Transmit Power Control Using Probabilistic Target
for DS-CDMA Packet Mobile Radio
ZhiSen WANG, Eisuke KUDOH, Fumiyuki ADACHI
Dept. of Electrical and Communication Engineering, Graduate School of Engineering, Tohoku University
05 Aza-Aoba, Aramaki, Aoba-ku, Sendai, 980-8579 Japanwang@mobile.ecei.tohoku.ac.jp, kudoh@mobile.ecei.tohoku.ac.jp, adachi@ecei.tohoku.ac.jp
Abstract
A new transmit power control (TPC) is proposed thatchanges TPC target randomly in order to obtain the capture
effect for DS-CDMA packet mobile radio. The uplink
capacity of a DS-CDMA packet mobile radio system withproposed random TPC in a frequency selective fading
channel is evaluated by computer simulation. The simulation
results show that random TPC provides larger link capacity
than with slow TPC irrespective of the number of
propagation paths.
Keywords: DS-CDMA, packet communication, capture
effect, transmit power control, link capacity
1.
Introduction
In a packet mobile communication system, the packet
with larger power can survive when packets collide. This is
known as the capture effect [1]. In DS-CDMA, transmit
power control (TPC) and Rake combining are necessary to
reduce the multiple access interference (MAI) [2]. There are
two types of TPC: fast TPC and slow TPC [3]. Since fast
TPC keeps the instantaneous received signal power constant,the capture effect cannot be expected. On the other hand,slow TPC keeps intact the instantaneous received signal
power variation due to multipath fading, thereby yielding alarger capture effect. Therefore, slow TPC achieves a larger
link capacity than fast TPC [4]. However, as the number of
propagation paths increases, the received power variations
become shallower due to the increased effect of Rake
combining and thus, the capture effect obtainable by slow
TPC decreases. In order to obtain a sufficiently large capture
effect irrespective of the number of propagation paths, it
may be effective to control the transmit power so as tointentionally fluctuate the received signal power.
In this paper, a new TPC called random TPC is
proposed that changes TPC target randomly in order toobtain a large capture effect irrespective of the number ofthe paths. The uplink capacity of a DS-CDMA packet
mobile radio system with proposed random TPC is evaluatedby computer simulation. The remainder of this paper isorganized as follows. Sect. 2 presents proposed random TPC.
Sect. 3 introduces the throughput and outage probability andpresents the throughput computation method for a multi-cellsystem under an interference-limited condition. Sect. 4
evaluates the link capacity by computer simulation. Sect.5
gives some conclusions.
2.

Random TPC

A.

Principle of operation
For simplicity, no fading is assumed. The received
signal power PR at the base station is give by−η

PR = PT ⋅ r −α ⋅10 10 ,(1)

where PT represents the mobile transmit power, r the

distance between the base and mobile stations, α the pathloss exponent, and η the shadow fading loss in dB.
Denoting the TPC target by Ptarget, the base station received
signal power PR is kept at PR = Ptarget. Therefore, the mobiletransmit power with TPC become−η

PT = Ptarget ⋅ (r −α ⋅ 10 10 )−1 .

(2)

If this TPC is applied to all users, all users’ signals arereceived with the same power Ptarget at the base station.
Hence, no capture effect is obtained. In this paper, we
propose a random TPC that controls the transmit power so as
to intentionally fluctuate the received signal power.
The mobile station intentionally fluctuates its transmit
power by ± ∆ dB, with the probability of ε ± (ε++ε−=1),
from its nominal power given by Eq.(2). By doing so, thebase station received signal power from a certain user
becomes Ptarget ± ∆ dB with a probability of ε ± . Fig.1 shows
probability density function (pdf) of the received signal
power with proposed random TPC. For comparison, the fast
TPC case is also illustrated.
PT can be determined using Eq.(1), but the sum of pathloss and shadowing loss (propagation loss) must be known.
The uplink and downlink propagation channel is symmetric
except for the effect of multipath fading. Therefore, thepropagation loss can be assumed the same for both links. If
the mobile station is informed of the base station transmit−

