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EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONSEuro. Trans. Telecomms.2005; 16:107111Published online 29 September 2004 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/ett.997

Letter

Communication Theory

Evaluation of SIR statistics in a DS/CDMA system with signal-level-based

power control and multipath dispersion

Y.-H. You1*, H.-K. Song1, Han-Jong Kim2, Chang-Kyu Song3 and We-Duke Cho4

1uT Communication Research Institute, Sejong University, Seoul, Korea2

School of Information Technology Electronics Engineering, Korea University of Technology and Education, Chungnam, Korea3School of Electrical and Computer Engineering, Chungbuk National University, Chungbuk, Korea

4National Center of Excellence in Ubiquitous Computing and Networking (CUCN), Kyounggi-Do, Korea

SUMMARY

The statistical evaluation of the estimated short-term signal-to-interference ratio (SIR) for power control ispresented in many-to-one reverse link. As mentioned in other previous works, the statistical evaluationshows that the estimated short-term SIR can be approximated by a log-normal distribution. The analysis hasapplications to a cellular system employing direct-sequence spread-spectrum code-division multiple access(CDMA) with M-ary orthogonal modulation on the uplink. Copyright # 2004 AEI.

1. INTRODUCTION

In recent years, there has been a growing interest for

direct-sequence code-division multiple access (DS/

CDMA) cellular communication networks. The well-

known ability of cellular system is to both combat multi-

path fading and allow multiple users to access a channel

simultaneously. However, as pointed out in recent studies

[1, 2], because of the near/far problem and all adjacent

interferences, to fully exploit the potential advantages of

cellular system, power control must be used. Among these

schemes, closed-loop power control based on received sig-

nal strength, where power is adjusted at the portable every1.25 ms based on commands from the base station, has

been suggested for a cellular radio communication system

[2, 3]. This power control scheme is intended to overcome

the uplink near/far problem.

In this letter, the estimated signal-to-interference ratio(SIR) statistics are evaluated in a cellular system employ-

ing direct-sequence spread-spectrum system with the sig-

nal-level-based power control and M-ary orthogonal

modulation on the uplink. With the assumption of the clas-

sical multipath fading model, for which there is ample

experimental evidence for wideband signals and a conven-

tional waveform, the signal level distribution is determined

forM-ary orthogonal modulation with noncoherent envel-

ope detector modulation. As mentioned in Reference [3], it

is shown from the evaluated SIR statistics that the signal

level distribution can be approximated by a log-normal

distribution. The statistical analysis has potential applica-tions to cellular system with M-ary orthogonal modulation

on many-to-one reverse link. Next section provides SIR-

based power control model in a DS/CDMA cellular sys-

tem. In Section 3, the SIR statistic for power control is

Received 11 June 2002

Revised 14 November 2003

Copyright # 2004 AEI Accepted 11 June 2004

* Correspondence to: Y.-H. You, uT Communication Research Institute, Sejong University, Seoul, Korea. E-mail: yhyou@sejong.ac.kr

Contract/grant sponsors: Ubiquitous Autonomic Computing and Network Project; The Ministry of Science & Technology (MOST) 21st CenturyFrontier R&D Program, Korea.

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evaluated in many-to-one reverse link. Section 4 provides

some examples and finally the concluding remarks are

given in Section 5.

2. POWER CONTROL MODEL

Figure 1 illustrates the feedback power control model,

where the user transmitting signal powerpi[dB] is updated

by a fixed stepDp [dB] everyTp s. Duringith interval, the

signal power received at the base station is the sum of the

variation due to channel xi and the transmit power of

mobile unit pi, i.e. pi xi [dB], which is compared to adesired signal level at the base station assumed to be

0 dB. Then, a hard-quantized power command bit is trans-

mitted back to the user over the return channel and the

power control error ei [dB] represents the received signal

level after power control. This model includes the possibi-lity of return channel errors and the extra loop delay kTp.

Figure 2 shows the power control method to estimate the

received signal strength expressed as the sum of the varia-

tion due to channel xi and the transmit power of mobile

unit pi. The signal strength-based power control uses a

method for estimating the short-term average SIR as the

power information.

The transceiver structure used in our analysis is

described in Reference [2]. It employs a combination of

convolutional coding and orthogonal signaling. M-ary

orthogonal waveforms can be generated using Hadamard

or Walsh functions whose duration is Mchip times. In a

base station receiver, the outputs of the corresponding

Hadamard correlators from each diversity branch are

square-law combined, weighted with equal gain. Thus,the output of the square-law combiner is made up with

Mvalues, which is used for power control and for the soft

decision Viterbi decoder. The deinterleaver performs the

inverse operation of the interleaver.

