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 PDF created with pdfFactory Pro trial version www.pdffactory.com

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 2 PDF created with pdfFactory Pro trial version www.pdffactory.com

Research Focus OSI Layers Application Logical Link Presentation Control Session (LLC) Transport Media Access Network Control (MAC) Data Link Physical (PHY) Consider IEEE 802.11g (WiFi) Broadcast Communications Channel telecommunications standard ‘Ad-hoc’ mode Infrastructure mode 3 PDF created with pdfFactory Pro trial version www.pdffactory.com

DCF Mode Operation n Distributed Coordination Function (DCF) is a randomized channel access scheme n Packet corruption and collisions are handled by Successful Tx Automatic Repeat reQuest (ARQ) mechanism that relies on packet retransmission n Retransmission obscures Unsuccessful Tx real channel situation for the upper layers as the actual number of retransmissions is a random variable 4 PDF created with pdfFactory Pro trial version www.pdffactory.com

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) 5 PDF created with pdfFactory Pro trial version www.pdffactory.com

Expected MAC Throughput Follow Bianchi (2000) approach n to calculate throughput in saturation conditions e l b i s s o p t m u p u h m Gap between PHY rate and g i x u a o n M r h t MAC throughput increases as rate grows Main considerations To measure actual throughput adequately retransmission n should be disabled! Existing tools are incapable of measuring throughput with high n time resolution* * see discussion in S. Andreev, S. Semenov, A. Turlikov “Methods of estimation 6 of radiochannel parameters”, 2007 PDF created with pdfFactory Pro trial version www.pdffactory.com

Proposed Measuring Methodology Sender t Experiment ‘Tail’ packets finish ‘Head’ packet ... ... N − N − n 1 2 N 0 1 2 t ′ Receiver T Experiment Time finish Lost L bytes packet ... ... N − N − n 1 2 N 0 1 T ′ Time Initial Delay delay ‘User-to-AP’ scenario Measured throughput accords with Bianchi theoretical estimation! 7 PDF created with pdfFactory Pro trial version www.pdffactory.com

Packet Error Rate (PER) Measurement Packet error trace : i Average PER with disabled retransmission is below 1% n A model is needed to describe PER behavior for realistic n packet error traces Main target: maintain simplicity – precision balance n Renown technique is to use Hidden Markov Models (HMM) n 8 PDF created with pdfFactory Pro trial version www.pdffactory.com

Hidden Markov Model (HMM) Summary Given by transition and emission probability matrices State transitions   ... i p p ... ... s1 s2 s3 s0 States 1,1 1,2   = = = =  Pr{ | } ... p s j s i p p  + , 1 2,1 2,2 ... i j t t    ... ... ...  State emissions   i ... e e x0 x1 x2 x3 1,1 1,2 Emitted tokens   = = = =  Pr{ | } ... e x j s i e e  , 2,1 2,2 i j t t   Canonical problems  ... ... ...  Compute the probability of a particular output sequence for known n parameters (forward-backward algorithm) Find the most likely sequence of hidden states for known parameters n (Viterbi algorithm) Find the most likely set of state transition and emission n i probabilities given an output sequence of (Baum-Welch algorithm*) * is highly complex and requires initial estimates of the transition and emission matrices 9 PDF created with pdfFactory Pro trial version www.pdffactory.com

Binary Symmetric Channel (BSC) Assumption PMF for the number of successful packets between two consecutive error packets : theory (dotted) and practice (solid) = ∈  Pr( ), X x x S =  ( ) PMF x ∈  0, \ x R S CDF for the number of successful packets between two consecutive error packets : theory (dotted) and practice (solid) = ≤ ( ) Pr( ) CDF x X x : i 10 PDF created with pdfFactory Pro trial version www.pdffactory.com

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) 11 PDF created with pdfFactory Pro trial version www.pdffactory.com

2-state HMM Definition n Markov chain transition probabilities:   ( / ) ( / ) p g g p b g =   P  ( / ) ( / )  p g b p b b n Matrix 2-state model:     a = ( / ) ( / ) ( / ) ( / ) q p g g q p b g p p g g p p b g ( ( ), ( )) p g p b =  =  g b g b 0 (0)   A (1) A 0 = ( / ) ( / ) ( / ) ( / ) q p g b q p b b p p g b p p b b     T ( 1 , 1 ) b g b g b n Probability of a given error sequence: n ∏ = = ⋅ instead of ( ) ( , ,..., ) ( ) p e p e e e a A e b 1 2 0 0 n i = 1 i ∑∑ ∑ = ⋅ ⋅ ⋅ ⋅ ⋅ ( ) K ( ) ( | ) ( | ) K ( | ) ( | ) p e p s p s s p e s p s s p e s − 0 1 0 1 1 1 n n n n s s s 0 1 n n Easy way to calculate characteristics ( , ) P m n 12 PDF created with pdfFactory Pro trial version www.pdffactory.com

Model Parameters Derivation n Denote and the sequences of zeros and ones: 0 i 1 j j i − − − 2 2 3 3 2 a a (0 ) (0) (0 ) (0 ) (0) (0 ) p p p p p p = + = = 00 10 1 A a a + − − − 00 01 2 2 2 2 1 a a (0 ) (0) (0 ) (0) p p p p 11 01 − − − 2 2 3 3 2 a (1 ) (1) (1 ) (1 ) (1) (1 ) p p p p p p = = = 10 B a a + − − − 10 11 2 2 2 2 1 a a (1 ) (1) (1 ) (1) p p p p 11 01 n The resulting expressions* for the 2-state model: p g g = + − − − 2 2 ( / ) 0.9999 4 4 A A B A A B = = p p p b b = b g 2 2 ( / ) 0.9188 − + + − ( ) ( ) a a p a a p a a p = 0.0044 = = 11 01 g 11 11 b 11 01 ( / ) p g g ( / ) p b b g − − p = p p 0.5423 p p g b g b b * see discussion in S. Andreev, A. Vinel “Gilbert-Elliott Model Parameters Derivation 13 for the IEEE 802.11 Wireless Channel”, 2007 PDF created with pdfFactory Pro trial version www.pdffactory.com

Conclusion n Achievements A method to measure MAC throughput with high time q resolution is introduced 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 q n Open problems Perform goodness-of-fit check of a introduced model q Account for ‘peaks’ in the experimental PMF q Compare the derived model with alternatives q (e. g. D. Moltchanov “Cross-layer performance evaluation and control of wireless channels in NG All-IP networks”, Ph.D. thesis, 2006) 14 PDF created with pdfFactory Pro trial version www.pdffactory.com

Discussion 15 PDF created with pdfFactory Pro trial version www.pdffactory.com