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510 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 55, NO. 2, MARCH 2006 Capacity Improvement in CDMA Downlink With Orthogonal Code-Hopping Multiplexing Sung Ho Moon, Student Member, IEEE, Suwon Park, Member, IEEE, Jae Kyun Kwon, Member, IEEE, and Dan Keun Sung, Senior Member, IEEE Abstract—Orthogonal code-hopping multiplexing (OCHM) is a statistical multiplexing scheme designed to increase the number of allowable downlink channels in code division multiple access (CDMA) systems. OCHM is expected to compensate for a lack of codewords in future communication systems. In CDMA systems including OCHM, system capacity is limited by the number of codewords and power (or interference), and the maximum system capacity is determined by a stronger limitation between them. Call blockings due to power limitation may occur firstly if downlink channels demand large E b /I 0 values and a high-channel activity. On the other hand, code limitation may occur prior to power lim- itation in CDMA. The maximum system capacities determined by both code and power limitations must be known, even in OCHM. However, previous studies on OCHM system capacity focused only on increasing the number of multiplexed users with no considera- tion of the power limitation. In this paper, the overall system ca- pacity of OCHM considering both code and power limitations was evaluated. For this analysis, the transmission chip energy of base station (BS) and inner/outer-cell interference is mathematically derived in a multicell and multiuser environment. The downlink system capacity for OCHM is larger than for orthogonal code division multiplexing (OCDM) as other cell interference (OCI), mean channel activity, and the required E b /I 0 value decrease. Index Terms—Code division multiple access (CDMA), down- link capacity, orthogonal code-hopping multiplexing (OCHM), perforation, synergy. I. I NTRODUCTION P ACKET-TYPE services, such as hypertext transfer pro- tocol (HTTP), file transfer protocol (FTP), and wireless application protocol (WAP), have gradually increased and may become dominant in future wireless communications. In con- trast to voice traffic, which is a major service in 2G, these packet-based services have two different characteristics. First, they exhibit high burstiness with low activity and second, Manuscript received October 25, 2004; revised April 24, 2005 and July 12, 2005. This work was supported in part by MIC, Korea, under the BrOMA Information Technology Research Center (ITRC) support program supervised by Institute of Information Technology Assessment (IITA). The review of this paper was coordinated by Prof. T. Lok. S. H. Moon and D. K. Sung are with the Department of Electrical Engineer- ing and Computer Science, Korea Advanced Institute of Science and Technol- ogy (KAIST), Daejeon 305-701, Korea (e-mail: [email protected]). S. Park was with the Department of Electrical Engineering and Computer Science, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 305-701, Korea. He is now with the Department of Electronics and Communications Engineering, Kwangwoon University, Seoul 139-701, Korea (e-mail: [email protected]). J. K. Kwon was with the Department of Electrical Engineering and Com- puter Science, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 305-701, Korea. He is now with Electronics and Telecommunications Research Institute (ETRI), Daejeon 305-701, Korea. Digital Object Identifier 10.1109/TVT.2005.863468 packet-based traffic is generally concentrated on the downlink since mobile users often demand information from servers. Based on these characteristics, demands for downlink code channels will increase more for packet-based services in 3G and 4G systems than for voice traffic. However, orthogonal code allocation/deallocation mechanisms in conventional code divi- sion multiple access (CDMA) systems are inefficient for serv- ing the bursty downlink packet-type traffic since code channels are allocated to mobile stations (MSs) by a base station (BS) at each initial call setup, and are released from the connection after each call termination. Waste of orthogonal code channels due to many inactive periods of bursty traffic and increased demands for orthogonal code channels may result in a lack of orthogonal codewords (OCs) in spite of remaining BS power. Orthogonal code-hopping multiplexing (OCHM) [1] can solve the problem of efficient multiplexing of data packets. Systems based on OCHM can accommodate more downlink channels than the number of OCs by using statistical multi- plexing. This means that OCHM can compensate for a lack of OCs without significant changes in conventional systems. In CDMA 3G and 4G packet services, more OCs may be needed. A multiscrambling code for wideband code division multiple access (W-CDMA) [2] and a quasi-orthogonal function for cdma2000 [3] were proposed to alleviate this code shortage. However, these techniques result in a loss of perfect orthogo- nality between codewords. Orthogonality is a valuable property of synchronous downlink since it yields a natural cancellation of interference. Thus, OCHM is an attractive multiplexing scheme. There are two limitations in CDMA downlink for determi- nation of the maximum system capacity. First, the number of connecting MSs in a code-limited system cannot exceed the number of OCs available in the system. Second, in a power (or interference) limited system like 2G CDMA, the number of voice users is limited by interference due to mean channel- activity values of 0.4 0.5. Thus, the maximum allowable number of users is less than the number of OCs. There have been previous studies regarding the maximum system capacity in power-limited CDMA downlinks. The maximum number of simultaneous users with a downlink pole equation was analyzed in [4] and [5] and the downlink Erlang capacity and outage probability were evaluated in [6]. In previous studies [7]–[11] on OCHM, capacity analysis was only focused on code capacity, which is defined as the maximum allowable number of users limited by the number of codewords under the assumption that system has no power limitation. Since a power shortage rarely occurs prior to a lack 0018-9545/$20.00 © 2006 IEEE

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510 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 55, NO. 2, MARCH 2006

Capacity Improvement in CDMA Downlink WithOrthogonal Code-Hopping Multiplexing

Sung Ho Moon, Student Member, IEEE, Suwon Park, Member, IEEE, Jae Kyun Kwon, Member, IEEE, andDan Keun Sung, Senior Member, IEEE

Abstract—Orthogonal code-hopping multiplexing (OCHM) is astatistical multiplexing scheme designed to increase the numberof allowable downlink channels in code division multiple access(CDMA) systems. OCHM is expected to compensate for a lack ofcodewords in future communication systems. In CDMA systemsincluding OCHM, system capacity is limited by the number ofcodewords and power (or interference), and the maximum systemcapacity is determined by a stronger limitation between them. Callblockings due to power limitation may occur firstly if downlinkchannels demand large Eb/I0 values and a high-channel activity.On the other hand, code limitation may occur prior to power lim-itation in CDMA. The maximum system capacities determined byboth code and power limitations must be known, even in OCHM.However, previous studies on OCHM system capacity focused onlyon increasing the number of multiplexed users with no considera-tion of the power limitation. In this paper, the overall system ca-pacity of OCHM considering both code and power limitations wasevaluated. For this analysis, the transmission chip energy of basestation (BS) and inner/outer-cell interference is mathematicallyderived in a multicell and multiuser environment. The downlinksystem capacity for OCHM is larger than for orthogonal codedivision multiplexing (OCDM) as other cell interference (OCI),mean channel activity, and the required Eb/I0 value decrease.

Index Terms—Code division multiple access (CDMA), down-link capacity, orthogonal code-hopping multiplexing (OCHM),perforation, synergy.

I. INTRODUCTION

PACKET-TYPE services, such as hypertext transfer pro-tocol (HTTP), file transfer protocol (FTP), and wireless

application protocol (WAP), have gradually increased and maybecome dominant in future wireless communications. In con-trast to voice traffic, which is a major service in 2G, thesepacket-based services have two different characteristics. First,they exhibit high burstiness with low activity and second,

Manuscript received October 25, 2004; revised April 24, 2005 and July 12,2005. This work was supported in part by MIC, Korea, under the BrOMAInformation Technology Research Center (ITRC) support program supervisedby Institute of Information Technology Assessment (IITA). The review of thispaper was coordinated by Prof. T. Lok.

