Wireless Personal Communications14: 29–47, 2000.© 2000Kluwer Academic Publishers. Printed in the Netherlands.

Capacity Estimation in Multiple-Chip-Rate DS/CDMA SystemsSupporting Multimedia Services∗

YOUNG WOO KIM, SEUNG JOON LEE, JEONG HO KIM, YOUNG HOON KWON andDAN KEUN SUNGDepartment of Electrical Engineering, Korea Advance Institute of Science and Technology, 373-1 Kusong-dong,Yusong-gu, Taejon 305-701, KoreaE-mail: dksung@ee.kaist.ac.kr or ywkim@cnr.kaist.ac.kr

Abstract. This paper is concerned with capacity estimation in multiple-chip-rate (MCR) DS/CDMA systemssupporting multimedia services with different information rates and quality requirements. Considering both powerspectral density (PSD) over a radio frequency (RF) band and the effect of RF input filtering on the receiver, capacitythat satisfies the requirement of the bit energy-to-interference PSD ratio is derived. The optimum value of the re-ceived power which causes the least interference for other users while maintaining an acceptable quality-of-service(QoS) requirement is also derived. The results show that system performance is strongly affected by a selectedchannel assignment strategy. Therefore, it is critical to efficiently assign radio resources in MCR-DS/CDMAsystems that support high capacity and a low blocking rate.

Keywords: multiple-chip-rate DS/CDMA, capacity estimation, optimum received power.

1. Introduction

Third-generation wireless systems, such as the IMT-2000 and the UMTS, are required toaccommodate a wide variety of services, including high quality voice, data, facsimile, video,and interactive applications, with information bit rates ranging from a few kb/s to 2 Mb/s[1]. Code division multiple access (CDMA) is a promising technique that complies with theabove requirements. Direct sequence (DS)-CDMA is attractive because of its flexibility insupporting multimedia traffic, as well as low interference coexistence with other CDMA ornarrow-band systems operating in the same frequency band [2].

Two approaches for accommodating multi-rate services in DS-CDMA systems have beenproposed. One is to use either a single-code or a multi-code DS-CDMA system in a single RFchannel bandwidth [3]. The other is to use an MCR-DS/CDMA system in multiple RF channelbandwidths [1, 5, 6, 7]. The frequency bandwidth of an MCR-DS/CDMA system is selectedaccording to the maximum information rate to be supported. MCR-DS/CDMA systems wereproposed by the Code Division Testbed (CODIT) project [1, 5], OKI [6], and ETRI [7]. In theexperimental CODIT testbed, an MCR-DS/CDMA system was proposed with three differentchip rates corresponding to three different RF channel bandwidths of approximately 1, 5, and20 MHz. The three RF channel bandwidths of this system are referred to as narrow-band,medium-band, and wide-band RF channels. In this system, low-rate services (e.g., voice) canbe optionally accommodated on narrow-band or on medium-band channels. The 1 MHz chan-nel can be allocated as a standard RF channel for low-rate voice mobile phones, and 5 MHz

∗ This study was supported in part by the Korea Science and Engineering Foundation.

30 Young Woo Kim et al.

can be used as an option for providing a higher grade-of-service (GoS). High-rate services(64 kb/s and above) require RF channels of 5 or 20 MHz. For flexible use of limited RFresources, MCR-DS/CDMA systems are preferable to single RF channel bandwidth systems[5]. However, due to the complexity of obtaining quantitative results on the performance ofMCR-DS/CDMA systems, only a few results have been reported [8, 9]. These reported resultsdid not consider the shape of the PSD of all spread signals in the system or the effect of RFinput filtering on the receiver.

In this paper, system capacity supporting multimedia services in MCR-DS/CDMA systemsis investigated. The number of users per cell is limited by the total interference receivedat each base station (BS). When a system encounters congestion, admitting a new call canonly cause deterioration of the link quality for some active calls and may result in droppingcalls. Thus, in order to maintain acceptable connections for existing users, a system requirescall admission criteria for new call requests. Gilhousen et al. [10] derived the number ofaccepted voice calls in order to represent the capacity of CDMA systems. Evans and Everitt[11] reported results regarding the capacity of multiple service DS-CDMA cellular networks,but they neglected background noise and considered the target signal in the interference. Leeet al. [12] derived the capacities of single-code and multi-code DS-CDMA systems accom-modating multi-class services and also proposed call admission criteria. This paper presentscapacity estimation for multimedia traffic in MCR-DS/CDMA systems. The optimum valueof the received power which causes the least interference to other users while maintaining anacceptable QoS requirements is also derived.

This paper is organized as follows. In Section 2, an MCR-DS/CDMA system model is de-scribed. In Section 3, criteria for capacity estimation in MCR-DS/CDMA systems supportingmultimedia services are derived. In Section 4, numerical examples are presented and resultsare discussed. Finally, conclusions are given in Section 5.

