BYMR.BHARGABJYOTI SAIKIA;DUDR.RUPABAN SUBADAR;NEHU

Effect of perfect &imperfect CSI on OPRA Technique

for M-QAM over Nakagami-m fading channel

I3CS15_Conference;NEHU;9-10 April-2015

OUTLINE

Introduction and motivation.System model.Nakagami-m fading channels.OPRA for perfect CSI.OPRA for imperfect CSI.Result and AnalysisConclusion.References.

Introduction and motivation

Fading is a major problem in wireless communication.

Received signal quality and channel capacity decrease due to fading.

Adaptive transmission can increase channel capacity.CSI is required for adaptive techniques.Perfect CSI is a ideal consideration.Imperfect CSI is very much important to wireless

system design.

System model

Fig1: System model for adaptive transmission

Optimum Power and Rate Adaptation Technique has been considered[1][15].

[15]Saikia Bhargabjyoti, Subadar Rupaban , “Capacity Analysis of Adaptive Techniques for MQAM over TWDP Fading Channel” Proceeding of IEEE International Conference on Power and Energy [ICPEN 2012];NERIST; Nirjuli;p.p:1-4;December (2012)

[1]Ali Olfat and Mohammad Shikh-Bahaei , ”Optimum Power and Rate Adaptation with Imperfect ChannelEstimation for MQAM in Rayleigh Flat Fading Channel” IEEE Transactions and Vehicular Technology,vol 57,No 4,pp. 2622,July 2008

Nakagami-m fading channels

Nakagami-m is a central chi-square distribution.

‘m’ parameter range is from ½ to The SNR per symbol is distributed

according to the Gamma distribution given by [12],

1

exp( )

m mm m

m

[12] M. Nakagami, “The m-distribution-A general formula of intensity distribution of rapid fading,” Statis-tical Methods in Radio Wave Propagation, W. G. Hoffman, Ed. Oxford, England: Pergamon, 1960.

OPRA for perfect CSI

For an adaptive system as shown in fig.1 the channel capacity (in bits/sec) for OPRA is given by [15],

Where, and ; is the cut off SNR .

The cut off SNR must satisfies the condition,

For uncoded MQAM the BER is given by ,

2logk

oprak

B dC

0k s

1.5

ln / 2S

BER

0

1 1

k k

d s

1.512

SNR

MBER e

OPRA for perfect CSI

The channel capacity for OPRA over a perfect channel considering uncoded MQAM can be expressed as,

(1) Where, the incomplete Gamma functionIn above equation should satisfy, (2)

1

20

,1 !

log!

km m

opra mkk

mk

mC B e

km

,a b

k

1

11,

21 , 1

m

k

m

m mm mm

s m

m mmm

OPRA for imperfect CSI

For imperfect CSI the model shown in Fig. 1 considering the BER bounds and flat-fading channels with MQAM is given by [1],

(3)

Where,C1 and C2 indicate two positive constant. M is

the size of transmitting constellation.

21

( )( , ) exp

1

C SBER C

M S

OPRA for imperfect CSI

For an instantaneous BER the conditional expectation of BER ,when the is known is given by [1],

(4)

where denotes the conditional probability density function of and .

( , )

2

1

0

exp ,1

SCBER C d

SM

OPRA for imperfect CSI

The conditional PDF for Nakagami-m distribution (for and )is given by [5],

(5)

Where, and and and is the modified Bessel function of

order m-1.

12

m 1

1

2I exp

1 1

m

m

mm

E E 1 2cov , var var

m 1I (.)

[5] Jun Zhang, Marios Kountouris, Jeffrey G. Andrews, Robert W. Heath, ”Multi-Mode Transmission forthe MIMO Broadcast Channel with Imperfect Channel State Information” IEEE Transaction On Communications, Vol. 59, No. 3, pp.803-814, March 2011.

OPRA for imperfect CSI

Substituting equation (5)into equation (4) and using PSAM the expression can be bounded as,

(6)

Where,

Assuming and it can be said that always lies between 0 and 1 for all values of .

1 exp 11

mBER C f f

1

2 111

SCf

m S M

( ) 0S 1M f

OPRA for imperfect CSI

From given eq. (6)it is difficult to express optimum power and rate adaptation in its closed form.

But if we consider the approximation of eq.(6) then it is easy to expressed OPRA in to its closed form, which is named as Sub-OPRA .The equation can be modified as,

(7)

1 exp 11

mBER C f

OPRA for imperfect CSI

Fig:2 shows a comparison between the OPRA and Sub-OPRA for different values of ‘m.’

The difference is negligible between OPRA and SUB OPRA as .

1

OPRA for imperfect CSI

For Nakagami-m the sub optimal solution for power adaptation is given by,

Where, and should satisfies the condition,

0

0

1 1max

0................................

T

TT

S

SOtherwise

11

ln .T

C

m

0 T

0 0

1 11T

TT

d

OPRA for imperfect CSI

In this way for rate adaptation the expression can be given by,

Now the spectral efficiency can be calculated as,

Where,

00( )

1............................