S. H. Moon and D. K. Sung are with the Department of Electrical Engineer-ing and Computer Science, Korea Advanced Institute of Science and Technol-ogy (KAIST), Daejeon 305-701, Korea (e-mail: [email protected]).

S. Park was with the Department of Electrical Engineering and ComputerScience, Korea Advanced Institute of Science and Technology (KAIST),Daejeon 305-701, Korea. He is now with the Department of Electronics andCommunications Engineering, Kwangwoon University, Seoul 139-701, Korea(e-mail: [email protected]).

J. K. Kwon was with the Department of Electrical Engineering and Com-puter Science, Korea Advanced Institute of Science and Technology (KAIST),Daejeon 305-701, Korea. He is now with Electronics and TelecommunicationsResearch Institute (ETRI), Daejeon 305-701, Korea.

Digital Object Identifier 10.1109/TVT.2005.863468

packet-based traffic is generally concentrated on the downlinksince mobile users often demand information from servers.Based on these characteristics, demands for downlink codechannels will increase more for packet-based services in 3G and4G systems than for voice traffic. However, orthogonal codeallocation/deallocation mechanisms in conventional code divi-sion multiple access (CDMA) systems are inefficient for serv-ing the bursty downlink packet-type traffic since code channelsare allocated to mobile stations (MSs) by a base station (BS) ateach initial call setup, and are released from the connection aftereach call termination. Waste of orthogonal code channels due tomany inactive periods of bursty traffic and increased demandsfor orthogonal code channels may result in a lack of orthogonalcodewords (OCs) in spite of remaining BS power.

Orthogonal code-hopping multiplexing (OCHM) [1] cansolve the problem of efficient multiplexing of data packets.Systems based on OCHM can accommodate more downlinkchannels than the number of OCs by using statistical multi-plexing. This means that OCHM can compensate for a lackof OCs without significant changes in conventional systems. InCDMA 3G and 4G packet services, more OCs may be needed.A multiscrambling code for wideband code division multipleaccess (W-CDMA) [2] and a quasi-orthogonal function forcdma2000 [3] were proposed to alleviate this code shortage.However, these techniques result in a loss of perfect orthogo-nality between codewords. Orthogonality is a valuable propertyof synchronous downlink since it yields a natural cancellationof interference. Thus, OCHM is an attractive multiplexingscheme.

There are two limitations in CDMA downlink for determi-nation of the maximum system capacity. First, the number ofconnecting MSs in a code-limited system cannot exceed thenumber of OCs available in the system. Second, in a power(or interference) limited system like 2G CDMA, the numberof voice users is limited by interference due to mean channel-activity values of 0.4 ∼ 0.5. Thus, the maximum allowablenumber of users is less than the number of OCs. There havebeen previous studies regarding the maximum system capacityin power-limited CDMA downlinks. The maximum number ofsimultaneous users with a downlink pole equation was analyzedin [4] and [5] and the downlink Erlang capacity and outageprobability were evaluated in [6].

In previous studies [7]–[11] on OCHM, capacity analysiswas only focused on code capacity, which is defined as themaximum allowable number of users limited by the numberof codewords under the assumption that system has no powerlimitation. Since a power shortage rarely occurs prior to a lack

0018-9545/$20.00 © 2006 IEEE

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MOON et al.: CAPACITY IMPROVEMENT IN CDMA DOWNLINK WITH OCHM 511

of codewords for packet services with relatively low-channelactivities, the code capacity and bit-error-rate (BER) perfor-mance were evaluated and compared with conventional multi-plexing schemes. However, system capacity may be also limitedby power (or interference) even if downlink channels experi-ence low-mean channel activities. Therefore, power capacity,which is defined as the maximum allowable number of userslimited by the maximum transmission power of a BS under theassumption that system has no code limitation, should also beevaluated in OCHM because the overall system capacity is aminimum value between code and power capacities.

In this paper, we briefly introduce OCHM based on previousstudies and evaluate the capacity improvement in OCHM-baseddownlink considering both code and power capacities. Theeffect of an increase in code capacity and OCHM link per-formance has already been evaluated by mathematical analysisand simulation [1]. Based on these previous results, the powercapacity of OCHM is mathematically analyzed based on themaximum number of users, and the overall system capacityis obtained, and numerical examples for the code and powercapacities are shown.

The rest of this paper is organized as follows: the previouslyproposed OCHM scheme is briefly introduced in Section II.Notations for analysis are summarized in Section III. InSection IV, we review a system capacity improvement in codecapacity in OCHM. The power capacity of OCHM is evaluatedin Section V, and numerical examples of the analysis are shownin Section VI. Finally, conclusions and further studies arepresented in Section VII.

II. OCHM

Several previous studies have analyzed code-hoppingschemes in spread spectrum systems [12]–[14]. These previousstudies focused mainly on showing that code-hopping sys-tems exhibit better BER performance than conventional spreadspectrum systems because cochannel interference is averagedwith time diversity. However, OCHM [1] is distinguished fromthese previous code-hopping methods because code-hopping inOCHM is used for downlink multiplexing in order to increasethe utilization of code channels. Moreover, OCHM is onlyapplicable to the downlink because a BS knows all downlinkdata transmitted to all MSs in its cell.

Fig. 1 shows the basic operations of OCHM and the con-ventional downlink multiplexing scheme, here called orthogo-nal code division multiplexing (OCDM). In the conventionalOCDM [Fig. 1(a)], each modulation symbol during a modula-tion symbol time Ts is spread by a specific OC. During a call foreach MS, an OC allocated to the MS is maintained. The MSsindexed from #a to #g maintain only one of the OCs indexedfrom #A to #G, regardless of the inactive periods for MS#c andMS#g. Thus, many OC resources are wasted in a bursty trafficenvironment.

On the other hand, OCHM allows change of the OCs in everymodulation symbol time Ts and multiplexing of a larger numberof MSs than the number of OCs. For example, in Fig. 1(b),MS #f changes an OC for each modulation symbol based on itshopping pattern (HP) indexed by #f. An MS-specific HP can be

generated based on the MS identifier (ID), such as an electronicserial number (ESN) at an initial channel allocation time.

From the random hopping of OCs, the BS can multiplexmore downlink channels than the number of OCs. However,code collisions between codewords are inevitable with higherutilization of OCs. Fortunately, the BS can monitor all informa-tion on the downlink channels. The BS compares each channelto all other channels during multiplexing to determine whichsymbols collide and deals with the colliding symbols beforetransmission.

When a code collision occurs among the HPs of activedownlink channels, a comparator and controller in the OCHMtransmitter performs one of the following two operations: per-foration or synergy.

1) Perforation: If code-collision symbols do not have anidentical symbolic value, i.e., +1 or 0 for binary phase-shift keying (BPSK), then none of the data symbolscolliding during a symbol time of Ts are transmitted.

2) Synergy: If code-collision symbols have an identical sym-bolic value, the data symbols colliding during a symboltime of Ts are transmitted and the transmission signalamplitude of the OC during the symbol time is the sum ofthe signal amplitudes assigned to all of the correspondingdownlink channels.

This perforation/synergy scheme for code collision in a code-hopping system is a unique concept. Fig. 2 shows the resultant,transmitted signal after perforation and synergy for MS#f.One of the code collisions related to OC#A from (n+ 2)Ts to(n+ 3)Ts is managed by a perforation, and there is no trans-mission. For the other interval from (n+ 7)Ts to (n+ 8)Ts,the code collision experiences a synergy, and an additive signalof the two symbols due to the synergy effect is transmitted.

