Capacities of single-code and multicode DS-CDMA systems accommodating multiclass services

376 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 48, NO. 2, MARCH 1999

Capacities of Single-Code and Multicode DS-CDMASystems Accommodating Multiclass Services

Seung Joon Lee,Student Member, IEEE,Hyeon Woo Lee,Member, IEEE,and Dan Keun Sung,Member, IEEE

Abstract—This paper is concerned with capacities of direct-sequence (DS) code-division multiple-access (CDMA) systemsaccommodating multiclass services with different transmissionrates and bit error rates (BER’s). The capacities are expressedby inequalities to which the number of accepted calls of eachclass should conform. Those inequalities are necessary and suffi-cient conditions satisfying the requirement of the bit energy-to-interference power spectral density ratio. The optimal receivedpower is derived to cause the least interference to other signalswhile maintaining the acceptable bit energy-to-interference powerspectral density ratio. It is shown that if the maximally receivablepower of a call of each class is identical in the multicode systemand the single-code system using a variable processing gain,the capacities of both systems are also identical in nonfadingchannels. However, in multipath fading channels, the multicodesystem is shown to be better than the single-code system in termsof capacity. Capacity is also derived in a dynamic multiple-cellenvironment.

Index Terms—Capacity, DS-CDMA, multicode system, optimalreceived power, variable processing gain.

I. INTRODUCTION

FUTURE wireless systems such as FPLMTS/IMT-2000[1], [2] and UMTS [3] are required to support multirate

services (voice, video, data, etc.) with different quality of ser-vices (QoS’s) [bit error rate (BER), delay, etc.]. Code divisionmultiple access (CDMA) is a promising technique to complywith the above requirements [4]–[6]. It has many attractivefeatures such as high-spectrum efficiency, soft handover, softcapacity, and low-frequency reuse factor [7], [8].

Two approaches have been proposed for supporting multi-rate services in direct-sequence (DS)-CDMA systems [4], [9].One is a single-code transmission scheme using a variableprocessing gain which is defined as the ratio of chip rate to userinformation bit rate [10]. With the single-code transmissionscheme, each user terminal transmits its signal on only oneCDMA channel with a processing gain that varies inverselyproportional to the user information bit rate. The other is amulticode transmission scheme [11]–[14]. With the multicodetransmission scheme, a high-rate data stream is first split intoseveral fixed low-rate streams. The multiple data streams arespread by different short codes with the same chip rate andare added together. Multiple short codes for one high-ratecall should be orthogonal over an information bit interval to

Manuscript received October 28, 1996; revised April 10, 1997. This workwas supported in part by the Korea Science and Engineering Foundation underGrant 95-0100-15-01-3.

The authors are with the Department of Electrical Engineering, KoreaAdvanced Institute of Science and Technology (KAIST), Taejon 305-701,Korea.

Publisher Item Identifier S 0018-9545(99)00779-3.

reduce the intercode interference. A random scrambling longpseudonoise (PN) code common to all parallel short codechannels can be applied after spreading. The long PN codedoes not affect any orthogonality property between the parallelchannels, but makes the transmission performance independentof the time-shifted auto- and cross-correlation properties of thespreading codes, which is one of the distinguished features ofconcatenated orthogonal/PN spreading sequences [14].

In this paper, we are concerned with the capacities ofsingle-code and multicode DS-CDMA systems accommodat-ing multiclass services, on which call admission criteria can bebased. Gilhousen [15] developed the expression for the numberof accepted voice calls in order to represent the capacity ofCDMA systems. Liu [16] proposed call admission controlalgorithms based on the measured signal-to-interference ratiofor dynamically changing multiple-cell CDMA systems whereonly voice calls are accommodated. Yang [17] derived admis-sion policies for integrated voice and data traffic in packetradio DS-CDMA networks. Evans [18] reported some resultson capacities of multiple-service DS-CDMA cellular networks.However, he neglected background noise and put the targetsignal in the interference. Liu [13] presented a power allocationmethod and a constraint on the number of accepted calls ofeach class in the multicode DS-CDMA system. However, heassumed that the required signal-to-interference ratio is equalfor all services. In this paper, the capacities are presented asthe necessary and sufficient conditions for the requirementof the bit energy-to-interference power spectral density ratioin DS-CDMA systems accommodating multiclass services inmultipath fading channels.

The rest of this paper is organized as follows. In Section II,we describe the system model and briefly review the capacityof a DS-CDMA system accommodating only voice calls. Wederive the capacities of single-code and multicode DS-CDMAsystems accommodating multiclass services in a single-cellenvironment without background noise in Section III andwith background noise in Section IV. In Section V, we givenumerical examples and discuss the effect of multipath fadingon capacities, including comparison between the single-codesystem and the multicode system. In Section VI, we derivecapacities in a dynamic multiple-cell environment, given theintercell interference from the outer cells. We draw conclusionsin Section VII.

