January 2004
doc.: IEEE 802.11-04-0064-00-000n
Time-Correlated Packet Errors in
MAC Simulations
Angelo Poloni and StefanoValle
STMicroelectronics
Gianluca Villa
Politecnico di Milano
([email protected], [email protected],
[email protected])
Submission
Slide 1
A. Poloni, S. Valle, STMicroelectronics
January 2004
doc.: IEEE 802.11-04-0064-00-000n
Introduction
• MAC simulations require time-correlated packet
errors in order to emulate PHYs in a realistic way.
• Simple Markov chains (Good/Bad channel),
proposed so far, seem to be a rough approximation
of the channel behavior [1].
• Information Theory provides the “Channel
Capacity” (CC) concept; CC is a suitable metric to
predict PHY performances [2].
• The “instantaneous” value of the CC can be used
to predict the “instantaneous” packet error
probability.
Submission
Slide 2
A. Poloni, S. Valle, STMicroelectronics
January 2004
doc.: IEEE 802.11-04-0064-00-000n
Basic idea
• “Instantaneous” CC at time t is a function of the channel
transfer function H  f , t  and of the average SNR;
C  CH  f , t , SNR
• The “instantaneous” CC can be considered a stochastic
process.
• It can be proved experimentally that, once the PHY is
defined, the instantaneous PER is a function of CC
PERt   CH  f , t , SNR
• If PER versus CC is available from link-level simulations
(e.g. as a Look-Up-Table[LUT]), it is sufficient to generate
the stochastic process that represents the CC versus time in
the MAC simulator. Its instantaneous value can be used to
read the PER LUT.
Submission
Slide 3
A. Poloni, S. Valle, STMicroelectronics
January 2004
doc.: IEEE 802.11-04-0064-00-000n
CC for frequency selective SISO channel
• Assumption: channel flat in each OFDM subcarrier (SC) bandwidth
• Capacity on k-th OFDM sub-carrier is given by
 Pk H kf  2 

Ck  f log 2 1 


N 0 f


• CC can be considered as the sum of the Capacities
on each SC
C
NFFT
C
k 1
Submission
Slide 4
k
A. Poloni, S. Valle, STMicroelectronics
January 2004
doc.: IEEE 802.11-04-0064-00-000n
Instantaneous PER versus instantaneous CC
80
• Erroneous packets
are in correspondence
of low CC
70

Erroneous packets
Erroneous Packet
60
Capacity [Mbps]
Simulation conditions
802.11a standard
Rate 6 Mbps
Channel model “B” (as
defined by 802.11n
standard)
Es/N0 = 8 dB
1
50
40
30
20


10
0
8
8.1
8.2

Submission
8.3
8.4
8.5
8.6
time [s]
8.7
8.8
8.9
9
0
Correct packets
Slide 5
A. Poloni, S. Valle, STMicroelectronics
January 2004
doc.: IEEE 802.11-04-0064-00-000n
PER versus CC
0
10
-1
10
PER
•802.11a
•Rate 6 Mbps
•Channel model “B”
(802.11n standard)
•Es/N0 [0:4:20] dB
SNR = 8
10
12
14
16
18
20
-2
10
-3
10
-4
10
Submission
0
10
20
Slide 6
30
40
Capacity [Mbps]
50
60
70
A. Poloni, S. Valle, STMicroelectronics
January 2004
doc.: IEEE 802.11-04-0064-00-000n
CC stochastic process
• In order to simulate the CC stochastic process in
MAC simulators it is necessary to have its
statistical characterization.
• This is done in the next two slides.
• After that an approach to reproduce such process
in a MAC simulator is proposed.
Submission
Slide 7
A. Poloni, S. Valle, STMicroelectronics
January 2004
doc.: IEEE 802.11-04-0064-00-000n
Characterization of CC: pdf
Channel model “B” (802.11n standard)
-1
10
SNR = 8
10
12
14
16
18
20
-2
Probability
10
-3
10
-4
10
-5
10
Submission
0
20
40
60
80
100
capacity [Mbps]
Slide 8
120
140
160
180
A. Poloni, S. Valle, STMicroelectronics
January 2004
doc.: IEEE 802.11-04-0064-00-000n
Characterization of CC: mean and
standard deviation
110
mean
std
100
90
Capacity [Mbps]
80
70
60
50
40
30
20
10
8
Submission
10
12
14
Es/N0
Slide 9
16
18
20
A. Poloni, S. Valle, STMicroelectronics
January 2004
doc.: IEEE 802.11-04-0064-00-000n
Generation of CC stochastic process
• Emulate the stochastic process with a Birth-Death Markov
process [3]
0 Mbps
…
5 Mbps
# Mbps
• Pros :
– easy to implement;
– low loading of MAC simulator.
• Cons :
– Relative high number of LUTs.
Submission
Slide 10
A. Poloni, S. Valle, STMicroelectronics
January 2004
doc.: IEEE 802.11-04-0064-00-000n
Characterization of Markov chain1/2
• Transition probabilities are given by the following
matrix (4 state Markov chain is assumed for
simplicity)
0
0 
 1,1  1, 2




