looks like you're stuck with a passive system, which actually is good, because you won't need a duplexer (ir diplexer.... the differnce between the two is a minor one)...
if you build a high gain antenna, and place it in a spot where signal is good, then locate another high gain omnidirectional antenna in your house, and connect the two with low loss coax (look at the specs for loss per 100m at 1Ghz, choose the one with the lowest loss, that you can afford to buy). the loss of the coax run should be less than the signal loss at your location. if you lose 20db of signal going from where you want to place the outside antenna, to inside your home, then the cable loss should be much lower than that. let's say the cable length will be 50m, and the cable loss is 20db/100m (that's a ridiculously high number for good cable, but it will illustrate what i'm talking about), so that's a 10db loss for 50m. that's a net gain of 10db though, because inside your house was a 20db loss to begin with. with 9 or 18db gain antennas, the margin gets even better.
if you build a high gain antenna, and place it in a spot where signal is good, then locate another high gain omnidirectional antenna in your house, and connect the two with low loss coax (look at the specs for loss per 100m at 1Ghz, choose the one with the lowest loss, that you can afford to buy). the loss of the coax run should be less than the signal loss at your location. if you lose 20db of signal going from where you want to place the outside antenna, to inside your home, then the cable loss should be much lower than that. let's say the cable length will be 50m, and the cable loss is 20db/100m (that's a ridiculously high number for good cable, but it will illustrate what i'm talking about), so that's a 10db loss for 50m. that's a net gain of 10db though, because inside your house was a 20db loss to begin with. with 9 or 18db gain antennas, the margin gets even better.