II. PRELIMINARY

A. System Description

We consider only the reverse link because it is far morecritical to total capacity than the forward link. The capacity in

0018–9545/99$10.00 1999 IEEE

LEE et al.: CAPACITIES OF SYSTEMS ACCOMMODATING MULTICLASS SERVICES 377

CDMA systems is limited by interference. Given the numberof accepted calls of each class, all powers of the same classcalls received by a base station are assumed to be made equaland constant through a perfect power control. For a measureof QoS in the DS-CDMA system accommodating only voicecalls, we define the bit energy-to-interference power spectraldensity ratio as

(1)

where denotes the total number of mobile terminals transmit-ting simultaneously, the information bit rate, the chip

rate of the spreading sequence, the processinggain, the received power of a call, the information bitenergy, and the two-sided power spectral density ofadditive white Gaussian noise (AWGN). The definition of (1)is motivated by the fact that the bit error rate is approximatelygiven by

BER Q

where Q , when coherent de-tection and asynchronous transmission among multiple userterminals are used in AWGN channels [19]–[21]. In (1), weassume a rectangular chip pulse, from which the coefficient

results: see [22, eq. (29)].For the DS-CDMA systems supporting multirate services,

(1) can be readily modified as follows. We assume that thereare service classes with each information bit ratewhichis an integer multiple of the basic rate. When multiple codesare used to transmit high-rate information, the informationbit rate of the th class call is given by where

is the number of codes for transmittingthe th class call. Suppose that calls of the th class

are connected to a base station. Then, in thesingle-code DS-CDMA system having a variable processinggain, the bit energy-to-interference power spectral density ratioof the th class call can be given by [10]

(2)

where is the received power of theth class call atthe base station. In the multicode DS-CDMA system, the

bit energy-to-interference power spectral density ratio of eachcode of the th class call can be given by [13]

(3)

where is the received power of each code of thethclass call. A code does not interfere with the others in the samemulticode call because of the orthogonality property [13], [14].

Next we consider a frequency-selective Rician fading mul-tipath channel which is modeled as a wide-sense-stationaryuncorrelated scattering (WSSUS) channel. If

is the input to the WSSUS channel, then the correspondingoutput is given by [23]

where is the AWGN term, and

Here, is the transmission coefficient for the fading channeland is a zero-mean complex Gaussian random process.The covariance function for the fading process in the WSSUSchannel

E

is assumed to be zero for where isthe chip duration and is assumed to be less than the minimumof the processing gain. For a frequency-selective Rician fadingchannel, using the result of [23], (2) and (3) can be modifiedto (4) and (5), respectively, given at the bottom of the page,where is the processing gain of theth classcall in the single-code system, the processinggain of each code of any calls in the multicode system, and

depends on the covariance function . In the case ofa triangular covariance function, is given by [23]

(4)

(5)


for , where and .Here, denotes the greatest integer less than. In (4) and(5), and represent the received powers of thenonfaded (specular or line-of-sight) signal components.

B. Capacity of the DS-CDMA System AccommodatingOnly Voice Calls in Nonfading Channels

Given the required bit energy-to-interference power spectraldensity ratio by , the constraint on the number of acceptedcalls can be given by

S / R

or

(6)

Equation (6) represents the capacity.

III. SINGLE-CELL ENVIRONMENT

WITHOUT BACKGROUND NOISE

We first introduce a lemma and a proposition which willbe used to determine the capacities of DS-CDMA systemsaccommodating multirate services in a single-cell environmentwithout background noise.

Lemma 1): Let be positive real numbersand nonnegative integers. We assume thereexists some such that . Then, thefollowing statements are equivalent.

i) There exists a set of positive suchthat

(7)

ii) There exists a set of positive suchthat

(8)

and

(9)

Proof: : Let satisfy (7).Choose for every .Then

and

Therefore, satisfy (8) and (9).

: It is trivial since (8) and (9) result in

Proposition 1): Let be positive realnumbers and nonnegative integers. Weassume there exists some such that .Then, there exists a set of positive such that

if and only if

(10)

Proof: According to Lemma 1, it can be proved byshowing that of Lemma 1 holds if and only if (10) does.

(If): Suppose that (10) holds. Then, there existssuch that

Selecting yields

and

(Only if): Suppose that of Lemma 1 holds. Then, wecan obtain

Corollary 1): Let be positive real num-bers and nonnegative integers. We assumethere exists some such that . Then,there exists a set of positive such that

if and only if

Proof: It can be proved as in Proposition 1, if “” and“ ” are replaced by “ ” and “ ,” respectively.Corollary 1 will be used for proof of Proposition 2 inSection IV.