2. System Model

2.1. MCR-DS/CDMA SYSTEM MODEL

In MCR-DS/CDMA systems, as in other cellular systems, a service area is divided into cells,and each cell is served by a BS. In each cell, the same RF channels can be reused. Therefore,the CDMA system capacity is interference limited [10]. A separation of different user signalsis achieved by means of signature sequences which are used to spread the spectrum of userinformation signals.

A system model is shown in Figure 1. The system consists of several subsystems.rchipmj and

fmj denote the spreading chip rate and the RF carrier frequency of subsystem{m, j}, m =1, · · · ,M andj = 1, · · · ,2m−1, respectively.

Calls are classified intoi different classes of bearer services,i = 1, · · · , I , and the bearerservices are arranged in order, according to the required QoS, spreading chip rates, and RFcarrier frequencies. Table 1 shows an example of relation between three types of calls andclass-i bearer service,i = 1, · · · ,12.

The MCR-DS/CDMA system model and the associated assumptions used in this paper aresummarized as follow:

1. A service area is divided into cells of equal size.

Capacity Estimation in MCR-DS/CDMA Systems Supporting Multimedia Services31

Figure 1. Frequency assignment of an MCR-DS/CDMA system.

Table 1. Example of relation between three types of calls and class-i bearer service.

Type-t Calls RequiredEb/Io, γt Class-i Remarks

1 Low γ1 1 Subsystem {1,1},f11

resolution 2 Subsystem {2,1},f21

video 3 Subsystem {2,2},f22

2 Facsimile γ2 4 Subsystem {1,1},f11

5 Subsystem {2,1},f21

6 Subsystem {2,2},f22

3 Voice γ3 7 Subsystem {2,1},f21

8 Subsystem {2,2},f22

9 Subsystem {3,1},f31

10 Subsystem {3,2},f32

11 Subsystem {3,3},f33

12 Subsystem {3,4},f34

2. Separate frequency bands are used for forward and reverse links. Thus, mobile stationsexperience interference only from BSs and BSs experience interference only from mobilestations.

3. Each mobile station is power-controlled by the BS of its home cell.4. A mobile station making a call request to the system chooses its home cell such that the

radio propagation attenuation between the mobile station and the BS of its home cell isminimized.

5. Only the reverse link is considered because it is more critical to the system capacity thanthe forward link.

6. There areI classes of bearer services with each information bit rateRi andni bearerservices of the class-i (i = 1, · · · , I ) are connected to the BS.

7. Given the number of accepted bearer services for each class, the received power at a BSis assumed to be equal for each bearer service in the same class through perfect powercontrol.

8. Coherent detection and asynchronous quaternary DS spread-spectrum multiple-accesssystems are used in additive white Gaussian noise (AWGN) channels.

32 Young Woo Kim et al.

9. Inter-cell interference is assumed to be measured from the received power at the BS.

2.2. QUALITY -OF-SERVICE (QOS)

As a QoS measure in an MCR-DS/CDMA system supporting multi-class bearer services, thebit energy-to-interference PSD ratio for class-i bearer service,〈Eb/Io〉i , is given by:

〈Eb/Io〉i = Si/Ri(∑Ik=1 λkinkSk + Ii − Si

)/(3

4Rchipi )+No

, (1)

whereRchipi denotes the chip rate of the spreading sequence of class-i bearer service,Si the

received power at the BS,Ri the information bit rate,Eb the information bit energy,λki (0 ≤λki ≤ 1) the interference factor for the class-k bearer service signal to the class-i bearer servicesignal (refer to subsection 2.3),nk the number of class-k bearer services transmitting,Ii theinter-cell interference received by the BS receiver for the class-i bearer service signals, andNo/2 the two-sided PSD of AWGN. Equation (1) is based on the fact that the bit error rate

(BER) is approximately given by BER≈ Q(√

2〈Eb/Io〉), whereQ(x) = ∫∞x

1√2πe−

y2

2 dy,when coherent detection and asynchronous transmission among multiple user terminals areused in AWGN [13, 14].

The coefficient34 arises in Equation (1) for the Gaussian approximation because rectangularchip pulses are assumed, and it needs to be changed with the assumption of other chip shapes[15].

2.3. INTERFERENCEFACTOR, λki

Sk is the power of the class-k bearer service signal(k = 1, · · · , I ) received at a BS. Theinterference factorλki (refer to Appendix) is defined as:

λki ,Ski

Sk, (2)

whereSki (0 ≤ Ski ≤ Sk) is the power portion of the class-k bearer service signal receivedby the BS receiver for the class-i bearer service signal (i = 1, · · · , I ). In the case of using asingle RF channel bandwidth, all of the interference factorsλki are ones (1’s).

