There is few ways to go about it depends on the envioroment, and amount of money you can afford.
The simplest is to buy an Access point like the D-Link 900AP+, and to set it as a repeater some where in the house, to extend the coverage.
If I was starting from scratch, I would get rid of the Linksys and get a regular Wired Router and plug into it a good Access Point with a good external Antenna installed in a key position of the envioroment.
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Wireless, Network Configuration Mode.
Access Point (AP) Configurations:
Mode 1 - Gateway.
All Entry Level Wireless Access Point (AP) can act as Wireless Hub to connect to Wireless Clients that are installed on computers (Wireless PCNCIA, WirelesS USB, Wireless PCI).
Mode 2. Bridge -
Some APs can also be configured as a Bridge. In such a Configuration the AP can only communicate with another AP that is configured as a Bridge. This mode is useful to Bridge two LANs segments that are apart, and it is preferred to connect them wirelessly. Plug one AP Bridge to a Switch on the first LAN, the other AP to a Switch on the second LAN, and they are connected.
Mode 3. Client -
Few APs can also be configured as Clients. In such a configuration they act as a "Fancy" regular Wireless card that usually goes on a computer. Under such configuration The AP can only communicate with Wireless Cable/DSL Router or an AP configured as a Gateway.
Mode 4. Repeater - One or two APs thus far (D-Link 900AP+) can work as a Repeater. It acts like a client to receive a signal from any 802.11b source (regular Router or AP), and then switches to AP mode to broadcasts to regular clients. Such a configuration can be used to extend the range of a Wireless LAN.
Since basic repeaters have only one Radio it alternates between Client and AP mode, thus reduces the "Speed" of the extended segment by 50%.
Mode 5. Independent Bridges - These are units that are actually
Wireless clients that are Independent of Drivers. As a result they can be connected to a device that supports Wireless but it is not a regular computer.
They can turn printers and game boxes that are equipped with Ethernet connection into 802.11b Wireless compatible devices. (Linksys WET11, D-Link DWL-810).
Let capture.
Mode 1 can only communicate with Mode 3.
Mode 2 can only communicate with Mode 2.
Mode 3 can communicate with Mode 1,
Mode 4 can communicate with Mode 1, and Mode 3.
Mode 5 can communicate with Mode 1 (and Mode 2 if it can be configured as a real bridge).
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As far as I know. To date, almost all the APs that are part of a Wireless Cable/DSL Routers are hard set as Gateways, and can not be configured as Bridges.
This is the one Cable/DSL Router that Claims capacity to work as a Repeater, and compliant with the pre draft of 802.11g.
AirStation G54 Broadband Router.