CDMA Cellular Systems Performance With Fading, Shadowing, And

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450 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 47, NO. 2, MAY 1998

CDMA Cellular Systems Performance with Fading,Shadowing, and Imperfect Power Control

Giovanni Emanuele Corazza, Giovanni De Maio, and Francesco Vatalaro

Abstract This paper addresses capacity estimation for cel-lular code-division multiple-access (CDMA) systems, assumingthe IS-95 standard as a reference. Extending the analyticalmethod from [6], we obtain a sequence of bounds on capacity,and then we introduce an accurate approximation to reducecomputation complexity. The analysis accounts for interferenceinternal and external to the reference cell, fading, shadowing,and imperfect power control. Outage probability is expressed interms of the characteristic functions (cfs) of the interferenceand imperfect power control random variables (rvs). The in-terference contributions are computed on the basis of a Poissondistribution for the number of users in a lognormally shadowedchannel. Results are provided for different channel conditions

and are validated against Monte Carlo simulations. A comparisonagainst previously published CDMA capacity estimates is carriedout, aimed at clarifying some controversial issues. It is alsoconfirmed that large system capacity is achievable under tightpower control.

Index TermsCellular systems, code-division multiple access,lognormal channels, outage probability, power control, spread-spectrum systems.

I. INTRODUCTION

THE code-division multiple-access (CDMA) technique ex-hibits some well-known theoretical advantages for wire-less personal communications [1]. An outstanding feature

of a CDMA cellular system is universal frequency reuse,which gives the potential for large spectrum efficiency, yields

maximum flexibility in resource assignment, and allows im-

plementation of soft handover algorithms. Universal frequency

reuse is accomplished by proper use of signature sequences in

a classical direct-sequence spread-spectrum transmission. In

the forward link (base station to mobile users), it is possible,

within a cell, to have synchronous CDMA. Conversely, in

the return link, asynchronous CDMA is usually adopted. The

return link is generally considered to limit system capacity [2],

i.e., the average number of users per cell which can be served

with a specified quality. We will only consider the return link

in the following.

Since all users in a cell share the same frequency band,a stronger signal (possibly sent from a terminal nearer to

the base station) virtually uses a larger part of the available

resource, thus lowering the total number of users that a base

station can serve. This is usually identified as the nearfar

problem. Therefore, power control must be implemented to

Manuscript received September 19, 1996; revised February 27, 1997.The authors are with the Dipartimento di Ingegneria Elettronica, Universit a

di Roma Tor Vergata, 00133, Rome, Italy (e-mail: [email protected]).Publisher Item Identifier S 0018-9545(98)03292-7.

ensure that all received signals have very closely the same

power level. However, power control regulates interference

from users within the same cell, i.e., those connected with

the same base station (internal interference), but interference

from other cells (external interference) will not, in general, be

power controlled.

Another feature of CDMA is that any improvements on the

receiver performance have an immediate and direct influence

on system capacity. In other words, if the threshold value for

the energy per bit-to-noise power spectral density ratio can be

lowered, then more users can be accommodated without any

change in system architecture. Measures such as diversity andchannel coding are used for this purpose in the recently in-

troduced IS-95 CDMA cellular standard [3]. In addition, there

is a widespread interest in interference-reduction techniques.

In particular, IS-95 adopts voice activity detection, multirate

speech coding, and 120 sectorized base-station antennas.

In the future, further advantages may be obtained through

adaptive antennas and multiuser estimation techniques at the

base station.

Estimation of capacity for a CDMA system requires that a

large number of cells is considered, each loaded with a user

population of given spatial distribution. This is in contrast

with the analysis of frequency- or time-division multiple-

access systems for which worst case conditions can easily beidentified involving only a small number of users. The two

key aspects that need to be properly accounted for in CDMA

capacity estimation are cell selection and power control. Cell

selection by the generic user entails a search for the return

link with least attenuation, which, through power control, also

corresponds to least interference to/from surrounding cells.

It follows that external interference not only depends on the

attenuation in the paths from the interferers to the base station

serving the desired user, but also on the attenuation in the paths

from the interferers to their own serving base stations. Power

control imperfections and shadowing must be considered for

any analysis to be realistic.In spite of the vast literature on cellular CDMA, some

important issues are not fully assessed as yet. Gilhousen et al.

