CHAPTER 4

SUBCHANNEL POWER CONTROL THROUGH INTELLIGENT CONTROLLERS

Power control is essential for MC-CDMA systems to maintain the

communication link quality and capacity under fading and interference conditions.

SlNR based closed loop power control (CLPC) reduces the interference [64] in the

system and hence increases the capacity with guaranteed QoS. The performance of

CLPC depends on the power update rate, the feedback loop delay, the number of

command bits, power step size and fading characteristics of the radio channels. A

subchannel power control mechanism suitable for MC-CDMA systems with the

adaptive adjustment of power and threshold SINR to each user is suggested in this

chapter. A fuzzy PI controller is introduced in the feedback path to perform inner

power control loop and an outer threshold SINR control loop in an adaptive CLPC

scheme. Tuning of fuzzy systems is achieved through genetic algorithm. The

proposed fuzzy genetic algorithm (FGA) controller effectively reduces the

interference with a considerable reduction in BER. This scheme improves the system

capacity and reduces the outage probability significantly even under adverse radio

conditions. Better channel tracking ability of the controller is achieved and is

analyzed through the standard deviation of power control error.

4.2 FUZZY GENETIC ALGORITHM

Power control techniques such as fixed step and multilevel control can be used

in CLPC to accommodate the effects of fading. In these algorithms the transmitted

power is updated using the discrete power control command. Thus, these algorithms

are only a slight modification of integral control. Philip and Nagle [I301 showed that

the integral control alone may make the system unstable. Sripada el a!. [85] proposed

a fuzzy logic controller (FLC) to overcome the drawbacks of the integral control.

Further the above schemes cannot compensate for large channel attenuation around

deep fades, where the occurrence of the bit error is high. This mismatch between the

controllers and time varying error statistics can be compensated by adaptive power

control. In adaptive power control algorithm, mobile station selects the power control

step-size according to the power control bit patterns and mobile speed [65] . The

adaptive power control technique can be effectively implemented through intelligent

controllers.

Initial step of designing a control system is to obtain a mathematical model for

the plant and the controller. This model represents the formulation of prior

information into an analytic structure, but many real world systems have unknown

parameters or highly complex and non linear characteristics. Attempts to overcome

these difficulties paved the way for intelligent controllers like FLC.

In FLC, the measured variables are represented as fuzzy variables [84, 1311. A

representation of the control signals as a fuuy variable is computed from the

measurements using fuzzy logic. In essence, the FLC provides an algorithm which

can convert the linguistic control strategy based on the characteristics of mobile radio

channels into a power control strategy. By using the defuuification, the fuuy control

decisions are converted to a crisp power command which is used to adjust the level of

power step.

Tuning of fuzzy systems is an important step to achieve optimum performance

in the design of fuuy logic controllers. Conventional optimization methods may not

be suitable for the dynamic and nonlinear nature of the wireless channel, as they

require exclusively deterministic operators. Genetic algorithm (GA) is found to be the

better choice for tuning fuzzy systems [I321 which uses only probabilistic transition

operators. The GA is initialized with a set of solutions represented by chromosomes

called a population. Each solution can be represented as either real valued numbers or

a binary string of ones and zeros. These solutions are known as individuals.

Initialize Population + Measure Fitness =

4 Selection

1 1

Mutation

1 Crossover

Not Optimal Solutions

Optimal Solutions

Figure 4.1 Basic outlay of genetic algorithm

Figure 4.2 Fumy genetic algorithm

SIN& +

-dp

- d-

Fuzzy Logic Controller

G A based learning

Initial

f"? partitions

- +

- +

-- - CC

--

Fuuy Rule Base

Figure 4.1 shows the basic outlay of GA. After evaluation the finest individual

from the initial population is selected. Then the genetic operations, mutation and cross

over of each of the selected individuals are carried out. The purpose of mutation is to

change one of the parameters of the parent based on a non-uniform probability

distribution. Crossover is basically meant to create a new individual from two of the

mutated individuals. These individuals ideally contain the best pans of each parent's

genetic material. This process of fitness evaluation, selection, mutation and crossover

continues until the optimum solutions to the problem in question are obtained.

