion s a e p ob-
abili ies ha e been de i ed. The p o ocol’s sensi i i y o e o s
in he de ec ion o he s a e o he con ol minislo s has been
s udied.P o ocol modi ica ions ha ebeenin oduced o manage
he possible e o scena ios, showing g ea obus ness and li le
e iciency loss in ealis ic channel condi ions.
I has been shown ha he p o ocol ou pe o ms o he widely
used mul iple access schemes in e ms o he maximum s able
h oughpu and he delay cha ac e is ics.
APPENDIX I
We a e o ind he exp ession o he numbe o combina ions
o use s ha a e able o gene a e a peaks i hey a e assigned
a unique pai o sequences be ween di e en a ailable ones.
We mus make an abs ac ion o he p oblem as ollows.
Le be he i s in ege numbe s. Tha is, we
numbe he ecei ed peaks om 1 o .
Le be he di e en possible pai s we can c ea e.
Each pai ep esen s one use . Le his be all he possible g oups
o pai s o numbe s, ha is, all he possible g oups o use s
ha ing 1 o use s pe g oup. We mus e alua e, o
any om 1 o , which o hese g oups con ain a
leas once all he numbe s om 1 o , being able o epea he
numbe s as many imes as desi ed, and how many use s he e
a e in each g oup.
Calling his numbe , we will suppose ha we know he
alue o o any alue , and wi h hese alues we
will e alua e he unc ion o ( he a ge alue).
We calcula e all he di e en g oups o use s we can make
om he o al possible use s, and hen we sub ac
hose ha dono ha eall henumbe s om1 o . Whichg oups
do no ul ill his condi ion? Fi s o all, hose ha lea e one
numbe unselec ed, which will be he numbe o pai s ha gen-
e a e peaks mul iplied by he a posi ions whe e we can
loca e he blank. Then, we mus sub ac he pai s ha lea e wo
unselec ed numbe s mul iplied by he numbe o combina ions
lea ing wo blanks o a numbe , and so on. The esul is hus
We ha e explici ly elimina ed he e ms o and
because heya eze o. Weonly need heini ial alues oe alua e
he ecu si e exp ession. These a e
ALONSO e al.: NEAR-OPTIMUM MAC PROTOCOL BASED ON DQRAP 1717
Fig. 18. Recei e s uc u e o each ecei e il e .
APPENDIX II
I is shown in [16] ha he op imum ecei e scheme o a se-
quence de ec ion il e is he one shown in Fig. 18. Each b anch
o he ecei e p esen ed in Fig. 3 has his s uc u e.
As shown in he igu e, o a gi en use , he inpu signal
ollows he exp ession, whe e ep esen s he ene gy pe chip,
is he impulse esponse o he channel, and is he in o -
ma ion ha modula es hecodesequence .Wechose
o all , ha is, we send a single bi , wi hou modula ing
. Wi h hese assump ions, he expec ed alue o he co -
ela ion be ween he inpu signal and he local copy o he se-
quence, o he in-phaseandquad a u esequences , has he
ollowing exp ession [16]:
(39)
whe e
(40)
and is henumbe o chipsin hesequence(i heyco espond
o one bi , his alue will be equal o he sp eading ac o ). The
ma ched il e ou pu peak co esponds o , which implies
ha o any inpu il e . As bo h signals
a e squa ed and added, he phase e m becomes i ele an ,
always supposing ha his alue emains cons an du ing he
-chip ansmission ime.
On he o he hand, he a iance o bo h componen s is [16]
Va Va (41)
whe e
(42)
ep esen s he he mal noise , plus he o al in e e ence
caused by he es o use s. Fo a ime-limi ed il e , he alue
o he in eg al in (42) is 2/3. Thus, assuming a powe con ol
ha main ains he same o all use s, he a iance o bo h
in-phase and quad a u e componen s is
Va (43)
wi h being he numbe o simul aneous access eques ans-
mi ed. To ind he de ec ion and alse ala m p obabili ies o
he ecei e scheme, we mus ake in o accoun he p opaga ion
channelcondi ions. Wewill conside aRayleigh adingen i on-
men .
