January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 1
doc.: IEEE 802.11-04-0064-00-000n
Submission
Time-Correlated Packet Errors in MAC Simulations
Angelo Poloni and StefanoValle
STMicroelectronics
Gianluca Villa
Politecnico di Milano
January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 2
doc.: IEEE 802.11-04-0064-00-000n
Submission
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.
January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 3
doc.: IEEE 802.11-04-0064-00-000n
Submission
Basic idea• “Instantaneous” CC at time is a function of the channel
transfer function and of the average 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
• 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.
t tfH ,
SNRtfHCC ,,
SNRtfHCtPER ,,
January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 4
doc.: IEEE 802.11-04-0064-00-000n
Submission
CC for frequency selective SISO channel
• Assumption: channel flat in each OFDM sub-carrier (SC) bandwidth
• Capacity on k-th OFDM sub-carrier is given by
• CC can be considered as the sum of the Capacities on each SC
fN
fkHPfC k
k0
2
2 1log
NFFT
kkCC
1
January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 5
doc.: IEEE 802.11-04-0064-00-000n
Submission
Simulation conditions 802.11a standard Rate 6 Mbps Channel model “B” (as defined by 802.11n standard) Es/N0 = 8 dB
Instantaneous PER versus instantaneous CC
• Erroneous packets are in correspondence of low CC
8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 90
10
20
30
40
50
60
70
80
time [s]
Ca
pa
city
[M
bp
s]
Erroneous packets
Correct packets
Err
on
eo
us
Pa
cke
t
0
1
January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 6
doc.: IEEE 802.11-04-0064-00-000n
Submission
PER versus CC
•802.11a•Rate 6 Mbps•Channel model “B” (802.11n standard)•Es/N0 [0:4:20] dB
0 10 20 30 40 50 60 7010
-4
10-3
10-2
10-1
100
Capacity [Mbps]
PE
R
SNR = 8 10 12 14 16 18 20
January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 7
doc.: IEEE 802.11-04-0064-00-000n
Submission
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.
January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 8
doc.: IEEE 802.11-04-0064-00-000n
Submission
Characterization of CC: pdf
0 20 40 60 80 100 120 140 160 18010
-5
10-4
10-3
10-2
10-1
capacity [Mbps]
Pro
babi
lity
SNR = 8 10 12 14 16 18 20
Channel model “B” (802.11n standard)
January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 9
doc.: IEEE 802.11-04-0064-00-000n
Submission
Characterization of CC: mean and standard deviation
8 10 12 14 16 18 2010
20
30
40
50
60
70
80
90
100
110
Es/N0
Ca
pa
city
[M
bp
s]meanstd
January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 10
doc.: IEEE 802.11-04-0064-00-000n
Submission
Generation of CC stochastic process• Emulate the stochastic process with a Birth-Death Markov
process [3]
• Pros :– easy to implement;– low loading of MAC simulator.
• Cons : – Relative high number of LUTs.
0 Mbps 5 Mbps # Mbps…
January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 11
doc.: IEEE 802.11-04-0064-00-000n
Submission
Characterization of Markov chain1/2
• Transition probabilities are given by the following matrix (4 state Markov chain is assumed for simplicity)
• Matrix can be estimated form a discrete version of the CC versus time curve.
4,44,3
4,33,32,3
3,22,21,2
2,11,1
00
0
0
00
SNR
SNR
January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 12
doc.: IEEE 802.11-04-0064-00-000n
Submission
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);
– The condition for having a capacity step less than C in a time step t is
tfCC
tC D2sin2
minmax
minmax CCf
Ct
D
January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 13
doc.: IEEE 802.11-04-0064-00-000n
Submission
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
January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 14
doc.: IEEE 802.11-04-0064-00-000n
Submission
0 20 40 60 80 100 120 140 160 180 200
10-0.07
10-0.04
10-0.01
capacity [Mbps]
ii
0 20 40 60 80 100 120 140 160 180 20010
-3
10-2
10-1
capacity [Mbps]
i,i-1
0 20 40 60 80 100 120 140 160 180 20010
-4
10-2
100
capacity [Mbps]
i,i+
1
SNR = 0 4 8 12 16 20 24
Example of Markov chain characterization2/2
i,i
i,i-1
i,i+1
January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 15
doc.: IEEE 802.11-04-0064-00-000n
Submission
Markov chain in MAC simulator
Channel Capacity
Emulation
(Markov Chain)
Erroneous Packet
Random draw
Packet OK
Mean SNR
ShadowingPropagation
Law
LUT:Markov chain
transition probabilities
LUT:PER vs SNR vs CC
Distance
January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 16
doc.: IEEE 802.11-04-0064-00-000n
Submission
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).
January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 17
doc.: IEEE 802.11-04-0064-00-000n
Submission
Preliminary Model validation
• Validation metrics are: – average PER;– Average Burst Error Length (ABEL);– Standard Deviation of Burst Error Length
(STDBEL).
January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 18
doc.: IEEE 802.11-04-0064-00-000n
Submission
Validation results1/3
8 10 12 14 16 18 2010-3
10-2
10-1
100
snr
PHY behaviorMarkov model
8 10 12 14 16 18 200
2
4
6
8
10PHY behaviorMarkov model
8 10 12 14 16 18 200
5
10
15PHY behaviorMarkov model
PER
ABEL
STDBEL
SNR
SNR
SNR
C = 15 Mbps t = 1 ms Channel: IEEE B Random draw:
method 1
January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 19
doc.: IEEE 802.11-04-0064-00-000n
Submission
C = 15 Mbps t = 1 ms Channel: IEEE B Random draw:
method 28 10 12 14 16 18 20
10-4
10-2
100
8 10 12 14 16 18 200
20
40
8 10 12 14 16 18 200
20
40
Validation results2/3
PER
ABEL
STDBEL
SNR
SNR
SNR
January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 20
doc.: IEEE 802.11-04-0064-00-000n
Submission
Validation results3/3
PER
ABEL
STDBEL
8 10 12 14 16 18 2010
-4
10-2
100
8 10 12 14 16 18 200
5
10
15
8 10 12 14 16 18 200
10
20
30
SNR
SNR
SNR
PHY behaviorMarkov model
PHY behaviorMarkov model
PHY behaviorMarkov model
C = 2 Mbps t = 1 ms Channel: IEEE B Random draw:
method 2
January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 21
doc.: IEEE 802.11-04-0064-00-000n
Submission
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.
January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 22
doc.: IEEE 802.11-04-0064-00-000n
Submission
Summary of the simulation method
Link level simulator
PER versus SNR CC
Channel only simulator(SNR, channel model)
CC versus TIME versus SNR
CCMARKOV CHAIN
(transition probabilities)
Statistical analysis
MAC simulator
N.B., Channel only simulator,Link level simulator and MAC simulator run separately
January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 23
doc.: IEEE 802.11-04-0064-00-000n
Submission
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.
January 2004
A. Poloni, S. Valle, STMicroelectronics
Slide 24
doc.: IEEE 802.11-04-0064-00-000n
Submission
References1. J. M. McDougall, “Low Complexity Channel Models for
Approximating Flat Rayleigh Fading in Network Simulations”, PhD Dissertation, Texas A&M University, August 2003.
2. IST- FITNESS D4.3, “Simulation Platform Structure and System Level Performance Evaluation” (http://www.telecom.ntua.gr/fitness/ )
3. 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.