FGA integrates fuzzy inference systems with GA as shown in Figure 4.2 to

improve their advantages and strength [88, 1331. FGA utilizes fuzzy logic to model

the knowledge base and GA to assist in the initial selection and dynamic online

adjustment of the control parameters. An application of controller based on fuzzy

logic combined with GA has been suggested for strength-based [91] and SIR based

power control in CDMA systems. The same technique can be extended to

MC-CDMA systems with SINR based power control.

4.3 OUTER LOOP POWER CONTROL

SINR based CLPC suffers from the problem of power escalation (positive

feedback). When a mobile station is under adverse radio conditions, it increases its

power to compensate for interference from other mobile stations. This increase in

signal power interferes more on all the other mobile stations, which in turn increase

their transmission power, forming a vicious cycle. Instability and power escalation

(also defined as positive feedback) can result [76] while the threshold SINR for each

mobile station remains fixed. This is particularly prevalent when the system is

operating at or closer to the maximum capacity. The increase in capacity causes

interference to the existing users, resulting in positive feedback. In reality, though the

transmission power is controlled, the received SINR at the base station may still have

some variations leading to imperfect CLPC. The level of error may vary from user to

user depending on propagation conditions, mobility speeds, etc. Therefore, in order to

achieve the desired QoS, each user may require a different SINR level. The threshold

SINR of each user needs to be adjusted [73-761 through outer loop power control.

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Data Input I Base band

Amplitier

Spreading

Cyclic Prefix Insertion

Data Output

L7-J Base band

Controller

H Intefligent 1 -1 Controller

d e r Controller

I FFT I

Cyclic Prefix Removal

Mobile Radio

Figure 4.4 Fuzzy llogc power controllers for MC-CDMA reverse link

The PCC is computed for each subchannel separately and sent to the mobile

station through the fonvard link. The power amplifier adjusts the mobile transmitted

power of each subchannel according to their respective PCC issued by the Intelligent

Controller.

4.5 DESIGN OF FUZZY PI CONTROLLER

The controller performance is improved by a fuzzy proportional-plus integral

(PI) control [85, 861, whose input variables are error and error change. In order to

equalize all signal powers received at the base station, the proportional term of fuzzy

PI control will effectively improve transient response, and eliminate the system

instability. Its integral term, however, forces the steady-state error to zero.

The fuzzy logic PI controller generates the fuzzy rule-base, based on the error

( e ) , error change (de) and the dynamics of the process. This provides fast rise time

and minimal peak overshoot with a possible oscillatory behaviour around the set point.

The f u v y PI controller is less sensitive to large parametric changes. The membership

functions (MF) are fuzzified using seven variables such as Large Positive (LP),

Medium Positive (MP). Small Positive (SP), Zero (ZE), Small Negative (SN),

Medium Negative (MN) or Large Negative (LN). The Knowledge base defines the

linguistic control rules and fuzzy data manipulation in fuzzy logic control (FLC) [131].

The control rule tracks the convergence of the closed loop time step response in the

phase plane in the form of IF-THEN statement [86]. The 7x7 fuzzy rules are given in

table 4.1.

Table 4.1 F u z y control rules

fN MN Sh' ZE SP 41P LP

LN LN LN MN M N SN SN ZE MN LN MN M N SN SN ZE SP SN M N MN SN SN ZE SP SP ZE MN SN SN ZE SP SP M P

SP SN SN ZE SP SP MP M P

M P SN ZE SP SP MP MP LP

LP ZE SP SP M P M P LP LP

The inference engine infers the control action by employing fuuy implication

and the control rules. The crisp non-fuzzy control command is obtained by the

centroid defuzzification procedure [84] explained using equation (4.1).

where dp is the adaptive power step size

U , is the nfh sample support value in the universe of discourse and

U is the membership function of U,

The performance of the system is analyzed under the following two situations

i. Fixed SINRth and adaptive power control.

i i . Adaptive SINRth and adaptive power control.

4.5.1 Fixed SINR,h and Adaptive Power Control

The typical fuzzy logic power controller with fixed SlNR threshold is shown

in Figure 4.5. The triangular membership functions for SlNR error (e), the SlNR error

change (de) and the power control step size (dp) as shown in Figure 4.6 are

considered.

