Capacity Estimation in Multiple-Chip-Rate DS/CDMA Systems ...

Wireless Personal Communications 14: 29–47, 2000. © 2000 Kluwer Academic Publishers. Printed in the Netherlands.

Capacity Estimation in Multiple-Chip-Rate DS/CDMA Systems Supporting Multimedia Services ∗ YOUNG WOO KIM, SEUNG JOON LEE, JEONG HO KIM, YOUNG HOON KWON and DAN KEUN SUNG Department of Electrical Engineering, Korea Advance Institute of Science and Technology, 373-1 Kusong-dong, Yusong-gu, Taejon 305-701, Korea E-mail: [email protected] or [email protected]

Abstract. This paper is concerned with capacity estimation in multiple-chip-rate (MCR) DS/CDMA systems supporting multimedia services with different information rates and quality requirements. Considering both power spectral density (PSD) over a radio frequency (RF) band and the effect of RF input filtering on the receiver, capacity that satisfies the requirement of the bit energy-to-interference PSD ratio is derived. The optimum value of the received 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 selected channel assignment strategy. Therefore, it is critical to efficiently assign radio resources in MCR-DS/CDMA systems 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 to accommodate 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 the above requirements. Direct sequence (DS)-CDMA is attractive because of its flexibility in supporting multimedia traffic, as well as low interference coexistence with other CDMA or narrow-band systems operating in the same frequency band [2]. Two approaches for accommodating multi-rate services in DS-CDMA systems have been proposed. One is to use either a single-code or a multi-code DS-CDMA system in a single RF channel bandwidth [3]. The other is to use an MCR-DS/CDMA system in multiple RF channel bandwidths [1, 5, 6, 7]. The frequency bandwidth of an MCR-DS/CDMA system is selected according to the maximum information rate to be supported. MCR-DS/CDMA systems were proposed by the Code Division Testbed (CODIT) project [1, 5], OKI [6], and ETRI [7]. In the experimental CODIT testbed, an MCR-DS/CDMA system was proposed with three different chip rates corresponding to three different RF channel bandwidths of approximately 1, 5, and 20 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) can be optionally accommodated on narrow-band or on medium-band channels. The 1 MHz channel 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.

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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 RF resources, 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 of MCR-DS/CDMA systems, only a few results have been reported [8, 9]. These reported results did not consider the shape of the PSD of all spread signals in the system or the effect of RF input filtering on the receiver. In this paper, system capacity supporting multimedia services in MCR-DS/CDMA systems is investigated. The number of users per cell is limited by the total interference received at each base station (BS). When a system encounters congestion, admitting a new call can only cause deterioration of the link quality for some active calls and may result in dropping calls. Thus, in order to maintain acceptable connections for existing users, a system requires call admission criteria for new call requests. Gilhousen et al. [10] derived the number of accepted 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. Lee et al. [12] derived the capacities of single-code and multi-code DS-CDMA systems accommodating multi-class services and also proposed call admission criteria. This paper presents capacity estimation for multimedia traffic in MCR-DS/CDMA systems. The optimum value of the received power which causes the least interference to other users while maintaining an acceptable QoS requirements is also derived. This paper is organized as follows. In Section 2, an MCR-DS/CDMA system model is described. In Section 3, criteria for capacity estimation in MCR-DS/CDMA systems supporting multimedia services are derived. In Section 4, numerical examples are presented and results are discussed. Finally, conclusions are given in Section 5. 2. System Model 2.1. MCR-DS/CDMA S YSTEM M ODEL 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 signals is achieved by means of signature sequences which are used to spread the spectrum of user information signals. chip A system model is shown in Figure 1. The system consists of several subsystems. rmj and fmj denote the spreading chip rate and the RF carrier frequency of subsystem {m, j }, m = 1, · · · , M and j = 1, · · · , 2m−1 , respectively. Calls are classified into i different classes of bearer services, i = 1, · · · , I , and the bearer services are arranged in order, according to the required QoS, spreading chip rates, and RF carrier frequencies. Table 1 shows an example of relation between three types of calls and class-i bearer service, i = 1, · · · , 12. The MCR-DS/CDMA system model and the associated assumptions used in this paper are summarized as follow: 1. A service area is divided into cells of equal size.

