The research paper published by IJSER journal is about Modified Variable Step Size Power Control Algorithm for CDMA Systems 1

ISSN 2229-5518

Modified Variable Step Size Power Control

Algorithm for CDMA Systems

Anand Gachhadar

AbstractPower control mechanism is an important issue for Code Division Multiple Access (CDMA) systems which helps in achieving higher capacity, combating against near far effect and provides high link performance. Unless a suitable power control mechanism is developed cellular systems cannot perform better. Power control allows to minimize the transmit power while keeping the system performance above the required value. In previous research [4], variable step size for closed loop power control system has been studied and results showed an increase in convergence speed and stability by properly choosing the step size. The new algorithm presented in this paper shows that it can perform better than variable step size power control algorithm and can obtain higher stability and convergence speed for step size δ at 0.1.

Index TermsCode Division Multiple Access (CDMA), Closed Loop Power control, Frame Error Rate (FER), Modified Variable Step Size Power Control Algorithm (MVSPCA), Near far Effect, Step Size (δ ), Signal to Interference Ratio (SIR) , Variable Step Size Power Control Algorithm (VSPCA).

—————————— ——————————

1 INTRODUCTION

Code Division Multiple Access (CDMA) technique provides a significant increase in capacity of cellular mobile radio systems as compared to Time Division Multiple Access (TDMA) and Frequency Division Multiple Access (FDMA) [1]. However this improvement in capacity depends on the power control of the system.

Power control in CDMA systems is a critical issue because
it helps to alleviate from “near far” problem, increases capacity, improves quality of service (QoS) and prolongs the
life of battery. Closed loop power control algorithms [2] are mostly in implementation, which helps to combat multipath fading. Open loop power control algorithm is used to combat against path loss and shadowing effects [3]. IS-95B and CDMA2000 uses Fixed Step Size Power Control Algorithm which updates transmits power every 1.25ms. In forward
closed loop power control system is used to bring the estimated Signal-to-Interference Ratio (SIR) closer to the target Signal-to-Interference Ratio. Whereas Outer closed loop power control system adjusts the target SIR based upon the frame error rate (FER). Inner closed loop compares the SIRest with SIRtarget and if target SIR is greater than the estimated SIR up command is sent through feedback channel to increase the transmit power whereas, if estimated SIR is greater than the target SIR than down command is sent to decrease the transmit power. Transmit power must not exceed the maximum allowed power.

2 SYSTEM MODEL

Consider the uplink power control (mobile-base) in this paper. Assume the system consists of M base stations (BS) and each BS consists of N number of mobile stations (MS) out of which only U users is active at a time. Hence, Signal-to- Interference Ratio (SIR) at the jth BS due to ith MS is given by
traffic channel a 20ms frame is organized into 16 time interval

S

E R


b i

g ji Pi

and each time interval consist of a power control group

   

I N W U i

(1)

(PCG). Inner loop sends power control bits at a rate of 800Hz.
Transmitter adjusts their power according to the power

i i

0

g

k i

jk Pk

j

control bits sent on the feedback channel. Speed of
Where

Eb stands for information bit-energy,

N 0 is the

convergence is an important factor for a good power control
interference power spectral density. The power transmitted
algorithm and also control overhead must be less. Variable
step closed loop power control algorithm [4] employ one bit
by each mobile is given by

Pi for 0  i U . Ri

stand for
for power signaling, provides stability and decrease loop delay.
Closed loop power control system consists of two systems.
i) Inner closed loop and ii) Outer closed loop system [5]. Inner

————————————————

information bit rate of each mobiles and W is the chip rate of
the system. g ji denotes the link gain from ith MS to jth BS and i denotes the background noise. Interference in CDMA system is mainly due to intercellular interference and intracellular interference. Thus, objective of power control is

Anand Gachhadar, Masters degree program completed in year 2010 from NIT, Warangal, Andhra Pradesh, India.

to find a non-negative power vector

p  ( p1 , p2 ,...... pU )

Currently working as a Pre-Sales Transmission and Planning

Engineer in ZTE Corporation (Nepal Branch).

for 0  i U which satisfies the maximum power constraint

E-mail: gachhadar.anand@gmail.com

i T

for all values of i Where

T is the minimum

threshold SIR for the system to maintain the required voice quality and medium BER.

IJSER©2012 http://www.ijser.org

The research paper published by IJSER journal is about Modified Variable Step Size Power Control Algorithm for CDMA Systems 2

ISSN 2229-5518

Zander [6] proved that the maximum achievable SIR is given by

SIRtarget is greater power up command is generated to increase transmitter power. Transmit power is given by

SIR

1


 1

(2)

p (t)  p (t 1)  exp(*)

(3)

Where, is the largest real positive value of the link gain matrix G and the Eigen vector obtained for corresponding

i

Where,

i

pi (t) is the power of the ith mobile at tth iteration

Eigen value is the maximum power vector for the system.