No e ha he decision a iable is .I
can be p o ed ha he diag am shown in Fig. 18 is op imal o
signals wi h unknown phase, acco ding o ei he he Bayes o
he Newman–Pea son op imali y c i e ia [17]. Using he la e ,
he sys em design consis s in ixing he decision h eshold alue
o ob ain a ce ain allowable alse ala m p obabili y. The c i-
e ion gua an ees ha he chosen alue is ha which maximizes
he de ec ion p obabili y o ha alse ala m p obabili y alue.
These p obabili ies a e ob ained om in eg a ing wo likelihood
unc ions o , depending on he ini ial possible hypo hesis:
unde he assump ion ha no signal has been ansmi ed,
and unde he assump ion ha he a ge sequence has
been ansmi ed. Using an enna and pos de ec ion di e si y o
o de , ha is (simila ly o he ime pos de ec ion in eg a ion
used in [16]), adding he con ibu ions o independen sig-
nals coming om he same numbe o di e en an ennas and
ecei e s, hese unc ions a e gi en by
(44)
(45)
whe e is wice he a iance o each componen , and is
he mean squa e, which is ob ained as he sum o he squa es o
he in-phase and quad a u e componen means. De ining
, he likelihood unc ions a e inally
(46)
The alse ala m and de ec ion p obabili ies a e ob ained by
e alua ing he in eg al o he co esponding unc ion om he
h eshold alue o in ini y, hus gi ing
(47)
(48)
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Luis Alonso (M’99) ecei ed he Enginee deg ee in elecommunica ions om
he Uni e si a Poli ècnica de Ca alunya (UPC), Spain, in 1997.
He joined he Escola Tècnica Supe io d’Enginye ia de Telecomunicació de
Ba celona, Spain, as Visi an P o esso in 1998. In 1999, he joined he Escola
Uni e si á ia Poli écnica del Baix Llob ega , Spain, whe e he became Assis an
P o esso .He is cu en ly doing hisPh.D. hesisabou mediumaccess p o ocols,
scheduling algo i hms, packe adio echniques, and sp ead-spec um sys ems
o mobile communica ions.
Ramon Agus í (M’78) was bo n in Riba- oja d’Eb e, Spain, on Augus 15,
1951. He ecei ed he Enginee o Telecommunica ions deg ee om he Uni-
e sidad Poli écnica de Mad id, Spain, in 1973, and he Ph.D. deg ee om he
Uni e si a Poli ècnica de Ca alunya, Spain, 1978.
In 1973, he joined he Escola Técnica Supe io d’Enginye s de Telecomuni-
caciódeBa celona, Spain,whe ehebecame FullP o esso in 1987.Hehasbeen
wo king in he ield o digi al communica ions wi h pa icula emphasis on dig-
i al adio, bo h ixed adio elay, and mobile communica ions. He has also been
conce nedwi h hepe o manceanalysisand de elopmen o equency-hopped
sp ead-spec um sys ems. He pa icipa ed in he COST 231, RACE, and ACTS
Eu opean esea ch p og ams, and cu en ly is pa icipa ing in he IST p og am.
His esea ch in e es s a e in he a ea o mobile communica ions wi h special
emphasis on CDMA sys ems and packe adio ne wo ks.
O iol Sallen (M’98) ecei ed he Enginee and Doc o Enginee deg ees
in elecommunica ion om he Uni e si a Poli ècnica de Ca alunya (UPC),
Spain, in 1994 and 1997 espec i ely. He ecei ed he Doc o a e Awa d om
he Telecommunica ion Enginee Associa ion o Spain in 1997 o his Ph.D.
disse a ion on mul iple access p o ocols o CDMA-based sys ems.
He joined he Escola Tècnica Supe io d’Enginye ia de Telecomunicació de
Ba celona, whe e he became Assis an P o esso in 1994 and Associa e P o-
esso in 1998. His esea ch in e es s a e in he ield o mobile communica ion
sys ems, especially packe adio echniques and sp ead-spec um sys ems.
