Signal distance would have nothing to do with your device.
Correct, the device itself does not, in a perfect world. Let me explain what i'm driving at here...
The display device you are using connects to the controller via 2.4ghz WiFi. The controller then connects to the copter via 5.8ghz for control and 2.4ghz for video downlink. The theory i'm trying to establish here is that the mobile device design and the orientation of the device on the controller can all impact the RF performance of the system.
let's start with purely blocking theory. Because of how the mobile device mount orients your device on the controller, it's easy to obstruct both the 5.8ghz aerial antenna and the 2.4ghz patch antennae inside the controller. For example, if i hold my phone 10 feet from my router, i can run repeated speedtests that usually land +/- 5% of eachother. If i grab my windows surface tablet and space it two inches from the phone, between the router and the phone, my results become more erratic, ranging from the same to +/- 20%. There's no black magic in the P3S controller setup, it's susceptible to the same types of interference.
Couple the RF blocking with interference from your mobile device constantly searching for 2.4ghz and 5.8ghz networks, RF and EMF from poorly shielded electronics, etc, there's huge potential for the phantom RF system to be impeded. If you're using something larger like a 7 or 8 inch tablet, assuming you hold the RC parallel to the ground, with the phantom directly above you, you basically have an 8-inch RF-emitting metal plate obstructing RF signal to the copter.
The point i'm trying to make here is that these are important variables to keep in mind while evaluating and attempting to maximize the range of the P3S. One user very clearly noted that his range doubled when he removed his device from the mount and had someone else hold it, which all but confirms my theory.
Sorry for hijacking your thread with this, i'll post it elsewhere as well, but i think it's something the community should look out for and try to mitigate as best they can for best performance.