3 MODIFIED VARIABLE STEP SIZE POWER CONTROL

SCHEME

This algorithm is a modified form of variable step size closed loop power control algorithm [4], which controls power
and δ is the step size or convergence parameter.
α is increased by one unit until the estimated SIRest is greater than the target SIRtarget. If the estimated SIRest is closer to target

SIRtarget by less than 1dB then the power is increased in small steps rather than increasing it by larger steps to decrease large

oscillations in received power. At this point, variable x is increased by one unit and transmit power is given by
adaptively rather than at fixed steps. Exponential function
pi (t )  pi (t  1)  exp (* x)
(4)
which has both increasing and decreasing characteristics has been used for controlling the power updates. Exponential function has already been used as power update function in most of Distributed Power Control [7], [8], [9], [10] algorithms.
Negative step size is employed to increase or decrease
power in small steps. At times, if the channel condition
changes and estimated SIRest is greater than target SIRtarget than power down command is send to the mobile station to decrease transmit power. Transmit power is now given by

pi (t)  pi (t  1)  exp (* )
(5)
At this instant, α is set to zero and β is increased by one unit until the estimated SIRest becomes less than the target SIRtarget. If the estimated SIRest is closer to target SIRtarget by greater than -1dB then the power is decreased in small steps. Now y is increased by one unit and transmit power is given by
pi (t )  pi (t  1)  exp (* y)
(6)
Table 1 shows generation of power control bits and algorithm is given below

TABLE 1

Fig. 1. Uplink power control mechanism

Fig. 1. depicts the block diagram of uplink power control mechanism studied in this paper. Power received at base station measures estimated SIRest which is then compared with the target SIRtarget to calculate error (err). It is then send to power control command decision block which decides power control bits and is then embedded with the traffic stream to be sent through the channel. No error protection is done for power control bits to reduce delay. Power control bits are then separated from traffic stream and are detected by power control command detector which then increments and decrements power based on the bits detected given in Table 1. After done with suitable power adjustments it is then transmitted back to the base station.
Two power control bits are used for sending power
control command and mobile station updates its power based upon the received power control bits. (α, β, x, y) are the

INFORMATION BITS AND UPDATE FUNCTION

Bits

Power increment/decrement

00

exp (* )

01

exp (* y);

10

exp (*);

11

exp (* x);

It should be noted that as soon as power control bits are changed from up command to down command or vice versa the value of and β is also changed to zero respectively and
their values start increasing from zero in the next iteration.

3.1 ALGORITHM

Step 1. Compute received SIR. i (t)

Step 2. Set α=0,β=0,x=0,y=0;
variables used in this algorithm. In the start of the algorithm T T
all these variables are initialized to zero. Power received at base station is measured and estimated SIRest is calculated which is then compared with the target SIRtarget. If target
Step 3. Compare it with target SIR. . err= - i (t)
Step 4. If err>0
If err<1
x=x+1;

IJSER©2012 http://www.ijser.org

The research paper published by IJSER journal is about Modified Variable Step Size Power Control Algorithm for CDMA Systems 3

ISSN 2229-5518

pi (t  1)  pi (t)  exp(

Else
α =α+1;β=0;

pi (t  1)  pi (t)  exp(

* x);

15

10

*); 4 3

Endif
Else
If err>-1`
pi (t  1)  pi (t)  exp(* y);
Else
β =β+1;α=0;

pi (t  1)  pi (t)  exp(* );

Endif

5

0

-5

-10

15

5 1 2

6 7

Endif

4 SIMULATION AND RESULTS

We consider a uplink (reverse link) transmission (i.e., from mobile to base station) for the entire simulation. The simulation was performed under static user condition and the propagation model consists of two components i) one component is due to multipath propagation where signal power decays with path loss component α=4. ii) The other component is due to the log normally distributed shadow effects which is a Gaussian random variable with zero mean and standard deviation of 8 dB. Hence the attenuation factor is represented by

ij / 10

-

-15 -10 -5 0 5 10 15

Fig. 2. Circular Cell

4.1 Convergence Performance

Convergence speed of Modified variable step size power control algorithm (MVSPCA) was found to be higher than the convergence speed of variable step size power control algorithm (VSPCA). Convergence speed of variable step size power control algorithm was measured at different values of step size whereas; step size of modified variable power control algorithm at value 0.1 gives better results. Variable step size power control algorithm shows a tradeoff between convergence and fluctuations in measured SIR. If chosen step

g ij

 10

d

(7)

size is less than convergence speed is low and fluctuations are
less if step size is high than convergence is faster whereas
fluctuations in measured SIR increase. So, step size must be
gij is the gain between the mobile user ith and the base station

jth. ij is the Gaussian random variable with zero mean and standard deviation of 8 dB. d is the distance between mobile

user and the base station. α is the path loss component and is
assumed to be 3.64.
Though in practical environmental conditions the gain is not
constant but theoretically we assume it to be constant.
We consider a circular cell of each of radius 5km with the
base station at the center of the cell. The number of cells
considered for simulation in this thesis is 7 and total number of users in each cell is considered to be 100. The active users in each cell are generated using a MATrix LABoratory (MATLAB) randn() function. The number of active users in cell 1 is fixed manually as 50. The transmit power of all the active users are assumed to be constant and fixed at 2W. Maximum power taken for the simulation equals to 3W. Small circles show the active users. The circular cell structure is shown in Fig. 2.
chosen properly for better results.
Choosing large value of step size or convergence
parameter in modified variable step size power control algorithm causes power to increase and decrease by large a amount which causes large oscillations. So convergence parameter must be chosen properly for faster convergence and less oscillation.
From above Fig. 3, Fig. 4 and Fig. 5 we can see that at larger values of step size of VSPCA convergence speed becomes almost comparable to MVSPCA, but it causes large amount of oscillations which is not desirable.