ηpower PT, then (r −α ⋅10 10 ) can be computed using Eq.(1).
However, this is only applicable when there is no fading.
The most possible applicable system may be thetime-division-duplex (TDD) system, in which the same
carrier frequency is used for both uplink and downlink.
pdf

pdf

εε+
target Received
Power (dB)(a) Received power pdf ofRandom TPC

target Received
Power (dB)(b) Fast TPC

Fig. 1 Pdf of received signal power.
B. Application to TDD system
The above described random TPC can be easily
implemented in a TDD system. Fig.2 illustrates the uplink(mobile to base)/downlink (base to mobile) timing structure.
The mobile station can estimate the uplink propagation loss−η(r −α ⋅10 10 ) in Eq.(1), by measuring the received power ofthe signal transmitted from the base station since the same
frequency channel is used for uplink and downlink. Thus,
the mobile station can determine its transmit power by itself.
The base station transmits pilot signals with the known

power (PBTp) periodically and the mobile station estimates
the sum of path loss and shadowing using its measured
received signal power PMRp to determine its transmit power
PT frame by frame as follows.

where p(k) is the conditional average packet error rate whenkinterfering
packetsarereceived
andPT = Ptarget ± ∆ + ( PBTp − PMRp ) in dB.

Assuming a slotted packet transmission and a block
fading (the fading stays almost constant over a packet), p(k)can be computed using(3)§ K − 1·( K − 1)!
is the binomial coefficient.
¨¨¸¸ =© k ¹ k!( K − k − 1)!

1 frame

···

···

(

p (k ) = 1 − 1 − pb (γ k )

···

)N ,

(8)

Time

Base → Mobile
Pilot

Mobile → Base
PacketBase → Mobile
PacketFig.2 Timing structure.

3. Throughput Computation Method
The throughput computation method for the fast TPC
case is presented in Ref.[4], which is used also in this paper.

where pb (γ k ) is the average bit error rate (BER) when kinterfering packets are received and N is the number of bits
in a packet. pb(γk) represents the instantaneous BER when
the received SINR is γk. Mathematical expression for γk ispresented in Sect. 3.3. Assuming coherent BPSK data
modulation and that the sum of colliding packets isapproximated as a Gaussian process, pb(γk) is given by [5]pb (γ k ) =3.1 Definition of throughput and link capacity

Outage occurs if the transmission quality drops below
the required quality of services (QoS), i.e., packet
throughput and delay. The link capacity is defined as the
maximum number of active users that satisfies the allowable
outage probability (Qallow) and Qallow is defined as the
maximum outage probability that satisfies the system
requirement. In a packet communication system, automatic
repeat request (ARQ) is used. Assuming infinite number ofretransmissions (infinite delay is allowed before successfultransmission of a packet), the throughput S is given by

S = 1 − p( K , λ ) ,(4)

where p(K, λ) is the average packet error rate with K and λbeing the number of active users and the packet occurrence
rate, respectively. The outage occurs only if throughput isless than the required value. The outage probability Q isgiven by
Q = Prob[ S < Sreq ] ,(5)

3.2 Obtaining p(K,λ)

error function.

(6)

There exist K-1 active interfering users. Assuming that theoriginal and retransmitted packets are randomly produced,p(K,λ) can be computed using
K −1§ K − 1· k

¦ p(k ) ⋅ ¨¨© k ¸¸¹λ (1 − λ )k =0∞³ e dt is the complimentary−t 2

x

3.3 Mathematical expression for SINR γk

We assume an interference-limited channel. A
frequency selective block fading channel having L discretepaths is assumed. Below, we derive an expression for γk tocompute the packet error rate p(k) using Eqs. (8) and (9).
The received signal r0(t) at the 0th base station is expressed,using equivalent baseband representation, as [6]k −1§ L −1·l)(l )(i ) ¸
2 PR ,i →0 ¨
ξi(→,
0 di (t − τ i →0 )ci (t − τ i →0 ) ¸¨i =0© l =0¹(10)where i denotes the user index, PR ,i →0 is the average signal

r0 (t ) =

¦

¦

(l )
(l )
chip waveform, respectively. ξi→j and τ i→ j are the lthpath complex gain and time delay, respectively, associatedwith ith user seen at the jth base station. It is assumed that
L −1

For the throughput computation we need to obtainp(K,λ). We assume that the occurrence rate of original
packets is the same for all active users and is denoted by λ0.
The total packet occurrence rate λ is (1+(packet
retransmission rate)) × λ0. When TPC is used, since packet
errors occur equally likely for all active users, λ is given byp( K , λ ) =where erfc( x) = (2 / π )(9)power of the ith user received at the 0th base station and di(t)and ci(t) are the data-modulated waveform and the spreadingwhere Sreq is the required throughput which is defined as theminimum throughput that satisfies the required QoS.

