Why a standard ceiling AP struggles above about 7.5 m, why turning up the transmit power or fitting a high-gain omni antenna makes things worse, and what a downward-pointing directional antenna does instead. Change the ceiling height and antenna, and drag the person across the floor.
The shape around the AP is its radiation pattern in the vertical plane: the further out, the more gain in that direction (on a dB scale). The coloured strip on the floor is the downlink signal the selected client would receive there.
Power only raises the downlink (AP → client). The client keeps transmitting at its own fixed power (11–18 dBm for the profiles here), so the uplink stays exactly where it was. The client shows full bars, but the AP can't hear it well enough: retries, low data rates, dropped calls.
Meanwhile every +6 dB pushes the AP's interference reach about 60% further across a typical warehouse (it would double in completely open space).
An omni antenna can't create gain; it only reshapes where the energy goes. A high-gain omni squeezes its pattern into a flat "pancake" around the horizon: more signal sideways, towards walls and the other APs, and much less downwards, where the clients are.
The dead zone under and around the AP grows, and so does the interference reach.
A directional (patch) antenna pointed down puts its gain into a cone below the AP. Because an antenna has the same gain for sending and receiving, that helps both directions: the client hears the AP and the AP hears the client.
Very little energy goes sideways, so neighbouring APs barely hear each other. Cells become small and predictable, and channels can be reused.