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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

Required Eb /Io , γt

1

Low resolution video

γ1

1 2 3

Subsystem {1,1}, f11 Subsystem {2,1}, f21 Subsystem {2,2}, f22

2

Facsimile

γ2

4 5 6

Subsystem {1,1}, f11 Subsystem {2,1}, f21 Subsystem {2,2}, f22

3

Voice

γ3

7 8 9 10 11 12

Subsystem {2,1}, f21 Subsystem {2,2}, f22 Subsystem {3,1}, f31 Subsystem {3,2}, f32 Subsystem {3,3}, f33 Subsystem {3,4}, f34

Class-i

Remarks

2. Separate frequency bands are used for forward and reverse links. Thus, mobile stations experience interference only from BSs and BSs experience interference only from mobile stations. 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 is minimized. 5. Only the reverse link is considered because it is more critical to the system capacity than the forward link. 6. There are I classes of bearer services with each information bit rate Ri and ni bearer services 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 BS is assumed to be equal for each bearer service in the same class through perfect power control. 8. Coherent detection and asynchronous quaternary DS spread-spectrum multiple-access systems are used in additive white Gaussian noise (AWGN) channels.

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9. Inter-cell interference is assumed to be measured from the received power at the BS. 2.2. Q UALITY- OF -S ERVICE (Q O S) As a QoS measure in an MCR-DS/CDMA system supporting multi-class bearer services, the bit energy-to-interference PSD ratio for class-i bearer service, hEb /Io ii , is given by: Si /Ri

hEb /Io ii = P I

 , 3 chip /( λ n S + I − S R ) + N i i o k=1 ki k k 4 i

(1)

chip

where Ri 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 service signal (refer to subsection 2.3), nk the number of class-k bearer services transmitting, Ii the inter-cell interference received by the BS receiver for the class-i bearer service signals, and No /2 the two-sided PSD of AWGN. Equation (1) is based on the fact that the bit error rate R∞ √ y2 (BER) is approximately given by BER ≈ Q( 2hEb /Io i), where Q(x) = x √12π e− 2 dy, when coherent detection and asynchronous transmission among multiple user terminals are used in AWGN [13, 14]. The coefficient 34 arises in Equation (1) for the Gaussian approximation because rectangular chip pulses are assumed, and it needs to be changed with the assumption of other chip shapes [15]. 2.3. I NTERFERENCE FACTOR , λki Sk is the power of the class-k bearer service signal (k = 1, · · · , I ) received at a BS. The interference factor λki (refer to Appendix) is defined as: λki ,

Ski , Sk

(2)

where Ski (0 ≤ Ski ≤ Sk ) is the power portion of the class-k bearer service signal received by the BS receiver for the class-i bearer service signal (i = 1, · · · , I ). In the case of using a single RF channel bandwidth, all of the interference factors λki are ones (1’s). 2.4. C HARACTERISTICS S YSTEMS

OF

C O -C HANNEL I NTERFERENCE

IN

MCR-DS/CDMA

In order to investigate characteristics of co-channel interference in MCR-DS/CDMA systems, chip chip a system model of a two-chip-rate (i.e., r1 and r2 ) system shown in Figure 2 [8] is considered. The system consists of 1 + 2m−1 subsystems. For convenience, we consider only two types of calls and denote the higher-rate call by type-1 and the lower-rate call by type-2. In addition, we assume that type-1 calls are only accommodated in subsystem {1,1} and type-2 calls in subsystem {m, j }. Consider a binary DS-CDMA system with rectangular chip pulses. Let n11 be the number of users in subsystem {1, 1}, nmj be the number of users in subsystem {m, j }; then the n-th transmitted signal of subsystem {1, 1}, s11n (t) (1 ≤ n ≤ n11) and the n-th transmitted signal

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

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

of subsystem {m, j }, smj n (t) (1 ≤ n ≤ nmj ) are [13] p s11n (t) = 2P1 β11n(t)α11n (t)cos (2πf11 t + θ11n), p smj n (t) = 2Pm βmj n (t)αmj n (t)cos (2πfmj t + θmj n ).

