Analytical Expression for Spatial Angles with 1st-Order Reflection

This submission in September 2015 presents an analytical expression for the probability density function (PDF) of spatial angles with 1st-order reflection from the ceiling in a conference room channel model. It discusses the development of channel models in the 60 GHz band, focusing on the statistics of arriving and departure angles based on experimental results. The document emphasizes the need for updated and improved models for IEEE 802.11ad. The PDF of the elevation angle is analyzed, comparing experimental results with analytical expressions.

• Spatial angles
• Reflection
• Probability density function
• Channel model
• IEEE 802.11
• 60 GHz band

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1. September 2015 doc.: IEEE 802.11-15/1028r0 PDF of Spatial Angles Reflected from Ceiling in the Conference Room Channel Model Date: 2015-09-14 Authors: Name Affiliations Address Phone Email Shouxing Simon Qu BlackBerry, Ltd. 1001 Farrar Rd., Ottawa, ON, Canada 1-613-595-4205 squ@blackberry. com James Lepp BlackBerry, Ltd. 1001 Farrar Rd., Ottawa, ON, Canada 1-613-595-4156 jlepp@blackberr y.com Submission Slide 1 Shouxing Simon Qu, BlackBerry, Ltd..

2. September 2015 doc.: IEEE 802.11-15/1028r0 Abstract This submission presents an analytical expression for the probability density function (PDF) of the spatial angles with 1st-order reflection from the ceiling in the conference room channel model specified in [1]. [1]Alexander Maltsev et al.: Channel models for 60 GHz WLAN systems , IEEE 802.11-09/0334r8. Submission Slide 2 Shouxing Simon Qu, BlackBerry, Ltd.. ..

3. September 2015 doc.: IEEE 802.11-15/1028r0 Introduction The IEEE 802.11ad group has developed a set of channel models in 60 GHz band based on the results of experimental measurements. The developed models include conference room, living room, and enterprise cubicle environments [1]-[2]. Statistic characteristics of arriving and departure angles were reported in [1] based on experimental results. No analytical results were available. As proposed in [3] for NG60, the set of 802.11ad model is to be updated and improved. Submission Slide 3 Shouxing Simon Qu, BlackBerry, Ltd.. ..

4. September 2015 doc.: IEEE 802.11-15/1028r0 Ray Tracing Model for Conference Room in [1] (Figure copied from [1]) Submission Slide 4 Shouxing Simon Qu, BlackBerry, Ltd.. .

5. September 2015 doc.: IEEE 802.11-15/1028r0 Spatial Angles with 1st-Order Reflection from Ceiling Submission Slide 5 Shouxing Simon Qu, BlackBerry, Ltd.. .

6. September 2015 doc.: IEEE 802.11-15/1028r0 What is the PDF of the elevation angle (EA) ? 2 ? 2 ? = ? = tan 1 = tan 1 (?? ??)2+(?? ??)2 h: distance between table surface and the ceiling. (??,??) specifies the location of Tx. (??, ??) specifies the location of Rx. (??,??)and (??, ??) are independently and uniformly distributed on the table surface. No general and accurate analytical expression for the PDF of EA was available. Submission Slide 6 Shouxing Simon Qu, BlackBerry, Ltd.. .

7. September 2015 doc.: IEEE 802.11-15/1028r0 Experimental Result of the PDF Reported in [1] (Figure copied from [1]) Submission Slide 7 Shouxing Simon Qu, BlackBerry, Ltd.. .

8. September 2015 doc.: IEEE 802.11-15/1028r0 Approximate PDF from Experimental Result [1] An approximate PDF of EA with 1st-order reflection from ceiling has been proposed in [1]. For Lx = 2.5m, Ly = 1m, h = 2m only. 0.0023? 0.1302 0.0087? + 0.7810 0 56.6 ? 83 83 ? 90 ?? ?????? ? ? Submission Slide 8 Shouxing Simon Qu, BlackBerry, Ltd.. ..

9. September 2015 doc.: IEEE 802.11-15/1028r0 Comments on the Approximate PDF Piece-wise linear approximation. Error is relatively large around the peak. Yielding negative values around = . Submission Slide 9 Shouxing Simon Qu, BlackBerry, Ltd.. .