Regardless of perforated symbols, the channel decoderin the receiver of the corresponding MS can recover thetransmitted data. The synergy operation allows the code-collision symbols to maintain and share their transmissionpowers in common. Thus, the synergy operation results in atransmission power gain.

III. NOTATIONS FOR MATHEMATICAL ANALYSIS

(i, b) ith MS in the bth cell.(i, j, b) ith MS scrambled by the jth scrambling code in the

bth cell.α(i,0,b) Correlation factor of OCs at MS (i, 0, b).α Mean correlation factor of OCs.b Index of a cell or a BS.d Distance between a BS and an adjacent BS.ε MS closer than ε are considered to be ε-distant from

the BS [15].E

(t)c,b Total transmission chip energy of BS b.

E(t)c,max Maximum downlink transmission chip energy.

E(t)c,b→m Transmission chip energy from BS b to MSm.

E(r)c,b→m Received chip energy from BS b to MSm.γ Propagation loss factor (= 4).I0,(i,0,b) Total interference chip energy at MS (i, 0, b).Iic,(i,0,b) Inner-cell interference chip energy at MS (i, 0, b).

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512 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 55, NO. 2, MARCH 2006

Fig. 1. Basic operations of (a) OCDM and (b) OCHM.

Ioc,(i,0,b) Outer-cell interference chip energy at MS (i, 0, b).m Index of an MS, wherem = (i, b) or (i, j, b).M c

b Code capacity in the bth cell.Mp

b Power capacity in the bth cell.N0 One-sided power spectral density of additive white

Gaussian noise (AWGN).NOC Number of OCs for the downlink.νb→m Channel activity of a downlink channel from BS b

to MSm.ν Mean channel activity of downlink channels.pc,OC Code-collision probability.pp,OC Perforation probability.ps,OC Synergy probability.rb→m Distance from BS b to MSm.ρ Proportion of maximum downlink transmit power

for downlink common control channels.re Equivalent cell radius of a hexagonal cell.rh Radius of a circumcircle surrounding a hexagonal

cell.R1 Random variable representing the distance between

a BS and an MS in a cell covered by the BS.

R2 Random variable representing the distance from aBS and an MS in an adjacent cell of the cell coveredby the BS.

RFECm Channel (or forward error correction) coding rate of

downlink channel for MSm.s Number of possible constellation points (i.e., s = 2

for BPSK).θ Transmission antenna main lobe width (θ = 120◦

for three-sectorized cell).ζb→m Shadow fading from BS b to MSm.

IV. CODE CAPACITY OF OCHM

As defined in Section I, code capacity is obtained under anassumption that there is no power limitation. In OCDM, ifthere are NOC codewords, NOC MSs can maintain maximalconnections. The (NOC + 1)th connection attempt is not per-mitted even if most connections are inactive. Therefore, codecapacity in OCDM is always fixed to NOC. However, the codecapacity in OCHM can increase more than NOC depending onthe perforation (or code collision) probability.

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MOON et al.: CAPACITY IMPROVEMENT IN CDMA DOWNLINK WITH OCHM 513

Fig. 2. Downlink transmission signal for MS#f.

For a given number of allocated orthogonal downlink chan-nels and available number of codewords, the more active theallocated channels are, the more often the downlink channelsmay experience code collisions. Therefore, for each modulationsymbol, we have the following probabilities [8]:

pc,OC =1 −(

1 − ν

NOC

)Mcb−1

(1)

pp,OC =1 −(

1 − s− 1s

· ν

NOC

)Mcb−1

(2)

ps,OC = pc,OC − pp,OC. (3)

Given pp,OC, the code capacity in OCHM is obtained as

M cb = 1 +

ln(1 − pp,OC)

ln(1 − (s−1)·ν

s·NOC

) . (4)

As shown in (4), the code capacity is determined by the per-foration probability. With a larger perforation probability, moredownlink channels can be accommodated for a given meanchannel-activity factor. Therefore, “code limited” in OCHMcan be also called “perforation limited.”

Fig. 3 shows the code capacity for a given allowable perfo-ration probability pp,OC with 64 OCs and QPSK modulation.In case of QPSK, we can set s = 2 from the independencebetween I- and Q-axes. If we have no limitation in the trans-mission power, OCHM increases code capacity up to 287, 370,and 458 with a mean channel activity of 0.1 and pp,OC valuesof 0.2, 0.25, and 0.3, respectively.

The allowable perforation probability for code capacity can-not increase infinitely because a larger allowable perforationprobability requires a larger Eb/I0 value. Therefore, from link-level simulation, we can determine a proper allowable perfora-

tion probability to satisfy a link quality. Fig. 4 [1] shows theframe-error-rate (FER) performance of OCHM in an AWGNchannel. The FER performance of OCHM with convolutionalcoding (CC) and turbo coding (TC) is evaluated by simulation.The code rate is 1/4, and all parameters follow the cdma2000specification [3]. The curve of pp,OC = 0.00 corresponds to theconventional OCDM scheme without perforation. The resultshows that additional transmission power is a maximum of1 dB compared to OCDM in order to meet a target FER valueof 0.01. From Figs. 3 and 4, OCHM enhances the code capacityfrom 64 to 370 with a slightly increased Eb/I0 value of 0.5 dBfor a mean channel-activity factor of 0.1 and an FER value of0.01 with TC.

V. POWER CAPACITY OF OCHM

In this section, we analyze the power capacity of OCHMdownlink channels in a cell, and assume that there is no code (orperforation) limitation. In addition, soft and softer handoversare not considered because we analyze the power capacity ofpacket services with relatively high burstiness. It is generallyknown that hard handoffs are more efficient for packet trafficthan are soft and softer handoffs.

A. Constraint for Estimating Power Capacity

Fig. 5 shows a CDMA system consisting of one inner andsix outer cells. CDMA systems are generally known to belimited by power (or interference). Since the maximum down-link transmission power is limited to avoid interference withMSs in adjacent cells, downlink channels need to be admittedwithin the maximum downlink transmission power. Therefore,a main constraint in downlink is that a BS can transmit withinthe maximum downlink transmission power. Since the chip

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514 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 55, NO. 2, MARCH 2006

Fig. 3. Code capacity in OCHM.

Fig. 4. FER versus Eb/I0 in AWGN.

duration Tc is fixed, the chip energy is proportional to power.Thus, the total transmission chip energy of BS b must satisfythe following condition:

E(t)c,b = ρE(t)

c,max +∑m

νb→mE(t)c,b→m ≤ E(t)

c,max (5)

where ρ is the energy portion for downlink broadcasting chan-nels (typically, ρ = 0.1 ∼ 0.3) [16].

Equation (5) is a requirement to determine the power ca-pacity in CDMA systems. Thus, our final goal here is to findthe number of downlink connections accommodated in a givencondition using this inequality.

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MOON et al.: CAPACITY IMPROVEMENT IN CDMA DOWNLINK WITH OCHM 515

Fig. 5. One inner cell and six outer cells.

B. Wireless Channel: Propagation Loss and Shadowing

For simplicity of analysis, we consider only propagation lossand shadow fading. Short-term fading due to the movement ofan MS is not considered. Short-term fading is assumed to beaveraged out by fast power control. In real environments, a BSrequires additional transmission power in order to overcomeshort-term fading.