(3) (4)

In Equations (3) and (4), the phases introduced by the modulators, θ11n and θmj n , are modeled as i.i.d. (independent and identically distributed) random variables uniformly distributed over [0, 2π ]. The data waveforms β11n (t) and βmj n (t) consist of sequences of mutually independent rectangular pulses with duration T1 = 1/R1 and Tm = 1/Rm and with equally probable amplitudes +1 or −1. Since random signature sequences are assumed, the code waveforms α11n(t) and αmj n (t) are also sequences of mutually independent rectangular pulses of duration chip chip Tc1 = 1/r11 and Tcm = 1/rmj having amplitude +1 or −1 with the equal probability. P1 and Pm 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. Imj l , m 6 = 1 and l = 1, · · · , nmj , denotes the interference at the l-th receiver output of subsystem {m, j } [8], then nmj Z Tm X 1 Imj l = cmj n (t − τmj n )αmj l (t)dt · cosφmj n Tm 0 n=1 n6=l

n11 X 1 + T n=1 m

s P1 Pm

Z

Tm

c11n (t − τ11n )αmj l (t) · cos(−2π Fmj t + φ11n )dt,

(5)

0

where c11n (t) = β11n (t)α11n (t); cmj n (t) = βmj n (t)αmj n (t); Fmj = fmj − f11 ; φ11n = θ11n − 2πf11 τ11n ; and φmj n = θmj n − 2πfmj τmj n . τ11n and τmj n are the delays modeled as uniformly distributed random variables in the interval [0, T1 ] and [0, Tm ], respectively. It is shown from [16] that φ11n and φmj n are uniformly distributed on [0, 2π ]. From Equation (5), Imj l is composed of the interference from its own subsystem and that from subsystem {1, 1}. The cos(−2π Fmj t + φ11n ) term causes different levels of interferences for different values of j . Therefore, we know that the farther the carrier frequency fmj is from f11 , the lower interference the corresponding subsystem can experience.

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Young Woo Kim et al.

3. Criteria for Capacity Estimation 3.1. C ALL A DMISSION Call admission control is important to prevent the system from becoming overloaded and to maintain an acceptable QoS for existing users. BS w is assumed to transmit a pilot signal at a constant power level P (w) on a separate channel at all times. When a new user l makes a call attempt, he measures and compares the pilot signal strength of all adjacent BSs. User l is assigned to the BS with the strongest pilot signal. That is, the new user l is assigned to BS w ∗ such that ∗

P (w ) · hlw∗ = max{P (w) · hlw }, w

(6)

where hlw denotes the gain for user l to BS w. After user l is assigned to BS w ∗ , a spreading code c is chosen in the set of codes at BS w ∗ that are not previously assigned to other users. Given the spreading code c, a constraint has to be satisfied: the estimated bit energy-to-interference PSD ratio of the class-i bearer service after admitting the new user cannot be less than γi , the required bit energy-to-interference PSD ratio for every i (i = 1, . . . , I ). 3.2. C RITERIA

FOR

C APACITY E STIMATION

A new class-i bearer service is accepted at a BS on spreading code c only if P I k=1

Si /Ri

 ≥ γi (i = 1, . . . , I ) . chip λki nk Sk + Ii − Si /( 34 Ri ) + No

(7)

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

I X

λki nk Sk + bi (i = 1, . . . , I ) ,

(8)

k=1

where − in general case: 3Gi 3 chip ai = 1 + and bi = Ri No + Ii , 4γi 4 − in case of using the inter-cell interference factor, f [17]: 3 3 Gi chip ai = 1 + and bi = Ri No , 4(1 + f ) γi 4(1 + f ) and Gi ,

chip

Ri Ri

denotes the spreading factor.

The parameter ai is determined according to the spreading bandwidth in a subsystem and QoS requirements of the call. Therefore, for the same type of call with different chip rates, the values of ai are different depending on the chip rate. In a single RF channel bandwidth system, all of λki in Equation (7) are ones (1’s).

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35

3.3. C APACITY E STIMATION Conditions on the capacity maximization i.e., conditions of the minimum transmitted power of the class-i bearer service that still meets the required bit energy-to-interference PSD ratio γi are achieved when an equality holds in Equation (7). Thus, we have the following constraints on the vectors N = [n1 , · · · , nI ] and S = [S 1 , · · · , S I ]T that provide the maximum capacity: ai S i =

I X

λki nk S k + bi (i = 1, . . . , I ).