[2] clearly posed the problem of CDMA capacity estimation,

but their results are limited by the following assumptions:

1) cell selection is governed by minimum distance rather

than minimum attenuation; 2) power control is perfect; 3) the

number of users per cell is fixed; and 4) the overall interfering

power is modeled as a Gaussian random variable (rv). The

minimum distance criterion leads to overestimation of interfer-

ence due to errors in cell selection, for shadowing can easily

00189545/98$10.00 1998 IEEE


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Fig. 2. Normalized mean E f Ie x t

= W g = N as a function of s

, the dB spreadin the channel ( N

c

= 4 and 9 , = 4 , no sectorization, and continuous voiceactivity). Results from [2] and [6] are shown for comparison.

Fig. 3. Normalized variance Varf I

e x t

= W g = N

as a function of

s

, the dBspread in the channel ( Nc

= 4 and 9 , = 4 , no sectorization, and continuousvoice activity).

typical values of the dB spread (i.e., around 8 dB), the value

needed for becomes very large. To solve this problem,

we introduce here an alternative method for the computation

of the external interference moments in , which yields a

very accurate approximation even for large dB spread with

relatively small values of . In essence, the modification

consists in adding BS0 to the set of nearest stations to a

given point in . When the attenuation is lowest toward BS0,

Fig. 4. Normalized mean E f Ie x t

= W g = N for Nc

= 1 , 2 , 3 , 4 , 9 , and 7 0as a function of the dB spread in the channel

s

( = 4 , no sectorization,and continuous voice activity). The result of the approximation for N

c

= 9

is also reported.

the contribution to the external interference is nulled. This is

somewhat similar to the weight function approach from [2], but

here we have a much larger number of base stations, which

are checked before the contribution is neglected. Following

this approach, (16) must be substituted with

(21)

where, as before, it is assumed that for each point ( ) the

nearest stations are numbered for . Note

the strong similarity of (17) and (21). In Figs. 4 and 5, we

report and Var as a function of

the dB spread for , with as a parameter, for both

the bounding and the approximation approaches. Contrasting

the approximation for against the bound for ,it is apparent that (21) can be used to match the results of

the bounding approach obtained for extremely large, even

for large values of the dB spread. In particular, this applies to

the evaluation of the external interference variance, which, ingeneral, needs large values to be accurately estimated.

C. Internal Interference

To derive the cf of the overall normalized internal interfer-

ence, we first consider that the probability of having internal

interferers is connected to the probability of having users

within the region , given by (5), conditioned on having one


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Fig. 6. Outage probability for different values of the path-loss exponent and

s

= 6 dB as a function of the average number of users per cell N(N

c

= 4 , = 7 dB, 120 sectorization, voice activity factor = 3 = 8 , andideal power control).

of the path-loss exponent. Outage probability increases

very significantly with decreasing . The agreement

with simulation results is very satisfactory. Analogously,

Fig. 7 provides system capacity results for dB.

Comparing Figs. 6 and 7, it can be noted that for smaller

values of , the capacity loss due to higher dB spread

is larger.

2) It is interesting to note the influence of on outageprobability, as reported in Fig. 8: at ,

every 1-dB decrease translates into a capacity gain of

at least 20 users per cell. This fact motivates the use of

coding, diversity, and interference cancellation as much

as receiver complexity allows.

3) Releasing the ideal power control assumption, Fig. 9

shows outage probability with the power control error

standard deviation as a parameter for ,

dB, and dB. At , every 1-dB increase

translates into a capacity loss of at least 20 users per

cell: a specification of dB for the power control

procedure seems necessary. This specification for is

in substantial agreement with that reported for the IS-95system based on experimental evidence [14].3

Referring to a dB spread of dB, Fig. 10 compares

under different assumptions the average number of users per

120 sectorized cell, , which was the parameter assumed

in [2] for CDMA capacity estimates. The dotted curve cor-

responds to the so-called surrounding cells full case in

[2]. For the sake of comparison, we modified our modeling

according to the assumptions of Gaussian interference power

and fixed number of users. By doing so, we find excellent

3 Note that the measured standard deviation in [14] is not directly compa-rable to

p

for it contains other contributions too.

Fig. 7. Outage probability for different values of the path-loss exponent and

s

= 4 dB as a function of the average number of users per cell N( N

c

= 4 , = 7 dB, 120 sectorization, voice activity factor = 3 = 8 , andideal power control).

