stochastic power control for short-term flat fading wireless networks: almost sure qos measures c....
TRANSCRIPT
Stochastic Power Control for Short-Term Flat Fading Wireless Networks: Almost Sure QoS
Measures
C. D. Charalambous1, S. Z. Denic2,
S. M. Djouadi3, N. Menemenlis4
University of Ottawa1,2, University of Arkansas3,
McGill University4
2001 CDC, Dec. 4-7, Orlando, FL
2
Outline
Review of the Power Control Problem Probabilistic QoS Measures Modeling of Log-Normal Shadowing
• Log-Normal SDE’s Stochastic Optimal Control
• Predictable Strategies• Linear Programming
3
QoS Measures
Review of the Power Control Problem
4
QoS Measures
Vector Form [Yates 1981]
Then
)(;10
min GPPGp Ii
M
ip j
5
QoS Measures
Probabilistic QoS MeasuresDefine
The Constraints are equivalent to
MnpI n ,...,2,1,0)(
6
QoS Measures Decentralized Probabilistic QoS
7
QoS Measures
8
QoS Measures Centralized Probabilistic QoS
9
Log-Normal Shadowing
Received Power
Power Path Loss
10
Large-Scale Shadowing
Attenuation Coefficient
11
Large-Scale Shadowing
Log-Normal Attenuation Coefficient
Log-Normal power Path Loss
12
Stochastic Models
Attenuation Coefficient
Power Path Loss
13
Temporal Power-Loss/ Attenuation
Mean-Reverting Power-Loss
14
Space-Time Mean-Reverting Power-Loss
15
Space-Time Mean-Reverting Power-Loss
16
QoS Measures
Stochastic Optimal Control• Received Signal
• State Space Representation
)()()()( tdtStstu nnjjj
}]exp{[ njnj kXS
njdnj
njnjnjnjnjnj
dBdPLtX
tdBtdttXtttdX
])[(),(
)(),()),()),()(,(),(
0
17
QoS Measures
• Pathwise QoS and Predictable Strategies
Define
Then
where
Sts j )( )()( tSts njj
nkS;)( dttpi
18
QoS Measures
Define
)()( tSts nini
19
QoS Measures• Predictable Strategies over the interval
• Predictable Strategies Linear Programming
],[ 1kk tt
)(tSnk
20
QoS Measures
21
QoS Measures
)()( tSts nn
)()( tSts nn
)()( tSts jj nnSs
)( 1kt
22
QoS Measures
Generalizations• Linear Programming
• Stochastic Optimal Control with Integral/Exponential-of-Integral Constraints
)(tSnk
)(tSnk
23
Conclusions
Predictable Strategies and Dynamic
Models Linear Programming
Probabilistic QoS Measures
Stochastic Optimal Control Linear Programming