(9)

k=1

We can rewrite the above constraints as a set of linear equations as follows: (a1 − n1 λ11 )S 1 − n2 λ21 S 2 − ··· −nI λI 1 S I = b1 −n1 λ12 S 1 + (a2 − n2 λ22 )S 2 − · · · −nI λI 2 S I = b2 .. .. .. .. . . . . −n1 λ1I S 1 − n2 λ2I S 2 − · · · +(aI − nI λI I )S I = bI .

(10)

We may write Equation (10) in a matrix form, AS = b, where

(11)



a1 − n1 λ11 −n2 λ21 · · · −nI λI 1  −n1 λ12 a2 − n2 λ22 · · · −nI λI 2  A ,  .. .. .. ..  . . . . −n1 λ1I −n2 λ2I · · · aI − nI λI I     b1 S1  b2  S     2 S ,  ..  , and b ,  ..  .  .   .  SI

   , 

bI

For a given b, Equation (11) may be regarded as a system of I linear equations with I unknowns S 1 , . . . , S I and we know from the Fundamental theorem for systems of linear equations 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 as S i (i = 1, . . . , I ), the admissible set of network traffic is given by: {(n1 , n2 , . . . , nI ) ∃ S i such that 0 ≤ S i ≤ S i and S i satisfies Equation (11)}.

(12)

Here, the maximum receivable power of the class-i bearer service means the maximum power that can be received by the BS even in the case of the largest propagation loss between the BS and the mobile station. In addition, S i implies the optimum received power causing the least interference to other signals while maintaining an acceptable bit energy-to-interference PSD ratio, 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

Required Eb /Io , γt

1 2 3

Low resolution video Facsimile Voice

128 kb/s 64 kb/s 32 kb/s

10−5 10−4 10−3

9.095 (= 9.6 dB) 6.916 (= 8.4 dB) 4.775 (= 6.8 dB)

Consider the following three types of calls, as shown in Table 2, where we refer to [18] for the required BERs. For simplicity, we consider only a single cell environment. We assume No = 10−14 mW/Hz and S i = 10−3 mW. 4.1. S YSTEM

CAPACITY

In order to compare the capacity of an MCR-DS/CDMA system with that of an one-chipchip rate system, we consider an MCR-DS/CDMA system with two chip rates (i.e., r1 = 5 chip Mchips/s and r2 = 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 allocated for RF channels for video, facsimile, and voice calls and 1.25 MHz bandwidth channels for chip chip chip chip chip voice calls. Therefore, we assume R1 = R2 = R3 = r1 = r11 = 5 Mchips/s and chip chip chip chip chip chip R4 = R5 = R6 = R7 = r2 = r3j = 1.25 Mchips/s. In addition, we assume chip

chip

chip

chip

R1 = R2 = R3 = r1 = 5 Mchips/s in the one-chip-rate system. We can obtain the parameters ai and bi in Equation (8) in Table 3. Next, the interference factors λki are considered in Appendix, which are summarized in Table 4. MCR-DS/CDMA System: We may write matrix A in Equation (11).  a1 − n1 λ11 −n2 λ21 · · ·  −n1 λ12 a2 − n2 λ22 · · ·  A =  .. .. ..  . . . 

−n1 λ17

−n2 λ27

4.221 − n1 −n2  −n 9.472 − n2 1  =  .. ..  . . −0.0716n1 0

−n7 λ71 −n7 λ72 .. .

    

· · · a7 − n7 λ77 ··· ··· .. .

−n7 0 .. .