2.4. CHARACTERISTICS OFCO-CHANNEL INTERFERENCE INMCR-DS/CDMASYSTEMS

In order to investigate characteristics of co-channel interference in MCR-DS/CDMA systems,a system model of a two-chip-rate (i.e.,rchip

1 andrchip2 ) system shown in Figure 2 [8] is con-

sidered. The system consists of 1+ 2m−1 subsystems. For convenience, we consider only twotypes of calls and denote the higher-rate call by type-1 and the lower-rate call by type-2. Inaddition, we assume that type-1 calls are only accommodated in subsystem {1,1} and type-2calls in subsystem{m, j}.

Consider a binary DS-CDMA system with rectangular chip pulses. Letn11 be the numberof users in subsystem{1,1}, nmj be the number of users in subsystem{m, j}; then then-thtransmitted signal of subsystem{1,1}, s11n(t) (1 ≤ n ≤ n11) and then-th transmitted signal

Capacity Estimation in MCR-DS/CDMA Systems Supporting Multimedia Services33

Figure 2. Frequency assignment of a two-chip-rate system.

of subsystem{m, j}, smjn(t) (1≤ n ≤ nmj) are [13]

s11n(t) =√

2P1β11n(t)α11n(t)cos(2πf11t + θ11n), (3)

smjn(t) =√

2Pmβmjn(t)αmjn(t)cos(2πfmj t + θmjn). (4)

In Equations (3) and (4), the phases introduced by the modulators,θ11n andθmjn, are modeledas i.i.d. (independent and identically distributed) random variables uniformly distributed over[0,2π ].

The data waveformsβ11n(t) andβmjn(t) consist of sequences of mutually independentrectangular pulses with durationT1 = 1/R1 and Tm = 1/Rm and with equally probableamplitudes+1 or−1. Since random signature sequences are assumed, the code waveformsα11n(t) andαmjn(t) are also sequences of mutually independent rectangular pulses of durationTc1 = 1/rchip

11 andTcm = 1/rchipmj having amplitude+1 or−1 with the equal probability.P1

andPm are the transmitted powers of type-1 and type-2 calls, respectively.A correlation receiver (or matched filter) is assumed to match the corresponding signal. In

addition, it is assumed that subsystem{m, j} do not interfere with each other.Imjl,m 6= 1 andl = 1, · · · , nmj , denotes the interference at thel-th receiver output of subsystem{m, j} [8],then

Imjl =nmj∑n=1n6=l

1

Tm

∫ Tm

0cmjn(t − τmjn)αmjl(t)dt · cosφmjn

+n11∑n=1

1

Tm

√P1

Pm

∫ Tm

0c11n(t − τ11n)αmjl(t) · cos(−2πFmj t + φ11n)dt, (5)

wherec11n(t) = β11n(t)α11n(t); cmjn(t) = βmjn(t)αmjn(t); Fmj = fmj − f11; φ11n = θ11n −2πf11τ11n; andφmjn = θmjn − 2πfmjτmjn.τ11n and τmjn are the delays modeled as uniformly distributed random variables in the

interval[0, T1] and[0, Tm], respectively. It is shown from [16] thatφ11n andφmjn are uniformlydistributed on[0,2π ]. From Equation (5),Imjl is composed of the interference from its ownsubsystem and that from subsystem{1,1}. The cos(−2πFmj t + φ11n) term causes differentlevels of interferences for different values ofj . Therefore, we know that the farther the carrierfrequencyfmj is fromf11, the lower interference the corresponding subsystem can experience.

34 Young Woo Kim et al.

3. Criteria for Capacity Estimation

3.1. CALL ADMISSION

Call admission control is important to prevent the system from becoming overloaded and tomaintain an acceptable QoS for existing users. BSw is assumed to transmit a pilot signal at aconstant power levelP (w) on a separate channel at all times.

When a new userl makes a call attempt, he measures and compares the pilot signal strengthof all adjacent BSs. Userl is assigned to the BS with the strongest pilot signal. That is, thenew userl is assigned to BSw∗ such that

P (w∗) · hlw∗ = max

w{P (w) · hlw}, (6)

wherehlw denotes the gain for userl to BSw.After userl is assigned to BSw∗, a spreading codec is chosen in the set of codes at BSw∗

that are not previously assigned to other users. Given the spreading codec, a constraint hasto be satisfied: the estimated bit energy-to-interference PSD ratio of the class-i bearer serviceafter admitting the new user cannot be less thanγi, the required bit energy-to-interferencePSD ratio for everyi (i = 1, . . . , I ).

3.2. CRITERIA FOR CAPACITY ESTIMATION

A new class-i bearer service is accepted at a BS on spreading codec only if

Si/Ri(∑Ik=1 λkinkSk + Ii − Si

)/(3

4Rchip

i )+No≥ γi (i = 1, . . . , I ) . (7)

Otherwise, the new call is blocked. Equation (7) can be rewritten as:

aiSi ≥I∑k=1

λkinkSk + bi (i = 1, . . . , I ) , (8)

where

− in general case:

ai = 1+ 3Gi

4γiand bi = 3

4R

chipi No + Ii ,

− in case of using the inter-cell interference factor,f [17]:

ai = 1+ 3

4(1+ f )Gi

γiand bi = 3

4(1+ f )Rchipi No ,

andGi , Rchipi

Ridenotes the spreading factor.

