if i am working on antenna tilting angel to change the cell shape and size but i am using algorithm that understand the amount of shift in the antenna radiation pattern boundary how can i relate the change in tilt with the amount of shifting
If I understand your question correctly, the boundary of the cell would shift according to the antenna pattern at different elevation angles. Antenna gain is not going to be the same at different elevation angles. If it's an omnidirectional antenna, then that's how omni antenna achieve gain. They limit the radiation pattern at high (and low) elevation angles. So perhaps you are using this reduced gain at higher elevation angles to fine-tune your cell size or shape?
If you are asking for specific contours, that would depend on the antenna design itself. They vary. That information should be available from the manufacturer.
Antenna performance depends on: array (polarization) pattern, power, elevation angle, the frequency in use, terrain, atmospheric state, height from ground. The manufacturer's specifications could assist you
i am using dynamic tilting strategy to increase the capacity of a system with six sector antenna and each sector would change it tilting angle according to its traffic density i use soft boundary shifting each sector would be shrink or expand with a specific shifting value but how to calculate this value from tilt angle changing
The SINE of tilt angle will give you distance from the radiation point. You consider triangle having one side is your antenna mounting height (Vertical distance of antenna from earth), other side is horizontal distance where pattern top point touches the ground to the antenna mounting base. Ar tilting angle gets changed, the horizontal distance from antenna will vary in accordance with sinusoide of tilting angle (tilting is on a down ward side)
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