Watch my local tv on my Android device

I have a somewhat fancy tv that supports an external wi-fi module. If you connect that to the tv, you'll be able to stream media from a pc or other compatible device. At which point I thought, is there a way to consume that stream with an Android device? I have searched google play, there's a fair amount of tv apps that are just shortcuts to some online tv websites. I don't want that, the idea is to watch exactly what I have on my tv, turning my phone into a portable tv. What I imagine is a server box connected to the tv cable that streams it over WiFi, and then there's an app on my phone that consumes the stream. I understand that may involve a combination of software and hardware that would need to be purchased. Happy with that, just can't figure what it would be. Have done my Google homework to no avail. Please advice if there's a solution for that, or whether it's feasible at all.