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A Game theoretic Power Control algorithm with Pricing for Spectral Efficient Communication in MIMO MC-DS/ CDMA System V.Nagarajan and P.Dananjayan† Department of Electronics and Communication Engineering, Pondicherry Engineering College, Pondicherry -605014, India [email protected], [email protected] †Corresponding author A distributed non cooperative power control game with pricing (NPGP) for multiple-input multiple-output (MIMO) multi-carrier direct sequence code division multiple access (MC -DS/ CDMA) system for different modulation is considered in this work. The utility functions for assaying the performance of MIMO MC-DS /CDMA for spectral efficient communication of the system carrying wireless data are envisaged. The spectral efficiency and power efficiency are referred as utility which divulges the level of satisfaction a user may get. According to the utility functions, two NPGP’s are propounded, which determines the existence and individuality of the Nash equilibria. A novel power control algorithm that delves the performance of the anticipated power control games to achieve the Nash equilibria is presented in this paper. The simulated results elucidate that a significant amelioration in terms of utilities specifically spectral efficiency for all users can be achieved using this approach. Also the propounded scheme exhibits better performance in the MIMO MC-DS /CDMA in terms of spectral efficiency as compared to the traditional system. Index Terms—MC-DS CDMA, MIMO, Pricing

I. INTRODUCTION The enormous growth of wireless services during the last decade gives rise to the need for a bandwidth efficient modulation technique that can reliably transmit high data rates. As Multi carrier technique combine good bandwidth efficiency with an immunity to channel dispersion, these technique have received considerable attention. In tandem the demand for wireless services increases, efficient use of resources has gained a significant importance. Also there is need for obtaining very high data rate which is the prime aim of future communication. Hence there has always been a need for spectral efficient communication. The elemental component of radio resource management is transmitter power control. It is well know that mitigating interference using power control algorithm increases the capacity and also extends battery life. Ever increasing need for wireless systems to provide high data transmission rates needs a system which performs well under severe fading conditions. To meet these demands MIMO MCDS /CDMA is an excellent candidate. In spite of the fact that, the performance of MC-DS/CDMA is limited by multiple access interference (MAI) in addition to the near-far effect, power control algorithm plays a vital role in combating these effects. Though MIMO MC-DS/CDMA system has much better performance compared with single antenna MC-DS /CDMA, it still comes into the CDMA traditional impairments [1]. The challenge to augment the performance of a MIMO MC-DS /CDMA consequently lies in the techniques of interference suppression and power control for a MIMO multi user system. Recently, an alternative approach to the power control problem in wireless systems based on an economic model has been offered. In this model, service preferences for each user

are represented by a utility function. As the name implies, the utility function quantifies the level of satisfaction a user gets from using the system resources. Game theoretic methods are applied to study power control under this new model [2]. Game theory is a powerful tool in modeling interactions between self-interested users and predicting their choice of strategies. Each player in the game maximizes some function of utility in a distributed fashion [3]. The game settles at Nash equilibrium if one exists. Since users act selfishly, the equilibrium point is not necessarily the best operating point from a social point of view. Pricing the system resources appears to be a powerful tool for achieving a more socially desirable result [2,3]. In the MC-DS/CDMA, raising one’s power level not only increases their signal-to interference-and–noise ratio (SINR), but also increases the interference observed by other users. This drives the SINR of other users to decrease which in turn will force other users to increase their own power levels to reach the Nash equilibrium. To overcome this situation a distributed game theoretic power control algorithm to provide efficient use of the radio resources in CDMA system has been established [4, 5]. The power control problem in multi-user MIMO MC-DS-CDMA system, using game theory framework for various modulation techniques has been proposed in this work. A new utility functions for the NPG (non cooperative power control game) by using singular value decomposition (SVD) is proposed to solve the problem. The new utility functions, which are based on MIMO MC-DS /CDMA system for wireless data, refer to the spectral efficiency, power efficiency. Then Nash equilibria and the performance of the power control games in a single cell MIMO MC- DS/ CDMA system is considered. In this paper the power control for MlMO MC- DS /CDMA systems is considered for various modulation techniques. The game theory approach is implemented to use the system resource more efficiently

The paper is organized as follows. Section II explains MIMO MC–DS/CDMA system and the utility function of the power control game. Section III shows the two NMPCGs (non cooperative MIMO power control game with pricing) for the MIMO MC–DS/ CDMA system. Section IV discusses the existence and uniqueness of the games and the algorithm to reach the Nash equilibrium with proposed game theoretic power control algorithm for MIMO MC-DS/CDMA system for different modulation. Simulation results are given and discussed in section V. Finally, Section VI draws the conclusion. II. MIMO MC FUNCTIONS:

–DS/

CDMA SYSTEM

AND

.

H i =U i

where

iV i =

U i( k )

{

k =1

Vi( k )

and

}

U i ( k ) i ( k )V i ( k )

are

M r×I

and

(1) M t×I

unitary

( k )

are the singular values of Hi. vectors, respectively, and i The per-user attainable normalized throughput, in bit per second Hertz, of MIMO MC- DS /CDMA system is the sum of the normalized throughputs of the min (Mt, Mr) decoupled sub channels. Then the normalized throughput of ith user is given in Eq.(2).