We assume that the required bit energy-to-interferencepower spectral density ratio of theth class call is set tobe .


A. Single-Code DS-CDMA System

The requirement of the bit energy-to-interference powerspectral density ratio for theth class call is written as

(11)for . Equation (11) can be rewritten as

(12)From Proposition 1, the constraint on forsatisfying (12) is given by

(13)

B. Multicode DS-CDMA System

The requirement of the bit energy-to-interference powerspectral density ratio for each code of theth class call iswritten as

(14)for . Equation (14) can be rewritten as

(15)From Proposition 1, the constraint on forsatisfying (15) is given by

(16)

IV. SINGLE-CELL ENVIRONMENT WITH BACKGROUND NOISE

We introduce two lemmas and a proposition to derivecapacities considering background noise.

Lemma 2): Let be positive real num-bers, a positive real number, and nonneg-ative integers. We assume there exists somesuch that . Then, the following statements are equiv-alent:

i) There exists a set of positive suchthat

(17)

ii) There exists a set of positive suchthat

(18)

Proof: : It is trivial.: Let satisfy (18). And let

Choose . Then, we can obtain

Therefore, satisfy (17).Lemma 3): Let be positive real num-

bers, a positive real number, andnonnegative integers. Suppose

Then

i) satisfy

ii) And if satisfy

(19)

then

Proof:

i)

ii) Let . From (19), it holds that, and


That is,

Therefore, we can obtain

Lemma 3 implies that consist ofthe minimal values of ’s satisfying (19).

Proposition 2): Let be positive realnumbers and nonnegative integers. Weassume there exists some such that .Let be positive real numbers. Then, thereexists a set of positive such that

(20)

and

(21)

for every , if and only if

and (22)

where

Proof: (If): If (22) holds, it follows that

for some , . By Lemma 3-i),

satisfy (20). Also

(Only if): From Lemma 2 and Corollary 1, if there existsa set of positive such that (20) holds, itfollows that

that is, for some , . FromLemma 3-ii) and (21), it holds that for every

, and it follows that forevery . Therefore, and

Finally, we can obtain

A. Single-Code DS-CDMA System

If background noise is considered, the requirement of thebit energy-to-interference power spectral density ratio for theth class call in the single-code system is written as shown

in (23), given at the bottom of the page, for .Equation (23) can be rewritten as

Given the maximally receivable power of the nonfaded com-ponent of the th class call by , theconstraint on is, from Proposition 2, givenby

(24)

and , where

B. Multicode DS-CDMA System

In the multicode system with background noise, the require-ment of the bit energy-to-interference power spectral densityratio for each code of theth class call is written as

(23)


for . Given the maximally receivable power ofthe nonfaded component of each code of theth class call by

, the constraint onis, from Proposition 2, given by

(25)and , where

C. Optimal Received Power

The optimal received power is defined as the receivedpower causing the least interference to other signals whilemaintaining the acceptable bit energy-to-interference powerspectral density ratio. Lemma 3 states that the optimal receivedpower of the nonfaded component of theth class call in thesingle-code DS-CDMA system is given by

for and that the optimal received power of thenonfaded component of each code of theth class call in themulticode DS-CDMA system is given by

for .

V. DISCUSSION

We define the normalized bandwidth of theth class call inthe single-code system and the multicode system as

and

TABLE IREQUIRED PERFORMANCE FORMULTICLASS SERVICES

respectively. Then, (24) and (25) correspond to

and

respectively. The normalized bandwidth means the bandwidthoccupied by one call when the total bandwidth is consideredto be one.

Let

and

Then, we know and. A service with the larger (or

) may affect, through (or ), the normalizedbandwidth of a service with the less (or ). How-ever, (or ) is generally too small to significantlyaffect the normalized bandwidth.

Example 1): Consider the following three classes of ser-vices as shown in Table I, where we refer to [24] for theacceptable maximum bit error rates. We assume that

Mcps, mW/Hz, the covariance function ofthe fading process has a triangular form, and the maximallyreceivable power of the nonfaded component of a call of anyclass is mW in both the single-code system and themulticode system (that is, mW).The number of codes for each call of voice, facsimile, andlow-resolution video services is assumed to be one, two, andfour, respectively, in the multicode system.

Figs. 1 and 2 show the normalized bandwidth of a callof each service class according to various transmission co-efficients for the fading channel and correlation durationcoefficients , respectively. From Fig. 1, we can observe thatwithout multipath fading the normalized bandwidthis identical in both single-code and multicode systems. How-ever, when multipath fading is considered , thenormalized bandwidth of a multirate call (facsimile or low-resolution video) in the multicode system is smaller than that


Fig. 1. Normalized bandwidth according to various squared transmissioncoefficients for the fading channel where� = 30.

