As far as I know, they could only have used Iridium satellites for communications. All of the alternatives that I'm aware of have satellites on geostationary orbit, which makes it impossible to cover anywhere outside 80 degrees North and South, whereas Iridium has 75 (originally 77, one failed, another collided with a defunct Russian satellite) satellites on the polar LEO orbit that covers literally the whole earth.

Iridium constellation consists of LEO satellites which have an orbital period of less than two hours.

Trivia: Iridium is #77 in the periodic table.