Again I pointed out like a lot of stuff size is decreasing, amount of data and reliability is increasing. Troposcatter antenna are still not carried by soldiers, but on trucks and trailers. Troposcatter antennas need to be larger than a satellite antenna with the current technology we have.
This link says that a Troposcatter terminal can be as small as a "portable transit case system":
http://www.comtechsystems.com/industries-capabilities/troposcatter-overview/
A troposcatter system is a point-to-point link that requires a terminal on each end, with each terminal both transmitting and receiving. Terminals can range in size from a portable transit case system to a vehicle-mounted system or large fixed installation.
The portable transit antennas are about 3 feet in diameter. A little over in my experience. They are not cosidered man portable over long distances like the satellite antenna I carried that was 1 foot in diameter. Usually deployed by being transported in a vehicle then set up when the vehicle arrives at a location. It also has a decreased range, max being about 150km in good conditions. Sometimes a little further in ideal conditions.
I am telling you I work with communications systems rather frequently and received a lot training. You are wrong in assuming that troposcatter is used to send things like satellite tv signals and GPS. It is highly directional and can not be used for wide spread coverage.
This page is about hobbyist Troposcatter tech, and says that a 70 cm receiver is better for a greater range than a 2 meter receiver:
http://www.qsl.net/oz1rh/troposcatter99/troposcatter99.htm
Greater range on 70 cm than on 2 m
70 cm may have greater range than 2 m, because:
a. lower noise level in the sky means you can take better advantage of a low-noise preamplifier in your 70 cm receiver
b. greater path loss is compensated by a larger antenna gain, given the same physical dimensions of the antenna
c. more frequent ducting because a smaller duct will do
Why do most amateurs then think that 70 cm has shorter range?
fewer other amateurs are active
greater antenna gain => smaller beam width
difficult to have the same transmitter power output
in the old days it was more difficult to make a low-noise preamplifier for 70 cm than for 2 m
greater cable loss
That is 2'4" and still could not send a signal from the Middle East to North Carolina like I could with sat-comm. Which used a dish about 1/2 that size. Not only was it 1/2 the size it was not solid but made of mesh material. Which decrease the effectiveness at transmitting and receiving. Even then it worked 100% of the time I used it.
It is still directional the size of the antenna is not going to change that and it still does not provide wide spread coverage like GPS or satellite TV.
You are missing one rather important thing. The amount of data that needs to be transmitted effects the effective range. The less data needed to transmit the further apart you can have the antennas.
In most applications the range is around 150km to 300km. Depending on frequency, power, antenna size and environment. If you have been researching you will notice that most modern set ups have less range than the earlier ones from the 1960's. Partly due to the amount of data needed to transmit increased. Methods and technology is starting to get to the point where that will likely not be the case. More sensitive equipment and better data compression will start changing that.
I will point out again I have real world experience with the equipment and have successful and unsuccessfully sent data and transmissions using that equipment. I have bounced HF radio waves across the globe from the Middle East to Germany and the US a couple of hundred times. I have set up the equipment you posted pictures of and used it. I have used satellite communication and had to set up antennas hundreds of times.
Here is a relatively simple thing to do. Go to a site that tells you the direction and elevation a satellite dish needs to be pointed to receive a signal from a satellite of your choosing. Maybe even one that is in the time lapse photo I posted in this thread. Then figure out the altitude and direction the signal source is. This is one of the things I pointed out before. You dismissed it becasue you said it would not prove the shape of the Earth. Now since you are questioning the existence of satellites in this thread and you are seeking the truth I see no reason for you to dismiss it.