1. September 2005
doc.: IEEE /0029r0
September 2005
Estimating Packet Error Rate Caused by Interference – A Coexistence Assurance Methodology
Date:
Authors:
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Steve Shellhammer, Qualcomm Inc.
Steve Shellhammer, Qualcomm Inc.

2. Presentation Outline Geometric Model Path Loss Model PHY Layer Model
September 2005
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 /0028r0
Steve Shellhammer, Qualcomm Inc.

3. Geometric Model Two networks
September 2005
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
Steve Shellhammer, Qualcomm Inc.

4. Possible Geometric Model
September 2005
Possible Geometric Model
Steve Shellhammer, Qualcomm Inc.

5. September 2005
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
Steve Shellhammer, Qualcomm Inc.

6. September 2005
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
Steve Shellhammer, Qualcomm Inc.

7. September 2005
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
Steve Shellhammer, Qualcomm Inc.

8. Path Loss Path Loss formula (example at 2.4 GHz)
September 2005
Path Loss
Path Loss formula (example at 2.4 GHz)
Signal-to-Interference Ratio (SIR)
Steve Shellhammer, Qualcomm Inc.

9. September 2005
Path Loss
Steve Shellhammer, Qualcomm Inc.

10. September 2005
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
Steve Shellhammer, Qualcomm Inc.

11. Packet Structure General packet structure
September 2005
Packet Structure
General packet structure
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
Steve Shellhammer, Qualcomm Inc.

12. September 2005
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
Steve Shellhammer, Qualcomm Inc.

13. Notation A symbol error is signified by the event SE
September 2005
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
Steve Shellhammer, Qualcomm Inc.

14. September 2005
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
Steve Shellhammer, Qualcomm Inc.

15. September 2005
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
If the interference bandwidth is greater than the signal bandwidth we scale by the bandwidth ratio,
Steve Shellhammer, Qualcomm Inc.

16. Simulation Based PHY Model
September 2005
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
Steve Shellhammer, Qualcomm Inc.

17. September 2005
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
Steve Shellhammer, Qualcomm Inc.

18. September 2005
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
Steve Shellhammer, Qualcomm Inc.

19. September 2005
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.
Steve Shellhammer, Qualcomm Inc.

20. Probability Calculations
September 2005
Probability Calculations
Introduce some more notation
A packet error event is called PE
The packet error rate is the probability of a packet error
The number of symbol collisions is a discrete random variable, which we will call M
This random variable has a probability mass function,
Steve Shellhammer, Qualcomm Inc.

21. Probability Calculations
September 2005
Probability Calculations
To assist in calculating the PER we use a Total Probability formula
Probability mass function of the number of symbol collisions
Probability of a packet error conditioned on m symbol collisions
Steve Shellhammer, Qualcomm Inc.

22. Probability Calculations
September 2005
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,
Steve Shellhammer, Qualcomm Inc.

23. Probability Calculations
September 2005
Probability Calculations
Therefore the PER formula is,
Next step is to determine the probability mass function of the number of symbol collisions
Steve Shellhammer, Qualcomm Inc.

24. Probability Calculations
September 2005
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
Steve Shellhammer, Qualcomm Inc.

25. General Format of Probability Mass Function
September 2005
General Format of Probability Mass Function
Case 1 – Packet shorter than the interference pulse
The Figure shows three possible collisions
Steve Shellhammer, Qualcomm Inc.

26. General Format of Probability Mass Function
September 2005
General Format of Probability Mass Function
There is some probability that there will be no symbol collisions (like possibility 2 in the figure)
There is some probability that all the symbols will collide with an interference pulse (like possibility 1 in the figure)
It turns out for fixed pulse durations and pulses spacing that the probability of all other number of collisions is a constant
Steve Shellhammer, Qualcomm Inc.

27. General Format of Probability Mass Function
September 2005
General Format of Probability Mass Function
The PER formula for this case is given by,
Steve Shellhammer, Qualcomm Inc.

28. General Format of Probability Mass Function
September 2005
General Format of Probability Mass Function
Case 2 – Packet longer than the interference pulse
The Figure shows three possible collisions
Steve Shellhammer, Qualcomm Inc.

29. General Format of Probability Mass Function
September 2005
General Format of Probability Mass Function
There is some probability that there will be no symbol collisions (like possibility 2 in the figure)
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
There is some probability exactly K symbols will collide
Steve Shellhammer, Qualcomm Inc.

30. General Format of Probability Mass Function
September 2005
General Format of Probability Mass Function
There is no probability that more than K symbols collide
The PER formula for this case is given by,
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
Steve Shellhammer, Qualcomm Inc.

31. Simplification of Probability Calculations
September 2005
Simplification of Probability Calculations
These PER formula can be simplified
We will focus on the summation term
We can begin the summation at zero since that term is zero
Steve Shellhammer, Qualcomm Inc.

32. Simplification of Probability Calculations
September 2005
Simplification of Probability Calculations
We can pull out a constant term
Next we utilize the following algebraic identity
Steve Shellhammer, Qualcomm Inc.

33. Simplification of Probability Calculations
September 2005
Simplification of Probability Calculations
If we apply that identity we get,
Which simplifies to,
Steve Shellhammer, Qualcomm Inc.