'-a'--' Figure 4.5 Controller for fixed SINRtb and adaptive power control

Figure 4.6 Membership functions for r. de, dp and dSI.YR,b

The fuzzy control of the power at the n" sampling period is

dpln) = F(e(n), de(n)l

where

e(n) = SINR,hW - SINRln)

deln) = efn) *(n- / )

SINRh) is the received SINR at the n" sampling period.

F ( l is the fuzzy inference function.

The transmitted power of the f' mobile user with subcamer at (n+l)Ih

power control period is

P,(n+l) = P(n) + dp(n) (4.3)

4.5.2 Adaptive SINR,b and Adaptive Power Control

The fuzzy logic controller incorporating the adaptive power (inner loop) and

the adaptive SINR threshold (outer loop) control [87] is shown in Figure 4.7. The

error (e(n)) and the change in error (de(n)) form the inputs, the outputs are power

control step size (dp(n)) and the threshold SINR control step size (dSINR,h(n)). The

outer loop is performed first, according to the BER requirements of the user, with

fixed a SlNRh value.

Figure 4.7 Controller for adaptive SINRth and adaptive power control

The inner loop is allowed to adjust the transmitted power of the user. The

membership functions for 'e', 'de', 'dp', and ' ~ S ~ N R B ' are as in Figure 4.6. The same

fuzzy inference rules as in Table 4.1 are utilized. Based on the input of e(n) and &(n)

at then" sampling period, the SINRth at the (n+l) "sampling period is,

The values of e(n) and de(n) are defined in (4.2). The SINR* of the mobile at

the (n+l) I h power control period is

The threshold SlNR is adjusted at each sampling period so that it enables a

quick adjustment of SlNR to keep track of fast fading environment. The transmitted

power is controlled with reference to the newly adjusted threshold SMR. Therefore,

e,, ( n ) = SIA'F,, (n + I) - SlNR(n) (4.6)

where em&) is the new SINR error and

de,(n) is SlNR error change at the n" sampling period

The Fuuy control of power at the n" sampling period is

The transmitting power of the mobile at the ( n + ~ ) ' ~ power control period is

The power is updated and transmitted for the next power control period (T,).

The power update rate (I/T,) is an important design parameter to be considered as it

accommodates the effects of channel fading rate and the velocity of the mobile.

4.6 DESIGN O F FGA CONTROLLER

GA is an optimization method based on the mechanism of natural evolution

like selection, recombination and mutation. Compared with the conventional

optimization methods GA manipulates coded versions of the problem instead of

parameters themselves. GA always operates on the whole population points (strings)

[90], while almost all conventional methods search from a single point. This

contributes to the robustness of GA. This improves the chance of reaching global

optimum and, vice versa, reduces the risk of becoming trapped in a local stationary

point. Normally it does not use any auxiliary information about the objective function

value such as derivatives. It is easier to implement. FGA systematically integrates the

GA and fuzzy inference systems. FGA can properly choose and adjust online the

control parameters to new situations. Though the conventional methods are faster,

they can be applied only if the fitness function is sufficiently smooth.

The first step in the optimization of fuzzy systems is to encode the fuzzy sets

into binary strings (chromosomes). The parameters in each chromosome shown in

Table 4.2 include the shape and position of membership functions (MFs), and the rule

bases.

Table 4.2 Chromosome of genetic algorithm

The shape of the MF may be triangular or trapezoidal. The triangular MF is

considered here for simplicity. Three values per fuvy variable are used to

characterize the position of the triangular membership function. The position of each

variable in the MF is coded in binary. There are 7x7 rules in the rule base as given in

Table 4.1. Each rule can be represented by nine parameters.

Position of

MF Output

'dp'

Position of

MF Input

'de'

Shape of

MF

Position of

MF Input

'e'

Position of

MF

'dSMRh'

Rules

In general any control variable like SINR, power etc., may be taken as the

fitness function. As the goal of FGA controller is to minimize the error, average error

is chosen as the fitness function.

The average error (AE) is given by

AE = SINR,, - SINR

B

where SINR,h is the threshold SINR required at the base station

SlNR is the estimated value of SINR at the base station

B is the number of bits of information.

