September 2005
doc.: IEEE 802.19-05/0029r0
Estimating Packet Error Rate Caused by Interference
– A Coexistence Assurance Methodology
Date: 2005-09-14
Authors:
Name
Company Address
Phone
E-mail
Steve
Shellhammer
Qualcomm
(858) 658-1874
shellhammer@ieee.org
5775 Morehouse Dr
San Diego, CA 92121
Notice: This document has been prepared to assist IEEE 802.19. It is offered as a basis for discussion and is not binding on the contributing individual(s) or organization(s). The material in
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Submission
Slide 1
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Presentation Outline
•
•
•
•
Geometric Model
Path Loss Model
PHY Layer Model
Temporal Model
– Temporal collision
– Probability Calculations
• Calculation of Performance Metrics
• Examples
– BPSK with periodic interference
– QAM with periodic interference
– BPSK with random interference
• Detailed Word document IEEE 802.19-05/0028r0
Submission
Slide 2
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Geometric Model
• Two networks
– Affected wireless network (AWN) – i.e. victim
– Interfering wireless network (IWN) – i.e. assailant
• Need to select the number of stations in each
wireless network
– Use a simplified model if at all possible
• Need to specify the location of stations
– Vary distance between stations in two networks to see
the effect of proximity of the two networks on packet
error rate and other performance metrics
Submission
Slide 3
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Possible Geometric Model
L
Affected Wireless Network
(0, L)
d
Interfering Wireless Network
(0, 0)
Submission
(d, 0)
Slide 4
(e, 0)
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Geometric Model
• Station that is affected by interference is
located at the origin.
• Assume station at (0, L) is not affected by
interference
• Distance L determines receive signal power
• Distance d determines interference power
• In this simplest case e is selected to be large
enough so that the station at (e, 0) does not
cause interference
Submission
Slide 5
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Geometric Model
• Vary distance d to see how the proximity
between the two wireless networks affects
network performance
• It is also necessary to specify any directional
gains of the antennas in the geometric model
Submission
Slide 6
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Path Loss
• The parameters of the geometric model need to
be converted into power levels for the station
located at the origin
• This conversion is accomplished using a path
loss model
Submission
Slide 7
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Path Loss
• Path Loss formula (example at 2.4 GHz)
 40.2  20 Log10 (d ) 0.5m  d  8m

pl (d )  
d 
58.5  33Log10  
d  8m

8
• Signal-to-Interference Ratio (SIR)
  [ PS  pl ( L)]  [ PI  pl (d )]
Submission
Slide 8
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Path Loss
Submission
Slide 9
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
PHY Layer Model
• The goal of the PHY Layer model is to calculate
the symbol error rate (SER) assuming
continuous interference
• The temporal model will then convert SER into
packet error rate (PER)
• All this assumes packet oriented protocol
Submission
Slide 10
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
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 11
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
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 12
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
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 13
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
First Order PHY Model
• If an analytic expression for the symbol error
rate for additive white Gaussian noise (AWGN)
then we may in certain circumstances use this
as a reasonable estimate of the SER
• Typical formula are available in terms of ES/N0
• This can be converted into ratio of signal power
to interference power
Submission
Slide 14
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
First Order PHY Model
• If the interference bandwidth is less than or equal to
the signal bandwidth we can show that in order to use
the common SER formula in terms of ES/N0 we make
the following substitution
ES
PS
 r 
N0
PI
if BI  B
• If the interference bandwidth is greater than the signal
bandwidth we scale by the bandwidth ratio,
ES
PS
B
 r 

