We use the 4G-XPOL-A0001 antenna from Solwise. It is omni-directional, with 5m of cable (which eats some of the gain, of course). We use it attached to a mobile MiFi device, rather than at home - though it gets used as emergency backup there too.
We find that, even when it is fixed to the outside of a window, it gives better reception than when the modem is sat on the inside of the same window. Often, of course, we can site the antenna better than we could the modem, so get very much better reception.
Solwise have this helpful info:
and a selection of other antenna, including directional ones, and could, for example, even use two yagi antenna for MIMO use.
This Australian site gives you an idea about how extreme you could go for a high-gain, directional, MIMO setup:
I'm pretty sure you could mount it on the same pole as the TV aerial, and run cable down to the modem. Technically it should work fine... but with 15m of cable, you might indeed be best with directional antenna and the best, lowest-loss cable you can find.
The Australian site has info on cable loss too:
Which shows applications for 4 different cable types.
Ironically, your biggest/strangest challenge might be planning permission: Without approval, you are limited to two microwave antenna on your property, which is defined as anything for 1,000MHz or above. Satellite dishes are considered as microwave antenna, as would be 4G antenna and WiFi antenna.