Methodology for NR V2X Power Imbalance Testing

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This document discusses the methodology for testing power imbalance in NR V2X, including ICS levels, distance between links, and test configurations. It also covers HARQ buffer combining tests and MCS propagation conditions for soft combining in AWGN channels.

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Coordinate Geometry Circles

Starter Write each expression in the form (? + ?)2+? 1) ?2+ 4? + 7 2) ?2 6? + 9 3) ?2+ 3? 4

Recall coordinate geometry skills Midpoint of a line segment ?1+ ?2 2 ,?1+ ?2 2 Perpendicular gradients 1 ?1?2= 1 ?? ?1= ?2 Distance between two points (?2 ?1)2+ (?2 ?1)2

Practising these skills Groups A, B and C: choose a point each! Group A: find the perpendicular bisector of AB: ?1 Group B: find the perpendicular bisector of BC : ?2 Group C: find the perpendicular bisector of AC : ?3 Group A: find the intersection of ?1 and ?2 Group B: find the intersection of ?2 and ?3 Group C: find the intersection of ?1 and ?3 Each group find the distance from the intersection to your original point What do we think is going on??

Applying these skills to circles in coordinate geometry The points ? ?, 2 and ?(3,?) are the ends of a diameter of a circle with centre ?(2, 4) Find ? and ? The points ? 3,4 and B 1,6 are the ends of a diameter. Find the centre and radius of the circle

The equation of a circle with radius r, centre the origin is ?2+ ?2= ?2 How has this equation been derived from the diagram?

Now consider a circle with centre (2,1) and radius 3 Using Pythagoras: (? 2)2+(? 1)2= 32 (? 1) 3 General equation: (? 2) (? ?)2+(? ?)2= ?2 Centre: (a,b) Radius: r https://www.desmos.com/calculator/q6hzmgf6nv

Equation of a circle with radius ? and centre ?(?,?) (? ?)2+(? ?)2= ?2 Write down the equation of the circle with centre (-3,2) and radius 4

Matching Activity: Circles 1 - From Susan Wall STEM website login required https://www.stem.org.uk/resources/elibrary/resource/31887/circle- geometry

Example: Find the centre and radius of the circle with equation: ?2+ 6? + ?2 4? = 4

Practice: 1) ?2+ 2? + ?2 2? = 2 ( 1,1) ? = 2 2) ?2+ ?2 6? + 2? = 6 (3, 1) ? = 4 3) ?2+ ?2+ 4? = 6 ( 2,0) ? = 10 4) ?2+ ?2 4? 6? = 12 (2,3) ? = 5 5) ?2+ ?2 6? + 8? = 7 (3, 4) ? = 4 2 6) ?2+ ?2 14? 4? + 13 = 0 (7,2) ? = 2 10

Finding the equation of a circle given the end points of its diameter: The line AB is a diameter of the circle C. Given that A is (2,2) and B is (8,10), find the equation of C.

Practice: 1) (? 3)2+(? 4)2= 25 1) (0,0) and (6,8) 2) ?2+ (? 6)2= 10 2) (-1,3) and (1,9) 3) (? 1)2+(? 3)2= 169 3) (-4,-9) and (6,15) 4) (? 1)2+(? 5 2)2=25 4) (3,1) and (-1,4) 4

Determine the area inside the circle defined by ?2+ ?2 8? + 4? + 4 = 0 but outside the triangle bounded by the three lines below: ? = ? 7 ? =1 52? 29 ? = 7