0
2 ,1
2, 2
2,3

 SNR   
 0  3 , 2  3, 3  3, 4 


0
0


3, 4
4, 4 

• Matrix SNR can be estimated form a discrete
version of the CC versus time curve.
Submission
Slide 11
A. Poloni, S. Valle, STMicroelectronics
January 2004
doc.: IEEE 802.11-04-0064-00-000n
Characterization of Markov chain2/2
• Only contiguous states transitions are allowed
• Contiguous states are uniformly spaced; capacity step is C.
• The assumption of transitions towards contiguous states only is not
obvious. In order to guarantee that such assumption is correct, it is
necessary that Markov chain time clock (t) is sufficiently small.
• A conservative condition is obtained through the following
considerations:
– Assume the capacity process to be a sinusoid with frequency fD (Doppler
Spread);
 C  Cmin 
C t    max
 sin 2f D t 
2


– The condition for having a capacity step less than C in a time step t is
t 
Submission
C
f D Cmax  Cmin 
Slide 12
A. Poloni, S. Valle, STMicroelectronics
January 2004
doc.: IEEE 802.11-04-0064-00-000n
Example of Markov chain characterization1/2





C = 15 Mbps
t = 1 ms
Channel: IEEE B
SNR = 0,4,8,12,16,20,24 dB
Transition probabilities for each SNR are plotted in the
next slide
Submission
Slide 13
A. Poloni, S. Valle, STMicroelectronics
January 2004
doc.: IEEE 802.11-04-0064-00-000n
Example of Markov chain characterization2/2
10
i,i
-0.04
ii
10
-0.01
10
-0.07
10
i,i-1
i,i-1
10
10
10
i,i+1
i,i+1
10
10
0
20
40
60
80
100
120
capacity [Mbps]
140
160
180
200
0
20
40
60
80
100
120
capacity [Mbps]
140
160
180
200
-1
-2
-3
0
SNR = 0
4
8
12
16
20
24
-2
-4
0
Submission
20
40
60
80
100
120
capacity [Mbps]
Slide 14
140
160
180
200
A. Poloni, S. Valle, STMicroelectronics
January 2004
doc.: IEEE 802.11-04-0064-00-000n
Markov chain in MAC simulator
Distanc
e
Propagation
Law
Shadowing
Mean
SNR
LUT:
Markov chain
transition
probabilities
LUT:
PER vs SNR vs CC
Channel
Capacity
Emulation
(Markov
Chain)
Rando
m draw
Erroneous
Packet
Submission
Slide 15
Packet
OK
A. Poloni, S. Valle, STMicroelectronics
January 2004
doc.: IEEE 802.11-04-0064-00-000n
Erroneous packet event:
drawing methods
• Random draw methods:
– draw for erroneous packet event every new
packet (Method 1);
– draw for erroneous packet event every new
capacity state (Method 2).
Submission
Slide 16
A. Poloni, S. Valle, STMicroelectronics
January 2004
doc.: IEEE 802.11-04-0064-00-000n
Preliminary Model validation
• Validation metrics are:
– average PER;
– Average Burst Error Length (ABEL);
– Standard Deviation of Burst Error Length
(STDBEL).
Submission
Slide 17
A. Poloni, S. Valle, STMicroelectronics
January 2004
doc.: IEEE 802.11-04-0064-00-000n
Validation