The parameterai is determined according to the spreading bandwidth in a subsystem andQoS requirements of the call. Therefore, for the same type of call with different chip rates, thevalues ofai are different depending on the chip rate.

In a single RF channel bandwidth system, all ofλki in Equation (7) are ones (1’s).

Capacity Estimation in MCR-DS/CDMA Systems Supporting Multimedia Services35

3.3. CAPACITY ESTIMATION

Conditions on the capacity maximization i.e., conditions of the minimum transmitted powerof the class-i bearer service that still meets the required bit energy-to-interference PSD ratioγiare achieved when an equality holds in Equation (7). Thus, we have the following constraintson the vectorsN = [n1, · · · , nI ] andS = [S1, · · · , SI ]T that provide the maximum capacity:

aiSi =I∑k=1

λkinkSk + bi (i = 1, . . . , I ). (9)

We can rewrite the above constraints as a set of linear equations as follows:

(a1− n1λ11)S1 − n2λ21S2− · · · −nIλI1SI = b1

−n1λ12S1 + (a2− n2λ22)S2− · · · −nIλI2SI = b2...

.... . .

...

−n1λ1IS1 − n2λ2IS2− · · · +(aI − nIλII )SI = bI .

(10)

We may write Equation (10) in a matrix form,

AS = b, (11)

where

A ,

a1− n1λ11 −n2λ21 · · · −nIλI1

−n1λ12 a2 − n2λ22 · · · −nIλI2...

.... . .

...

−n1λ1I −n2λ2I · · · aI − nIλII

,

S ,

S1S2...

SI

, and b ,

b1

b2...

bI

.For a givenb, Equation (11) may be regarded as a system ofI linear equations withIunknownsS1, . . . , SI and we know from the Fundamental theorem for systems of linearequations that it has a unique solution if and only if an(I × I )matrix,A is nonsingular.

Given the maximum receivable power of the class-i bearer service asSi (i = 1, . . . , I ),the admissible set of network traffic is given by:

{(n1, n2, . . . , nI ) ∃ Si such that 0≤ Si ≤ Si andSi satisfies Equation (11)}. (12)

Here, the maximum receivable power of the class-i bearer service means the maximum powerthat can be received by the BS even in the case of the largest propagation loss between the BSand the mobile station. In addition,Si implies the optimum received power causing the leastinterference to other signals while maintaining an acceptable bit energy-to-interference PSDratio, which can be obtained from Equation (12), given existing calls.

4. Numerical Results and Discussion

We now show examples of how system capacities can be estimated, given some parameters.In addition, characteristics of co-channel interference between subsystems are investigated.

36 Young Woo Kim et al.

Table 2. Required performance for multi-class services.

Type-t Calls Information bit rate Required BER RequiredEb/Io, γt

1 Low resolution video 128 kb/s 10−5 9.095 (=9.6 dB)

2 Facsimile 64 kb/s 10−4 6.916 (=8.4 dB)

3 Voice 32 kb/s 10−3 4.775 (=6.8 dB)

Consider the following three types of calls, as shown in Table 2, where we refer to [18] forthe required BERs. For simplicity, we consider only a single cell environment. We assumeNo = 10−14 mW/Hz andSi = 10−3 mW.

4.1. SYSTEM CAPACITY

In order to compare the capacity of an MCR-DS/CDMA system with that of an one-chip-rate system, we consider an MCR-DS/CDMA system with two chip rates (i.e.,r

chip1 = 5

Mchips/s andrchip2 = 1.25 Mchips/s) and five subsystems (i.e.,m = 3) in total, as shown

in Figure 2. In the MCR-DS/CDMA system, a 5 MHz bandwidth channel can be allocatedfor RF channels for video, facsimile, and voice calls and 1.25 MHz bandwidth channels forvoice calls. Therefore, we assumeRchip

1 = Rchip2 = R

chip3 = r

chip1 = r

chip11 = 5 Mchips/s and

Rchip4 = R

chip5 = R

chip6 = R

chip7 = r

chip2 = r

chip3j = 1.25 Mchips/s. In addition, we assume

Rchip1 = R

chip2 = R

chip3 = r

chip1 = 5 Mchips/s in the one-chip-rate system. We can obtain

the parametersai and bi in Equation (8) in Table 3. Next, the interference factorsλki areconsidered in Appendix, which are summarized in Table 4.

MCR-DS/CDMA System:We may write matrixA in Equation (11).

A =

a1− n1λ11 −n2λ21 · · · −n7λ71

−n1λ12 a2− n2λ22 · · · −n7λ72...

.... . .

...

−n1λ17 −n2λ27 · · · a7− n7λ77

=

4.221− n1 −n2 · · · −n7

−n1 9.472− n2 · · · 0...

.... . .

...

−0.0716n1 0 · · · 7.135− n7

.

