1. March 2010
Project: IEEE P Working Group for Wireless Personal Area Networks (WPANs)
Submission Title: [SFD Design for SUN FSK]
Date Submitted: [March 2010]
Source: [Tim Schmidl, Khanh Tuan Le, Trond Rognerud] Company [Texas Instruments]
Address [12500 TI Blvd, Dallas, TX USA]
Voice:[ ], FAX: [ ],
Abstract: [This presentation gives two SFD’s for SUN FSK]
Purpose: [For information]
Notice: This document has been prepared to assist the IEEE P 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 acknowledges and accepts that this contribution becomes the property of IEEE and may be made publicly available by P
Tim Schmidl, Texas Instruments Inc.

2. SFD Proposals Evaluated
March 2010
SFD Proposals Evaluated
Three proposals for SFD pairs (Plan A, B, C) are given in g-sfd-and-fec-proposal.pdf
This document proposes Plan D:
Plan
SFD Value for FEC
SFD value for Non-FEC A
0xF68D
0x7BC9 B
0x6F4E
0x904E C
0x21F6
0xC9C2 D
0x632D
0x7A0E
Tim Schmidl, Texas Instruments Inc.

3. Optimization Metric for SFD Design
March 2010
Optimization Metric for SFD Design
Plans A, B, and C are optimized by minimizing rms. Problems with rms include:
Correlation of 6 is weighted the same as correlation of -6, while correlation of 6 is much more likely to cause a false alarm
Highest rms value occurs with correlation of -16, which is largest distance away from the SFD and the least likely to cause a false alarm
Weights for rms do not vary much from correlation of 6 to correlation of 4, while the probability of false alarm varies greatly
Plan D was found by directly optimizing the probability of false alarm, so this gives a low probability of false alarm
False alarm probability is what affects system performance
Tim Schmidl, Texas Instruments Inc.

4. <month year>
doc.: IEEE
March 2010
Computation of False Alarm Probability for a Single Shift with Correlation = 6
Assumption is that the threshold is set at a correlation of 10, which means that out of 16 bits there are 13 matching bits and 3 different bits
Correlation of 6 means that 11 bits match and 5 bits differ. If 2 of the 5 different bits are received in error, then there is a false alarm
False Alarm Probability = (5 Choose 2)p2 (1-p)14 = 10p2(1-p)14, where p = prob. of a bit error
Assuming i.i.d. errors, for p = 0.01 ( SNR of 4 dB), FA probability = 8.710-4
11 same bits
5 different bits
Correlation = 6
13 same bits
3 different bits
Correlation = 10, FALSE ALARM
2 bit errors cause a false alarm
Tim Schmidl, Texas Instruments Inc.
<author>, <company>

5. False Alarm Probability for Each Correlation Value
<month year>
doc.: IEEE
March 2010
False Alarm Probability for Each Correlation Value
Correlation values of 6 is ~50 times more likely to cause false alarms than correlation values of 4
Correlation Value
Coefficient
Formula for False Alarm Probability
False Alarm Probability for p=0.01
False Alarm Probability Normalized to Correlation of 4 6
(5 choose 2)=10
10p2(1-p)14
8.710-4
49.5 4
(6 choose 3)=20
20p3(1-p)13
1.810-5
1.0 2
(7 choose 4)=35
35p4(1-p)12
3.110-7
0.0177
(8 choose 5)=56
56p5(1-p)11
5.010-9
0.0003
Tim Schmidl, Texas Instruments Inc.
<author>, <company>

6. RMS is not the same as False Alarm Probability
<month year>
doc.: IEEE
March 2010
RMS is not the same as False Alarm Probability
Correlation Value
False Alarm Probability
False Alarm Probability Normalized to Correlation of 4
RMS Weighting relative to correlation of 4 (before taking root)
RMS Underweighting/Overweighting 6
8.7e-4
49.5
2.25
Underweight by factor of 22 4
1.8e-5 1
1.00
Correct weight 2
3.1e-7
1.8e-2
0.25
Overweight by factor of 14
5.0e-9
2.9e-4
0.00
Underweight by factor of infinity -2
7.6e-11
4.3e-6
Overweight by factor of 5.8e4 -4
1.1e-12
6.2e-8
Overweight by factor of 1.6e7 -6
1.5e-14
8.7e-10
Overweight by factor of 2.6e9 -8
2.1e-16
1.2e-11
4.00
Overweight by factor of 3.4e11
-10
2.7e-18
1.5e-13
6.25
Overweight by factor of 4.1e13
-12
3.5e-20
2.0e-15
9.00
Overweight by factor of 4.6e15
-14
4.4e-22
2.5e-17
12.25
Overweight by factor of 4.9e17
-16
5.4e-24
3.1e-19
16.00
Overweight by factor of 5.2e19
The rms metric treats the correlation of -16 as the worst case even though it is the best case because all 16 bits differ from the correct SFD and 13 bit errors would be required to generate a false alarm. The rms metric is not appropriate for estimating false alarm when the false alarm probabilities can be directly calculated
Tim Schmidl, Texas Instruments Inc.
<author>, <company>

