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The amplifier gain does add to the power level of the signal, but the amplifier also amplifies the noise floor, plus its own internal noise. In order to have successful reception, the signal must meet ALL of the following qualifications:
1) Adequate signal power at the input to the tuner. Generally, -82 to -85 dBm is the weakest signals usable.
2) Adequate ratio between the desired signal power and the (simplified) background noise level. Bare minimum is usually around 15-16 dB differential under ideal conditions.
3) The quality of the signal must be such that the tuner is able to decode it reliably. Generally, quality is adversely affected by such things as multi-path and external electrical interference (noise).
The concept of the "noise margin" is such that, if, at the input to the tuner, it is greater than zero, then reception should occur provided ALL of the above requirements are met.
Increasing the gain of the antenna is the only way to improve the power level of the signal without simultaneously raising and degrading the noise floor. Bottom line, it's the only way to improve the signal to noise ratio or the "noise margin".
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