One-Chip-Rate System:

A = a1− n1 −n2 −n3

−n1 a2− n2 −n3

−n1 −n2 a3− n3

= 4.221− n1 −n2 −n3

−n1 9.472− n2 −n3

−n1 −n2 25.541− n3

.

Capacity Estimation in MCR-DS/CDMA Systems Supporting Multimedia Services37

Table 3. Parameters.

Type-t Calls Class-i MCR-DS/CDMA system One-chip-rate system Remarks

ai bi ai bi

1 Low resolution video 1 4.221 3.75× 10−11 4.221 3.75× 10−11 Subsystem {1,1}

2 Facsimile 2 9.472 3.75× 10−11 9.472 3.75× 10−11 Subsystem {1,1}

3 Voice 3 25.541 3.75× 10−11 25.541 3.75× 10−11 Subsystem {1,1}

4 7.135 9.375× 10−12 Subsystem {3,1}

5 7.135 9.375× 10−12 Subsystem {3,2}

6 7.135 9.375× 10−12 Subsystem {3,3}

7 7.135 9.375× 10−12 Subsystem {3,4}

Table 4. The interference factors,λki .

k \ i 1 2 3 4 5 6 7

1 1 1 1 0.0716 0.4284 0.4284 0.0716

2 1 1 1 0.0716 0.4284 0.4284 0.0716

3 1 1 1 0.0716 0.4284 0.4284 0.0716

4 1 1 1 1 0 0 0

5 1 1 1 0 1 0 0

6 1 1 1 0 0 1 0

7 1 1 1 0 0 0 1

Figure 3 shows the admissible sets (or capacities) for an MCR-DS/CDMA system and anone-chip-rate system.N1(= n1), N2(= n2), andN3(= n3) are the admissible numbers forvideo, facsimile, and voice call, respectively. Each admissible point(N1, N2, N3) within theadmissible set means the admissible number of each type of calls that the system can supportat a specified level of QoS.

Figure 3. Admissible sets: (a) MCR-CDMA system; (b) One-chip-rate system.

38 Young Woo Kim et al.

Table 5. Admissible sets.

Items MCR-DS/CDMA system One-chip-rate system

Number of admissible points 386 283

Figure 4. MCR-DS/CDMA system model for simulation.

In Table 5, the admissible points in admissible sets are summarized. From the result, it isshown that the MCR-DS/CDMA system supports at least 36% more capacity than the one-chip-rate system.

4.2. CHARACTERISTICS OFCO-CHANNEL INTERFERENCE BETWEENSUBSYSTEMS

In order to investigate characteristics of co-channel interference between subsystems, we con-sider an MCR-DS/CDMA system with three chip rates (i.e.,r

chip1 , rchip

2 , andrchip3 ) and seven

subsystems, as shown in Figure 4. The PSDs of DS waveforms in a system configuration areshown in Figure 5. The PSD of each spreading signal follows a curve of sinc2{2(f − fc)Tc},

Figure 5. Psd of DS waveforms in a system configuration.

Capacity Estimation in MCR-DS/CDMA Systems Supporting Multimedia Services39

Table 6. Parameters.

Type-t Calls Class-i ai bi Remarks

1 Low resolution 1 13.884 1.5× 10−10 Subsystem {1,1}

video 2 7.442 7.5× 10−11 Subsystem {2,1}

2 Facsimile 3 17.944 7.5× 10−11 Subsystem {2,1}

4 9.472 3.75× 10−11 Subsystem {3,1}

5 9.472 3.75× 10−11 Subsystem {3,2}

6 9.472 3.75× 10−11 Subsystem {3,3}

7 9.472 3.75× 10−11 Subsystem {3,4}

3 Voice 8 50.084 7.5× 10−11 Subsystem {2,1}

9 25.541 3.75× 10−11 Subsystem {3,1}

10 25.541 3.75× 10−11 Subsystem {3,2}

11 25.541 3.75× 10−11 Subsystem {3,3}

12 25.541 3.75× 10−11 Subsystem {3,4}

(Tc: chip duration,fc: carrier frequency) with a rectangular chip pulse. Considering both PSDover an RF band and the effect of RF input filtering on the receiver, admissible sets in thefollowing four cases are estimated and the characteristics of co-channel interference betweensubsystems are investigated:

− Case-1: Using subsystem {1,1}, subsystems {2,1} and {3,1},− Case-2: Using subsystem {1,1}, subsystems {2,1} and {3,2},− Case-3: Using subsystem {1,1}, subsystems {2,1} and {3,3},− Case-4: Using subsystem {1,1}, subsystems {2,1} and {3,4}.

