At the moment I have a small wireless camera that transmits well at about 50 feet. What kind of camera/broadcaster would I need for signals to go about 1 mile through a few walls (not line of sight)
Same camera, more powerful transmitter and properly tuned aerial (antenna to those across the pond). Unsing a directional aerial (yaggi) will improve performance
What kind of camera/broadcaster would I need for signals to go about 1 mile through a few walls (not line of sight)
Your camera will be 1 mile away from your router?
Then you will also need to upgrade the router as well, to have a 1 mile range. Remember, the communication (Tx/Rx) is bi-directional.
You should also consider that if you want 1 mile range through several walls then you are probably looking at something with a 5 to 10 miles line-of-sight range. Depending upon country of use you are probably looking at a device that needs a licence-to-use.
I don't think there is any commercial WiFi device with this kind of range. The max range for Class 1 WiFi is 300-500m, open-field.
Natures warning sign: if long range cams as specified were cheap/easy/available, you would already see many people using them in their projects.
not by router, an actual camera and 1 way broadcast from camera
Longer range video stuff.
It really depends on the setup. As people have mentioned, you probably have to go through all sorts of regulations when you have high power stuff.
However, having a camera that can send signals over 1 mile directly is not the only way to do things.
If camera being set up is in a fixed location, and you have internet access there and where the base station is. Then you set up a small computer, that gets the feed, and sends the information over the internet. For security, you probably want to set up a VPN (virtual private network) that logically creates a new network between the sites, and uses encryption over the public part of the internet.
If your camera is in a plane but is close enough to a computer that can act as relay via the current wireless setup, you can use that.
If the camera is mobile, then you could use a network created from a cell phone. With a cell phone, you need to watch the data bandwidth to make sure you don't go above your monthly quota, and bring about unplanned extra phone charges. Of course with cell phones, many have the ability to do video chats in the first place, so you might want to use that.
You could of course lay wire or fiber, but for that you need to make sure it is safe, and that you have permission of all land owners whose property you cross.