In order to express (5) in terms of the number of downlinkconnections, we must know the average transmission chipenergy and the channel activity per MS. Under an assumptionof perfect power control, the average transmission chip energyper MS is determined depending on the required (Ec/I0)targetvalue in receiver. The received chip energy at MSm is given as

E(r)c,b→m = E(t)

c,b→m · r−γb→m · 10

−ζb→m

10 . (6)

The propagation loss is closely related to the distance be-tween a transmitter and a receiver. We consider two distances,as shown in Fig. 5. Distance R1 is between a BS and an MS ina cell covered by the BS, and distance R2 is between a BS andan MS in a cell adjacent to the cell covered by the BS.

When MSs are uniformly distributed in a cell, the probabilitydensity functions for R1 and R2 are derived as

fR1(r) =2rr2e

(7)

fR2(r) �2√3·√

4d2r2e − (d2 + r2e − r2)2d3

. (8)

The detailed derivation of (8) is given in the Appendix.

If MS m is served by a BS of index b, from (7), the γthmoment of distance R1 from BS b to MSm is derived as

E[rγb→m

]=

re∫ε

2rγ+1

r2edr � 2

γ + 2(rγe − εγ) (9)

where ε � 10 [m].When MS m is not served by BS b, the γth moment of

rz→m(z = b) using (8) is derived as

E[rγz→m

]=

(√

3+1)re∫(√

3−1)re

2rγ√3·√

4d2r2e − (d2 + r2e − r2)2d3

dr

(10)

where re � rh = d/√

3.Typically, shadowing in a wireless channel is modeled as a

log-normal distribution with zero mean. Thus, the expectationof a log-normally distributed random variable with a mean ofmζ = 0 and a variance of σ2

ζ is written as

E

[10

−ζb→m

10

]=10

−mζ10 · exp

{(ln 1010 σζ

)22

}

= exp

{(ln 1010 σζ

)22

}. (11)

C. Total Transmission Chip Energy From BS b

If we assume that the required (Ec/I0)target value in receiveris determined for an MS, the transmission chip energy per MSfrom a BS can be obtained. We assume that MSs have threedimensional indexes such as m = (i, 0, b). MS (i, j, b) is theith MS scrambled by the jth scrambling code in a cell coveredby a BS of index b. For simplicity of mathematical analysis, weassume that only one scrambling code is used (j = 0). Then

E(t)c,b→(i,0,b) = E

(r)c,b→(i,0,b) · rγb→(i,0,b) · 10

ζb→(i,0,b)10 . (12)

The required chip energy at the MS (i, 0, b) is calculated asa multiplication of (Ec/I0)target and I0,(i,0,b). Thus, the totaltransmission chip energy from BS b is expressed as

E(t)c,b = ρE(t)

c,max +∑

(i,0,b)

(νb→(i,0,b) · E(t)

c,b→(i,0,b)

)

= ρE(t)c,max +

∑(i,0,b)

(νb→(i,0,b) · E(r)

c,b→(i,0,b)

· rγb→(i,0,b) · 10ζb→(i,0,b)

10

)

= ρE(t)c,max +

∑(i,0,b)

(νb→(i,0,b) ·

(Ec

I0

)target

· I0,(i,0,b)

· rγb→(i,0,b) · 10ζb→(i,0,b)

10

). (13)

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516 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 55, NO. 2, MARCH 2006

D. Interference at MS (i, 0, b)

For complete derivation of (13), I0,(i,0,b) must be calculated.The total interference chip energy at an MS is the sum of theinner-cell interference chip energy, the outer-cell interferencechip energy, and the thermal noise. In (9) and (10), we calculatethe expectations of propagation losses from a home cell andan adjacent cell. Thus, all received power from BSs can beexpressed, and inner/outer-cell interference chip energy canbe calculated. Since a BS has a maximum transmission chipenergy of E(t)

c,max, the total interference chip energy at MS(i, 0, b) is bounded as

I0,(i,0,b) = Iic,(i,0,b) + Ioc,(i,0,b) +N0

≤E(t)c,max · r−γ

b→(i,0,b) · 10−ζb→(i,0,b)

10

+∑z =b

E(t)c,max · r−γ

z→(i,0,b) · 10−ζz→(i,0,b)

10 +N0

=E(t)c,max

(r−γb→(i,0,b) · 10

−ζb→(i,0,b)10

+∑z =b

r−γz→(i,0,b) · 10

−ζz→(i,0,b)10

)+N0

(14)

where the subscripts ic and oc denote the inner-cell and theouter-cell interference, respectively.

Inner-cell interference occurs from cross correlation amongspreading codes in the downlink. Usually in the downlink ofCDMA, if a perfectly orthogonal code set is used, i.e., Walshcodes, no inner-cell interference occurs. However, the multipatheffect corrupts the perfect orthogonality. For modeling of thiseffect, we set α as a correlation factor. If the downlink from BSb to MS (i, 0, b) is perfectly orthogonal, i.e., α(i,0,b) = 1, thenthe inner-cell interference is 0, or Iic,(i,0,b) = 0.

Since the inner-cell interference chip energy cannot exceedthe total transmission chip energy of BS b denoted as E(t)

c,b , theinner-cell interference chip energy at MS (i, 0, b) is expressedand bounded as

Iic,(i,0,b) =

ρE(t)

c,max +∑

{(x,0,b)|x=i}νb→(x,0,b)E

(t)c,b→(x,0,b)

· r−γb→(i,0,b) · 10

−ζb→(i,0,b)10 · (1 − α(i,0,b)

)

≤E(t)c,b · r−γ

b→(i,0,b) · 10−ζb→(i,0,b)

10

≤E(t)c,max · r−γ

b→(i,0,b) · 10−ζb→(i,0,b)

10 . (15)

Other cell interference (OCI) chip energy is determined bya summation of the transmission chip energy of adjacent BSs.OCI chip energy at MS (i, 0, b) is given as

Ioc,(i,0,b) =∑z =b

E(t)c,z · r−γ

z→(i,0,b) · 10−ζz→(i,0,b)

10

=∑z =b

ρE(t)

c,max +∑

(x,0,z)

νz→(x,0,z)E(t)c,z→(x,0,z)

· r−γz→(i,0,b) · 10

−ζz→(i,0,b)10

≤∑z =b

E(t)c,max · r−γ

z→(i,0,b) · 10−ζz→(i,0,b)

10

=E(t)c,max ·

∑z =b

r−γz→(i,0,b) · 10

−ζz→(i,0,b)10 . (16)

E. Expectations of Interferences andTotal Transmission Chip Energy

From previous sections, the total transmission chip energyof a BS and the interference chip energy at an MS are ex-pressed from the transmission chip energy per MS. To obtainthe average system capacity, the expectation values of theinterference and the total transmission chip energy must bederived. From (15) and (16), the expectation of the inner/outer-cell interference at MS (i, 0, b) can be expressed.

Since propagation loss and shadowing are independent ofeach other, the expectation values from (9) and (11) are used forcalculating the expectation of the inner-cell interference chipenergy as follows:

E[Iic,(i,0,b)

]

=

ρE(t)

c,max +∑

{(x,0,b)|x=i}ν · E

[E

(t)c,b→(x,0,b)|active

]

· 2−γ + 2

(r−γe − ε−γ

) · exp

{(ln 1010 σζ

)22

}· (1 − α)

≤ E[E

(t)c,b

]· 2−γ + 2

(r−γe − ε−γ

) · exp

{(ln 1010 σζ

)22

}

≤ E(t)c,max · 2

−γ + 2(r−γe − ε−γ

) · exp

{(ln 1010 σζ

)22

}.