The GA starts with a population of randomly generated solutions,

chromosomes, and advances toward better solutions by applying genetic operators.

The population of solutions for a given problem undergoes evolution in a form of

natural selection. The Roulette Wheel selection algorithm [I321 is used to pick up the

chromosome which gives minimum AE. The two genetic operators, mutation and

crossover are used during the reproduction phase of the GA. The fitness function

returns a single numerical value for a particular chromosome.

4.6.1 Mutation

Mutation is the random deformation of the genetic information of an

individual by radiation or other influences. In real reproduction the probability of

mutation for a single gene is almost the same for all the genes. The most common

method used is to select a sub-tree of a derivation-tree and replaced randomly with

another sub-tree generated randomly by the same method. The non-uniform mutation

technique [90, 132, 1331 used can be explained as follows.

If C,' = (c,. ... ..... ch, ...., cd is a chromosome and the element ch. The position

of 'E' in Figure 4.8 is selected for this mutation. The result is a vector

c, '+l = ( c l , ... c ' i .,,cH/.withh E l . . .H

The new position of E is given by

c 'h = ch+ A(1, chU- chi f a = 0

ch - A(1, ch- chL) f a = 1 (4.1 1)

where

a is random digit in the chromosome that can have a value of 0 or 1

chU is the upper position of point E

chL is the lower position of point E

E is the point selected for mutation

The function A (r,y), the mutation function, returns a value in the range [O,y]

such that the probability of A(t,y) being close to 0 increases as f increases

where

r is a random number in the interval [0,1]

G, is the maximum number of generations and

p is a parameter chosen by the user which determines the degree of

dependency with the number of mutations.

This property causes the operator to perform a uniform search in the initial

space when f is small and varies locally at later stages.

The progress of the mutation algorithm for the MF 'de' is partly illustrated in

Figure 4.8. A random point 'E' is hacked for the study. This undergoes non-uniform

mutation. Part of the path haced by 'E' is given in this figure. The best shape of the

MF obtained after convergence, which is the final result of mutation programme

G t t e n in Marlab is shown in Figure 4.9.

Figure 4.8 Mutation algorithm

Figure 4.9 Best shape of membership functions

Figure 4.10 Crossover algorithm

4.6.2 Crossover

Crossover [90, I321 is the exchange of genes between the chromosomes of

two parents. The selection of an appropriate crossover operator is a more subtle task

for f u v y membership functions. However, if the fitness function is smooth and not

very chaotic, modified crossover operations can speed up the convergence. If the

fitness function is chaotic, which is the case when GA is typically applied, these

operations speed up convergence but with the risk of becoming trapped at local

stationary points.

Figure 4.10 describes the one point crossover algorithm of parent 1 with

parent 2 for the MF of the input 'de ' . The chromosome parents, the cut point

membership function in parent I are randomized first and then allowed to crossover

with parent 2.

The iterative procedure of selection, mutation and crossover is continued till

convergence.

4.6.3 Threshold SINR and Power Control

A similar analysis for power control with fixed threshold SINR as in fuzzy PI

control algorithm is carried out with FGA controller. The adaptive adjustment of

threshold SINR and power 1911 is explained here. Based on the input of e(n) and de(n)

at the nIh sampling period, the dSINR,h at the (n+ 1) I h sampling period is

The SINR,h of the mobtle at the n+I lh power control penod IS*/* ---*'" -b,, ,/- .- x

SINR, ( n +I) = SINR, ( n ) - &NR, ( n + I) 1'

The adjustment of SMFQh of each user follows the variation trend of the

received SINR. The SIN& is n d j u ~ d (I al sampling p.'ifbaso.that it enables a

quick adjustment to SINQ to keep track of the fast fading environment. The power

control is performed after each SINRth adjustment. The transmitted power is

controlled with reference to the newly adjusted target SINR,h. Therefore,

The FGA controlled power at the nIh sampling period is

The transmitted power of the mobile at the ( ~ + I J ' ~ power control period is

Thus the power control command at the ( n + l f h power control period is used

to adjust the transmitted power of the mobile through a power amplifier.

4.7 SIMULATION RESULTS AND DISCUSSION

The simulation is performed using Marlab. The simulation parameters are given

in Table 4.3.

