A question about Repeater

Hi,everybody! I've got trouble with understanding Repeater. Have you ever thought about the scene that the UE signal level at the repeater's antenna port is static sensitivity level, such as -104dBm with -121dbm noise level for GSM. After the amplification of the repeater, the signal level is improved but the s/n is degraded. Assumption: 40dB Gain & 4dB NF, the out signal will be -64dBm with -77dBm noise signal. Can the repeated signal be decoded by the BTS whose sensitivity is just -104dBm?
Thanks

the mobile signal arrive the repeater donor antenna is about -70dBm to -60dBm, not -104dBm