SIM800L module on Arduino nano
Thanks to @PeterPaulKiefer here is the answer.
External power for SIM800L module GND pin needs to be connected to both SIM800L module GND pin and Arduino nano GND pin. (e.g between RST and R2 pin on Arduino nano)
In order for the calling function to work, you also need to use a capacitor on SIM800L VCC and GND pins. I used 35V, 3300µF.
Schema:
                  Antena
                   \_/
                    |
Arduino    SIM800L  |  External 4.0V
             NET ---/
             VCC ----- +4.0V
 D2 --------- RST   |
 D3 ---------  RX  === Capacitor (35V, 3300µF)
 D4 ---------  TX   |
GND --------- GND ----- GND