λ0,
λ=1 − p( K , λ )γ
1erfc k ,22

K −1− k

, (7)

E[

¦ξ

(l )
i→ j

2

] = 1 ,where E[*] denotes ensemble average

l =0

operation. Time dependency of the path gain is dropped forthe sake of simplicity. PR ,i →0 is given byPR ,i →0 = PTi ri−→α010

η

→0
− i10

,

(11)

where PTi , ri →0 , α, and η i → 0 are the transmit power, thedistance to the base station normalized by the cell radius, thepath loss exponent, and the shadowing loss (dB),respectively, for the ith user. We assume an ideal Rake
receiver with the number of fingers equal to L. The mobile
station communicate with the base station that the received
signal power is largest.
Each user finds the best base station having theminimum path loss. The best base station is indexed as k(i).
The ith users signal power PRake,i after Rake combing at theTable 1 Simulation parameters
Uniform
distribution
FadingBlock RayleighNumber of paths L=1~16
Data mod. /BPSK withand demod.
coherent detection
Spreading factor SF=1~512
LengthN=128~4096 bits
Data packet
λ0=0.01~0.1
generation
probability
Required
Sreq=0.9
throughput
Qallow=0.001~0.1
Allowable
outageprobabilityk(i) th base station is given by
PRake,i = PTi ri−→αk (i )10

ηi→k i L −1
− 10 ( )¦ξ(l )i → k (i )2User location
,(12)

l =0

where
L −1
­°
η
2½
°
− i→k
l)
k (i ) = arg max ®ri−→αk 10 10
ξi(→
k ¾ . (13)
k °̄
°¿
l =0

¦

Propagation
channelTransmitterand receiverPacketWhen random TPC is applied, the transmit power PTi
becomes∆ ⋅δPtarget 10 10 i

PTi =ri−→αk (i )10

L −1η
− i→10k ( i )

¦ξ

(l )
i → k (i )

2

,

QoS

(14)

l =0

where δ i (1 or -1) represents the power state. δi=1
represents the target value of Ptarget+∆dB and δi=-1
represents the target value of Ptarget-∆dB with
Prob(δi=±1)=ε±, where ε++ε−=1.
The received SINR γ k after Rake combining is givenby2¦§ L −1 L −1
·
2
∆δ
(l )
∗( m )¨¸ξξ
10 10 0
0
0
0
0
→
→
¨
¸
¨ m =0 l = 0
¸
l≠m
¨
¸
¨
¸
L −1 L −12(l ) ∗ ( m ) ¸¨η i →0
ξ
ξ
−
∆
i
→
0
0
→
0
k −1
¨ § L −1¸δ2·
10 10 i ⋅ ri−→α010 10 m = 0 l = 0¨+ ¨¸
ξ 0( l→) 0 ¸¸
2 ¸
η i→ k ( i )¨ ¨−§ L −12·¹ i =1−α¨ © l =0
10
(
m
)
¨
¸
ri → k ( i )10
ξ i → k ( i ) ¸ ¸¸¨¨¨¸© m =0
¹ ¹
©

¦¦
¦

¦¦

¦

¦

. (15)For the single cell case, Eq.(15) reduces to2γk =§ L −1
2·
∆δ
(l )
¸
10 0
2 SF ¨ξ
0 → 0 ¸ 10¨
© l =0¹¦§ L −1 L −1
·
2
∆δ
(m)
¨
¸
10 0
ξ 0(l→) 0ξ 0∗→0 10¨¸¨ m = 0 l =0
¸
l ≠m
¨
¸
¨
¸
L −1 L −1
2( l ) ∗( m ) ¸
¨
ξ
ξ
i
→
0
0
→
0
¨ § L −1¸
2 · k −1(l )¸ 10 10∆ δ i m = 0 l = 0
¨+ ¨
¸
ξ
0
→
0
2
¸
¨ ¨
¸
L −1
§
·
2
¹ i =1¨ © l =0
¸
(m) ¸
¨
ξ
i →0 ¸
¨¨
¸¸
¨
© m=0
¹
©
¹

.

