Code-Hopping as a New Strategy to Improve Performance of S-CDMA Cellular Systems
Transcript of Code-Hopping as a New Strategy to Improve Performance of S-CDMA Cellular Systems
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Code-Hopping
as a
New Strategy t o Improve
Perform ance of S CDMA ellular Systems
Berna Unal Yalqin Tanik
Department
of
Electrical and Electronics Engineering
Middle East Technical University
Ankara TURKEY
Abstract- An alternative coding strategy to the fixed
spreading code assignment of code-division multiple-access
CDMA) systems, called
code-hopping
is proposed for the up-
link path
of
synchronous CDM A S-CD MA ) system s. In
code-hopping S-CDMA,
mobile users swap their spreading
codes according to a predetermined hopping pattern. In this
way, mobile channels which are identified by the spreading
codes are exchanged.
Performance of code-hopping on the
uplink path of S-CDMA systems is evaluated numerically on
a typical S-CDMA system in the case of random hopping and
compared to that
of
conventional S-CDMA.
In performance
evaluation, the criterion is t he uplink ou tage probability which
is defined as the probability of the uplink interference power
exceeding a predetermined threshold. The numerical results
show that application of code-hopping to the uplink commu-
nication of S-CDM A system s decreases the outa ge probability
significantly.
I. INTRODUCTION
Synchronous code-division multiple-access (S-CDMA) sys-
tems which maintain perfect synchronization between mobile
units and base stations are good alternatives for picocellu-
lar mobile communications where propagation delays expe-
rienced by signals from the cell center to the cell border re-
main less than one chip period and mobile users roam at
walking speeds. Having achieved this perfect synchroniza-
tion between mobile units and base stations, S-CDMA can
make full use of the periodic correlation properties of the
spreading sequences. Research on S-CDMA has
so
far been
concentrated mostly on multiuser detectors for several types
of mobile radio channels [1]-[3]) and on various different
aspects of fiberoptic networks [4]-[SI).
The uplink interference of a mobile in a cellular S-CDMA
system depends both on the spatial positions of the ac-
tive mobiles in the system and on the periodic crosscor-
relation parameters between the spreading code sequences.
Since the S-CDMA mobile channel is assumed to be very
slowly-varying, the channel parameters do not vary during
successive signaling intervals.
If
the base station receiver of
a mobile receives excessive amount of interference in an arbi-
trary signaling interval, it will certainly suffer from the same
inferior situation in the next intervals. This will result in
failure of uplink communication for that mobile as long as
the channel remains in the same state. We will denote such
This work was suppoFted by the Turkish Scientific and Technical Re-
search Foundation (TUBITAK)
as
part
of
the European Cooperation
in the Field of Scientific and Technical Research (EURO-COST) 231
project
0-7803-3336-5/96 5.00 1996
IEEE
mobiles as
t rapped m obi les.
To
overcome this drawback of conventional S-CDM
we propose a new coding scheme for uplink, called
code-hopping, where mobile users swap their spreading cod
according to a predetermined hopping pattern. By changi
the spreading code sequences of the mobiles in consecut
signaling intervals, trapped mobiles have the probability
having less interference in the pursuing intervals. On t
other hand, utilization of code-hopping has a counter eff
on the situation of successfully communicating mobiles th
will bear the possibility of having more interference in t
succeeding intervals. In th is way, we introduce a code
vers i t y which brings the time-averaged inerference of all
mobiles to a moderate value. This reflects the notion of
individualist approach where the aim is to achieve success
communication of all the members simultaneously. That
the states of the trapped mobiles are improved at the expen
of deteriorating those of the over-successful ones, gradua
bringing all to a n acceptable point.
In this paper, we describe the code-hopping sche
for S-CDMA systems and evaluate the performance
code-hopping S-CDMA on the uplink path of a typical s
tem. System performance is measured by the
ou tage
pr
abili ty criterion which is defined as the probability of t
signal-to-interference ratio (SIR) being less than
a
predet
mined threshold. Section
I1
gives the general features of
S-CDMA system which employs the code-hopping strate
Section I11 describes the code-hopping scheme in the upli
communication of S-CDMA systems. Section IV includes
uplink performance evaluation of code-hopping S-CDMA
a
typical system, in terms of outage probability by giv
graphical illustrations and numerical results. Finally, s
tion V gives concluding remarks and comments about
proposed coding strategy.
