Here is a Noise Margin diagram for an indoor antenna with and without a preamp with moderately strong signals. Note that the preamp not only compensates for distribution losses but also allows reception of weaker signals than without a preamp. In this case the improvement is 5 dB, from a +13 dB NM signal to a +8 dB NM signal. The components of the improvement are preamp elimination of the 3 dB coax loss, 3 dB NF improvement of the preamp NF over the tuner NF, minus the 1 dB coax loss between the antenna and the preamp input.
3 + 3 -1 = 5 dB improvement in signal sensitivity from +13 NM to + 8 NM
If the tuner NF is more than 6 dB, or the preamp NF is less than 3 dB, or the loss between the antenna and the preamp input is less than 1 dB, then the improvement will be more than 5 dB.
Here is a Noise Margin diagram for an indoor antenna with a preamp and two weak signals. Note that neither signal is below the thermal noise floor. The antenna gain makes the Noise Margin more positive and improves the SNR.