{

}

min Mt ,Mr T = i

k=1

{

}

min Mt ,Mr N 1 L Tk ,i = log Mk ,i 1 BER ,i k 2 k=1 S=1

( ))

(

th

um = T / P i i i

{

=

th

k,i is to represent the SINR of i user in k sub channel, which

is using sub carrier for convenience. Since each antenna can accommodates sub carriers, the total throughput will be the summation of the throughput of individual carrier. In order to solve the power control problem in the MIMO MC –DS/

(

{

( ))

}

(3)

min Mt ,Mr N 1 Pk ,i k=1 S=1

The power control utility function is given in Eq (4)

{

}

min Mt ,Mr N 1 L log Mk ,i 1 2 BER k ,i 2 k=1 S=1

u = i

(

{

( ))

}

min Mt ,Mr N 1 Pk ,i k=1 S=1

{

=

where,

}

min Mt ,Mr N 1 log Mk ,i f k ,i 2 k=1 N=1

( )

{

(4)

}

min Mt ,Mr N 1 Pk ,i k=1 S=1 f

k ,i

=

(1 2 BER ( k ,i ))

L

is

called

efficiency

function. The frame successive rate (FSR) is approximated by f ( i ) , which closely follows the behaviour of the probability of correct reception while producing FSR equals zero at Pi =0. The pricing mechanism was introduced into the CDMA non-cooperative power control game. By using the pricing mechanism, the power control game was more efficient. A new utility function with pricing in MIMO MC-DS/CDMA power control game is developed. It is expressed in Eq. (5)

{

}

min M t , M r N 1 u

c i

k =1

=

S =1

log

Pi

{

(2) where

}

min Mt ,Mr N 1 L log M 1 BER 2 k ,i k ,i k=1 S=1

UTILITY

The uplink of a single cell N-users MIMO MC- DS/ CDMA system with feedback is considered for our analysis. Each user is assumed to have Mt transmit antennas and the base station is equipped with Mt x Mr antennas. Each antenna is capable of transmitting 1x Mr subchannel. Subcarriers and processing gain G are considered. In this system, the user's bit stream is demultiplexed among several transmitting antennas, each of which transmits an independently modulated signal, simultaneously and in the same frequency band. The base station receives these signal components by an antenna array whose sensor outputs are processed such that the original data stream can be recovered. Assume that the channel state information (CSI) is perfectly known to receiver, and the transmitter can get the CSI through feedback. Assume H, which is the channel matrix of user i can be decomposed using SVD is given in Eq. (1). m in M t ,M r

CDMA system, a marginal utility function which is expressed in Eq (3) is established.

}

min M t , M r N 1 Pi = k =1 Pk ,i S =1

2

M k ,i f

( k ,i ) tP i

(5)

where Pi is the total transmitting power of the ith user, and t is a positive scalar. This proposed utility function, which gives attention to both spectral efficiency and power efficiency, are based on MlMO MC- DS/ CDMA system.

III. NON COOPERATIVE MIMO POWER CONTROL GAME Let G = N ,{ Ai},{Ui (.)}

denote the non cooperative

A. The NMCPG, GI, G2 are supermodular games with appropriate strategy space Ai = P i , Pi

MlMO power control game (NMCPG) where N = {l, 2... N} is the index set for the mobile users currently in the cell. The ith

Consider the game G1 first.

user select a total transmit power strategy Pi , such that

P i A i where Ai , denotes the strategy space of ith user. Let the vector P =( P1,........, PN ) denote the outcome of the game in terms of the selected power levels of all users, and P-i, denotes the vector consisting of elements of P other than the ith element. The strategy space of all the users excluding the ith user is denoted A-i. According to the analysis, two NMCPGs are established. All of these games have the same player space and strategy space, but different utility functions The game G1 is given by, min{M t , M r } N G1 =

max Pi Ai

S =1

k =1

U1 i ( Pi , P i ) =

log

2

M

k ,i

f

=

1 Pi 2

{

k =1

2u 1 li = 2 Pi P j Pi

(

(

}

min M t , M r

k ,i

)

2

)

2f

( k ,i )

N 1 S =1

{

log 2 M k , i

min M t , M r k =1

}

N =1 S =1

( k ,i )

f

(

log 2 M k , i

( k ,i ) f ( k ,i ) k ,i )

( k ,i )

2f

(

(6)

}

Pi

form

(

can

be

2 k ,i

Ai = P i , Pi tPi

(7) for all i

( k ,i ) 2

k ,i

k ,i Pj

)

(9)

2u li

0

)

0,

it can guarantee

concluded

that

2u li Pi Pj

with

the 2f

min Mt ,Mr N 1 log2 Mk,i f k ,i k=1 S=1

(8)

, it can be concluded that P P for all jLi. k ,i i j Assume there exists a P-i such that 0