11.
S-CDMA
SYSTEM
DESCRIPTION
The S-CDMA system of concern is composed of a cellu
structure where cell size is sufficiently small
so
that the m
imum delay experienced by signals within a cell is less th
a chip duration. In this way, the spreading-despreading p
cesses can employ the periodic correlation properties of
spreading sequences. The mobile channel between the b
stations and the mobile units is assumed to preserve the
nal constellation during the course of transmission and
free of intersymbol interference (ISI).
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As a result of small cell size and channel properties, perfect
carrier and symbol synchronization can be achieved. This
permits the utilization of coherent reception a t the receiver.
The s tructure of the system involves typical CDMA blocks
forward error correction (FEC) and spreading followed by
modulation at the transmitter, matched-filtering and de-
spreading followed by the FEC decoder
at
the receiver. The
major source of deterioration is assumed to be thc multiuser
interference and thus thermal noise can be neglected.
Assuming perfect instantaneous power control on the up-
link path within the cell, the interferen'ce from mobiles within
the same cell (co-cell mobiles) will arrive at the base station
with equal power. Since mobiles in the neighboring cells are
power controlled by their cell sites, the interference power
from such mobiles (inter-cell mobiles), at the desired user's
base station will be given by
where
P,
is the received power by the desired user's base
station,
Pt
is the transmitted power by the inter-cell inter-
fering mobile, and
a2
s an attenuation factor which models
the combined effects of path loss and fading [9] xperienced
by the interfering mobile's signal
at
the desired user's base
station. Precise characterization of this at tenuation factor is
possible for different propagation models.
Several statistical assumptions are also made Transmit-
ted data of mobiles, carrier phases and attenuation factors
are assumed to be mutually statistically independent. Fur-
thermore, carrier phases are assumed to be uniformly
dis-
tributed between
-n, ]
Modulation is chosen typically as
QPSK as it is one of the most commonly used modulation
schemes in CDMA systems. Thus, successive information
symbols are transmitted on quadrature carriers after being
spread by the same spreading code sequence.
As a result of the abovementioned characterization of the
S-CDMA system, the uplink signal power Si and the inter-
ference power Ii in the decision variables at the output of
the despreading block pertaining to the receiver of mobile i
can be written respectively as
-2
s . 55
16
where L is the processing gain,
c s
is the received signal en-
ergy per symbol, CISi is the co-cell index set of mobile i,
IISi is the inter-cell index set of mobile i, a is the attenu-
ation parameter of
1)
experienced by the inter-cell mobile
j
interfering with the base station of mobile i, and p i j
is
the
value of the periodic crosscorrelation between spreading code
sequences of mobiles i and
j.
Note that
2)
and
3)
are valid
for an arbitrary mobile i and for an arbitrary signaling inter-
val.
111.
CODE-HOPPINGOR
T H E
U P L I N K
PATH OF
S-CDMA
SYSTEMS
Assignment of spreading sequences in conventional
S-CDMA is organized in
a
once
nd
for all basis. That is,
every mobile user is assigned
a
spreading code sequence and
performs the spreading-despreading process with the same
sequence. As can be observed in
3 ) ,
once the propagation
model is set, the uplink interference power of
a
mobile de-
pends both on the periodic crosscorrelation values between
the spreading codes and on the geometrical locations of the
active inter-cell interferers which are reflected by the atten-
uation parameters.
If a
mobile fails to communicate in a
signaling interval due to reception of excessive amount of
interference, it will fail to communicate in the subsequent
signaling intervals unless the spatial positions of the active
mobiles change, because of the constant crosscorrelation pa-
rameters. Therefore, the very slowly-varying nature of the
S-CDMA mobile channel causes mobiles to be trapped.
However in code-hopping S-CDMA, mobile users exchange
their spreading code sequences in successive signaling inter-
vals. As an interesting observation, we can interpret this
exchange of codes as having the effect of rapidly changing
the spatial positions of the mobiles
at
each signaling inter-
val. Thus, probability of having
a
mobile which suffers from
high interference jn
a
long burst of signaling intervals is con-
siderably decreased.