· · · 7.135 − n7

One-Chip-Rate  System:  a1 − n1 −n2 −n3 A =  −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 Services

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Table 3. Parameters. Type-t Calls

1 2 3

Class-i MCR-DS/CDMA system ai bi

Low resolution video 1 Facsimile 2 Voice 3 4 5 6 7

4.221 9.472 25.541 7.135 7.135 7.135 7.135

3.75 × 10−11 3.75 × 10−11 3.75 × 10−11 9.375 × 10−12 9.375 × 10−12 9.375 × 10−12 9.375 × 10−12

One-chip-rate system ai bi

Remarks

4.221 3.75 × 10−11 9.472 3.75 × 10−11 25.541 3.75 × 10−11

Subsystem {1,1} Subsystem {1,1} Subsystem {1,1} Subsystem {3,1} Subsystem {3,2} Subsystem {3,3} Subsystem {3,4}

Table 4. The interference factors, λki . k \i

1

2

3

4

5

6

7

1 2 3 4 5 6 7

1 1 1 1 1 1 1

1 1 1 1 1 1 1

1 1 1 1 1 1 1

0.0716 0.0716 0.0716 1 0 0 0

0.4284 0.4284 0.4284 0 1 0 0

0.4284 0.4284 0.4284 0 0 1 0

0.0716 0.0716 0.0716 0 0 0 1

Figure 3 shows the admissible sets (or capacities) for an MCR-DS/CDMA system and an one-chip-rate system. N1 (= n1 ), N2 (= n2 ), and N3 (= n3 ) are the admissible numbers for video, facsimile, and voice call, respectively. Each admissible point (N1 , N2 , N3 ) within the admissible set means the admissible number of each type of calls that the system can support at 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 is shown that the MCR-DS/CDMA system supports at least 36% more capacity than the onechip-rate system. 4.2. C HARACTERISTICS

OF

C O - CHANNEL I NTERFERENCE

BETWEEN

S UBSYSTEMS

In order to investigate characteristics of co-channel interference between subsystems, we conchip chip chip sider an MCR-DS/CDMA system with three chip rates (i.e., r1 , r2 , and r3 ) and seven subsystems, as shown in Figure 4. The PSDs of DS waveforms in a system configuration are shown 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 Services

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Table 6. Parameters. Type-t

Calls

1

Low resolution video

2

Facsimile

3

Voice

ai

bi

Remarks

1 2

13.884 7.442

1.5 × 10−10 7.5 × 10−11

Subsystem {1,1} Subsystem {2,1}

3 4 5 6 7

17.944 9.472 9.472 9.472 9.472

7.5 × 10−11 3.75 × 10−11 3.75 × 10−11 3.75 × 10−11 3.75 × 10−11

Subsystem {2,1} Subsystem {3,1} Subsystem {3,2} Subsystem {3,3} Subsystem {3,4}

8 9 10 11 12

50.084 25.541 25.541 25.541 25.541

7.5 × 10−11 3.75 × 10−11 3.75 × 10−11 3.75 × 10−11 3.75 × 10−11

Subsystem {2,1} Subsystem {3,1} Subsystem {3,2} Subsystem {3,3} Subsystem {3,4}

Class-i

(Tc : chip duration, fc : carrier frequency) with a rectangular chip pulse. Considering both PSD over an RF band and the effect of RF input filtering on the receiver, admissible sets in the following four cases are estimated and the characteristics of co-channel interference between subsystems 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 and facsimile calls, a 10 MHz bandwidth channel for voice, facsimile, and video calls, and a chip chip 20 MHz bandwidth channel for video calls. Therefore, we assume that R1 = r1 = 20 chip chip chip chip chip chip chip chip Mchips/s, R2 = R3 = R8 = r2 = 10 Mchips/s, and R4 = R5 = R6 = R7 = chip chip chip chip chip R9 = R10 = R11 = R12 = r3 = 5 Mchips/s. The parameters ai and bi are shown in Table 6 and the interference factors λki are summarized in Table 7. Finally, we may write matrix A in Equation (11). Case-1:



a1 − n1 λ11 −n2 λ21 · · · −n9 λ91  −n1 λ12 a2 − n2 λ22 · · · −n9 λ92  A =  .. .. .. ..  . . . . −n1 λ19 −n2 λ29 · · · a9 − n9 λ99  13.884 − n1 −n2 ··· −n9  −0.5n1 7.442 − n · · · −n9 2  =  .. .. .. . ..  . . . −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 2 3 4 5 6 7 8 9 10 11 12