T

TM

otherwise

0

0

2 2log ( ) log

T

TE M d

1

exp( )

mmm m

m

Result and Analysis

Fig 3: Spectral efficiency for OPRA considering a perfect Channel.

Result and Analysis

Fig 4: Spectral efficiency for OPRA considering an imperfect Channel.

Result and Analysis

Table:1: Comparison between different calculated values considering perfect and imperfect CSI for 20 dB SNR

Conclusion

In this paper analysis have been given to the spectral efficiency of an OPRA system considering MQAM modulation over slow varying Nakagami-m fading channels.

We compare the spectral efficiency considering perfect CSI with the calculated spectral efficiency for imperfect CSI.

The numerically evaluated results show that the spectral efficiency decreases considerably, for imperfect CSI.

References

[1] Ali Olfat and Mohammad Shikh-Bahaei , ”Optimum Power and Rate Adaptation with Imperfect ChannelEstimation for MQAM in Rayleigh Flat Fading Channel” IEEE Transactions and Vehicular Technology,vol 57,No 4,pp. 2622,July 2008

[2] Muriel Mdard , ”The Effect upon Channel Capacity in Wireless Communications of Perfect and ImperfectKnowledge of the Channel” IEEE Transactions on Information Theory, Vol. 46, No. 3,pp. 933-946, may2000

[3] Jos F. Paris, M. Carmen Aguayo-Torres, and Jos T. Entrambasaguas , ”Impact of Channel EstimationError on Adaptive Modulation Performance in Flat Fading” IEEE Transactions on Communications,pp. 716-720, May 2004

[4] Xiaoyi Tang, Mohamed-Slim Alouini and Andrea J. Goldsmith , ”Effect of Channel Estimation Error onM-QAM BER Performance in Rayleigh Fading” IEEE Transactions On Communications, Vol. 47, No.12, pp.1856-1864,December1999

[5] Jun Zhang, Marios Kountouris, Jeffrey G. Andrews, Robert W. Heath, ”Multi-Mode Transmission forthe MIMO Broadcast Channel with Imperfect Channel State Information” IEEE Transaction On Communications, Vol. 59, No. 3, pp.803-814, March 2011.

[6] Zouheir Rezki, Mohamed-Slim Alouini, ”Ergodic Capacity of Cognitive Radio Under Imperfect ChannelState Information” IEEE Transaction on Vehicular Technology, Vol. 61, No. 5, pp. 2108-2119June 2012.

[7] Xiangbin Yu, Wenting Tan, Shu-Hung Leung, Yun Rui, Xin Yin, Xiaoshuai Liu, ”Discrete-rate adaptivemodulation with optimum switching thresholds for space-time coded multipleinput multiple-outputsystem with imperfect channel state information” IET Communications, Vol. 7, Iss. 6, pp. 521-530,December 2012

[8] Hongyu Cui, Rongqing Zhang, Lingyang Song, Bingli Jiao, ”Capacity Analysis of Bidirectional AF RelaySelection with Imperfect Channel State Information” IEEE Wireless Communication Letters, Vol. 2, No.3, June 2013.

[9] Xiaoming Chen, Chau Yuen, and Zhaoyang Zhang, ”Wireless Energy and Information Transfer Tradeofffor Limited-Feedback Multiantenna Systems With Energy Beamforming ” IEEE Transaction on Vehic-ular Technology, Vol. 63, No. 1,pp. 407-412, January 2014

[10] Mehdi M. Molu and Norbert Goertz, ”Optimal Precoding in the Relay and the Optimality of LargestEigenmode Relaying with Statistical Channel State Information” IEEE Transaction on Wireless Com-munications,Vol. 13, No. 4,pp. 2113-2123, April 2014

[11] Ying Zhang, Huapeng Zhao, and Chuanyi Pan, ”Optimization of an Amplify-and-Forward Relay NetworkConsidering Time Delay and Estimation Error in Channel State Information ” IEEE Transactionon Vehicular Technology, Vol. 63, No. 5,pp.2483-2488,June 2014

 

References

[12] M. Nakagami, “The m-distribution-A general formula of intensity distribution of rapid fading,” Statis-tical Methods in Radio Wave Propagation, W. G. Hoffman, Ed. Oxford, England: Pergamon, 1960.

[13] Mohamed-Slim Alouini and Andrea J. Goldsmith , ”Adaptive Modulation over Nakagami Fading Channels” Wireless Personal Communications,Vol 13,issue 1-2,pp.119-143,May 2000

[14] Xiaodong Cai,, and Georgios B. Giannakis , ”Adaptive PSAM Accounting for Channel Estimation and Prediction Errors” IEEE Transactions on Wireless Communications, Vol. 4, No. 1, pp. 246256,January 2005

[15]Saikia Bhargabjyoti, Subadar Rupaban , “Capacity Analysis of Adaptive Techniques for MQAM over TWDP Fading Channel” Proceeding of IEEE International Conference on Power and Energy [ICPEN 2012];NERIST; Nirjuli;p.p:1-4;December (2012)

Thank you