The hopping pattern can be purely random or
it
can in-
volve heuristics. The latte r alternative requires the utiliza-
tion
of a dynamic channel al locat ion
algorithm. For the sake
of simplicity here, we are concerned with the case of ran-
dom hopping where mobiles exchange their spreading code
sequences in
a
purely random manner.
When code-hopping scheme is applied to the uplink com-
munication of the S-CDMA system,
p 's
in
3)
become ran-
dom variables. They can be treated as statistically inde-
pendent from the set of a&%. n code-hopping S-CDMA,
I; takes on different values in consecutive signaling intervals
whereas
in
the case of conventional S-CDMA because of the
very slowly-varying channel, Ii virtually remains constant.
Assuming the free distance of the FEC to be sufficiently
long,
so
that every possible code permutation can be ex-
perienced by the code-hopping mobile, we can evaluate the
interference values of the code-hopping S-CDMA in terms of
time-averages for equivalent comparative purposes. Averag-
ing
3)
with respect t o time which affects only the p terms,
we obtain the following expression for
z
he time-averaged
uplink interference of mobile i
where
G,
s the time-averaged
p j .
4)
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I v . PER FORM ANCE EVALUATION
A .
The cr i t e r ia
:
Outage probabi l i ty
The performance evaluation of the proposed coding strat -
egy is carried out by comparing the uplink outage proba-
bilities of the conventional and the code-hopping S-CDMA.
The uplink outage probabilities of the conventional and the
code-hopping S-CDMA can be written, respectively, as
here Po(i) nd Po(i) re the uplink outage probabilities of
an arbitrary mobile i in the conventional and code-hopping
S-CDMA respectively, and is a predetermined threshold.
This threshold is determined by the parameters of the sys-
tem, like the minimum tolerable bit error rate (BER) re-
quired by the type of communication and the minimum av-
erage SIR imposed by the FEC to achieve the specified BER.
Treating the attenuation parameters $ j s as
i nde pe nde n t
and ident i cal l y d is t ributed ran do m var iables
(iid), both Ii and
I become random variables. The number of random terms
in the second summation of (3) and
4)
an be assumed high
enough to invoke the Central Limit Theorem and approxi-
mate Ii and as Gaussian. Thus , we can express the outage
probabilities of
5)
and 6) analytically as
( 7 )
where
mi
and
oi
are the mean and standart deviation
of the corresponding interference term, and
e r f c ( u ) =
3 s
e z p (
z 2 ) d z .
Note that Po(i)s defined for
a
particular mobile. In sym-
metric code systems where mi and gi are equal for all mo-
biles,
Po(i)
Po
V i ,
so
Po
alone can be used as a valid
criterion. For non-symmetric code systems a meaningful per-
formance measure Po for the whole system can easily be de-
fined, e.g.
B.
Results
For illustrative purposes, the numerical comparison is car-
ried out on a typical S-CDMA system having the following
specifications
The cellular structure of the system include hexagonal cells.
Interfering signals of mobiles from the neighboring cells are
assumed to include signals only from the first tier, higher or-
der tiers are assumed not to contribute to interference signif-
icantly. The received signal power is assumed to fall off with
distance according to a fourth power law [SI, and t he mobile
channel is assumed to be non frequency selective. According
to this propagation model, the attenuation parameters
a
can be written as
where d j 3 is the distance from the j t h mobile
t o
its b
station, and d, is distance from the
j t h
mobile to the b
station of mobile i.
The system has a convolutional forward error correct
mechanism (FEC) of rate 1 / 2 and constraint length 7. Su
a FEC requires at least 3 dB of average SIR to provid
BER of which is sufficient for reliable voice commu
cations [ lo] Thus, the threshold of 7) equals
Sz/2
wh
corresponds to an average SIR of dB. Processing gain
the system ( L ) s 31 which is found to be a suitable value
indoor mobile communication applications. Maximal-len
shift-register sequences (m-sequences) of period 31 are u
as the spreading codes, so tha t phases of an m-sequence
assigned to mobile users of one cell and different m-sequen
are assigned to different cells.