Fig. 8. Outage probability for different values of the Eb

= N

0

threshold as afunction of the average number of users per cell N ( N

c

= 4 , = 4 , s

= 6

dB, 120 sectorization, voice activity factor = 3 = 8 , and ideal power control).

agreement between the result from [2] with this modified

bound calculated for (dasheddotted curve). If we

increase the number of tested base stations, all other conditions

being maintained, the capacity bound is increased, gaining

about two users per sector for (dotted curve), thus

showing that previous estimates could be improved. However,

when we return to the assumption of interference power


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CORAZZA et al.: CDMA CELLULAR SYSTEMS PERFORMANCE 457

Fig. 9. Outage probability for different values of imperfect power controlstandard deviation

p

as a function of the average number of users per cellN (N

c

= 4 , = 7 dB, = 4 , s

= 6 dB, 120 sectorization, and voiceactivity factor = 3 = 8 ).

Fig. 10. Outage probability as a function of the number of users per sectorN

s

. Comparison of results from [2] with our model for Nc

= 4 and 9 anddifferent assumptions on the number of users and external interference powerdistributions (

s

= 6 : 3 dB, = 7 dB, = 4 , 120 sectorization, and voiceactivity factor = 3 = 8 ).

and Poisson distribution of users, as the solid curve in Fig. 10

shows, the bound is decreased, providing a loss of about three

users per sector at .

As a final result, in Fig. 11 we provide capacity estimates

for dB. The dotted curve shows the bound on system

capacity when tested base stations are assumedthe

Fig. 11. Outage probability as a function of the number of users per cell N .Comparison of bounding technique for N

c

= 9 and 7 0 and approximationfor N

c

= 9 ( s

= 8 : 0 dB, = 7 dB, = 4 , 120 sectorization, and voiceactivity factor = 3 = 8 ).

capacity estimate is still far from its actual value as we can

show by evaluating the bound for an extremely large number of

tested stations (e.g., , see solid curve in Fig. 11). The

solid curve is practically coincident with the curve we achieve

with the approximation (21) and a much more reasonable value

of tested stations (e.g., , see dotted curve in Fig. 11).

VII. CONCLUSIONS

This paper presented a new approach to the evaluation

of system capacity for a CDMA cellular system. Havingextended to higher moments the analysis provided in [6], our

approach allows a complete system capacity evaluation. This

was carried out here on the basis of a sequence of bounds

and introducing an approximation which is often advisable to

reduce computation complexity of the former technique.

Our approach takes into account both internal and external

interference, fading, shadowing, and imperfect power control.

The approach is characterized by several features which distin-

guish it from previously proposed methods. The main featuresare:

1) adoption of a minimum attenuation criterion over

base stations to derive the interference statistics rather

than the minimum distance criterion ( );

2) use of a model for the number of users through a Poisson

distribution, which is more realistic than that based on

a fixed number of users per cell;

3) use of the one-sided form of the central limit theorem,

so that the interference power pdf is always null for

negative values, as opposed to the case of the Gaussian

approximation;


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CORAZZA et al.: CDMA CELLULAR SYSTEMS PERFORMANCE 459

variance , if we interchange in (36) integration with respect

to and , we have

(37)

Substituting (30) in (37) and after some manipulations similar

to those performed before, we achieve (17).

ACKNOWLEDGMENT

The authors gratefully acknowledge cooperation from Dr.

F. Ceccarelli in performing computer simulations and thank

the reviewers for their constructive criticism which led to

significant improvements in the paper.

REFERENCES

[1] A. J. Viterbi, Wireless digital communication: A view based on threelessons learned, IEEE Commun. Mag., vol. 29, pp. 3336, Sept. 1991.

[2] K. S. Gilhousen, I. M. Jacobs, R. Padovani, A. J. Viterbi, L. A. Weaver,Jr., and C. E. Wheatley III, On the capacity of a cellular CDMAsystem, IEEE Trans. Veh. Technol., vol. 40, no. 2, pp. 303312, 1991.

[3] TIA/EIA/IS-95, Mobile station-base station compatibility standard fordual-mode wideband spread spectrum cellular system, Telecommuni-cation Industry Association, July 1993.

[4] T. Chebaro and P. Godlewski, About the CDMA capacity derivation,in Int. Symp. Signals, Systems and Electronics, Paris, France, Sept. 14,1992, pp. 3639.

[5] , Average external interference in cellular radio CDMA sys-tems, IEEE Trans. Commun., vol. 44, pp. 2325, Jan. 1996.