(17)

For the outer-cell interference chip energy, the expectationvalue at MS (i, 0, b) is derived from (10), (11), and (16)

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MOON et al.: CAPACITY IMPROVEMENT IN CDMA DOWNLINK WITH OCHM 517

as follows:

E[Ioc,(i,0,b)

]=∑z =b

E[E(t)

c,z

]· E[r−γz→(i,0,b)

]· exp

{(ln 1010 σζ

)22

}

=∑z =b

ρE(t)

c,max +∑

(x,0,z)

ν · E[E

(t)c,z→(x,0,z)|active

]· E[r−γz→(i,0,b)

]· exp

{(ln 1010 σζ

)22

}

≤∑z =b

E(t)c,max · E

[r−γz→(i,0,b)

]· exp

{(ln 1010 σζ

)22

}

= E(t)c,max · exp

{(ln 1010 σζ

)22

}·∑z =b

E[r−γz→(i,0,b)

]. (18)

The expectation value of the total transmission chip energyfrom BS b is derived from the expectation of the transmis-sion chip energy and the activity factor for an MS. Thus, theexpectation of total transmission chip energy from BS b isexpressed as

∑(i,0,b)

E[E

(t)c,b→(i,0,b)

]=∑

(i,0,b)

(E[νc,b→(i,0,b)

] · E [E(t)c,b→(i,0,b)|active

])(19)

where νc,b→(i,0,b) is the channel activity of the downlink chan-nel from BS b to MS i.

We already know a relation of E[E(r)c,b→(i,0,b)|active] =

(Ec/I0)target · E[I0,(i,0,b)], and the equations for E[Iic,(i,0,b)]and E[Ioc,(i,0,b)]. Therefore, using the previous (17)–(19), theexpectation of the total transmission chip energy from BS b isderived as∑(i,0,b)

E[E

(t)c,b→(i,0,b)

]

= Mpb ·ν ·

(Ec

I0

)target

·

ρE(t)

c,max+∑

{(x,0,b)|x=i}ν ·E

[E

(t)c,b→(x,0,b)|active

]

· 4γ2 − 4

· (rγe − εγ)2

rγe εγ· exp

{(ln 1010

σζ

)2}·(1 − α)

+

∑z =b

ρE(t)

c,max+∑

(x,0,z)

ν ·E[E

(t)c,z→(x,0,z)|active

]

· E[r−γz→(i,0,b)

]· exp

{(ln 1010 σζ

)22

}+N0

· 2γ+2

(rγe − εγ)· exp

{(ln 1010 σζ

)22

}. (20)

The expectation of total transmission chip energy is expressedas the number of downlink channels, the mean channel activity,target received Eb/I0 value, and interference values in (20).The detailed derivation is given in Appendix.

F. Power Capacity of OCHM

Using (20), we can rearrange the inequality∑(i,0,b)E[E(t)

c,b→(i,0,b)] ≤ (1 − ρ)E(t)c,max from (5) and obtain

the power capacity in the bth cellMpb as follows:

Mpb ≤ (1 − ρ)E(t)

c,max

ν ·(

EcI0

)OCHM

target

/ρE(t)

c,max+∑

{(x,0,b)|x=i}ν ·E

[E

(t)c,b→(x,0,b)|active

]

· 4γ2 − 4

· (rγe − εγ)2

rγe εγ· exp

{(ln 1010

σζ

)2}·(1 − α)

+

∑z =b

ρE(t)

c,max+∑

(x,0,z)

ν ·E[E

(t)c,z→(x,0,z)|active

]

· E[r−γz→(i,0,b)

]· exp

{(ln 1010 σζ

)22

}+N0

· 2γ+2

(rγe − εγ) · exp

{(ln 1010 σζ

)22

}. (21)

Equation (21) shows the system capacity based on a power-limited situation. Mp

b is bounded by the terms proportional to

the maximum transmission chip energy of the BS, E(t)c,max, and

inversely proportional to the mean channel activity ν and thereceived target signal-to-interference-plus-noise ratio (SINR)(Ec/I0)OCHM

target .We define three different cases of outer-cell interference. The

first one is the maximum outer-cell interference case, whichis the worst case. Generally, the capacity or the number ofadmissible downlink channels is obtained in this case, and themaximum transmission power is also adjusted in this case.The second case is that all adjacent cells have no downlinkchannels, except common control channels such as a pilotcontrol channel. The third case is that there are no adjacentcells with the same serving frequency band. Thus, the frequencyreuse factor is far less than 1.

When the BSs of all adjacent cells transmit at the allowablemaximum transmission power, we can derive the probabilisti-cally worst system capacity. The probabilistically worst caseis not the worst case in reality. The real worst case heremeans the case where all MSs served by a BS are locatedaround the cell boundary covered by the BS. That is, the realworst case occurs when the transmission power per channel ismaximally allocated. However, the probabilistically worst caseoccurs when all MSs served by a BS are uniformly located

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518 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 55, NO. 2, MARCH 2006

within the cell covered by the BS, and the BSs of all adjacentcells transmit at the allowable maximum transmission power. Ifouter-cell interference is a maximum, (21) is expressed as

Mp,maxOCIb ≤ (1 − ρ)E(t)

c,max

ν ·(

EcI0

)OCHM

target

/

ρE(t)

c,max+∑

{(x,0,b)|x=i}ν ·E

[E

(t)c,b→(x,0,b)|active

]

· 4γ2 − 4

· (rγe − εγ)2

rγe εγ· exp

{(ln 1010

σζ

)2}·(1 − α)

+

∑z =b

E(t)c,max ·E

[r−γz→(i,0,b)

]· exp

{(ln 1010 σζ

)22

}+N0

· 2γ+2

(rγe − εγ)· exp

{(ln 1010 σζ

)22

} (22)

where Mp,maxOCIb is the power capacity when OCI has a

maximum value.When BSs of all adjacent cells transmit at the minimum

transmission power, such as the pilot channel power, we canderive the probabilistically best system capacity. The proba-bilistically best case is not the best case in reality. The real bestcase means the case where all MSs served by a BS are locatedat the nearest position to the BS and the transmission power perchannel is minimally allocated. However, the probabilisticallybest case occurs when all MSs served by a BS are uniformlylocated within the cell covered by the BS, and BSs of alladjacent cells transmit at the minimum transmission power,such as the pilot channel power. The number of downlinkchannels in a cell is bounded, as in the minimum OCI case

Mp,minOCIb ≤ (1−ρ)E(t)

c,max

ν ·(

EcI0

)OCHM

target

/ρE(t)

c,max+∑

{(x,0,b)|x=i}ν ·E

[E

(t)c,b→(x,0,b)|active

]

· 4γ2−4

· (rγe −εγ)2rγe εγ

· exp

{(ln 1010

σζ

)2}·(1−α)

+

∑z =b

ρE(t)c,max ·E

[r−γz→(i,0,b)

]· exp

{(ln 1010 σζ

)22

}+N0

· 2γ+2

(rγe −εγ)· exp

{(ln 1010 σζ

)22

} (23)

where Mp,minOCIb is the power capacity when OCI has a

minimum value.