3. EVALUATION OF SIR STATISTICS

The classical model for multipath is a delay line, with

delays corresponding to discernable paths each scaled by

a complex random variable with Rayleigh distributed

amplitude and uniformly distributed phase. Thus, the over-all complex transfer function of the L-component multi-

path channel can be defined as Reference [1]. If

assuming that all L paths are mutually independent, the

sum of all Lpaths for the correct signal correlator, y, has

probability density which is the L-fold convolution of that

for each path as [1]

fCy yL1ey=S1

LS 1L 1

Figure 1. Feedback power control model.

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with x x 1! for any integer x. For each of theincorrect signal correlator, it has a following probability

density

fIy yL1ey

L 2

It is assumed that automatic gain control has normalized

the noise variance to unity and Sis the normalized mean

received energy per path. As adopted in Reference [2], a

method for estimating the short-term average SIR for

power control uses the outputs from the square-law com-

biner of the base station. The short-term average SIR is

estimated by

1

Ns

XNsk1

k 3

where, Ns is the number of symbols in the power control

measurement interval ofTPms and

k maxyk1;. . .

;ykM1=M 1

PMi1

i6imaxyki

4

In Equation (4),imaxis the index of the largest value for the

given symbol interval,yki(i 1; . . . ;M) is the output fromthe square-law combiner for the kth information bit period

Tb, the numerator represents the signal power over Tb, and

the denominator denotes the noise and interference power

over Tb.

We first consider the probability density function (PDF)

ofk. The PDF of numerator ofkhas the following dis-

tribution,

fny fCyFIyM1 M 1fIyFCyFIy

M2

5

where,FCyand FIyare the corresponding distributionfunctions offCyand fIyrespectively, while the PDF ofdenominator ofk has the following distribution,

fdy M 1X3i1

Xmik1

Fik M 1yf gKi eaiM1y 6

where,

F11 PC

K1 1 7

and

Fik 1 PCikai

S 1LKi 1k8

In Equation (6), m1 1, m2 LM 2, m3 L,a1 a2 1, a3 1=S 1, K1 LM 1 1,Ki m i k(i 2; 3), and ikai andPCcan be written as

ikai 1k1mi k 1

mi 1

1i S

1 S

mi k1 9

Figure 2. Signal strength-based power control model.

EVALUATION OF SIR STATISTICS IN A DS/CDMA SYSTEM 109

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and

PC

Z 10

yL1ey=S1

LS 1L 1 ey

XM1k0

yk

k!

( )M1dy

XM1n0

1n M1n

1 n nSL

XnM1k0

bknL k

L

1 S

1 n nS

k10

For deriving Equation (10), we adopt the following

expansion

XM1k0

yk

k!( )

n

XnM1k0

bkn

yk

11

where,bkn is the set of coefficients in the above expansion

[4]. Using Equations (411), the distribution function of

kcan be expressed as

Fky

Z 10

fdxFCxyFIxyM1

dx

X3i1

M 1KiXmi

l1

FilXM1n0

1n M 1

n

XnM1k0

bknk Ki 1

ny aiM 1f gkKi1

yk

Xmil1

FilXL1j0

a3j

j 1

XM1n0

1n M 1

n

XnM1k0

bknk Ki l 1

ny a3y aiM 1f gkKil1

yjk

12

Using the above result, the distribution function of theshort-term average SIR can be easily obtained.

4. ANALYTIC EXAMPLES AND DISCUSSIONS

The uncoded bit rate is assumed to be 9.6 kbits/s. With a

rate of 1/3 convolutional code and M-ary orthogonal mod-

ulation (M 64), the symbol rate is 4800 symbols/s. We

assume that a power control command is sent every

1.25 ms, i.e. every six Walsh symbols (in which case

Ns 6). The normalized mean received energy per path Sis defined as S EE=N0=L, where EE is the total receivedenergy per orthogonal waveform summed over all Lpaths

andN0 denotes the additive noise density.

Figure 3 shows the distribution ofkversus normal-

ized signal level with L as a parameter. It is shown

from Figure 3 that the distribution function of kis approximated by log-normal. From these results,

we can make the approximation that (which is asum of log-normal r.vs) is also log-normal (this was

justified in [5, 6]). This result is consistent with the

results in Reference [3]. In addition, for high maximum

Doppler shift, it was suggested that the signal level

distribution can be approximated by a log-normal

distribution [1, 3].