¦¦
¦

¦

1.2

¦¦

S req=0.9, Q allow=0.1, λ 0=0.05, N =512bits, L =2, SF =32
1

¦

(16)
It is found from Eq.(14) that γ k is independent of the pathloss and the shadowing loss, but is randomly fluctuated byrandom TPC.
4.

4.1. Single cell caseFig. 3 plots the normalized link capacity C/SF as afunction of ∆ with ε- as a parameter for L=2. For
comparison, the cases with slow and fast TPC are alsoplotted. When ∆=0dB, the same link capacity as with the fast
TPC is achieved. As ∆ becomes larger, the link capacity
increases due to increased capture effect. The link capacity
approaches its maximum when ∆ is 3dB. When ∆ increases
beyond 3dB, however, the link capacity starts to reduce
since the increasing MAI offsets the capture effect. It can beseen that the proposed random TPC achieves a larger link
capacity than slow TPC when ∆ = 3 dB and ε − = 0.8 . Thisis because the random TPC provides a larger capture effectdue to controlled power fluctuations.

Computer Simulation

Table 1 shows the simulation parameters. BPSK data
modulation and ideal Rake combing based on maximum
ratio combining (MRC) are assumed.

Slow TPC

0.8
C/SF

γk =

§ L −12·∆δξ 0( l→) 0 ¸¸ 10 10 0
2 SF ¨¨© l =0¹

The uplink capacity is evaluated by the Monte-Carlosimulation using following procedure
Step1: set K=1.
Step2: increase the value of K by one.
Step3: obtain the throughput S as described in Sects.3 and4.
Step4: obtain the outage probability (Q) that S<Sreq.
Step5: repeat step 2 to step 4 until Q≥Qallow. The
maximum number of K that satisfies Q<Qallow is
the link capacity C.
The single cell case is considered first and then, the simulation
is extended to the multiple cell case.

0.6

Fast TPC

ε -=0.2
ε -=0.8

0.4

ε -=0.5
0.2
0
0

1

2

3

4

5

6

∆（dB)
Fig.3 Normalized link capacity C/SF as a function of ∆.

7

Fig. 4 plots the normalized link capacity C/SF as afunction of ε- for ∆=3dB and SF=32. When ε- = 0 or 1, since
the received signal power is constant, the same normalized
link capacity as with fast TPC is obtained. As ε- increases,
the link capacity becomes larger due to the increasing
capture effect and it approaches its maximum when ε-=0.8.

When SF > 8 , the proposed random TPC provides thelargest link capacity. When SF>64, the normalized link
capacity remains constant since the impact of inter-pathinterference can be neglected.
1.2
Rndom TPC

1.2

1

1

0.8

ε −=0.8, ∆ =3dB
Slow TPC

C/SF

Slow T PC

C/SF

0.8
Fast T PC

0.6

0.6

Fast TPC

0.4

0.4

0.2
S req=0.9, Q allow=0.1, λ 0=0.05, N =512bits, L =2

0.2

0

S req =0.9, Q allow=0.1, N =512bits, SF =32,∆=3dB

1

10

SF

100

1000

Fig. 6 Normalized link capacity C/SF as a function of SF.

0
0

0.2

0.4

ε-

0.6

0.8

1

Fig. 4 Normalized link capacity C/SF as a function of ε-.
Fig. 5 plots the normalized link capacity C/SF as afunction of L for ∆=3dB, ε−=0.8 and SF=32. For comparison,
the cases with slow and fast TPC are also plotted. For thecase of slow TPC, since the degrees of the received powerfluctuations after Rake combining depends on L, the link
capacity with slow TPC is sensitive to L. The link capacitywith random TPC always obtains a larger link capacity thanboth slow and fast TPC irrespective of L. This is because thereceived power fluctuations are controlled by random TPC
so that the capture effect can be maximized.