7. Textbook Method of Finding Probability of Error
March 2010
Textbook Method of Finding Probability of Error
dmin
dmin
Probability of error is dominated by the minimum distance to the nearest neighbor and the number of nearest neighbors
Tim Schmidl, Texas Instruments Inc.

8. RMS Method Does Not Give Probability of Error
March 2010
RMS Method Does Not Give Probability of Error d1 d2
darb d3 d4
Select arbitrary distance darb and then find rms from darb.
Distances from darb are minimized, but this does not necessarily minimize probability of error.
Tim Schmidl, Texas Instruments Inc.

9. Preamble for 802.15.4d/g The preamble is repeated bytes of “01010101”.
March 2010
Preamble for d/g
The preamble is repeated bytes of “ ”.
The receiver can detect that a preamble is present, but it needs to detect the SFD to determine the start of the frame
Once the “ ” pattern is detected, the receiver knows that the SFD must start on an even position, where the 0 positions are even. Therefore it can search only on even start positions in order to lower the false alarm probability.
For images a “ ” pattern is received, so the receiver can again search for the SFD on even positions where the 0 positions are defined as even.
Tim Schmidl, Texas Instruments Inc.

10. Simulation Assumptions
March 2010
Simulation Assumptions
The received sequence is a 32 bit preamble followed by an SFD. The receiver is assumed to detect the preamble and start searching for the SFD immediately thereafter
The receiver correlates with both of the defined SFD’s to determine which one was received
For the image, the received sequence is inverted so that 0 maps to 1 and 1 maps to 0
Tim Schmidl, Texas Instruments Inc.

11. Preamble Detector Types
March 2010
Preamble Detector Types
Type 0: The correlation values for all start positions are searched. This is the so-called “conventional” detector.
Type 1: The correlation values for only even start positions are searched because these are the only positions that can contain a valid SFD
Tim Schmidl, Texas Instruments Inc.

12. 105 * False Alarm Rates at 4 dB SNR
<month year>
doc.: IEEE
March 2010
105 * False Alarm Rates at 4 dB SNR
Type 0: Conventional detector
Interferer
Plan B, SFD 1
Plan B, SFD 2
Plan D, SFD 1
Plan D, SFD 2
SFD 1 7 5 4 23
SFD 2 2 20
SFD 4d
176 87 45 25
Image (SFD 1) 8 95
110
Image (SFD 2) 50 26
Plan B average false alarm rate = 7.0e-4
Plan D average false alarm rate = 7.1e-4
Tim Schmidl, Texas Instruments Inc.
<author>, <company>

13. 105 * False Alarm Rates at 4 dB SNR
<month year>
doc.: IEEE
March 2010
105 * False Alarm Rates at 4 dB SNR
Type 1: Search even positions
Interferer
Plan B, SFD 1
Plan B, SFD 2
Plan D, SFD 1
Plan D, SFD 2
SFD 1 4
0.03
SFD 2 2
SFD 4d 89 87
0.07
Image (SFD 1) 5
Image (SFD 2) 48 3
Tim Schmidl, Texas Instruments Inc.
<author>, <company>

14. Average False Alarm Rates at 4 dB SNR
<month year>
doc.: IEEE
March 2010
Average False Alarm Rates at 4 dB SNR
Type 1: Search even positions
Full correlation values for all shifts are shown in backup slides
Plan
Number of shifts with correlation of 6
Average False Alarm Rate at 4 dB SNR A 1
2.1e-4 B 2
4.9e-4 C
2.8e-4 D
5.2e-5
About a factor of 10 higher false alarm rate with Plan B versus Plan D!
Tim Schmidl, Texas Instruments Inc.
<author>, <company>

