Wilson electronics Sleek booster from Amazon for $85. Not free. Should give 18db +/- signal increase. Leverify ave phone near a window with strongest signal for free. Be sure to verify with the actual signal level. The bars tell very little.
Correct, the Wilson Cellular Repeaters are among the best out there, but like the "passive" method above, it requires installation of an antenna on the roof. The Repeater modules themselves have their own short "stubby" cellular antenna on them or built inside for mounting interior to the home. Also, the OP did say he was looking for a "free" solution, so I suggested the above. There are also ways to craft your own antenna, such as from a Pringles can or other container, to make a "cantenna". If you search on Youtube for them, there are plenty of DIY instruction videos.
There are better home solutions as you mentioned. OP mentioned free. The better home solutions can carry Upto 5 different devices at one time. They also allow roaming throughout a single room. They are also far from cheap. I didn't mention the yagi due to cost. For whole house solution a femtocell would be best. Cheapest room/multi device from Wilson is about $300. The sleek was closest to free. It can also be powered by battery pack for emergency while hiking.
I've noticed since rooting and using custom roms that my phone does a better job at staying on 3g in the house
Another suggestion worthy of consideration.
Ok, trying to wrap my head around how rooting would have any effect on signal reception. I mean this seams it would be a perception as opposed to actual signal gain. Rooting does nothing to enhance signal reception at all. It is simply unlocking the phone's operating system to allow you full access to change things they don't want you messing with, like their proprietary apps etc. Making this software change does nothing to enhance signal reception. Am I missing something here.I've noticed since rooting and using custom roms that my phone does a better job at staying on 3g in the house