We consider that 5 MHz bandwidth channels can be allocated for RF channels for voice andfacsimile calls, a 10 MHz bandwidth channel for voice, facsimile, and video calls, and a20 MHz bandwidth channel for video calls. Therefore, we assume thatR

chip1 = r

chip1 = 20

Mchips/s,Rchip2 = Rchip

3 = Rchip8 = rchip

2 = 10 Mchips/s, andRchip4 = Rchip

5 = Rchip6 = Rchip

7 =R

chip9 = Rchip

10 = Rchip11 = Rchip

12 = rchip3 = 5 Mchips/s. The parametersai andbi are shown in

Table 6 and the interference factorsλki are summarized in Table 7.Finally, we may write matrixA in Equation (11).

Case-1:

A =

a1− n1λ11 −n2λ21 · · · −n9λ91

−n1λ12 a2− n2λ22 · · · −n9λ92...

.... . .

...

−n1λ19 −n2λ29 · · · a9− n9λ99

=

13.884− n1 −n2 · · · −n9

−0.5n1 7.442− n2 · · · −n9...

.... . .

...

−0.0716n1 −0.5n2 · · · 25.541− n9

.

40 Young Woo Kim et al.

Table 7. Interference factors.

k \ i 1 2 3 4 5 6 7 8 9 10 11 12

1 1 0.5 0.5 0.0716 0.4284 0.4284 0.0716 0.5 0.0716 0.4284 0.4284 0.0716

2 1 1 1 0.5 0.5 0 0 1 0.5 0.5 0 0

3 1 1 1 0.5 0.5 0 0 1 0.5 0.5 0 0

4 1 1 1 1 0 0 0 1 1 0 0 0

5 1 1 1 0 1 0 0 1 0 1 0 0

6 1 0 0 0 0 1 0 0 0 0 1 0

7 1 0 0 0 0 0 1 0 0 0 0 1

8 1 1 1 0.5 0.5 0 0 1 0.5 0.5 0 0

9 1 1 1 1 0 0 0 1 1 0 0 0

10 1 1 1 0 1 0 0 1 0 1 0 0

11 1 0 0 0 0 1 0 0 0 0 1 0

12 1 0 0 0 0 0 1 0 0 0 0 1

Case-2:

A =

13.884− n1 −n2 · · · −n10

−0.5n1 7.442− n2 · · · −n10...

.... . .

...

−0.4284n1 −0.5n2 · · · 25.541− n10

.

Case-3:

A =

13.884− n1 −n2 · · · −n11

−0.5n1 7.442− n2 · · · −n11...

.... . .

...

−0.4284n1 0 · · · 25.541− n11

.

Case-4:

A =

13.884− n1 −n2 · · · −n12

−0.5n1 7.442− n2 · · · −n12...

.... . .

...

−0.0716n1 0 · · · 25.541− n12

.Figure 6 and Table 7 show the admissible sets in case-1, case-2, case-3, and case-4.

In Figure 6,N1(= n1+n2),N2(= n3+· · ·+n7), andN3(= n8+· · ·+n12) are the admissiblenumbers for video, facsimile, and voice call, respectively. The admissible set in each case isgiven by simulations. Each admissible point(N1, N2, N3) within the admissible set means theadmissible number of each type of calls that the system can support at a specified level of QoS.The number of admissible points in case-2 is approximately 55% less than in case-4, and thecapacity boundaries in cases -2 and -3 are more similar to that in one-chip-rate system, thanthe capacity boundaries in other cases. This is because mutual-interferences in cases -2 and -3

Capacity Estimation in MCR-DS/CDMA Systems Supporting Multimedia Services41

Table 8. Admissible sets.

Items Case-1 Case-2 Case-3 Case-4

Number of admissible points (= N) 3,590 3,379 6,007 7,568

Proportion (= NN in case-4) 0.4744 0.4465 0.7937 1

Figure 6. Admissible sets: (a) case-1, (b) case-2, (c) case-3, (d) case-4.

are larger than in other cases. Then, it can be observed that subsystem {3,2} (or {3,3}) suffersmore interferences from subsystem {1,1} than does subsystem {3,1} (or {3,4}), as shown inFigure 5. In addition, subsystems {2,j }, (j = 1,2) (or {3,j }, (j = 1, . . . , 4)) interfere witheach other by way of subsystem {1,1}, which yields a change in the number of admitted usersin subsystems 1, 2, and 3. From these observations, it is noted that adjusting the allocation ofthe number of calls to subsystems can reduce the blocking probability in MCR-DS/CDMAsystems.

5. Conclusions

System capacity and optimum received power in MCR-DS/CDMA systems supporting mul-timedia services are considered. In addition, in order to account for other user interferencein the same frequency band, interference factorλki in the requirement is introduced. Numer-ical results show that MCR-DS/CDMA systems support more capacity than one-chip-rate

42 Young Woo Kim et al.

Figure 7. PSD and Bandpass filters: (a) PSD of QPSK spreading signal; (b) Transfer function of ideal output filterin a transmitter; (c) PSD of output signal in a transmitter; (d) Transfer function of ideal input filter in a receiver;(e) PSD of input signal in a receiver.

system and that subsystems {3,j }, (j = 1, . . . , 4) experience different interferences fromsubsystem {1,1}. From the results, system performance is strongly affected by a selectedchannel assignment strategy. Therefore, it is important to efficiently assign radio resources inMCR-DS/CDMA systems that support high capacity with a low blocking rate [19].