G. Power Capacity in Sectorized Cell Environments

Even if omnicells are sectorized, the total transmission chipenergy from BS b is assumed to be identical to (20). A pro-portion of the total transmission power from sector antennasof adjacent BSs affects the BS b as OCI. The interferencepower is determined by the sector antenna characteristics, suchas the main lobe width and the side lobe attenuation. As anideal approximation, we assume that an antenna with a mainlobe width of θ directly reduces the average OCI power bya factor of θ/360. Thus, when a cell is sectorized with atransmission antenna of main lobe width θ(0 ≤ θ ≤ 360), thepower capacities in a sectorized cell are modified from (22) and(23) and are expressed as

Mp,maxOCI,θb ≤ (1 − ρ)E(t)

c,max

ν ·(

EcI0

)OCHM

target

/

ρE(t)

c,max +∑

{(x,0,b)|x=i}ν · E

[E

(t)c,b→(x,0,b)|active

]

· 4γ2 − 4

· (rγe − εγ)2

rγe εγ· exp

{(ln 1010

σζ

)2}

· (1 − α)

+

∑z =b

E(t)c,max · E

[r−γz→(i,0,b)

]

· exp

{(ln 1010 σζ

)22

}· θ

360+N0

· 2γ + 2

(rγe − εγ) · exp

{(ln 1010 σζ

)22

} (24)

Mp,minOCI,θb ≤ (1 − ρ)E(t)

c,max

ν ·(

EcI0

)OCHM

target

/

ρE(t)

c,max +∑

{(x,0,b)|x=i}ν · E

[E

(t)c,b→(x,0,b)|active

]

· 4γ2 − 4

· (rγe − εγ)2

rγe εγ· exp

{(ln 1010

σζ

)2}

· (1 − α)

+

∑z =b

ρE(t)c,max · E

[r−γz→(i,0,b)

]

· exp

{(ln 1010 σζ

)22

}· θ

360+N0

}

· 2γ + 2

(rγe − εγ) · exp

{(ln 1010 σζ

)22

}. (25)

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MOON et al.: CAPACITY IMPROVEMENT IN CDMA DOWNLINK WITH OCHM 519

TABLE IASSUMPTIONS FOR NUMERICAL EXAMPLES

VI. OVERALL SYSTEM CAPACITY AND NUMERICAL

EXAMPLES OF OCHM

A. Overall System Capacity in OCHM

In previous sections, we evaluated the code capacity in (4)and the power capacity in (21). Therefore, the overall systemcapacity Mmax

b considering both code and power limitationscan be expressed as

Mmaxb = min (M c

b ,Mpb ) (26)

where M cb and Mp

b represent the code and power capacitiesdetermined by (4) and (21), respectively.

In OCHM, both power capacity and code capacity varydepending on the perforation probability, the mean channelactivity, and the number of codewords. The overall capacitydetermined by Mp

b can be called a power limited state. On theother hand, the overall capacity equal to M c

b can be called acode-limited or perforation-limited state since the code capacityis limited by the allowable perforation probability in OCHM.

B. Numerical Examples for the Overall System Capacity

The physical layer parameter (Eb/I0)OCHMtarget has a typical

range from 0 to 7 dB, and the channel code rate is fixed at1/4. The total transmission chip energy E(t)

c,max is calculated bymultiplication of the maximum transmission power of a BS andthe chip duration. A typical value of the maximum transmissionpower is 15 W, and the chip duration is 1/1.2288 [MHz] incdma2000 [3]. We consider two typical channel-activity valuesof 0.1 and 0.2 since OCHM targets packet services. In thisexample, the tolerable value of ∆(Eb/I0)target, which is thedifference between the target Eb/I0 values of OCDM andOCHM, is set at 0.5 dB with an FER value of 0.01. Thus,the allowable perforation probability is 0.25, and the required(Eb/I0)OCHM

target value is approximately 2.0 dB with TC fromFig. 4. The detailed environment is shown in Table I.

Fig. 6 shows the code and power capacities versus the(Eb/I0)OCHM

target value. A horizontal solid line without markscorresponds to the code capacity of OCDM, which is equalto 64 codewords, and six parallel solid lines with marks cor-respond to the six code capacities of OCHM. For a meanchannel activity of ν = 0.1, the six perforation probabilitiespp,OC = 0.30, pp,OC = 0.25, pp,OC = 0.20, pp,OC = 0.15,pp,OC = 0.10, and pp,OC = 0.05 correspond to code capac-ities M c

b = 458(> 64), M cb = 370(> 64), M c

b = 287(> 64),M c

b = 209(> 64),M cb = 136(> 64), andM c

b = 67(> 64), re-spectively, which are obtained from Fig. 3. The five curves

with marks represent the OCHM power capacities calculatedfrom (21).

Fig. 6(a) shows the code and power capacities of OCHM inan omnicell environment with a maximum value of OCI. If weassume that the system can support a perforation probabilityof 0.25 and the proportion of the maximum downlink trans-mission power for the downlink common control channel ρ is0.20, the code capacity is 370 and the power capacity followsthe “+” marked curve. In this case, the OCHM system withpp,OC = 0.25 is not code (or perforation) limited but is powerlimited because a code capacity of 370 is always larger thanthe power capacity curve. Thus, the overall system capacityof OCHM follows the “+” marked power capacity curve inthe whole range of (Eb/I0)OCHM

target values. The overall systemcapacity of OCHM is approximately 180 for an (Eb/I0)OCHM

target

value of 2.0 dB. For other ρ values, the overall system capacitiesof OCHM are always power limited in this environment.

Fig. 6(b) illustrates the code and power capacities in anomnicell environment with a minimum OCI value. In this case,the system is code (or perforation) limited for a small value of(Eb/I0)OCHM

target since the power capacities increase regardless ofthe same code capacities. Crossover points depend on the powerproportion of the downlink common channels ρ. Since OCIhas a minimum value, ρ affects the power capacity more thanfor the maximum OCI case. If ρ = 0.20 and (Eb/I0)OCHM

target ≤5.5 dB, the overall system capacity of OCHM is determinedby the code capacity. However, if (Eb/I0)OCHM

target > 5.5 dB,the overall system capacity follows the power capacity curveof ρ = 0.20. Therefore, the overall system capacity can be370 at an (Eb/I0)OCHM

target value of 2.0 dB. Compared to themaximum OCI case, an increase in the power capacity makesit possible for the system to utilize the whole code capacityof 370.

Fig. 7 shows the code and power capacities with a meanchannel activity of 0.2. Compared to the code and powercapacities in Fig. 6, the higher channel activity of 0.2 yieldsa smaller code capacity due to a small statistical multiplexinggain, and a smaller power capacity due to a large average inter-ference. The code capacities for pp,OC = 0.30, pp,OC = 0.25,pp,OC = 0.20, pp,OC = 0.15, pp,OC = 0.10, and pp,OC = 0.05are M c

b = 230(> 64), M cb = 185(> 64), M c

b = 144(> 64),M c

b = 105(> 64), M cb = 69(> 64), and M c

b = 34(< 64), re-spectively. The power capacity curve values decrease to approx-imately half of the curve values for a mean channel activityof 0.1. In Fig. 7(a) and (b), the overall system capacities arelimited by power or code (or perforation). The trend is similar tothat shown in Fig. 6(a) and (b). Only the y-axis is scaled downsince both code and power capacities decrease. Therefore, theoverall system capacities at an (Eb/I0)OCHM

target value of 2.0 dBdecrease to 80 and 185 for ν = 0.2 compared to 180 and 370for ν = 0.1, respectively. However, these values are still largerthan the number of codewords equal to 64.