5. CONCLUSIONS

In this letter, the estimated short-term average SIR statis-

tics are evaluated in cellular systems with the signal-level-

based power control and multipath dispersion. Based on

the assumption of the classical multipath fading model,

the signal level distribution is determined for M-ary ortho-

gonal modulation with noncoherent envelope detector

modulation. The statistical analysis has applications to a

cellular system with M-ary orthogonal modulation on the

reverse link.

Figure 3. Signal level distributions ofk: (i)L 3 (ii)L 6 (iii)L 9 (iv) L 12.

110 Y.-H. YOU ET AL.

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ACKNOWLEDGEMENTS

This research is supported by the Ubiquitous Autonomic Comput-ing and Network Project, the Ministry of Science and Technology(MOST) 21st Century Frontier R&D Program, Korea.

REFERENCES

1. Viterbi AJ, Viterbi AM, Zehavi E. Performance of power-controlledwideband terrestrial digital communication. IEEE Transactions onCommunications1993;41(4):559569.

2. Chang LF, Ariyavisitakul S. Performance of a CDMA radio commu-nications system with feed-back power control and multipath disper-sion.Globecom91, 1991; pp. 10171021.

3. Ariyavisitakul S, Chang LF. Signal and interference statistics of aCDMA system with feedback power control. IEEE Transactions onCommunications1993; 41(11):16261634.

4. Proakis JG. Digital Communications. McGraw-Hill: New York,

1989.5. Schwartz SC, Yeh YS. On the distribution function and moments of

power sums with log-normal components. Bell System TechnicalJournal1982;61(7):14411462.

6. Fenton LF. The sum of log-normal probability distributions in scattertransmission systems.IRE Transactions on Communications Systems1960;8(3):5767.

AUTHORS BIOGRAPHIES

Young-Hwan You received his B.S., M.S. and Ph.D. degrees in Electronic Engineering from Yonsei University, Seoul, Korea, in 1993,1995 and 1999 respectively. From 1999 to 2002, he was a senior researcher at the Wireless PAN Technology Project Office, KoreaElectronics Technology Institute (KETI), KyungGi-Do, Korea. Currently, he is with the School of Computer Engineering, SejongUniversity, Seoul, Korea. His research interests are in the areas of wireless/wired communications systems design, spread spectrumtransceivers and system architecture for realizing advanced digital communication systems.

Hyoung-Kyu Song received his B.S., M.S. degrees and Ph.D. in Electronic Engineering in 1990, 1992 and 1996 respectively fromYonsei University, Korea. From 1996 to 2000, he was a managerial researcher in Korea Electronics Technology Institute (KETI),Korea. Since 2000, he has been an associate professor of the Department of Information and Communications Engineering, SejongUniversity, Seoul, Korea. His research interests include digital and data communications, information theory and their applicationswith an emphasis on mobile communications.

Han-Jong Kim received his B.S. degree from Hanyang University, Korea, in 1986 and the M.S. degree and Ph.D. in YonseiUniversity, Korea, in 1988 and 1994 respectively. He is currently with the School of Information Technology Electronics Engineering

at Korea University of Technology and Education, Korea. His main areas of interest are communication systems, error control methodsand modulation and demodulation methods. In particular, he has been working on multicarrier modulation techniques, turbo codes andspace-time codes.

Chang-Kyu Songwas born in Cungcheong-Bukdo, Korea, on 12 January 1970. He received his B.S. and M.S. degrees in ElectricalEngineering from Chungbuk National University, Cheongju, Chungbuk, Korea, in 1995 and 1997 respectively. He has been a Ph.D.student in the School of Electrical and Computer Engineering, Chungbuk National University. His current research interests are inimage processing, image compression, image analysis and wavelets.

We-Duke Chowas born in Pusan, Rep of Korea on 17 November 1958. He received his M.S. degree and Ph.D. in Electronic Engi-neering from KAIST, Seoul, Korea, in 1983 and 1987 respectively. Since 2003, he has been a director of Center of Excellence inUbiquitous Computing and Networking (CUCN) (21-century Frontier Project office of MOST, Korea). From 1991 to 2002, he hadbeen a vice president of KETI and as head of System Research LAB. He had worked for developing GSM Modem, HDTV system andVOIP system. And from 1984 to 1990, he was project manager, LG Electronics (LGE) company, Korea. His main research interests are

ubiquitous system solution design, proactive fusion technology (BT IT CT) and self-growing interactive ubiquitous platformdesign.

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Copyright # 2004 AEI Euro. Trans. Telecomms. 2005; 16:107111