N0
BI
PI
Submission
Slide 15
if BI  B
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Simulation Based PHY Model
• In most modern systems the PHY layer is often too
complex to have an analytic formula for the SER
available
• However, it is very common to develop a simulation of
the PHY
• Thus a more accurate approach would be to use a
simulation-based model to develop the SER versus SIR
curves
• The data from these curves can be used for the SER
formula. This can be done with a table and
interpolation between data points as necessary
Submission
Slide 16
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
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 17
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
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 18
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
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 19
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
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 20
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
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 21
• Probability mass function
of the number of symbol
collisions
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
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 22
m
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Probability Calculations
• Therefore the PER formula is,
N
PER   [1  (1  p) m ] f M (m)
m 0
• Next step is to determine the probability mass
function of the number of symbol collisions
Submission
Slide 23
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Probability Calculations
• The probability mass function depends on a
number of factors
– The symbol duration
– The number of symbols in the packet
– The duration of the pulses. This may be a fixed number
or a random variable
– The spacing between pulses. This may be a fixed
number or a random variable
• We will give two example that demonstrate the
general format of the probability mass function
• Latter in the presentation numerical examples
will be given
Submission
Slide 24
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
General Format of Probability Mass Function
• Case 1 – Packet shorter than the interference pulse
• The Figure shows three possible collisions
Interference Pulse
Interference Pulse
Possibility 1
Possibility 2
Possibility 3
Submission
Slide 25
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
General Format of Probability Mass Function
• There is some probability that there will be no symbol
collisions (like possibility 2 in the figure)
f M (0)  c1
• There is some probability that all the symbols will
collide with an interference pulse (like possibility 1 in
the figure)
f M ( N )  c3
• It turns out for fixed pulse durations and pulses
spacing that the probability of all other number of
collisions is a constant
f M (m)  c2
Submission
m  1, 2...N 1
Slide 26
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
General Format of Probability Mass Function
• The PER formula for this case is given by,
N 1
PER  c2  [1  (1  p) m ]  c3 [1  (1  p ) N ]
m 1
Submission
Slide 27
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
General Format of Probability Mass Function
• Case 2 – Packet longer than the interference pulse
• The Figure shows three possible collisions
Interference Pulse
Interference Pulse
Possibility 1
Possibility 2
Possibility 3
Submission
Slide 28
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
General Format of Probability Mass Function
• There is some probability that there will be no symbol
collisions (like possibility 2 in the figure)
f M (0)  c1
• For all values from one up to K-1 (where K is the
number of symbols in the duration of a interference
pulse) the probability of m collisions is a constant
f M (m)  c2
m  1, 2...K 1
• There is some probability exactly K symbols will collide
f M ( K )  c3
Submission
Slide 29
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
General Format of Probability Mass Function
• There is no probability that more than K symbols
collide
f M (n)  0 m  K  1, K  2...N
• The PER formula for this case is given by,
K 1
PER  c2 [1  (1  p) m ]  c3 [1  (1  p) K ]
m 1
• This formula is similar to case 1 with the limit of the
summation being K and not N. We can use this format
in general and let K=N as appropriate
Submission
Slide 30
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Simplification of Probability Calculations
• These PER formula can be simplified
• We will focus on the summation term
K 1
  [1  (1  p) m ]
m 1
• We can begin the summation at zero since that term is
zero
K 1
   [1  (1  p ) m ]
m 0
Submission
Slide 31
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Simplification of Probability Calculations
• We can pull out a constant term
K 1
  K   (1  p ) m
m 0
• Next we utilize the following algebraic identity
K
1

a
m
a


1 a
m 0
K 1
Submission
Slide 32
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Simplification of Probability Calculations
• If we apply that identity we get,
K
1

(
1

p
)
  K   (1  p) m  K 
1  (1  p)
m 0
K 1
• Which simplifies to,
Kp  1  (1  p) K

p
Submission
Slide 33
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Simplification of Probability Calculations
• If we use this simplification and we substitute it
back into the general PER formula we get the
following PER formula which applies when the
probability mass function is of the form shown
previously,
Kp  1  (1  p) K
PER  c2
 c3 [1  (1  p) K ]
p
Submission
Slide 34
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Limits of PER Formula
• For small SER we get the following limit of the PER
formula,
Lim PER  0
p0
• For large SER we get the following limit of the PER
formula,
Lim PER  c2 ( K  1)  c3  1  c1
p1
Submission
Slide 35
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Random Pulse Model
• In some cases the interference pulses will not be
fixed duration and spacing
• In those cases it is most likely that a simulation
will be needed to calculate the probability mass
function
• Once the probability mass function is found
then the total probability formula can be
applied directly
• It is unlikely that the simplified probability
expressions can be used in this case
• An example will be given later
Submission
Slide 36
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Calculation of Performance Metrics
• Besides the packet error rate there may be
other metrics that are important
• Two common performance metrics are
throughput and latency
• Depending on the application there may be
other important metrics to consider
• It is often possible to estimate these
performance metrics from the PER estimate
Submission
Slide 37
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Calculation of Performance Metrics
• The actual throughput depends on the specifics of the
network being considered.
• Let us define TP0 as the throughput without interference
• Then the throughput with interference is given by,
TP  (1  PER)TP0
• Let us define τ0 as the latency without interference
• Similarly, the latency with interference is given by,

Submission
0
(1  PER)
Slide 38
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Example 1 – BPSK with Periodic Interference Pulses
• Use the geometric model given previously
• Affected wireless network station separation is L=30
meters
• Affected wireless network is WLAN-type network with
transmit power of 20 dBm
• Simple BPSK modulation with no coding on affected
wireless network
• Each packet includes 128 Kbytes (1024 bits)
• Interfering wireless network is WPAN-type network
with transmit power of 0 dBm
• The interference pulses are co-channel with the affected
wireless network with the same bandwidth
Submission
Slide 39
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Example 1 – BPSK with Periodic Interference Pulses
• The interference pulses in the interfering wireless
network are the same duration as the packets sent in the
affected wireless network
• The duty cycle of the interference pulses is 25%
Data Packet
Interference
Pulse
Submission
Interference
Pulse
Slide 40
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Example 1 – BPSK with Periodic Interference Pulses
• Since this is a simple BPSK example we can use the
AWGN approximation for the symbol error rate,
SERBPSK  Q[ 2 ]
• The Q Function is the tail probability of a Gaussian
random variable,