Fig. 8 shows the overall system capacity of OCHM andOCDM in an omnicell environment. The OCI values of thex-axis are normalized by the maximum OCI value. The foursolid lines represent the overall system capacities of OCHMwith (Eb/I0)OCHM

target values of 2.0, 3.0, 4.0, and 5.0 dB. InOCDM, the power capacity is also calculated by (21) replacing

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520 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 55, NO. 2, MARCH 2006

Fig. 6. Code and power capacities with a mean channel-activity value of 0.1 in an omnicell environment. (a) OCI = max. (b) OCI = min.

(Eb/I0)OCHMtarget with (Eb/I0)OCDM

target , which is (Eb/I0)OCHMtarget −

∆(Eb/I0)target. The four dashed lines represent the overallsystem capacities of OCDM with (Eb/I0)OCDM

target values of 1.5,2.5, 3.5, and 4.5 dB. With a mean channel-activity value of 0.1shown in Fig. 8(a), the OCDM system is always limited by thenumber of codewords, and the overall system capacity is fixedat an OCDM code capacity of 64. However, OCHM achieves

much larger capacities than OCDM in the entire range becauseOCHM with a small channel activity yields an increase in boththe power capacity and the code capacity due to a statisticalmultiplexing gain. In Fig. 8(b), OCHM also shows betteroverall system capacity with a small range of normalized OCIvalues and a small (Eb/I0)OCHM

target value. For normalized OCIvalues larger than 0.85 and 0.70 with (Eb/I0)OCHM

target = 4.0 dB

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MOON et al.: CAPACITY IMPROVEMENT IN CDMA DOWNLINK WITH OCHM 521

Fig. 7. Code and power capacities with a mean channel-activity value of 0.2 in an omnicell environment. (a) OCI = max. (b) OCI = min.

and (Eb/I0)OCHMtarget = 5.0 dB, respectively, OCHM performs

worse than OCDM because both OCHM and OCDM are lim-ited by the power capacity, which is smaller than the number ofcodewords, and the required Eb/I0 value of OCHM is largerthan that for OCDM.

Figs. 9 and 10 show the code and power capacities in athree-sectorized cell environment. Compared to Figs. 6 and 7,

the power capacities increase because interference from/toother cells in the three-sectorized cell environment is smallerthan in the omnidirectional cell environment. However, thecode capacities in Figs. 9 and 10 are identical to the valuesin Figs. 6 and 7, respectively. For the maximum OCI valuesshown in Figs. 9(a) and 10(a), the overall system capacity iscode (or perforation) limited or power limited, depending on

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522 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 55, NO. 2, MARCH 2006

Fig. 8. Overall system capacity of OCDM and OCHM in an omnicell environment. (a) OCI = max. (b) OCI = min.

(Eb/I0)OCHMtarget values, while the systems are always power

limited in the omnicell environment with a maximum OCIvalue. The sectorized cell fully achieves the code capacitiesof 370 and 185 at an (Eb/I0)OCHM

target value of 2.0 dB evenwith a maximum OCI value, as shown in Figs. 9(a) and 10(a),respectively. For the minimum OCI value shown in Figs. 9(b)and 10(b), the overall system capacities are always code (or per-foration) limited under the given conditions. Therefore, where

(Eb/I0)OCHMtarget = 2.0 dB and ρ = 0.20, the overall system ca-

pacities are still 370 and 185, as in the omnicell environmentshown in Figs. 6(b) and 7(b), respectively.

Fig. 11 shows the overall system capacity of OCHM andOCDM in a three-sectorized cell environment. The OCHMsystem is code (or perforation) limited in a range of normalizedOCI values larger than 0.8 or 0.7 with (Eb/I0)OCHM

target = 4.0 dBand (Eb/I0)OCHM

target = 5.0 dB, respectively. Compared to Fig. 8,

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MOON et al.: CAPACITY IMPROVEMENT IN CDMA DOWNLINK WITH OCHM 523

Fig. 9. Code and power capacities with a mean channel-activity value of 0.1 in a three-sectorized cell environment. (a) OCI = max. (b) OCI = min.

the sectorized cell yields a larger overall system capacity inOCHM while the OCDM system is still limited by the numberof codewords. OCHM always performs better than OCDM,even where ν = 0.2. An increase in the power capacity fromthe sectorized main lobe width is not effective in OCDM inrelatively low-channel-activity environments. In OCHM, anincrease in the power capacity from the sectorized main lobe

width contributes to an increase in the overall system capacitiesin large normalized OCI ranges in Fig. 8.

VII. CONCLUSION

For evaluating the overall system capacity of our previouslyproposed OCHM, the power capacity of OCHM is analyzed

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524 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 55, NO. 2, MARCH 2006

Fig. 10. Code and power capacities with a mean channel-activity value of 0.2 in a three-sectorized cell environment. (a) OCI = max. (b) OCI = min.

under assumptions of a one-tier hexagonal cell structure anduniformly distributed users. Even if the power capacity ismathematically derived in a simplified environment, we canestimate the effect of various downlink system parameters:mean channel activity, transmission power proportion of thedownlink common channels, OCI, and the required (or target)Eb/I0 value. From this power capacity and code capacity

previously analyzed, the overall system capacity, which isdetermined from the minimum value of the code and powercapacities, can be obtained in the CDMA downlink. In nu-merical examples, the code, power, and overall capacitiesare calculated and compared to the values of the conven-tional CDMA (OCDM). The proposed OCHM system canaccommodate more downlink channels than OCDM because

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MOON et al.: CAPACITY IMPROVEMENT IN CDMA DOWNLINK WITH OCHM 525

Fig. 11. Overall system capacity of OCDM and OCHM in a three-sectorized cell environment. (a) ν = 0.1. (b) ν = 0.2.

OCHM increases the code capacity by statistical multiplex-ing. The overall system capacity in OCHM is greatly im-proved for low-mean channel-activity values, small required(Eb/I0)target values, and small values of OCI. These condi-tions are well matched with expected future wireless communi-cation systems since packet-based services exhibit lower meanchannel activities than voice services, and enhanced modemtechnologies and strong channel coding schemes reduce the

required Eb/I0 values, and advanced antenna technologies,such as the switched-beam array antenna (SBAA) systemand the adaptive array antenna (AAA), reduce the amount ofinterference.

As further studies, we will perform feasibility studies ofsoft and hard handoffs in OCHM, and model the sectoredantenna with real parameters. These approaches may enhancethe capacity analysis of OCHM.

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526 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 55, NO. 2, MARCH 2006

Fig. 12. Approximation of probability density function for R2.

APPENDIX

A. Probability Density Function for R2

We obtain the probability density function fR2(r) of a ran-dom variable R2 that represents the distance between a BS andan MS in a cell adjacent to the cell covered by the BS. FromFig. 12, it can be approximated as fR2(r) � rφ/πr2e , where φis the angle between two lines from an adjacent BS to two crosspoints of a equivalent circle of the center cell and a circle withradius r from the adjacent BS. πr2e is the area of the equivalentcircle of the center cell, and rφ is the length of the arc betweenthe two cross points.

The probability density function fR2(r) can be appro-ximated as

fR2(r) �rφ

πr2e� 2xπr2e

(A1)

where 2x is the distance between the two cross points.Using a cross point, the center BS, and the adjacent BS,

a triangle can be constructed, where x is the length of aperpendicular line from the cross point to the base line. If we lety be the distance from the center BS to a contact point betweenthe perpendicular line and the base line, we can obtain twoequations from the two triangles:

x2 + y2 = r2e

x2 + (d− y)2 = r2. (A2)

From the above two equations, x can be derived, rh � re andd =

√3rh, and, finally, fR2(r) can be derived as

fR2(r) =2√3·√

4d2r2e − (d2 + r2e − r2)2d3

. (A3)

B. Expectation of Total Transmission Chip Energy

We can express the transmission chip energy from BS b forMS i, E(t)

c,b→(i,0,b) as a weighted sum of conditional expecta-

tion values E[E(t)c,b→(i,0,b)|active] and E[E(t)

c,b→(i,0,b)|inactive].

