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The short version: Don't use a 1S LiPo.
The long version: If you use a freshly-charged 1S battery it will "appear" to work, however the threshold voltage of the regulator IC is 1.0V, so the minimum input voltage to get 3.3V out of it is 4.3V... about 0.1V higher than what you get out of a just-charged LiPo cell. At the LiPo's nominal voltage of 3.7V, you don't have enough voltage to feed the regulator, so it basically acts like a diode dropping the the input voltage about 1.0V, to 2.7V. The minimum input voltage for the RF module is 2.4V, but for the GPS module it's only 3.0V, so you're 0.3V BELOW the recommended input voltage of the GPS. You'll probably get an RF feed (weaker, obviously because you're running at a lower voltage), but chances are that your GPS data will be sketchy at best. Bottom line: Use a 2S.
BTW, there are regulators with lower dropout voltages than 1.0V, however none of them can source enough current for a RF module and a GPS module. It takes 250 mA minimum to guarantee that there's enough current for the GPS' startup plus the RF module's nominal transmit power.
The long version: If you use a freshly-charged 1S battery it will "appear" to work, however the threshold voltage of the regulator IC is 1.0V, so the minimum input voltage to get 3.3V out of it is 4.3V... about 0.1V higher than what you get out of a just-charged LiPo cell. At the LiPo's nominal voltage of 3.7V, you don't have enough voltage to feed the regulator, so it basically acts like a diode dropping the the input voltage about 1.0V, to 2.7V. The minimum input voltage for the RF module is 2.4V, but for the GPS module it's only 3.0V, so you're 0.3V BELOW the recommended input voltage of the GPS. You'll probably get an RF feed (weaker, obviously because you're running at a lower voltage), but chances are that your GPS data will be sketchy at best. Bottom line: Use a 2S.
BTW, there are regulators with lower dropout voltages than 1.0V, however none of them can source enough current for a RF module and a GPS module. It takes 250 mA minimum to guarantee that there's enough current for the GPS' startup plus the RF module's nominal transmit power.
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