C = 15 Mbps
t = 1 ms
Channel: IEEE B
Random draw:
method 1
1/3
results
0
10
PHY behavior
Markov model
-1
PER
10
-2
10
-3
10
8
10
12
10
ABEL
14
SNR
16
18
20
PHY behavior
Markov model
8
snr
6
4
2
0
8
10
12
15
14
SNR
16
18
20
PHY behavior
Markov model
STDBEL
10
5
0
8
10
12
14
16
18
20
SNR
Submission
Slide 18
A. Poloni, S. Valle, STMicroelectronics
January 2004
doc.: IEEE 802.11-04-0064-00-000n
Validation




C = 15 Mbps
t = 1 ms
Channel: IEEE B
Random draw:
method 2
2/3
results
0
10
PER 10-2
-4
10
8
10
12
14
SNR
16
18
20
8
10
12
14 SNR
16
18
20
8
10
12
14
16
18
20
40
ABEL
20
0
40
STDBEL
20
0
Submission
Slide 19
SNR
A. Poloni, S. Valle, STMicroelectronics
January 2004
doc.: IEEE 802.11-04-0064-00-000n
Validation




C = 2 Mbps
t = 1 ms
Channel: IEEE B PER
Random draw:
method 2
ABEL
3/3
results
0
10
PHY behavior
Markov model
-2
10
-4
10
8
15
10
12
14
SNR
16
18
20
PHY behavior
Markov model
10
5
0
8
30
STDBEL
10
12
14
SNR
16
18
20
PHY behavior
Markov model
20
10
0
Submission
8
10
12
Slide 20
14
SNR
16
18
20
A. Poloni, S. Valle, STMicroelectronics
January 2004
doc.: IEEE 802.11-04-0064-00-000n
Comments on model validation
• PER matches the PHY behavior.
• Matching ABEL and STDBEL is the most critical
aspect:
– in the special case here presented, promising results
have been obtained by shortening the Capacity Step of
the Markov Chain and by using the Draw method
number 2;
– a general rule for calibrating the Capacity Step is still
unknown.
Submission
Slide 21
A. Poloni, S. Valle, STMicroelectronics
January 2004
doc.: IEEE 802.11-04-0064-00-000n
Summary of the simulation method
Channel only simulator
(SNR, channel model)
Link level simulator
CC versus TIME versus SNR
PER versus SNR CC
N.B., Channel only simulator,
Link level simulator and MAC
simulator run separately
MAC simulator
Statistical analysis
Submission
CC
MARKOV CHAIN
(transition probabilities)
Slide 22
A. Poloni, S. Valle, STMicroelectronics
January 2004
doc.: IEEE 802.11-04-0064-00-000n
Some comments
• Channel state is condensed in a single number (CC versus
time): overloading of MAC simulators is avoided.
• CC versus time can be easily reproduced by other parties
and thus it can be easily standardized.
• PHY behaviors (PER versus time) can be easily included
and updated with LUTs (PER versus CC).
• A method for including the effects of interferers will be
investigated in the near future.
• The same approach is applicable to MIMO channels and
PHYs.
Submission
Slide 23
A. Poloni, S. Valle, STMicroelectronics
January 2004
doc.: IEEE 802.11-04-0064-00-000n
References
1.
2.
3.
Submission
J. M. McDougall, “Low Complexity Channel Models for
Approximating Flat Rayleigh Fading in Network
Simulations”, PhD Dissertation, Texas A&M University,
August 2003.
IST- FITNESS D4.3, “Simulation Platform Structure and
System Level Performance Evaluation”
(http://www.telecom.ntua.gr/fitness/ )
Hong Shen Wang, Moayeri, N., “Finite-state Markov
Channel-a Useful Model for Radio Communication
Channels”, IEEE Transactions on Vehicular Technology,
Feb. 1995 Volume 44 Number 1.
Slide 24
A. Poloni, S. Valle, STMicroelectronics