1
y
Q( x ) 
exp

2
2 x
Submission
Slide 41
2
( ) dy
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Example 1 – BPSK with Periodic Interference Pulses
Submission
Slide 42
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Example 1 – BPSK with Periodic Interference Pulses
• Calculate Probability Mass Function
• The probability of exactly 1024 symbol collisions is,
1
f M (1024) 
4096
• The probability of other non-zero symbol collisions is
twice the probability of 1024 symbol collisions,
1
f M ( m) 
2048
Submission
m  1, 2,1023
Slide 43
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Example 1 – BPSK with Periodic Interference Pulses
• That leaves the following probability of zero symbol
collisions,
2049
f M ( 0) 
4096
• This gives the following PER formula,
1 1024 p  1  (1  p)1024
1
PER 

[1  (1  p)1024 ]
2048
p
2048
Submission
Slide 44
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Example 1 – BPSK with Periodic Interference Pulses
Submission
Slide 45
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Example 1 – BPSK with Periodic Interference Pulses
• Suggest two figures of merit based on PER curve
– Maximum PER
– Distance at which the PER is 1%
Submission
Slide 46
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Example 1 – BPSK with Periodic Interference Pulses
Max PER
1% PER
Distance
Submission
Slide 47
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Example 1 – BPSK with Periodic Interference Pulses
Submission
Slide 48
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Example 1 – BPSK with Periodic Interference Pulses
Submission
Slide 49
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Example 2 – QAM with Periodic Interference Pulses
•
•
•
•
•
•
•
Similar to Example 1
Include uncoded QPSK, 16QAM and 64QAM
Keep the packet payload at 128 Kbytes
The symbol error rate changes
The number of symbols in a packet change
Keep the interference pulses the same
Symbol error rate formula can be found in word
document
Submission
Slide 50
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Example 2 – QAM with Periodic Interference Pulses
Submission
Slide 51
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Example 2 – QAM with Periodic Interference Pulses
• Show how to find probability mass function for QPSK
case
• Number of symbols is now 512 (two bytes per symbols
Data
Packet
Interference
Pulse
Submission
Interference
Pulse
Slide 52
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Example 2 – QAM with Periodic Interference Pulses
• The probability of exactly 512 symbol collisions is,
513
f M (512) 
4096
• The probability of the other non-zero symbol collisions
is still the same as before,
1
f M ( m) 
m  1, 2,511
2048
• The probability of zero symbol collisions is what is left,
2561
f M ( 0) 
4096
Submission
Slide 53
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Example 2 – QAM with Periodic Interference Pulses
Submission
Slide 54
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Example 2 – QAM with Periodic Interference Pulses
• Figures of Merit for Example 2
1% PER Distance (meters) Maximum
PER
BPSK
QPSK
16QAM
13.8
17.1
27.5
0.499
0.374
0.312
64QAM
41.7
0.281
Submission
Slide 55
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Example 2 – QAM with Periodic Interference Pulses
Submission
Slide 56
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Example 2 – QAM with Periodic Interference Pulses
Submission
Slide 57
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Example 3 – BPSK with Random Interference Pulses
• Similar to Example 1
• Random pulse width
– Uniformly distributed between 512T and 1536T
– Same average duration as in Example 1
• Random pulse spacing
– Uniformly distributed between 2048T and 4096T
– Same average duration as in Example 2
• Probability mass function is found using a simulation
• Plot cumulative distribution function of the number of
symbol collisions
Submission
Slide 58
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Example 3 – BPSK with Random Interference Pulses
Submission
Slide 59
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Example 3 – BPSK with Random Interference Pulses
•
•
•
•
Calculate PER using Total Probability formula
Cannot use simplifications
Plot PER for both Example 1 and 3
The result shows that the PER is almost
identical for these two examples
• This indicates that in many cases using a fixed
pulse duration and spacing is likely a good
approximation
Submission
Slide 60
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Example 3 – BPSK with Random Interference Pulses
Submission
Slide 61
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Summary of the Process
•
•
•
•
•
•
Step 1 – Select Geometric Model
Step 2 – Select Path Loss Model
Step 3 – Develop Symbol Error Rate Formula
Step 4 – Develop Temporal Model
Step 5 – Develop Packet Error Rate Formula
Step 6 – Calculate and Plot PER and other
Performance Metrics
Submission
Slide 62
Steve Shellhammer, Qualcomm Inc.
September 2005
doc.: IEEE 802.19-05/0029r0
Conclusions
• A process has been described that illustrates
how to estimate the PER caused by interference
• The SER formula can be either analytic or
based on a simulation
• The probability mass function can be
developed analytically for periodic pulses or
through a simulation for random pulses
• The PER and other Performance Metrics can
then easily be plotted as a function of distance
• Two figures of merit were introduced
– Maximum PER
– 1% PER distance
Submission
Slide 63
Steve Shellhammer, Qualcomm Inc.