Is it possible to set up a DD-WRT router as a repeater or client bridge without having access to the gateway you are trying to repeat/bridge?
No. You can create your own WiFi that's routed to the existing WiFi. You can bridge wired clients to the existing WiFi. But bridging wireless clients will not work.
We tend to think of WiFi as working just like wired Ethernet. But unfortunately, it's really not. It has its own rules and this is one case where it's just different.
The short version of the problem is this: An access point will not accept packets with origin hardware addresses that are not paired with the access point. Since some clients won't be able to reach the existing WiFi network, they won't pair with it, and those access point will reject bridged/repeated packets from them.
What might work, and I stress might, is two bridges back-to-back, connected by wired Ethernet. The specifications say it shouldn't work, but in practice it seems to. Apparently, while the WiFi hardware isn't capable of proxy registration, the DD-WRT software is. Bridging from wired to wireless is done in software in these routers, and DD-WRT is smart enough to proxy register a software-bridged packet. (It knows it has to do the WiFi magic on behalf of its wired clients, since they obviously won't be able to do it themselves.)
For this setup, you connect two wireless routers, LAN-to-LAN. You configure the WiFi on one as a station on the existing WiFi. You configure the WiFi on the other as an access point on a new network. You will probalby need to use a different SSID though, so people will specifically have to choose to connect to your network.
Theoretically, you could use the same SSID and encryption, if any. This would allow clients to automatically connect to the strongest network. You will have two issues. First, you have to make sure your two routers don't connect to each other wirelessly. That obviously won't work. Second, clients will typically show a temporary disruption of service when they switch to and from your access point because the existing network won't know where to find them. MAC learning takes up to a minute. You might get complaints if you 'steal' people who momentarily came into range of your access point and experienced service disruptions as they switch to and from it.
Update: The way back-to-back bridges work is by a form of NAT. The bridge doesn't proxy register its clients but instead re-writes their source hardware addresses.
The Repeater Bridge mode does what you're looking for, without access to the configuration of the gateway you're trying to repeat. All you need is the SSID and security key of the source network, and follow the instructions (precisely). Especially make sure that the DD-WRT repeater uses the same channel as the gateway to be repeated.
There's one caveat: the gateway to be repeated needs to use a static wi-fi channel. If it's set to change its channel automatically, you'll have to reconfigure the DD-WRT every time the channel changes.
For example when repeating wi-fi network "MyNetwork" with WPA2 key "secret" on channel 6 from a gateway, the configuration of the DD-WRT should essentially be this:
- Set channel to 6, use wireless mode: Repeater Bridge, SSID "MyNetwork", security WPA2 with key "secret"
- Virtual access point (optionally), SSID "MyVap", security WPA2 with key "myVapKey"
- Additional config as per the Repeater Bridge instructions
What clients will see is three SSID's:
- "MyNetwork", channel 6, key "secret" (the original network)
- "MyNetwork", channel 6, key "secret" (the DD-WRT repeated network)
- "MyVap", channel 6, key "myVapKey" (the virtual access point of the DD-WRT)
When clients are configured with the SSID "MyNetwork" and key "secret" they will transparently connect to either the original (1) and repeated (2) networks. How the client handles this depends on the client, and in my experience this works smooth with most devices. When moving away from the original AP and toward the DD-WRT, eventually the client will detect that the wi-fi signal is low, search for a new access point and connect to the repeater. And vice versa.
The virtual access point (3) is not necessary for this to function, but it's practical if you want to make sure that you're connecting to the DD-WRT and not the original gateway.