Directional antenna for bluetooth for allowing connection under a "cone"

Hello,

I am starting a new project with Arduino and a CC2541 chip.
I am thinking to use a directional antenna to allow the chip to "talk" with mobile phones only a certain "cone": I am attaching an image to make it clear.

Is it possibile, or should a use a certain type o directional antenna?

Thank you

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Try mounting it in the bottom (toward the ceiling when inverted) of a very large (and tall) tin can. Not directly against the bottom; about 3 cm away.