1. doc.: IEEE 802.19-05/0044r0 Submission November 2005 Steve Shellhammer, Qualcomm Inc.Slide 1 Au Update on Estimating Packet Error Rate Caused by Interference 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 this document is subject to change in form and content after further study. The contributor(s) reserve(s) the right to add, amend or withdraw material contained herein. Release: The contributor grants a free, irrevocable license to the IEEE to incorporate material contained in this contribution, and any modifications thereof, in the creation of an IEEE Standards publication; to copyright in the IEEE’s name any IEEE Standards publication even though it may include portions of this contribution; and at the IEEE’s sole discretion to permit others to reproduce in whole or in part the resulting IEEE Standards publication. The contributor also acknowledges and accepts that this contribution may be made public by IEEE 802.19. Patent Policy and Procedures: The contributor is familiar with the IEEE 802 Patent Policy and Procedures, including the statement "IEEE standards may include the known use of patent(s), including patent applications, provided the IEEE receives assurance from the patent holder or applicant with respect to patents essential for compliance with both mandatory and optional portions of the standard." Early disclosure to the TAG of patent information that might be relevant to the standard is essential to reduce the possibility for delays in the development process and increase the likelihood that the draft publication will be approved for publication. Please notify the Chair as early as possible, in written or electronic form, if patented technology (or technology under patent application) might be incorporated into a draft standard being developed within the IEEE 802.19 TAG. If you have questions, contact the IEEE Patent Committee Administrator at.http:// ieee802.org/guides/bylaws/sb-bylaws.pdfpatcom@ieee.org Date: 2005-11-02 Authors:

2. doc.: IEEE 802.19-05/0044r0 Submission November 2005 Steve Shellhammer, Qualcomm Inc.Slide 2 Presentation Outline Background Review of Temporal Collision Model Extension to Model to use BER instead of SER Simplification of Probability Calculations Conclusions

3. doc.: IEEE 802.19-05/0044r0 Submission November 2005 Steve Shellhammer, Qualcomm Inc.Slide 3 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

4. doc.: IEEE 802.19-05/0044r0 Submission November 2005 Steve Shellhammer, Qualcomm Inc.Slide 4 Review of Temporal Collision Model

5. doc.: IEEE 802.19-05/0044r0 Submission November 2005 Steve Shellhammer, Qualcomm Inc.Slide 5 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

6. doc.: IEEE 802.19-05/0044r0 Submission November 2005 Steve Shellhammer, Qualcomm Inc.Slide 6 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

7. doc.: IEEE 802.19-05/0044r0 Submission November 2005 Steve Shellhammer, Qualcomm Inc.Slide 7 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

8. doc.: IEEE 802.19-05/0044r0 Submission November 2005 Steve Shellhammer, Qualcomm Inc.Slide 8 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

9. doc.: IEEE 802.19-05/0044r0 Submission November 2005 Steve Shellhammer, Qualcomm Inc.Slide 9 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

10. doc.: IEEE 802.19-05/0044r0 Submission November 2005 Steve Shellhammer, Qualcomm Inc.Slide 10 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.

11. doc.: IEEE 802.19-05/0044r0 Submission November 2005 Steve Shellhammer, Qualcomm Inc.Slide 11 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,

12. doc.: IEEE 802.19-05/0044r0 Submission November 2005 Steve Shellhammer, Qualcomm Inc.Slide 12 Probability Calculations To assist in calculating the PER we use a Total Probability formula Probability of a packet error conditioned on m symbol collisions Probability mass function of the number of symbol collisions

13. doc.: IEEE 802.19-05/0044r0 Submission November 2005 Steve Shellhammer, Qualcomm Inc.Slide 13 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,

14. doc.: IEEE 802.19-05/0044r0 Submission November 2005 Steve Shellhammer, Qualcomm Inc.Slide 14 Probability Calculations Therefore the PER formula is, Given the probability mass function of the number of symbol collisions we can calculate the PER Several examples we given in September

15. doc.: IEEE 802.19-05/0044r0 Submission November 2005 Steve Shellhammer, Qualcomm Inc.Slide 15 Extension of Temporal Collision Model to use BER instead of SER

16. doc.: IEEE 802.19-05/0044r0 Submission November 2005 Steve Shellhammer, Qualcomm Inc.Slide 16 Probability Calculations Total Probability Formula still applies 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

17. doc.: IEEE 802.19-05/0044r0 Submission November 2005 Steve Shellhammer, Qualcomm Inc.Slide 17 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 N CBPS The number of information bits per symbol is N BPS The two are related by the code rate The post-FEC bit error rate is,

18. doc.: IEEE 802.19-05/0044r0 Submission November 2005 Steve Shellhammer, Qualcomm Inc.Slide 18 Probability Calculations The number of information bit in m symbol is m N BPS 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, The resulting PER formula is then,

19. doc.: IEEE 802.19-05/0044r0 Submission November 2005 Steve Shellhammer, Qualcomm Inc.Slide 19 Simplification of Probability Calculations

20. doc.: IEEE 802.19-05/0044r0 Submission November 2005 Steve Shellhammer, Qualcomm Inc.Slide 20 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

21. doc.: IEEE 802.19-05/0044r0 Submission November 2005 Steve Shellhammer, Qualcomm Inc.Slide 21 Simplification of Probability Calculations Which simplifies to, Then the PER is given by, This is not as simple as the case when we use the SER but still not too difficult to calculate

22. doc.: IEEE 802.19-05/0044r0 Submission November 2005 Steve Shellhammer, Qualcomm Inc.Slide 22 Conclusions The process described in September has been extended to the case when we have the post- FEC 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