EXPERIMENTAL WIRELESS CHANNEL MODEL DERIVATION Sergey D. Andreev - - PowerPoint PPT Presentation

EXPERIMENTAL WIRELESS CHANNEL MODEL DERIVATION

Sergey D. Andreev State University of Aerospace Instrumentation (SUAI) Serge.Andreev@gmail.com

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Session Outline

n Research Focus n MAC Throughput Measurement n Packet Error Rate Measurement n Hidden Markov Models Summary n Appropriate State Space Selection n 2-state Model Description

and Parameters Derivation

n Conclusion

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Research Focus

Application Presentation Session Transport Network Data Link Physical (PHY)

OSI Layers Logical Link Control (LLC) Media Access Control (MAC) Broadcast Communications Channel

Consider IEEE 802.11g (WiFi) telecommunications standard Infrastructure mode ‘Ad-hoc’ mode

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DCF Mode Operation

n Distributed Coordination Function

(DCF) is a randomized channel access scheme

n Packet corruption and

collisions are handled by Automatic Repeat reQuest (ARQ) mechanism that relies

• n packet retransmission

n Retransmission obscures

real channel situation for the upper layers as the actual number of retransmissions is a random variable

Successful Tx Unsuccessful Tx

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Problem Statement

n Measure IEEE 802.11g MAC throughput

with high time resolution (required for real- time video transmission modeling)

n Obtain mean packet error rate without

packet retransmission

n Collect realistic packet error traces n Build appropriate error source model

(required to calculate transport coding parameters)

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Expected MAC Throughput

n

Follow Bianchi (2000) approach to calculate throughput in saturation conditions

n

Gap between PHY rate and MAC throughput increases as rate grows

Main considerations

n

To measure actual throughput adequately retransmission should be disabled!

n

Existing tools are incapable of measuring throughput with high time resolution*

M a x i m u m p

• s

s i b l e t h r

• u

g h p u t

* see discussion in S. Andreev, S. Semenov, A. Turlikov “Methods of estimation

• f radiochannel parameters”, 2007

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Proposed Measuring Methodology

1 2 1

‘Head’ packet ‘Tail’ packets Lost packet Initial delay Delay Time Time Experiment finish

n n

N N 1 N − 1 N −

T T′

... ...

t t′

... ... 2 N − 2 N −

Experiment finish

Lbytes

Sender Receiver

‘User-to-AP’ scenario Measured throughput accords with Bianchi theoretical estimation!

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Packet Error Rate (PER) Measurement

n

Average PER with disabled retransmission is below 1%

n

A model is needed to describe PER behavior for realistic packet error traces

n

Main target: maintain simplicity – precision balance

n

Renown technique is to use Hidden Markov Models (HMM)

: i

Packet error trace

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Hidden Markov Model (HMM) Summary

Canonical problems

n

Compute the probability of a particular output sequence for known parameters (forward-backward algorithm)

n

Find the most likely sequence of hidden states for known parameters

(Viterbi algorithm)

n

Find the most likely set of state transition and emission probabilities given an output sequence of (Baum-Welch algorithm*)

s0 s3 s2 s1

i

... ... x0 x1 x2 x3

i

...

State transitions State emissions Emitted tokens States

i

Given by transition and emission probability matrices

* is highly complex and requires initial estimates of the transition and emission matrices

1,1 1,2 , 1 2,1 2,2

... Pr{ | } ... ... ... ...

i j t t

p p p s j s i p p

+

    = = = =      

1,1 1,2 , 2,1 2,2

... Pr{ | } ... ... ... ...

i j t t

e e e x j s i e e     = = = =      

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Binary Symmetric Channel (BSC) Assumption

PMF for the number of successful packets between two consecutive error packets: theory (dotted) and practice (solid) CDF for the number of successful packets between two consecutive error packets: theory (dotted) and practice (solid)

( ) Pr( ) CDF x X x = ≤ Pr( ), ( ) 0, \ X x x S PMF x x R S = ∈  =  ∈ 

: i

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Previous Models

n Bit level models (PHY bit inversion probability)

q Gilbert model, 1960 q Gilbert-Elliott model, 1963 q Wang et al., Zorzi et al., 1995-96

(relevance of the 2-state model)

q Lyakhov et al., 2004

(2-state model for WiFi with retransmissions) n Packet level models (Use with packet error traces)

q Zorzi et al., 1997

(2-state model is good at packet level)

q Giao et al., Konrad et al., 1996-2001 (realistic data) q Wang et al., 1995 (larger Markov chain state space)

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2-state HMM Definition

n Markov chain transition probabilities: n Matrix 2-state model: n Probability of a given error sequence: n Easy way to calculate characteristics

      = ) / ( ) / ( ) / ( ) / ( b b p b g p g b p g g p P

( / ) ( / ) (0) ( / ) ( / )

g b g b

q p g g q p b g A q p g b q p b b   =     ( / ) ( / ) (1) ( / ) ( / )

g b g b

p p g g p p b g A p p g b p p b b   =    

)) ( ), ( ( b p g p a =

T

b ) 1 , 1 (

0 =

1 2 1

) ( ) ,..., , ( ) ( b e A a e e e p e p

n i i n

⋅ = =

∏

=

) , ( n m P

1

1 1 1 1

( ) ( ) ( | ) ( | ) ( | ) ( | )

n

n n n n s s s

p e p s p s s p e s p s s p e s

−

= ⋅ ⋅ ⋅ ⋅ ⋅

∑∑ ∑

K K

instead of

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Model Parameters Derivation

n Denote and the sequences of zeros and ones: n The resulting expressions* for the 2-state model:

0i

1j

i

j

2 2 3 00 2 2

(0 ) (0) (0 ) (0 ) (0) p p p a p p − = −

3 2 01 2 2

(0 ) (0) (0 ) (0 ) (0) p p p a p p − = −

2 2 3 10 2 2

(1 ) (1) (1 ) (1 ) (1) p p p a p p − = −

3 2 11 2 2

(1 ) (1) (1 ) (1 ) (1) p p p a p p − = −

00 10 11 01

1 1 a a A a a − = + + −

10 11 01

1 a B a a − = + −

2

4 2

b

A A B p + − =

2

4 2

g

A A B p − − =

11 01 11

( ) ( / )

g g b

a a p a p b b p p + − = −

11 11 01

( ) ( / )

b g b

a p a a p g g p p − + = −

( / ) 0.9999 p g g = ( / ) 0.9188 p b b =

0.0044

g

p =

0.5423

b

p =

* see discussion in S. Andreev, A. Vinel “Gilbert-Elliott Model Parameters Derivation for the IEEE 802.11 Wireless Channel”, 2007

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Conclusion

n Achievements

q

A method to measure MAC throughput with high time resolution is introduced

q

Realistic packet error traces of IEEE 802.11g are obtained

q

Appropriate hidden Markov model selection is addressed

q

2-state wireless experimental model is built

q

The results are published in 2 articles during 2007

n Open problems

q

Perform goodness-of-fit check of a introduced model

q

Account for ‘peaks’ in the experimental PMF

q

Compare the derived model with alternatives

(e. g. D. Moltchanov “Cross-layer performance evaluation and control

• f wireless channels in NG All-IP networks”, Ph.D. thesis, 2006)

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Discussion

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