Doc.: IEEE 802.11-04-0064-00-000n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 1 Time-Correlated Packet Errors in MAC Simulations

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

([email protected], [email protected], [email protected])

January 2004


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


Slide 19

doc.: IEEE 802.11-04-0064-00-000n

Submission


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


PER

ABEL

STDBEL

SNR

SNR

SNR

January 2004


Slide 20

doc.: IEEE 802.11-04-0064-00-000n

Submission


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





method 2

January 2004


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


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


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


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.

Documents

Doc.: IEEE 802.11-04-0064-00-000n Submission January 2004 A. Poloni, S. Valle, STMicroelectronicsSlide 1 Time-Correlated Packet Errors in MAC Simulations