Code-Hopping as a New Strategy to Improve Performance of S-CDMA Cellular Systems

8/9/2019 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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Code-Hopping as a New Strategy to Improve Performance of S-CDMA Cellular Systems