34. Simplification of Probability Calculations
September 2005
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,
Steve Shellhammer, Qualcomm Inc.

35. September 2005
Limits of PER Formula
For small SER we get the following limit of the PER formula,
For large SER we get the following limit of the PER formula,
Steve Shellhammer, Qualcomm Inc.

36. September 2005
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
Steve Shellhammer, Qualcomm Inc.

37. Calculation of Performance Metrics
September 2005
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
Steve Shellhammer, Qualcomm Inc.

38. Calculation of Performance Metrics
September 2005
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,
Let us define τ0 as the latency without interference
Similarly, the latency with interference is given by,
Steve Shellhammer, Qualcomm Inc.

39. Example 1 – BPSK with Periodic Interference Pulses
September 2005
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
Steve Shellhammer, Qualcomm Inc.

40. Example 1 – BPSK with Periodic Interference Pulses
September 2005
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%
Steve Shellhammer, Qualcomm Inc.

41. Example 1 – BPSK with Periodic Interference Pulses
September 2005
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,
The Q Function is the tail probability of a Gaussian random variable,
Steve Shellhammer, Qualcomm Inc.

42. Example 1 – BPSK with Periodic Interference Pulses
September 2005
Example 1 – BPSK with Periodic Interference Pulses
Steve Shellhammer, Qualcomm Inc.

43. Example 1 – BPSK with Periodic Interference Pulses
September 2005
Example 1 – BPSK with Periodic Interference Pulses
Calculate Probability Mass Function
The probability of exactly 1024 symbol collisions is,
The probability of other non-zero symbol collisions is twice the probability of 1024 symbol collisions,
Steve Shellhammer, Qualcomm Inc.

44. Example 1 – BPSK with Periodic Interference Pulses
September 2005
Example 1 – BPSK with Periodic Interference Pulses
That leaves the following probability of zero symbol collisions,
This gives the following PER formula,
Steve Shellhammer, Qualcomm Inc.

45. Example 1 – BPSK with Periodic Interference Pulses
September 2005
Example 1 – BPSK with Periodic Interference Pulses
Steve Shellhammer, Qualcomm Inc.

46. Example 1 – BPSK with Periodic Interference Pulses
September 2005
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%
Steve Shellhammer, Qualcomm Inc.

47. Example 1 – BPSK with Periodic Interference Pulses
September 2005
Example 1 – BPSK with Periodic Interference Pulses
Steve Shellhammer, Qualcomm Inc.

48. Example 1 – BPSK with Periodic Interference Pulses
September 2005
Example 1 – BPSK with Periodic Interference Pulses
Steve Shellhammer, Qualcomm Inc.

49. Example 1 – BPSK with Periodic Interference Pulses
September 2005
Example 1 – BPSK with Periodic Interference Pulses
Steve Shellhammer, Qualcomm Inc.

50. Example 2 – QAM with Periodic Interference Pulses
September 2005
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
Steve Shellhammer, Qualcomm Inc.

51. Example 2 – QAM with Periodic Interference Pulses
September 2005
Example 2 – QAM with Periodic Interference Pulses
Steve Shellhammer, Qualcomm Inc.

52. Example 2 – QAM with Periodic Interference Pulses
September 2005
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
Steve Shellhammer, Qualcomm Inc.

53. Example 2 – QAM with Periodic Interference Pulses
September 2005
Example 2 – QAM with Periodic Interference Pulses
The probability of exactly 512 symbol collisions is,
The probability of the other non-zero symbol collisions is still the same as before,
The probability of zero symbol collisions is what is left,
Steve Shellhammer, Qualcomm Inc.

54. Example 2 – QAM with Periodic Interference Pulses
September 2005
Example 2 – QAM with Periodic Interference Pulses
Steve Shellhammer, Qualcomm Inc.

55. Example 2 – QAM with Periodic Interference Pulses
September 2005
Example 2 – QAM with Periodic Interference Pulses
Figures of Merit for Example 2
1% PER Distance (meters)
Maximum PER
BPSK
13.8
0.499
QPSK
17.1
0.374
16QAM
27.5
0.312
64QAM
41.7
0.281
Steve Shellhammer, Qualcomm Inc.

56. Example 2 – QAM with Periodic Interference Pulses
September 2005
Example 2 – QAM with Periodic Interference Pulses
Steve Shellhammer, Qualcomm Inc.

57. Example 2 – QAM with Periodic Interference Pulses
September 2005
Example 2 – QAM with Periodic Interference Pulses
Steve Shellhammer, Qualcomm Inc.

58. Example 3 – BPSK with Random Interference Pulses
September 2005
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
Steve Shellhammer, Qualcomm Inc.

59. Example 3 – BPSK with Random Interference Pulses
September 2005
Example 3 – BPSK with Random Interference Pulses
Steve Shellhammer, Qualcomm Inc.

60. Example 3 – BPSK with Random Interference Pulses
September 2005
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
Steve Shellhammer, Qualcomm Inc.

61. Example 3 – BPSK with Random Interference Pulses
September 2005
Example 3 – BPSK with Random Interference Pulses
Steve Shellhammer, Qualcomm Inc.

62. Summary of the Process Step 1 – Select Geometric Model
September 2005
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
Steve Shellhammer, Qualcomm Inc.

63. September 2005
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
Steve Shellhammer, Qualcomm Inc.