Space based internet systems, like the one recently proposed by SpaceX and Google, are said to use satellites to communicate directly with end users, without using cellular ground stations. But how much power would a consumer device like a smartphone need to send data 1,000+ km? Wouldn't a separate outdoor antenna and amplifier be required anyway, reducing the mobility?
While power requirements are higher than for regular GSM service, they are not as high as one might think. Current satellite telephones use handsets of the size of 2000-era mobile phones and are able to transmit 15 kBit/s to geosynchronous satellites (the Thuraya system). These satellites are more than 30 times farther from Earth than the planned SpaceX system. Therefore, the received power is about 1000 times weaker.
Compared to e.g. Iridium, the planned satellite network has the advantage of a much larger number of satellites (4000 compared to 66), which allows the use of highly directional antennas with way better gain, even in the phone itself.
For high speed data transfer a larger antenna will be required, but lower bandwidth services are well within reach for smart phones, albeit with a slightly changed design to house a larger antenna. I don't have precise numbers, but a bandwidth of well above 100 kBit/s seems well possible when communicating with a satellite in LEO.
If it is a geosynchronous satellite it would not be a issue. The satellite itself would transmit with sufficient power to connect with the smart phone. The satellite would a high enough gain to receive the smart phone. Any phone within the footprint of the satellite would connect easily. This is because the path of the signal is straight upwards and as a result the signal would not have and terrestrial obstructions or signal propagation issues blocking the signal. The satellites transponder would down link the to the phone company.
A low earth orbiting (LEO) satellite would not be feasible for a any cell phone service due to elliptical nature of the orbit. It would be prone only being with usable for 6-10 minutes during each pass overhead. The satellite would then take 90 mins give or take to complete an orbit of the earth. The satellites orbit would not change. However since it is orbiting Planet Earth which is rotating east to west-90 mins later the satellite would 15 degrees west of you and would not be overhead for hours if not days. Furthermore because of the elliptical orbit the speed as it passes changes. This causes something referred to as Doppler Shift as a result both smart phones and satellite would constantly have to adjust their frequencies to remain in contact.
Doppler Shift is the effect one hears when stand next to a railway track as a passing train blows the whistle. As it approaches the pitch is higher, in front of you the actual pitch, and as it passes the frequency drops in pitch.