10. September 2015 doc.: IEEE 802.11-15/1028r0 Analysis of General and Accurate PDF of EA 2 ? = ? = tan 1 (?? ??)2+(?? ??)2. h: constant. ??,??, ?? and ?? are independent and uniform RVs. A general and accurate PDF of EA is derived analytically. Submission Slide 10 Shouxing Simon Qu, BlackBerry, Ltd.. ..

11. September 2015 doc.: IEEE 802.11-15/1028r0 Analytical PDF Expression for the Elevation Angles 2 ?? ? ? (1) for tan 1 2: 8 2 2?? 2tan ? ? ? = ???2(?) ?? 2 4 ??+?? tan ? 2 + ?????. tan ? Submission Slide 11 Shouxing Simon Qu, BlackBerry, Ltd.. .

12. September 2015 doc.: IEEE 802.11-15/1028r0 2 ?? 2 ??: (2) fortan 1 ? tan 1 8 2 2?? 2tan ? ? ? = ???2(?) ?? 2???2? 2 2 2 2 ?? 2 ????cos 1 2?? tan ? 2 2 2 2. ?? ?? tan ? Submission Slide 12 Shouxing Simon Qu, BlackBerry, Ltd.. .

13. September 2015 doc.: IEEE 802.11-15/1028r0 2 2 ??: 3) for tan 1 ? tan 1 2+?? 2 ?? 8 2 2?? 2tan ? ? ? = ???2(?) ?? 2 2???2? 2 2 2 2 ????cos 12 2 ?? 2???2? 2 2 cos 1?? 2 tan? 2 + 2?? ?? 2 2 2 tan? 2 tan? 2 2 ?? 2 . + 2?? ?? ?? Submission Slide 13 Shouxing Simon Qu, BlackBerry, Ltd.. .

14. September 2015 doc.: IEEE 802.11-15/1028r0 0.07 Accurate approximate in [1] 0.06 0.05 0.04 PDF 0.03 0.02 0.01 0 negative -0.01 55 60 65 70 (degr.) 75 80 85 90 (Lx = 2.5m, Ly = 1m, h = 2m) Submission Slide 14 Shouxing Simon Qu, BlackBerry, Ltd.. .

15. September 2015 doc.: IEEE 802.11-15/1028r0 New Approximate PDF of EA (Lx=2.5m, Ly=1m, h=2m) ? ? 0.00225338? 0.128168 0.00060672?2+ 0.097636? 3.87211 0 57 ? < 76 76 ? 90 ?? ?????? Submission Slide 15

16. September 2015 doc.: IEEE 802.11-15/1028r0 New Approximate PDF of EA (Lx=2.5m, Ly=1m, h=2m) 0.06 0.05 0.04 PDF 0.03 0.02 0.01 0 55 60 65 70 (degr.) 75 80 85 90 Submission Slide 16 Shouxing Simon Qu, BlackBerry, Ltd.. .

17. September 2015 doc.: IEEE 802.11-15/1028r0 Conclusions An accurate analytical expression for the PDF of the spatial angles with first-order reflection from the ceiling in the conference room model specified in [1] is presented. Only elementary functions are involved. No special function is needed. While the corresponding statistical distribution obtained from experiment in [1] is consistent with the analytical result for the specific example, the analytical result provides a theoretical, general and accurate PDF for the EA. A new approximate PDF with higher accuracy is proposed. Submission Slide 17 Shouxing Simon Qu, BlackBerry, Ltd.. .

18. September 2015 doc.: IEEE 802.11-15/1028r0 References [1]Alexander Maltsev et al.: Channel models for 60 GHz WLAN systems , IEEE 802.11-09/0334r8. [2] Alexander Maltsev et al.: Verification of IEEE 802.11ad channel model for enterprise cubical environment , IEEE 802.11-15/0630r0. [3] Alexander Maltsev et al.: NG60 channel modeling plan , IEEE 802.11-15/0614r1. Submission Slide 18 Shouxing (Simon) Qu, Blackberry, Ltd.