At last, after many weeks of battling with this project, I have now succeeded in amplifying the local 4G signal by 15 dBm. Part of the problem was that my iPhone 5, which I was using for testing, did not really work too well on 4G and since the signal is so poor where I live this made it fairly impossible to do proper experiments. After my neighbour came round with her iPhone 7 and helped me with the project, I went out and upgraded my phone to the 7. Now I can monitor the signal quality with relative ease.

Another factor was the type of indoor antenna. I switched out the normal 'whip' antenna to one with a square back plate as shown below:

The RF amp that I used was an NLB-310, with 2 of the cascaded together in series. I also had success with a low noise amplifier (LNA) the QPL9065.

Here's the LNA module:I also tried this variable gain amp, the Analog devices HMC742A, but I've not got it to work yet:

All the boards above are DIY custom design for testing purposes and can be linked together using U.FL RF cables to produce cascades.