Fig. 7 plots the normalized link capacity as a functionof packet length N. As the N becomes larger, the normalized
capacity decreases because the required SINR to achieve therequired packet error rate increases. However, it is seen thatthe proposed random TPC always yields the largest capacity
irrespective of the packet length N.
1.6
Q req=0.1, S req=0.9, SF =32, L =2
1.2

C/SF

Random T PC

1.2

0.8

Slow T PC

Random T PC

Fast T PC

1
0.4

C/SF

0.8

Slow TPC
0

0.6

100

Fast TPC
0.4

1000
Packet length N (bit)10000

Fig.7 Normalized link capacity C/SF as a function of N.
S req=0.9, Q allow=0.1, λ 0=0.05, N =512bit, SF =32

0.2

0
0

5

10
Number L of paths

15

20

Fig.5 Normalized link capacity C/SF as a function of L.
Fig. 6 plots the normalized link capacity as a functionof SF. When SF ≤ 4 , the link capacity is almost zero
because of large inter-path interference for all TPC schemes.

4.2 Multi-cell
So far single cell case has been considered. In the caseof multi-cell, the users communicating with other cells giveinterference to the cell of interest and this reduces the link
capacity per cell compared to the single cell. In this paper,
up to the second tiers of the surrounding cells are considered(i.e., 19 cells are considered in the simulation.) Fig. 8 plots
the normalized link capacity per cell as a function of thenumber L of propagation paths for the multi-cell case.
Similar to the single cell case, the link capacity with random
TPC has identical value irrespective of L. Fig. 9 plots thenormalized link capacity per cell as a function of the path1

0.8
Random TPC
0.6

C/SF per cellloss exponent α. As α becomes larger, the link capacity
increases. This is because the interference power from theother cell user decreases as α becomes larger. Fig. 10 plots
the normalized link capacity per cell as a function of thestandard deviation σ of the log-normally distributed
shadowing loss. As σ becomes larger, the link capacity
tends to decrease, but is not that sensitive to σ.
All the above results confirm that similar to the single
cell case, the random TPC can achieve the largest capacity.

Slow TPC

0.4
Fast TPC

1
Q req=0.1, S req=0.9, SF =32, N =512bits
multi-cell

Q req=0.1, S req=0.9, SF =32, N =512bits
α =3.5, L =2
multi-cell

0.2

C/SF per cell

0.8
0Random TPC∆=3dB, ε -=0.8

0.6

4

Fast TPC

5.

0.2

0
0

5

10

15

20

Number L of paths

Fig.8 Normalized link capacity C/SF as a function of L in
multi-cell environment.

1

0.8

C/SF per cell

Random TPC

0.6

Slow TPC

02

34
Path loss exponent α

We proposed the random TPC whose received signal
target power is randomly fluctuated in order to obtain thelarger capture effect. The uplink capacity of DS-CDMApacket mobile radio was evaluated by computer simulation.
The results obtained in this paper can be summarized asfollows.
(a) The proposed random TPC achieves a larger maximum
link capacity than slow TPC and fast TPC. This isbecause the random TPC gives adequate received signal
power fluctuations which can obtain a larger capture
effect.
(b) The maximum link capacity with random TPC isalmost insensitive to the number L of the propagation
paths. However, the capacity with slow TPC is sensitive
to L since the statistics of received signal powerfluctuation after Rake combining depends on L.
References

Q req =0.1, S req =0.9, SF =32, N =512bits,
σ =7, L =2
multi-cell

0.2

Conclusions[1] I. Widipangestu, at el., “Capture probability andthroughput analysis of slotted ALOHA and unslotted
np-ISMA in a Rician/Rayleigh environment,” IEEE
Trans. Veh. Technol. Vol. 43, no. 3, pp.457-465, Aug.
1994.

Fast TPC

0.4

12

Fig.10 Normalized link capacity C/SF as a function ofstandard deviation σ of shadowing loss in multi-cell
environment.

Slow TPC

0.4

8Standerd deviation σ of shadowing loss

5

6

Fig.9 Normalized link capacity C/SF as a function of pathloss exponent α in multi-cell environment.

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