Table 4 3 Simulation parameters for fuzzy logic power control scheme

PARAMETERS

Number of usen

Normalized Doppler frequency (fbT,) Mobile speed (Kmh)

Power control sampling period (ms) FFT size

Guard interval ps

VALUES

5 to 50

[0.01.0.1] 5 to 100

0.43

1024

3.75

The BER performance of the system under consideration is investigated as a

function of threshold SMR at a constant channel fading rate, with a mobile speed of

40 K m h and a power control period of 0.5 ms. Figures 4.1 1 to 4.13 show the BER

performance for various rypes of power control schemes with different number of

carriers (8, 32 and 64) per channel. From these figures it is evident that Figure 4.1 1

with 8 subcarriers per subchannel shows a better performance than the other two. As

the number of subcarriers in a subchannel increases the number of power conhollers

required is reduced. This causes low computational complexity at the cost of BER

performance. These figures also reveal that the adaptive threshold SINR outperforms

the fixed threshold SINR with respect to BER. Within adaptive or fixed threshold

SINR, the decreasing order of BER performance was noticed from FGA power

controller through the f w y PI to the conventional power controllers.

The fading rate of channels represented as Doppler frequency VD) varies with

the speed of the mobile. Effects of this time varying channel conditions required to be

tracked and compensated. The power control period (Tp) can be adjusted to improve

the performance. This channel tracking ability is analyzed by computing the standard

deviation of power control error as a function of the channel fading rate. It follows

from Figure 4.14 that the standard deviation of power control error for all the schemes

is different at high channel fading rates but this difference is reduced as the fading

rate decreases. The result of these curves can be used as design parameters to develop

a suitable power controller appropriate to the mobile speed.

The outage probability, the probability of failing to achieve the minimum

required SINR, is a measure of performance mobile system. The outage probability

curves in Figure 4.15 reveal that with increasing number of users the outage

probability increases. Among different power control schemes tested, better

performance was observed with the use of FGA controller with adaptive threshold

SINR.

- -- -- - --

Conventlonat C Fuzzy * FGA 4- Conmnt~onal j

Fuzzy " FGA

- - -

d 4 '. F~xed SINR th

\ I * . .\ lo4 Adaptlm SlNRth 4

A

lo5 - - . 0 2 4 6 8 10 12 14 16 18 20

SlNR In dB

Figure 4.1 1 BER as a function of SINR with 8 carriersisubchannel

- -

- * Conwnt~onal * Fuzzy * FGA

+ - Conwntlonal - Fuzzy

+ C FGA Y t - . - -

lo5 - 0 2 4 6 8 10 12 14 16 18 20

SINR In dB

Figure 4.12 BER function of SINR with 32 carriers /channel

- * F u z z y - t FGA

Conwnt~onal - Fuzzy

- FGA X

-

m 'r, 1

-,zxed SlNRfh

. m * /A a m - , - = =

l o 1 - - - - - - 0 2 4 6 8 10 12 14 16 18 20

SlNR In dB

Figure 4 13 BER function of S l N R with 64 carriers /channel

4 5 - - - - - -

' wlth fixed step power control ,A

wlth fuzzy PI power control 4 with FGA power control -

-,

1 - - 0 0 0 2 0 0 4 0 0 6 0 0 8 0 1 0 1 2 0 1 4 0 1 6 0 1 8 0 2

Normallzed speed fDTp

Figure 4.14 Power control error as a function of fDTp

- - - - - - - - -

-iF wlth fixed step Dower control - - mth fuzzy power control

- rL wth FGA control - - - - - -

Number of users

Figure 4.15 Outage probability curves with adaptive SINR,h

4.8 SUMMARY

A reverse link power control technique using intelligent controllers for

MC-CDM.4 radio interfacing has been proposed. The simulation study has shown that

the adaptabilit! of threshold SINR is crucial lo the SlNR based power controllers. The

power control and adaptive ad,justment of threshold SINR of each subchannel

according to the time varying conditions of the channel utilizing the FGA controller

has contributed to enhance the capacity with guaranteed QoS. 41so it has been shown

to reduce the outage probabilit) significantly and better channel tracking ability