IJSER©2012 http://www.ijser.org

The research paper published by IJSER journal is about Modified Variable Step Size Power Control Algorithm for CDMA Systems 4

ISSN 2229-5518

step-up=0.3,step-down=0.3 for VSPCA and step size=0.1 for MVSPCA

30

VSPCA MVSPCA

20

1

0.9

0.8

VSPCA MVSPCA

0.7

10 0.6

0.5

0

0.4

-10

0.3

0.2

-20

-30

0 10 20 30 40 50 60

Iterations

0.1

0

0 10 20 30 40 50 60

Number of Iterations

Fig. 6. Outage probability vs. Iterations

Fig. 3. Convergence speed of VSPCA for δup and δdown=0.3 and MVSPCA

for δ=0.1

step-up=0.6,step-down=0.6 for VSPCA and step size=0.1 for MVSPCA

30

VSPCA MVSPCA

20

Fig. 6. shows that the outage probability drastically decreases after each iterations and the number of mobiles reaching the target SIR after each iteration is higher in modified variable step size power control algorithm than in variable step size power control algorithm. This algorithm has higher speed, higher robustness against loop delay and higher stability (fewer fluctuations in closed loop power control process).

10

0

-10

-20

-30

0 10 20 30 40 50 60

Iterations

5 CONCLUSIONS

This paper presents a new power control algorithm for CDMA systems which depends upon the variation of convergence parameter. The convergence speed and outage probability of modified variable step size power control algorithm outperforms that of variable step size power control algorithms. The presented algorithm increases capacity and leads to greater stability.
The presented algorithm uses two bits as power control

Fig. 4. Convergence speed of VSPCA for δup and δdown=0.6 and MVSPCA

for δ=0.1

step-up=0.9,step-down=0.9 for VSPCA and step size=0.1 for MVSPCA

signaling whereas variable step size power control algorithm uses single bit and more bandwidth efficient which is the major drawback of Modified variable step size power control Algorithm.

30

20

10

0

-10

-20

-30

VSPCA MVSPCA

0 10 20 30 40 50 60

Iterations

Acknowledgment

I would like to thank Associate professor. Sri S.K.L.V. Sai Prakash, my advisor, for providing me guidance and assistance. He has been supportive, tolerant and lent me a patient ear at all times. I am also grateful to all the faculty members of National Institute of Technology, Warangal and my friends for their kind assistance, guidance and encouragement.

References

[1] T. S. Rappaport. Wireless Communications: Principles and Practice

IInd Edition. NJ: Upper Saddle River, Prentice-Hall, 2005

Fig. 5. Convergence speed of VSPCA for δup and δdown=0.9 and MVSPCA

for δ=0.1

[2] C. Lee, R. Steele, “Closed loop power Control in CDMA systems”,

IEE proc-commun vol. 143. No. 4, August 1996

IJSER©2012 http://www.ijser.org

The research paper published by IJSER journal is about Modified Variable Step Size Power Control Algorithm for CDMA Systems 5

ISSN 2229-5518

[3] A.J. Viterbi, CDMA: principles of spread spectrum communication, Addison-Wesley, 1995

[4] S. Hamed, A. Abbas, ”Variable Step Closed loop power Control in Cellular wireless CDMA systems under Multipath fading”, Islamic Azad University, Shahr_e_Rey branch, Tehran Iran, 2007

[5] L. Nuaymi, X. Lagrange, P. Godlewski, “A Power Control

Algorithm for 3-G WCDMA System”, email-loutfi.nuaymi

[6] J. Zander, “Transmitter power control for co-channel interference

management in cellular radio systems”, Radio Communication Systems laboratory, Dept. of Teleinformatics, Royal Institute of Technology, Electrum 207, Sweden.

[7] B. Cheng , W. Liu, C. Ma, “A Novel Power Control Algorithm for CDMA systems”, Information and Engineering University, Zhengzhon, china, @IEEE, 2005

[8] K. Dongwoo, C. Kun-Nyeong, K. Sehun, “Efficient Distributed

Power Control for Cellular Mobile Systems”, August-14, 1995.

[9] A. G. Sudheer, V. Rajiv and J.G. David, “Distributed Power Control in Cellular Radio Systems”, IEEE Transactions on communications, Vol. 42 No 2/3/4, February/March/April 1994.

[10] L. Lu, S. Zhu and S. Dong, “Fast Convergence Distributed power

control algorithm for WCDMA Systems”, IEE proc-commun. Vol.

150, No. 2. April 2003.

IJSER©2012 http://www.ijser.org