Transcript 19-05-0044-00-0000-Update-on-Estimating-PER-Caused-by-Interference.ppt

November 2005
doc.: IEEE 802.19-05/0044r0
Au Update on Estimating Packet Error Rate
Caused by Interference
Date: 2005-11-02
Authors:
Name
Company Address
Phone
E-mail
Steve
Shellhammer
Qualcomm
(858) 658-1874
[email protected]
5775 Morehouse Dr
San Diego, CA 92121
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Submission
Slide 1
Steve Shellhammer, Qualcomm Inc.
November 2005
doc.: IEEE 802.19-05/0044r0
Presentation Outline
•
•
•
•
•
Background
Review of Temporal Collision Model
Extension to Model to use BER instead of SER
Simplification of Probability Calculations
Conclusions
Submission
Slide 2
Steve Shellhammer, Qualcomm Inc.
November 2005
doc.: IEEE 802.19-05/0044r0
Background
• At the September meeting I gave a presentation on
estimating PER using analytic techniques
– Presentation 802.19-05/0029r0
– Document 802.19-05/0028r0
• The probability techniques utilized the symbol error
rate (SER) functions
• However, as was pointed out in the discussion, one
often has bit error rate (BER) and not SER
• This presentation is an update of how to extend the
work of the previous presentation to using BER
formula instead of SER formula
• The word document has be revised incorporating these
enhancements
– Document 802.19-05/0028r2
Submission
Slide 3
Steve Shellhammer, Qualcomm Inc.
November 2005
doc.: IEEE 802.19-05/0044r0
Review of Temporal Collision Model
Submission
Slide 4
Steve Shellhammer, Qualcomm Inc.
November 2005
doc.: IEEE 802.19-05/0044r0
Packet Structure
• General packet structure
PREAMBLE
DATA
• Typically the preamble is short compared to the data
• Typically the preamble is sent at a more robust
modulation and coding rate than the data
• Generally, the data portion breaks before the preamble
breaks
• Thus under most cases the packet error rate is based
predominantly on symbol errors in the data portion
Submission
Slide 5
Steve Shellhammer, Qualcomm Inc.
November 2005
doc.: IEEE 802.19-05/0044r0
Packet Structure
• Typically the data portion consists of a sequence
of symbols
–
–
–
–
The symbols may encode a single bit or multiple bits
Each symbol is of duration T seconds
This can represent the data portion of the packet
If the preamble is sent at a similar modulation and code
rate then this could represent both the data and preamble
S1
S2
S3
S4
S5
S6
...
SN
T
Submission
Slide 6
Steve Shellhammer, Qualcomm Inc.
November 2005
doc.: IEEE 802.19-05/0044r0
Notation
• A symbol error is signified by the event SE
• The symbol error rate is the probability of a symbol
error.
– Since this is used frequently we will call this probability p
• This SER is a function of the signal-to-interference
ratio (SIR)
– Will assume high signal to noise ratio (SNR) since we are
interested in the effect of interference not the effect of noise
p  p( )  SER  P( SE )
Submission
Slide 7
Steve Shellhammer, Qualcomm Inc.
November 2005
doc.: IEEE 802.19-05/0044r0
Temporal Model
• This model converts from symbol error rate to
packet error rate (PER)
• It models the temporal aspects of both the
packets sent over the affected wireless network
and the pulses sent by the interfering wireless
network
Submission
Slide 8
Steve Shellhammer, Qualcomm Inc.
November 2005
doc.: IEEE 802.19-05/0044r0
Temporal Collision
• A packet sent over the affected wireless
network may or may not collide in time with
one or more of the pulses sent by the
interfering wireless network
• When a collision occurs part or all of the
packet may collide with the interference pulse
Submission
Slide 9
Steve Shellhammer, Qualcomm Inc.
November 2005
doc.: IEEE 802.19-05/0044r0
Temporal Collision
• The following figure illustrates a typical collision
• In this example four of the symbols collided with an
interference pulse
• The number of symbol collisions is actually a random
variable.
S1
S2
S3
S4
S5
S6
...
SN
T
Interference Pulse
Submission
Interference Pulse
Slide 10
Steve Shellhammer, Qualcomm Inc.
November 2005
doc.: IEEE 802.19-05/0044r0
Probability Calculations
• Introduce some more notation
• A packet error event is called PE
• The packet error rate is the probability of a packet
error
PER  P(PE )
• The number of symbol collisions is a discrete random
variable, which we will call M