[6] A. J. Viterbi, A. M. Viterbi, and E. Zehavi, Other-cell interference incellular power-controlled CDMA, IEEE Trans. Commun., vol. 42, nos.2/3/4, pp. 15011504, 1994.

[7] F. Vatalaro, G. E. Corazza, G. De Maio, and F. Ceccarelli, CDMAcellular systems performance with imperfect power control and shad-owing, in Proc. IEEE Veh. Technol. Conf. VTC96, Atlanta, GA, pp.

874878.[8] A. M. Viterbi and A. J. Viterbi, Erlang capacity of a power controlled

CDMA system, IEEE J. Select. Areas Commun., vol. 11, no. 6, pp.892899, 1993.

[9] O. Andrisano, D. Dardari, and R. Verdone, Analytical methodologyfor F-TDMA and CDMA cellular systems performance evaluation, inProc. 3rd Int. Conf. Univers. Pers. Comm. (ICUPC94), San Diego, CA,Sept. 1994, pp. 3136.

[10] G. Falciasecca, C. Caini, M. Missiroli, and G. Riva, A general approachto spectral efficiency evaluation for high capacity mobile radio systemsin different scenarios, in Proc. 42nd IEEE Veh. Technol. Conf., Denver,CO, May 1992, pp. 10341037.

[11] A. Papoulis, Probability, Random Variables and Stochastic Processes.New York: McGraw-Hill, 1965.

[12] , The Fourier Integral and Its Applications. New York:McGraw-Hill, 1962.

[13] L. F. Fenton, The sum of log-normal probability distributions in scattertransmission systems, IRE Trans. Comm. Syst., pp. 5767, Mar. 1960.

[14] R. Padovani, Reverse link performance of IS-95 based cellular sys-tems, IEEE Personal Commun., vol. 1, no. 3, pp. 2834, 1994.

Giovanni Emanuele Corazza was born in Trieste,Italy, in 1964. He received the Dr.Ing. degree inelectronic engineering in 1988 from the Universityof Bologna, Italy, and the Ph.D. degree in 1995 fromthe University of Rome Tor Vergata, Italy.

From 1989 to 1990, he was with the Canadianaerospace company COM DEV, Ontario, wherehe worked on the development of microwave andmillimeter-wave components and subsystems. In1991, he joined the Department of Electronic En-

gineering, University of Rome Tor Vergata, wherehe is presently a Research Associate. During 1995, he visited ESA/ESTEC,The Netherlands, under a research fellowship granted from the EuropeanCommunity. During 1996, he visited the Communications Sciences Institute,University of Southern California, Los Angeles. His research interests are inthe areas of communication theory, personal communications systems, spread-spectrum techniques, and synchronization.

Dr. Corazza received the Marconi International Fellowship Young ScientistAward in 1995 (ex-aequo). He serves as an Editor for spread spectrum for theIEEE TRANSACTIONS ON COMMUNICATIONS.

Giovanni De Maio was born in Rome, Italy, in

1968. He received the electronic engineering degreefrom the University of Rome Tor Vergata, Rome,Italy, in 1995.

In 1997, he joined CoRiTel, Rome, a researchconsortium specializing in telecommunication dis-ciplines, where he currently deals with architecturedefinition and performance evaluation of proposalsfor the third-generation universal mobile telecom-munications systems (UMTSs) radio interface. Hispresent research interests include multiple-access

schemes for wireless personal communications and radio channel modeling.

Francesco Vatalaro received the Dr.Ing. degreein electronics engineering from the University ofBologna, Italy, in 1977.

From 1977 to 1980, he was with FondazioneUgo Bordoni at Pontecchio Marconi, Italy. Then, hewas with the FACE Standard Central Laboratory,Pomezia, Italy, from 1980 to 1985. While withSelenia Spazio, Rome, Italy, he was Group Leaderof Satellite Ground Segment System Engineering.In 1987, he became an Associate Professor of RadioSystems at the University of Roma Tor Vergata. He

is presently a Visiting Professor at the University of Southern California,Los Angeles, holding a course on spread spectrum for the spring semesterof 1998. He has been responsible for several research contracts both atItalian national and European levels. He is the author of more than 60scientific papers in international and national journals and in internationalconference proceedings. His research interests include mobile and personalcommunications, spread-spectrum communications, and satellite systems.

Dr. Vatalaro was a cowinner of the 1990 Piero Fanti INTEL-SAT/Telespazio international prize. He is a member of the AEI.

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