Fig. 2. Normalized bandwidth according to various correlation durationcoefficients where�2 = 0:2.

in the single-code system. From Fig. 2, we can notice that asis smaller, the normalized bandwidth is larger. This results

from the fact that a small reduces the smoothing effect ofthe correlation receiver on the diffused portion of the receivedsignal and degrades , as noted in [23].

Fig. 3. Normalized bandwidth according to various information bit rateswhere�

2= 0:2 and � = 30.

Fig. 3 shows the normalized bandwidth according to variousinformation bit rates, when only one service is accommodated.We can see that as the information bit rate increases, differencebetween the normalized bandwidth in the single-code systemand that in the multicode system is larger. This suggests theadvantage of the multicode system with a higher processinggain over the single-code system with a lower processing gainin terms of capacity.

VI. M ULTIPLE-CELL ENVIRONMENT

Thus far, we have examined capacity in a single-cell en-vironment. We now deal with capacity in a multiple-cellenvironment. Under a dynamic multiple-cell environment, thecapacity depends on interference from outer cells. We derivethe capacity, given the interference from outer cells.

Let be the intercell interference from outer cells.Then, we can express the requirement of the bit energy-to-interference power spectral density ratio for theth class callin the multiple-cell single-code DS-CDMA system as shownin (26), given at the bottom of the page, for .Equation (26) can be rewritten as

(26)


for . From Proposition 2, the constraint onis given by

(27)

and

where

Equation (27) can be rewritten as

or

where was defined in Section IV. The optimal receivedpower of the nonfaded component of theth class call in themultiple-cell single-code DS-CDMA system is, by Lemma 3,given by

for .

In a similar way, we can obtain the constraint onand the optimal received power in the multiple-cell

multicode DS-CDMA system.

VII. CONCLUSIONS

We determined the capacities of single-code and multicodeDS-CDMA systems accommodating multiclass services, byderiving the necessary and sufficient conditions on the numberof accepted calls of each class for the requirement of the bitenergy-to-interference power spectral density ratio. We alsoderived the optimal received power of a call of each class. Inmultipath fading channels, the multicode system was shown tohave advantages over the single-code system using a variableprocessing gain in terms of capacity, while capacities of bothsystems are identical in nonfading channels.

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Seung Joon Lee(S’95) was born in Kwangju, Ko-rea, in 1967. He received the B.S. and M.S. degreesin electrical engineering from the Korea AdvancedInstitute of Science and Technology (KAIST), Tae-jon, Korea, in 1991 and 1993, respectively. Cur-rently, he is working toward the Ph.D. degree inelectrical engineering at KAIST.

He has been with Hyundai Electronics IndustrialCorporation, Korea, since November 1994. His re-search interests include handoff schemes in wirelessATM and support of multimedia in CDMA systems.

Mr. Lee is a student member of KICS.

Hyeon Woo Lee (S’93–M’94) was born inKyeongju, Korea, in 1963. He received the B.S.E.E.degree from Seoul National University, Seoul,Korea, in 1985, the M.B.A. degree from SogangUniversity, Seoul, in 1989, and the M.S.E.E. degreefrom the Korea Advanced Institute of Science andTechnology (KAIST), Taejon, Korea, in 1994. Heis working toward the Ph.D. degree at KAIST.

He has been with the Telecommunication R&DCenter, Samsung Electronics Corporation, as aResearcher since 1984. His research interests

include radio resource allocation, mobile network architecture, and IMT-2000/FPLMTS radio transmission technology.

Mr. Lee is a member of KICS and KITE.

Dan Keun Sung (S’80–M’86) received the B.S.degree in electrical engineering from Seoul NationalUniversity, Seoul, Korea, in 1975 and the M.S. andPh.D. degrees in electrical and computer engineer-ing from the University of Texas, Austin, in 1982and 1986, respectively.

From May 1977 to July 1980, he was a ResearchEngineer with the Electronics and Telecommunica-tions Research Institute, where he was engaged inresearch on the development of electronic switchingsystems. In 1986, he joined the faculty of the Korea

Advanced Institute of Science and Technology (KAIST), Taejon, Korea, wherehe is currently a Professor in the Department of Electrical Engineering. Hisresearch interests include ISDN switching systems, ATM switching systems,wireless networks, and performance and reliability of systems.

Dr. Sung is a member of IEICE, KITE, KICS, and KISS.

Capacities of single-code and multicode DS-CDMA systems accommodating multiclass services

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