Appendix

A. Interference Factors

In this appendix, we first review the PSD and the autocorrelation function of power signals,and then derive interference factors.

A.1. POWER SPECTRAL DENSITY AND AUTOCORRELATION FUNCTION

The PSD of QPSK spreading signal is expressed in the form ofSg(f ) = sinc2{2(f −f11)Tc1},(Tc1: chip duration,f11: carrier frequency) with a rectangular chip pulse, as shown in Figure 7.

It is often convenient to work with filters having idealized transfer functions with rectan-gular response functions that are constant within the passband and zero elsewhere. Within thepassband, a linear phase response characteristic is assumed. Thus, 1/Tc1 and 1/Tc3 = 1/4Tc1are the bandwidths of the filters, the transfer functions of these two filters can be written asfollows:

Ho(f ) = [5{(f − f11)Tc1}]e−jwto , (13)

Hi(f ) = [5{4(f − f31)Tc1}]e−jwto , (14)

Capacity Estimation in MCR-DS/CDMA Systems Supporting Multimedia Services43

whereHo(f ) denotes the transfer function of transmitter output bandpass filter andHi(f ) thetransfer function of receiver input bandpass filter. Then, the PSD of the output signal in thetransmitter,Si(f ) is expressed by:

Si(f ) = |Ho(f )|2Sg(f ). (15)

Finally, the PSD of the input signal in the receiver,S(f ) is as follows:

S(f ) = |Hi(f )|2Si(f )= |Hi(f )|2|Ho(f )|2Sg(f )= |5{(f − f11)Tc1}|2|5{4(f − f31)Tc1}|2sinc2{2(f − f11)Tc1}. (16)

By the Wiener–Khinchine theorem, which says that the autocorrelation function of a signaland its PSD are Fourier transform pairs, the autocorrelation functionR(τ) is obtained by:

R(τ) = F−1[S(f )]= F−1[|5{(f − f11)Tc1}|2|5{4(f − f31)Tc1}|2sinc2{2(f − f11)Tc1}]=∫ ∞−∞|5{(f − f11)Tc1}|2|5{4(f − f31)Tc1}|2sinc2{2(f − f11)Tc1}ej2πfτ df

≈∫ f11− 1

4Tc1

f11− 12Tc1

sinc2{2(f − f11)Tc1}ej2πf τ df. (17)

The total average powerR(0) is given by:

R(0) =∫ f11− 1

4Tc1

f11− 12Tc1

sinc2{2(f − f11)Tc1}df. (18)

A.2. INTERFERENCEFACTORS

From the results of the previous subsection A.1, we can obtain the total power of transmittedsignalR(0)t as follows:

R(0)t =∫ f11+ 1

2Tc1

f11− 12Tc1

sinc2{2(f − f11)Tc1}df . (19)

The power portion of section I,R(0)1 is given by:

R(0)1 =∫ f11− 1

4Tc1

f11− 12Tc1

sinc2{2(f − f11)Tc1}df . (20)

The power portion of section II,R(0)2 is written as:

R(0)2 =∫ f11

f11− 14Tc1

sinc2{2(f − f11)Tc1}df . (21)

The power portion of section III,R(0)3 is given by:

R(0)3 =∫ f11+ 1

4Tc1

f11

sinc2{2(f − f11)Tc1}df . (22)

44 Young Woo Kim et al.

The power portion of section IV,R(0)4 is written as:

R(0)4 =∫ f11+ 1

2Tc1

f11+ 14Tc1

sinc2{2(f − f11)Tc1}df . (23)

From the previous subsection 2.3, we can determine the interference factors as follows:

λ11 = R(0)tR(0)t

= 1,

λ12 = R(0)tR(0)t

= 1,

λ13 = R(0)tR(0)t

= 1,

λ14 = R(0)1R(0)t

= 0.0716,

λ15 = R(0)2R(0)t

= 0.4284,

λ16 = R(0)3R(0)t

= 0.4284,

and λ17 = R(0)4R(0)t

= 0.0716.

In a similar way, we can obtain the remaining interference factors. The interference factors foreach case are shown in Tables 4 and 7.

References

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2. L.B. Milstein, D.L. Schilling, R.L. Pickholtz, V. Erceg, M. Kullback, E.G. Kanterakis, D.S. Fishman,W.H. Biederman and D.C. Salerno, “On the Feasibility of a CDMA Overlay for Personal CommunicationsNetworks”,IEEE J. Select. Areas Commun., Vol. 10, No. 4, pp. 655–668, 1992.

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7. S. C. Bang, “ETRI IMT-2000 Multiband CDMA System for Terrestrial Environments,” Mobile Comm.Research Div., ETRI, Taejon, Korea, 1997.