0.5 1 1 1 1 0 0 1 1 1 0 0

0.0716 0.5 0.5 1 0 0 0 0.5 1 0 0 0

0.4284 0.5 0.5 0 1 0 0 0.5 0 1 0 0

0.4284 0 0 0 0 1 0 0 0 0 1 0

0.0716 0 0 0 0 0 1 0 0 0 0 1

0.5 1 1 1 1 0 0 1 1 1 0 0

0.0716 0.5 0.5 1 0 0 0 0.5 1 0 0 0

0.4284 0.5 0.5 0 1 0 0 0.5 0 1 0 0

0.4284 0 0 0 0 1 0 0 0 0 1 0

0.0716 0 0 0 0 0 1 0 0 0 0 1

Case-2:

1 1 1 1 1 1 1 1 1 1 1 1

0.5 1 1 1 1 0 0 1 1 1 0 0



13.884 − n1 −n2  −0.5n1 7.442 − n2  A =  .. ..  . . −0.4284n1 −0.5n2

Case-3:



13.884 − n1 −n2  −0.5n1 7.442 − n2  A =  .. ..  . . −0.4284n1 0

Case-4:



13.884 − n1 −n2  −0.5n1 7.442 − n2  A =  .. ..  . . −0.0716n1 0

··· ··· .. .

−n10 −n10 .. .

   . 

· · · 25.541 − n10

··· ··· .. .

−n11 −n11 .. .

   . 

· · · 25.541 − n11

··· ··· .. .

−n12 −n12 .. .

   . 

· · · 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 ), and N3 (= n8 +· · ·+n12 ) are the admissible numbers for video, facsimile, and voice call, respectively. The admissible set in each case is given by simulations. Each admissible point (N1 , N2 , N3 ) within the admissible set means the admissible 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 the capacity boundaries in cases -2 and -3 are more similar to that in one-chip-rate system, than the capacity boundaries in other cases. This is because mutual-interferences in cases -2 and -3

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Table 8. Admissible sets. Items

Case-1

Case-2

Case-3

Case-4

Number of admissible points (= N) Proportion (= N in N case-4 )

3,590

3,379

6,007

7,568

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}) suffers more interferences from subsystem {1,1} than does subsystem {3,1} (or {3,4}), as shown in Figure 5. In addition, subsystems {2,j }, (j = 1, 2) (or {3,j }, (j = 1, . . . , 4)) interfere with each other by way of subsystem {1,1}, which yields a change in the number of admitted users in subsystems 1, 2, and 3. From these observations, it is noted that adjusting the allocation of the number of calls to subsystems can reduce the blocking probability in MCR-DS/CDMA systems. 5. Conclusions System capacity and optimum received power in MCR-DS/CDMA systems supporting multimedia services are considered. In addition, in order to account for other user interference in the same frequency band, interference factor λki in the requirement is introduced. Numerical results show that MCR-DS/CDMA systems support more capacity than one-chip-rate

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Figure 7. PSD and Bandpass filters: (a) PSD of QPSK spreading signal; (b) Transfer function of ideal output filter in 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 from subsystem {1,1}. From the results, system performance is strongly affected by a selected channel assignment strategy. Therefore, it is important to efficiently assign radio resources in MCR-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. P OWER S PECTRAL D ENSITY

AND

AUTOCORRELATION F UNCTION

The PSD of QPSK spreading signal is expressed in the form of Sg (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 rectangular response functions that are constant within the passband and zero elsewhere. Within the passband, a linear phase response characteristic is assumed. Thus, 1/Tc1 and 1/Tc3 = 1/4Tc1 are the bandwidths of the filters, the transfer functions of these two filters can be written as follows: Ho (f ) = [5{(f − f11 )Tc1 }]e−j wto , Hi (f ) = [5{4(f − f31 )Tc1 }]e−j wto ,

(13) (14)

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43

where Ho (f ) denotes the transfer function of transmitter output bandpass filter and Hi (f ) the transfer function of receiver input bandpass filter. Then, the PSD of the output signal in the transmitter, Si (f ) is expressed by: Si (f ) = |Ho (f )|2 Sg (f ).

(15)

Finally, the PSD of the input signal in the receiver, S(f ) is as follows: S(f ) = |Hi (f )|2 Si (f ) = |Hi (f )|2 |Ho (f )|2 Sg (f ) = |5{(f − f11 )Tc1 }|2 |5{4(f − f31 )Tc1 }|2 sinc2 {2(f − f11 )Tc1 }.

