On Linux, you can scan the connection with
device="$(ip -o -4 route show to default | awk '{print $5}')"
watch -d -n0,5 iw dev $device station dump
which will show something like:
Station dc:9f:db:f1:c2:88 (on wlp1s0)
inactive time: 668 ms
rx bytes: 41304484
rx packets: 33901
tx bytes: 2289023
tx packets: 12030
tx retries: 2573
tx failed: 0
signal: -46 [-46] dBm
signal avg: -46 [-46] dBm
tx bitrate: 144.4 MBit/s MCS 15 short GI
rx bitrate: 72.2 MBit/s MCS 7 short GI
authorized: yes
authenticated: yes
preamble: long
WMM/WME: yes
MFP: no
TDLS peer: no
On top you see the mac address dc:9f:db:f1:c2:88 which is the same that is shown on
iwconfig $device
wlp1s0 IEEE 802.11bgn ESSID:"yourWLAN-SSID"
Mode:Managed Frequency:2.462 GHz Access Point: DC:9F:DB:F1:C2:88
Bit Rate=144.4 Mb/s Tx-Power=22 dBm
Retry short limit:7 RTS thr:off Fragment thr:off
Encryption key:off
Power Management:on
Link Quality=64/70 Signal level=-46 dBm
Rx invalid nwid:0 Rx invalid crypt:0 Rx invalid frag:0
Tx excessive retries:0 Invalid misc:173 Missed beacon:0
but both only show the connection to the wlan networks BSSID
To analyze if your Router is working, try watching the output while switching the repeater on and of.
sit next to your repeater with your laptop.
watch the signal strength if it weakens, when you turn the repeater of