If you're looking for anime similar to Voices of a Distant Star, you might like these titles. All recommendations are made by Anime-Planet users like you!
Four months ago aliens invaded Earth, but they're not obliterating cities or abducting huge amounts of people. Instead, they send one single alien to the surface each day and, for reasons unknown, teenager Kakashi is the only person in the world who can fight them. However, this duty takes a huge toll on the boy's psyche, and after a while his memories have all but disappeared. Only his broken cell phone is there to remind him of the life he left behind, but Kakashi is afraid to fix it - for what if there are no new messages, and nobody cares that he's no longer around?
A light bleached pair of animated titles, that both have an alien invasion, but actually center around relationships. A boy and a girl in Voices and a trio of younger men in Kono
In both titles there is a cell phone used as a prop. And the sending, and or waiting of messages.
The animation in both are a bit experimental. Voices was more experimental in the day, Kono uses some new techniques.