I'm going to give you three options for fixing this problem. However, one thing you should do first is call up your cellular provider and let them know about your situation.
They might have a solution, but even if they can't fix it, you'll want it documented as an ongoing problem. That way when it comes time to buy some of the hardware I'm going to talk about, they might give you a discount or even cover the cost. In the worst cases, you might have an excuse to break your contract so you can switch to a carrier that can provide a suitable signal in your home.
Also called a "repeater," a signal booster does just what it says. Put the unit in an area of the house where you have a good signal, like near a window, and it will boost the signal to the rest of the house. Some repeaters also come with an external antenna you can mount outside for a better signal.
Your carrier might have a booster it sells (or that it can give you for free to correct its lousy service); however, there is a catch. That booster usually only works with that carrier's signal. So if you have family members or visiting friends who use another carrier, and they also have a weak signal, this won't help them.
A third-party company like zBoost or weBoost makes boosters that do work with multiple carriers. However, you're probably going to have to pay for this out of pocket. On the lower end, these gadgets set you back about $200.
Plus, if you want higher speed 4G coverage, count on those booster price tags bumping up to $300 or more. However, 4G is mainly an advantage only if you use your phone for internet connections. But if you have Wi-Fi at home, you can use your home internet connection on your phone and not need the more expensive 4G booster.