(16)

By the Wiener–Khinchine theorem, which says that the autocorrelation function of a signal and its PSD are Fourier transform pairs, the autocorrelation function R(τ ) is obtained by: R(τ ) = F −1 [S(f )] = F −1 [|5{(f − f11 )Tc1 }|2 |5{4(f − f31 )Tc1 }|2 sinc2 {2(f − f11 )Tc1 }] Z ∞ = |5{(f − f11 )Tc1 }|2 |5{4(f − f31 )Tc1 }|2 sinc2 {2(f − f11 )Tc1 }ej 2πf τ df −∞

Z ≈

f11 − 4T1

c1

f11 − 2T1 c1

sinc2 {2(f − f11 )Tc1 }ej 2πf τ df.

The total average power R(0) is given by: Z f11 − 1 4Tc1 R(0) = sinc2 {2(f − f11 )Tc1 }df.

(17)

(18)

f11 − 2T1

c1

A.2. I NTERFERENCE FACTORS From the results of the previous subsection A.1, we can obtain the total power of transmitted signal R(0)t as follows: Z f11 + 1 2Tc1 R(0)t = sinc2 {2(f − f11 )Tc1 }df . (19) f11 − 2T1

c1

The power portion of section I, R(0)1 is given by: Z f11 − 1 4Tc1 R(0)1 = sinc2 {2(f − f11 )Tc1 }df .

(20)

f11 − 2T1

c1

The power portion of section II, R(0)2 is written as: Z f11 R(0)2 = sinc2 {2(f − f11 )Tc1 }df .

(21)

f11 − 4T1

c1

The power portion of section III, R(0)3 is given by: Z f11 + 1 4Tc1 R(0)3 = sinc2 {2(f − f11 )Tc1 }df . f11

(22)

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The power portion of section IV, R(0)4 is written as: Z f11 + 1 2Tc1 R(0)4 = sinc2 {2(f − f11 )Tc1 }df .

(23)

f11 + 4T1

c1

From the previous subsection 2.3, we can determine the interference factors as follows: λ11 = λ12 = λ13 = λ14 = λ15 = λ16 = and

λ17 =

R(0)t R(0)t R(0)t R(0)t R(0)t R(0)t R(0)1 R(0)t R(0)2 R(0)t R(0)3 R(0)t R(0)4 R(0)t

= 1, = 1, = 1, = 0.0716, = 0.4284, = 0.4284, = 0.0716.

In a similar way, we can obtain the remaining interference factors. The interference factors for each case are shown in Tables 4 and 7. References 1. 2.

3. 4. 5.

6. 7. 8. 9. 10.

P.G. Andermo and L.M. Ewerbring, “A CDMA-Based Radio Access Design for UMTS”, IEEE Personal Commun., Vol. 2, No. 1, pp. 48–53, 1995. 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 Communications Networks”, IEEE J. Select. Areas Commun., Vol. 10, No. 4, pp. 655–668, 1992. E. Dahlman and K. Jamal, “Wide-Band Services in a DS-CDMA Based FPLMTS System”, in Proc. IEEE VTC, April 1996, pp. 1656–1660. C-L. I and R.D. Gitlin, “Multi-Code CDMA Wireless Personal Communication Networks”, in Proc. IEEE ICC, June 1995, pp. 1060–1064. A. Baier, U.C. Fiebig, W. Granzow, W. Koch, P. Teder and J. Thielecke, “Design Study for a CDMA-Based Third-Generation Mobile Radio System”, IEEE J. Select. Areas Commun., Vol. 12, No. 4, pp. 733–743, 1994. R. E. Fisher, A. Fukasawa, T. Sato, Y. Takizawa, T. Kato and M. Kawabe, “Wideband CDMA System for Personal Communications Services”, in Proc. IEEE VTC, April 1996, pp. 1652–1655. S. C. Bang, “ETRI IMT-2000 Multiband CDMA System for Terrestrial Environments,” Mobile Comm. Research Div., ETRI, Taejon, Korea, 1997. 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. D. Lyu, I. Song, Y. Han and H.M. Kim, “Analysis of the Performance of an Asynchronous Multiple-ChipRate DS/CDMA System”, Int. J. Electron. Commun., Vol. 51, Issue 4, pp. 213–218, 1997. K.S. Gilhousen, I.M. Jacobs, R. Padovani, A.J. Viterbi, L.A. Weaver and C.E. Wheatley, “On the Capacity of a Cellular CDMA System”, IEEE Trans. Veh. Technol., Vol. 40, No. 2, pp. 303–312, 1991.