Since E[E(t)c,b→(i,0,b)|inactive] = 0, the expectation of total

transmission chip energy from a BS b is derived as∑(i,0,b)

E[E

(t)c,b→(i,0,b)

]

=∑

(i,0,b)

(E[E

(t)c,b→(i,0,b)|active

]· E [νc,b→(i,0,b)

]

+ E[E

(t)c,b→(i,0,b)|inactive

]· (1 − E[νc,b→(i,0,b)

]))=∑

(i,0,b)

E[E

(t)c,b→(i,0,b)|active

]· E [νc,b→(i,0,b)

](B1)

where νc,b→(i,0,b) is the channel activity of the downlink chan-nel from BS b to MS i.

The received transmission chip energy can be expressed witha received (Ec/I0)target value and interference values, and theexpectation values of propagation loss and shadowing is alreadyderived in (9) and (11). Thus, the expectation of transmissionchip energy with an active condition is given by

E[E

(t)c,b→(i,0,b)|active

]

= E[E

(r)c,b→(i,0,b)|active

]·E[rγb→(i,0,b)

]·E[10

ζb→(i,0,b)10

]

=(Ec

I0

)target

·E[I0,(i,0,b)

]·E [rγb→(i,0,b)

]·E[10

ζb→(i,0,b)10

]

=(Ec

I0

)target

· (E [Iic,(i,0,b)

]+ E

[Ioc,(i,0,b)

]+N0

)

· 2γ + 2

(rγe − εγ) · exp

{(ln 1010 σζ

)22

}. (B2)

Substituting (B2), (15), and (16) in (B1), and using that theexpectation values for all MS i’s are identical, the expectationof total transmission chip energy is given by∑(i,0,b)

E[E

(t)c,b→(i,0,b)

]

= Mpb · ν ·

(Ec

I0

)target

·ρE(t)

c,max +∑

{(x,0,b)|x=i}ν · E

[E

(t)c,b→(x,0,b)|active

]

· 4γ2 − 4

· (rγe − εγ)2

rγe εγ· exp

{(ln 1010

σζ

)2}

· (1 − α)

+

{∑z =b

(ρE(t)

c,max +∑

(x,0,z)

ν · E[E

(t)c,z→(x,0,z)|active

])

· E[r−γz→(i,0,b)

]+N0

}

· 2γ + 2

(rγe − εγ) · exp

{(ln 1010 σζ

)22

}. (B3)

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MOON et al.: CAPACITY IMPROVEMENT IN CDMA DOWNLINK WITH OCHM 527

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Sung Ho Moon (S’01) received the B.S. and M.S. degrees in electricalengineering from the Korea Advanced Institute of Science and Technology(KAIST), Daejeon, Korea, in 1999 and 2001, respectively, where he is currentlyworking toward the Ph.D. degree.

Since March 1999, he has been a Teaching and a Research Assistant inthe Department of Electrical Engineering and Computer Science (EECS),KAIST. His research interests include frequency and code-hopping systemsfor packet data transmission, wireless scheduling algorithms, link and system-level simulations for 3G and 4G wireless communication systems, adaptivemodulation and coding, and multiple-input multiple-output (MIMO) systems.

Suwon Park (S’92–A’03–M’04) received the B.S. degree in electrical engi-neering and mathematics (double major) in 1994, the M.S. degree in electricalengineering in 1996, and the Ph.D. degree in the Department of ElectricalEngineering and Computer Science (EECS), all from the Korea AdvancedInstitute of Science and Technology (KAIST), Daejeon, Korea, in 2003.

From 1994 to 1998, he was a Research Engineer in Telecommunication R&DCenter of Samsung Electronics, where he worked for the standardization ofInternational Mobile Telecommunications (IMT)-2000. From 1999 to 2002, hewas a Research Assistant in the Department of EECS, KAIST, and a Part-TimeResearcher with the Electronics and Telecommunications Research Institute(ETRI), Daejeon. In 2002, he rejoined the Telecommunication R&D Centerof Samsung Electronics as a Senior Research Engineer, where he worked forthe development of terminal modems based on software-defined radio (SDR).In 2006, he joined the faculty of the Kwangwoon University, Seoul, Korea,where he is currently an Assistant Professor with the Department of Electron-ics and Communications Engineering. His research interests include mobilecommunication systems, statistical multiplexing, radio resource management,communication theory, and SDR.

Dr. Park is a member of the Institute of Electronics Engineers of Korea(IEEK) and the Korean Institute of Communication Sciences (KICS).

Jae Kyun Kwon (S’96–A’03–M’03) received the B.S., M.S., and Ph.D. de-grees in electrical engineering from Korea Advanced Institute of Science andTechnology (KAIST), Daejeon, Korea, in 1996, 1998, and 2003, respectively.

He is currently working for Electronics and Telecommunications ResearchInstitute (ETRI), Daejeon. His research interests include intercell interferencemanagement, air interface for 3G evolution systems, code-hopping systems forpacket data transmission, code division multiple access (CDMA) soft handoff,and indoor and urban area mobility modeling.

Dan Keun Sung (S’80–M’82–SM’00) received theB.S. degree in electronics engineering from SeoulNational University, Seoul, Korea, in 1975 and theM.S. and Ph.D. degrees in electrical and computerengineering from the University of Texas at Austinin 1982 and 1986, respectively.

His research interests include mobile communi-cation systems and networks, high-speed networks,next generation IP-based networks, traffic control inwireless and wireline networks, signaling networks,intelligent networks, performance and reliability of

communication systems, and microsatellites. From May 1977 to July 1980, hewas a Research Engineer at the Electronics ad Telecommunications ResearchInstitute (ETRI), where he had been engaged in various projects including thedevelopment of an electronic switching system. In 1986, he joined the facultyof the Korea Advanced Institute of Science and Technology (KAIST), Daejeon,Korea, where he is currently Professor with the Department of ElectricalEngineering and Computer Science (EECS). He was Director of the SatelliteTechnology Research Center (SaTReC) of KAIST from 1996 to 1999.

Dr. Sung is Editor of IEEE Communication Magazine. He is also DivisionEditor of the Journal of Communications and Networks. He was Vice-Chairof International Conference on Communications (ICC) 2002 Symposium onGlobal Service Portability and Infrastructure for Next Generation VirtualHome and Office Environments and Program Cochair of the Globecom 2002Symposium on Service Infrastructure for Virtual Enterprise Environments.He was also General Conference Chair of ICC 2005 and Technical ProgramProgram Committee Vice-Chair of ICC 2005. He received the National Orderof Merits, the Dongbaek Medal in 1992, the Research Achievement Awardin 1997, the MoMuc Paper Award in 1997, the Academic Excellent Awardin 2000, the Best Paper Award of the Asia-Pacific Conference on Commu-nications (APCC)2000, and This Month’s Scientist Award from the Ministryof Science and Technology (MOST) and the Korea Science and EngineeringFoundation (KOSEF) in 2004. He is a member of Institute of Electronics,Information, and Communications Engineers (IEICE) and the Korean Instituteof Communication Sciences (KICS). He is also a member of Phi Kappa Phi andTau Beta Pi.