15. <month year>
doc.: IEEE
March 2010
Conclusion
Probability of false alarm for each shift position can be calculated directly from the correlation value
Plans A, B, and C each contain a shift position with a correlation of 6 which leads to high false alarm rates
Plan B will have poor coexistence with d since high correlations with the 15.4d SFD are found for both SFD1 and SFD2
Plan B and Plan D have almost the same false alarm probability with the Type 0 conventional detector (7.0e-4 versus 7.1e-4), but Plan D offers about 10x lower false alarm probability when the preamble structure information is utilized with the Type 1 detector (4.9e-4 versus 5.2e-5)
Plan D offers the best correlation properties and should be selected as the g SFD’s
Tim Schmidl, Texas Instruments Inc.
<author>, <company>

16. March 2010
Backup
Tim Schmidl, Texas Instruments Inc.

17. Correlation with Plan A SFD’s
<month year>
doc.: IEEE
March 2010
Correlation with Plan A SFD’s
Correlation with 0xF68D
Shift from First 0 of Preamble 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
Preamble + SFD1 -2 -4
Preamble + SFD2
Preamble d SFD
Image (Preamble + SFD1) 1 -3 -1
Image (Preamble + SFD2) -5 3
Correlation with 0x7BC9
Shift from First 0 of Preamble 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
Preamble + SFD1 -2 -4
Preamble + SFD2
Preamble d SFD
Image (Preamble + SFD1) -6 1 3
Image (Preamble + SFD2) -1 -3
Tim Schmidl, Texas Instruments Inc.
<author>, <company>

18. Correlation with Plan B SFD’s
<month year>
doc.: IEEE
March 2010
Correlation with Plan B SFD’s
Correlation with 0x6F4E
Shift from First 0 of Preamble 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
Preamble + SFD1 -4 -2
Preamble + SFD2
Preamble d SFD
Image (Preamble + SFD1) 1 -1 -3
Image (Preamble + SFD2) 3 5
Correlation with 0x904E
Shift from First 0 of Preamble 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
Preamble + SFD1 -4 -2
Preamble + SFD2
Preamble d SFD
Image (Preamble + SFD1) 1 3
Image (Preamble + SFD2) -1 -3
Tim Schmidl, Texas Instruments Inc.
<author>, <company>

19. Correlation with Plan C SFD’s
<month year>
doc.: IEEE
March 2010
Correlation with Plan C SFD’s
Correlation with 0x21F6
Shift from First 0 of Preamble 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
Preamble + SFD1 -4 -2
Preamble + SFD2 -6
Preamble d SFD
Image (Preamble + SFD1) -3 1
Image (Preamble + SFD2) 5 -1
Correlation with 0xC9C2
Shift from First 0 of Preamble 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
Preamble + SFD1 -2 -6
Preamble + SFD2 -4
Preamble d SFD
Image (Preamble + SFD1) -1 1 3
Image (Preamble + SFD2)
Tim Schmidl, Texas Instruments Inc.
<author>, <company>

20. Correlation with Plan D SFD’s
<month year>
doc.: IEEE
March 2010
Correlation with Plan D SFD’s
Correlation with 0x632D
Shift from First 0 of Preamble 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
Preamble + SFD1 -4 -2 -6
Preamble + SFD2
Preamble d SFD
Image (Preamble + SFD1) 3 -1 -5
Image (Preamble + SFD2)
Correlation with 0x7A0E
Shift from First 0 of Preamble 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
Preamble + SFD1 -4 -2 -6
Preamble + SFD2
Preamble d SFD
Image (Preamble + SFD1) 1 -1 3
Image (Preamble + SFD2) -3
Tim Schmidl, Texas Instruments Inc.
<author>, <company>

21. SFD Selection Criteria
March 2010
SFD Selection Criteria
The criteria for the selection of 2 SFD’s is given in g-fsk-sub-group-resolution-update.pdf
Process to select the SFD values:
1. Will be selected based on the following prioritized criteria:
a. Autocorrelation and cross correlation to the other pattern
b. Good image rejection (low correlation against the image)
c. Correlation relative to the preamble (low side lobes against the preamble)
2. The following prioritized differentiators will be used to select SFD values if multiple solutions are found with identical performance. Supporting data for item 2a shall be provided by all proposals.
a. The selected code should have good orthogonality against the existing d SFD. (Co-existence with d is imperative)
3. Timeline:
a. Harada-san: proposals provided within one month (no later than 2/22 midnight PST) and exchanged among subgroup participants. Proposals will be ed to Harada-san and copied to all members of the SFD subgroup. Harada-san will send an to all SFD participants.
b. There will be a conference call the week of 2/22 to review the proposals. Harada-san will schedule the conference call for 2/25 (we propose using the normal 4g call time)
Tim Schmidl, Texas Instruments Inc.