Capacity Estimation in MCR-DS/CDMA Systems Supporting Multimedia Services 11. 12. 13. 14. 15.

16. 17. 18. 19.

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J. Evans and D. Everitt, “Call Admission Control in Multiple Service DS-CDMA Cellular Networks”, in Proc. IEEE VTC, April 1996, pp. 227–231. S.J. Lee, H.W. Lee and D.K. Sung, “Capacities of Single-Code and Multi-Code DS-CDMA Systems Accommodating Multi-Class Services”, IEEE Trans. Veh. Technol., to be published. M.B. Pursley, “Performance Evaluation for Phase-Coded Spread-Spectrum Multiple-Access Communication-Part I: System Analysis”, IEEE Trans. Commun., Vol. 25, No. 8, pp. 795–799, 1977. R.L. Pickholtz, L.B. Milstein and D.L. Schilling, “Spread Spectrum for Mobile Communications”, IEEE Trans. Veh. Technol., Vol. 40, No. 2, pp. 313–322, 1991. E. Geraniotis and B. Ghaffari, “Performance of Binary and Quaternary Direct-Sequence Spread-Spectrum Multiple-Access Systems with Random Signature Sequences”, IEEE Trans. Commun., Vol. 39, No. 5, pp. 713–724, 1991. M.B. Pursley, “Spread-Spectrum Multiple-Access Communications”, in G. Longer (ed.), Multi-User Communication Systems, Springer-Verlag: New York, NY, pp. 139–199, 1981. 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. P. Mermelstein, A. Jalali and H. Leib, “Integrated Services on Wireless Multiple Access Networks”, in Proc. IEEE ICC, Oct. 1993, pp. 863–867. Young W. Kim, Seung J. Lee, Min Y. Chung, Jeong H. Kim and Dan K. Sung, “Radio Resource Assignment 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 Aviation College in 1977 and the M.S. degree in electronic engineering from Seoul National University in 1983. He is working towards the Ph.D. degree in electrical engineering at Korea Advanced Institute of Science and Technology (KAIST) since 1994. From Dec. 1978 to Feb. 1985, he was a development engineer with Oriental Precision Company, Korea, where he had been engaged in research and development of military communication systems. Since March 1985, he has been with Hyundai Electronics Industries Company, Korea. His research interests include radio resource management and call admission control in IMT-2000. He is a member of KICS.

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Seung Joon Lee received the B.S., M.S., and Ph.D. degrees in electrical engineering from KAIST, in 1991, 1993, and 1998, respectively. He has been with Hyundai Electronics Industries Company, Korea since Nov. 1994. His research interests include handoff schemes in wireless ATM and support of multimedia in CDMA systems. He is a member of IEEE and KICS.

Jeong Ho Kim received the B.S. and M.S. degrees in electrical engineering from KAIST, in 1991 and 1993, respectively. Currently he is working towards the Ph.D. degree in electrical engineering at KAIST. He has been with LG Electronics Inc., Korea since Feb. 1993. His research interests include system analysis, power control, and multimedia multiple access protocol in CDMA systems. He is a student member of IEEE and a member of KICS.

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Young Hoon Kwon received the B.S. degree in electronics from Kyungpook National University in 1994 and the M.S. degree in electrical engineering from KAIST in 1996. He is working towards the Ph.D. degree in electrical engineering at KAIST since 1996. His research interests include 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 National University in 1975, the M.S. and Ph.D. degrees in electrical and computer engineering from University 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. In 1986, he joined the faculty of the Korea Institute of Technology and is currently a Professor of Dept. of Electrical Engineering at KAIST. His research interests include ISDN switching systems, ATM switching systems, wireless networks, and performance and reliability of systems. He is a member of IEEE, IEICE, KITE, KICS and KISS.