• This random variable has a probability mass function,
f M (m) m  0, 1,N
Submission
Slide 11
Steve Shellhammer, Qualcomm Inc.
November 2005
doc.: IEEE 802.19-05/0044r0
Probability Calculations
• To assist in calculating the PER we use a Total
Probability formula
N
PER  P( PE )   P( PE | m) f M (m)
m 0
• Probability of a packet
error conditioned on m
symbol collisions
Submission
Slide 12
• Probability mass function
of the number of symbol
collisions
Steve Shellhammer, Qualcomm Inc.
November 2005
doc.: IEEE 802.19-05/0044r0
Probability Calculations
• The probability of a packet error is one minus
the probability of no symbol errors
• Assuming the symbol error rate is p, then the
probability of no symbol errors is (1-p)m
• So the probability of a packet error if there are
m symbol collisions is,
P( PE | m)  1  (1  p)
Submission
Slide 13
m
Steve Shellhammer, Qualcomm Inc.
November 2005
doc.: IEEE 802.19-05/0044r0
Probability Calculations
• Therefore the PER formula is,
N
PER   [1  (1  p) m ] f M (m)
m 0
• Given the probability mass function of the
number of symbol collisions we can calculate
the PER
• Several examples we given in September
Submission
Slide 14
Steve Shellhammer, Qualcomm Inc.
November 2005
doc.: IEEE 802.19-05/0044r0
Extension of Temporal Collision Model to
use BER instead of SER
Submission
Slide 15
Steve Shellhammer, Qualcomm Inc.
November 2005
doc.: IEEE 802.19-05/0044r0
Probability Calculations
• Total Probability Formula still applies
N
PER  P( PE )   P( PE | m) f M (m)
m 0
• Where M is the number of symbol collisions
• Find probability mass function for M just as before
• Formula for conditional PER is needs to change
Submission
Slide 16
Steve Shellhammer, Qualcomm Inc.
November 2005
doc.: IEEE 802.19-05/0044r0
Notation
• We will assume that forward error correction (FEC) is
used in the affected wireless network
– If this is not the case then the code rate is one
• We assume the post-FEC bit error rate is know through
a simulation
• The number of coded bits per symbol is NCBPS
• The number of information bits per symbol is NBPS
• The two are related by the code rate
N BPS  R N CBPS
• The post-FEC bit error rate is,
pb  pb ( )  BER  P( BE )
Submission
Slide 17
Steve Shellhammer, Qualcomm Inc.
November 2005
doc.: IEEE 802.19-05/0044r0
Probability Calculations
• The number of information bit in m symbol is m NBPS
• The probability of no packet error conditioned on m
symbol collisions is the probability that all the
information bits in those symbols are correct. Hence,
P( PE | m)  1  (1  p b ) m N BPS
• The resulting PER formula is then,
N
PER   [1  (1  pb ) m N BPS ] f M (m)
m 0
Submission
Slide 18
Steve Shellhammer, Qualcomm Inc.
November 2005
doc.: IEEE 802.19-05/0044r0
Simplification of Probability Calculations
Submission
Slide 19
Steve Shellhammer, Qualcomm Inc.
November 2005
doc.: IEEE 802.19-05/0044r0
Simplification of Probability Calculations
• As was done for the case when the SER was used we
can simplify the PER calculations in specific cases.
• Given fixed pulse duration and spacing the probability
mass function for the number of symbol collisions is of
the form
f M (0)  c1
f M ( K )  c3
Submission
f M (m)  c2
m  1, 2...K 1
f M (n)  0 m  K  1, K  2...N
Slide 20
Steve Shellhammer, Qualcomm Inc.
November 2005
doc.: IEEE 802.19-05/0044r0
Simplification of Probability Calculations
• Then the PER is given by,
K
PER  c2 [1  (1  pb ) m N BPS ]  c3 [1  (1  pb ) K N BPS ]
m 1
• Which simplifies to,
PER  c2
[
1  (1  pb ) K N BPS
K N BPS
K

c
[
1

(
1

p
)
]
3
b
N BPS
1  (1  pb )
]
• This is not as simple as the case when we use the SER
but still not too difficult to calculate
Submission
Slide 21
Steve Shellhammer, Qualcomm Inc.
November 2005
doc.: IEEE 802.19-05/0044r0
Conclusions
• The process described in September has been
extended to the case when we have the postFEC BER and not the SER
• Like in the pervious case the PER formula can
be simplified for fixed pulse durations and
spacing. However, the simplification is not
quite a simple as the case of using SER
• This extension is significant since in many cases
we will have simulation results that supply
post-FEC BER and those results can be utilized
to estimate the PER
Submission
Slide 22
Steve Shellhammer, Qualcomm Inc.