8. T. H. Wu, “Issues in Multimedia Packet CDMA Personal Communication Networks”, Ph.D. Thesis, Dept.of Elec. Eng., Univ. of Maryland, College Park, Aug. 1994.

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10. K.S. Gilhousen, I.M. Jacobs, R. Padovani, A.J. Viterbi, L.A. Weaver and C.E. Wheatley, “On the Capacityof a Cellular CDMA System”,IEEE Trans. Veh. Technol., Vol. 40, No. 2, pp. 303–312, 1991.

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11. J. Evans and D. Everitt, “Call Admission Control in Multiple Service DS-CDMA Cellular Networks”, inProc. IEEE VTC, April 1996, pp. 227–231.

12. S.J. Lee, H.W. Lee and D.K. Sung, “Capacities of Single-Code and Multi-Code DS-CDMA SystemsAccommodating Multi-Class Services”,IEEE Trans. Veh. Technol., to be published.

13. M.B. Pursley, “Performance Evaluation for Phase-Coded Spread-Spectrum Multiple-AccessCommunication-Part I: System Analysis”,IEEE Trans. Commun., Vol. 25, No. 8, pp. 795–799, 1977.

14. R.L. Pickholtz, L.B. Milstein and D.L. Schilling, “Spread Spectrum for Mobile Communications”,IEEETrans. Veh. Technol., Vol. 40, No. 2, pp. 313–322, 1991.

15. E. Geraniotis and B. Ghaffari, “Performance of Binary and Quaternary Direct-Sequence Spread-SpectrumMultiple-Access Systems with Random Signature Sequences”,IEEE Trans. Commun., Vol. 39, No. 5, pp.713–724, 1991.

16. M.B. Pursley, “Spread-Spectrum Multiple-Access Communications”, in G. Longer (ed.),Multi-UserCommunication Systems, Springer-Verlag: New York, NY, pp. 139–199, 1981.

17. 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. 892–900, 1993.

18. P. Mermelstein, A. Jalali and H. Leib, “Integrated Services on Wireless Multiple Access Networks”, inProc.IEEE ICC, Oct. 1993, pp. 863–867.

19. Young W. Kim, Seung J. Lee, Min Y. Chung, Jeong H. Kim and Dan K. Sung, “Radio Resource Assign-ment in Multiple-Chip-Rate DS/CDMA Systems Supporting Multimedia Services”,IEICE Trans. Commun.,Vol. E82-B, No. 1, pp. 145–155, 1999.

Young Woo Kim received the B.S. degree in electronic engineering from Korea AviationCollege in 1977 and the M.S. degree in electronic engineering from Seoul National Universityin 1983. He is working towards the Ph.D. degree in electrical engineering at Korea AdvancedInstitute of Science and Technology (KAIST) since 1994. From Dec. 1978 to Feb. 1985, hewas a development engineer with Oriental Precision Company, Korea, where he had been en-gaged in research and development of military communication systems. Since March 1985, hehas been with Hyundai Electronics Industries Company, Korea. His research interests includeradio resource management and call admission control in IMT-2000. He is a member of KICS.

46 Young Woo Kim et al.

Seung Joon Leereceived the B.S., M.S., and Ph.D. degrees in electrical engineering fromKAIST, in 1991, 1993, and 1998, respectively. He has been with Hyundai Electronics In-dustries Company, Korea since Nov. 1994. His research interests include handoff schemes inwireless ATM and support of multimedia in CDMA systems. He is a member of IEEE andKICS.

Jeong Ho Kim received the B.S. and M.S. degrees in electrical engineering from KAIST, in1991 and 1993, respectively. Currently he is working towards the Ph.D. degree in electricalengineering at KAIST. He has been with LG Electronics Inc., Korea since Feb. 1993. Hisresearch interests include system analysis, power control, and multimedia multiple accessprotocol in CDMA systems. He is a student member of IEEE and a member of KICS.

Capacity Estimation in MCR-DS/CDMA Systems Supporting Multimedia Services47

Young Hoon Kwon received the B.S. degree in electronics from Kyungpook National Univer-sity in 1994 and the M.S. degree in electrical engineering from KAIST in 1996. He is workingtowards the Ph.D. degree in electrical engineering at KAIST since 1996. His research interestsinclude IMT-2000 network and satellite communications. He is a student member of IEEE.

Dan Keun Sung received the B.S. degree in electronic engineering from Seoul NationalUniversity in 1975, the M.S. and Ph.D. degrees in electrical and computer engineering fromUniversity of Texas at Austin, in 1982 and 1986, respectively. From May 1977 to July 1980,he was a research engineer with the Electronics and Telecommunications Research Institute,where he had been engaged in research on the development of electronic switching systems. In1986, he joined the faculty of the Korea Institute of Technology and is currently a Professor ofDept. of Electrical Engineering at KAIST. His research interests include ISDN switching sys-tems, ATM switching systems, wireless networks, and performance and reliability of systems.He is a member of IEEE, IEICE, KITE, KICS and KISS.