Utilization of m-sequences causes
Po(i)
alues to be eq
for all i due to the symmetric structure of m-sequen
Therefore, we can use Po
= Po i).
he code reuse fac
of the system is
4
which is chosen in accordance with
m-sequence code set, since there are a total of
6
m-seque
sets of period 31 [l l] nd thus it is impossible to utilize
next greater code reuse factor which is
7.
The code-hopping counterpart of this system will invo
purely random exchange of the spreading codes among
eo cell
mobi les
only. That is, the random hopping patt
will not permit code exchange between cells but there w
only be code exchanges among mobiles of a cell.
To justify the assumption of 1 and as being appro
mately Gaussian, we have determined their probability d
sity functions (pdfs) numerically. By (3) and 4),
I ,
and
are in the form of weighted sum of a;s which are trea
as iid random variables. Therefore, the pdfs of I , and I
be determined numerically by a series of scaling and con
lution operations, performed iteratively on the pdf of
1
To obtain the pdf of
QS a
simple computer program
used where the propagation environment of the uplink p
is simulated only for a single inter-cell interfering mob
The resulting numerical pdfs for I and are depicted
figure 1.
The pdfs of figure 1are approximately Gaussian as
pected. This justifies the utilization of (7) in outage pr
ability calculations. The outage probability values of
conventional and the code-hopping S-CDMA system ca
lated by (7) , ogether with the numerically computed m
and standart deviation values of the corresponding interf
ence terms are listed in table I. Note that the mean value
both pdfs remain constant whereas the standart deviatio
reduced by a factor of 1.4. Employment of the code-hopp
scheme is observed to cause a significant decrease (from
9
to
3.1%)
on the uplink path of the S-CDMA system. In ot
words, we can state that in the conventional S-CDMA s
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mean
st. dev.
P o ( )
P r o b a b i l i t y
d e n s i t y
S-CDMA code-hopping S-CDMA
370.99 370.99
82.78 58.51
9.3 3.1
5 OO 35 5
6 5
BOG
n t e r f e r e n c e
-CDMA
Code-Hopping S-CDYA
Fig.
1.
Pdfs of and
Ii
TABLE
I
N U M E R I C A LOM PA R I SON OF THE C ON V E N T I ON A L
A N D THE
C OD E -HOPPI N G SY ST E M
tem, the mobiles are likely to fail
3
times more tha n those of
the code-hopping system on the uplink path.
V. CO N CL U S I O N S
A new coding strategy in S-CDMA systems, called
code-hopping
has been presented in this paper. The im-
provement brought by this new scheme to the uplink com-
munication of S-CDMA systems is verified by performance
analysis. This analysis is carried out by comparing the up-
link performance of
a
typical S-CDMA system with that of
its code-hopping counterpart, the criterion being the ou tage
probabili ty.
Assuming a purely random hopping pattern, the numeri-
cal results have revealed tha t utilization of code-hopping on
the uplink path decreases the outage probability drastically
in S-CDMA systems. Specifically, the decrease in the out-
age probability, on the uplink path
of
our typical S-CDMA
system is one-third. Utilization of heuristics in the hopping
pattern is likely to decrease the outage probability more and
therefore it is worth the effort for implementation.
Although we have carried out our mathematical analysis
on the uplink path, the analyses are not resctricted to the
uplink path. Thus, an analogous approach can easily be
carried out for the downlink case.
The numerical analysis carried out in this paper for a spe-
cific type of channel model can be generalized t o other types
of channel models. The formulation
of
3) and
4)
is valid for
the uplink path of all types of channels. These expressions
offer complete flexibility in choosing the type of propagation
medium, cell shape and mobility pa ttern. The flexibility lies
in the key step of obtaining statistical information about
the attenuation parameters, because determination of the
channel model, cell shape and mobility pattern is directly
reflected in the statistical behaviour
of
attenuation parame-
ters
at
the end of this step. Therefore we can assume that
the results for these other cases are readily available.
Examples which may be of practical interest are the down-
link path of this propagation model and the uplink-downlink
analyses of fading channels.
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