You have several ways to do this. One is to replace your router's built-in antennas with better third-party ones, which will send out a more powerful signal. Such products are available in two flavors: Omnidirectional antennas (the kind that most routers come with) broadcast the signal in all directions, while directional antennas let you focus on a problem area. (Note that the FCC places limits on antenna signal strength, but these consumer products fall well within them.)
Since these antennas work only with routers that either let you remove the original antennas or provide a jack for third-party antennas, check your router to see whether replacing the antennas is even an option. Several vendors offer so-called high-gain antennas; when shopping, make sure to find one that supports your current Wi-Fi technology. A few older units on the market work with 802.11b/g gear, but if you've upgraded to 802.11n, confirm that the new antenna supports the latest and fastest Wi-Fi standard.
The $50 Buffalo Technology AirStation WLE-2DA Directional Antenna supports 802.11n and claims to boost a router's signal from the standard 1-2db to 6db; it's a big, flat gizmo that you point in the direction of your problem spots. Meanwhile, the Amped Wireless High Power 12dBi Omni-Directional WiFi Antenna ($40) promises even more robust amplification. Note that both of these work only with 2.4GHz 802.11n networks (which are backward-compatible with the most popular legacy standards, 802.11b/g) and are designed primarily for indoor use. Trendnet sells a full line of antennas designed for outdoor use, including some that support dual-band (2.4GHz and 5GHz) networks.
Do-it-yourself types can experiment with a homebrew antenna, such as the one I found on a site called FreeAntennas.com, which uses foil. (I've never done this, but links to testimonials are on several forums, and I've also seen the design referenced on Lifehacker.)
What if your router doesn't support external or replacement antennas? Investing in a repeater might help. This is basically a device that you position on the outskirts of--but definitely within--the range of your router's reliable coverage; it receives, amplifies, and rebroadcasts the original signal, thereby extending the range. Hawking Technology offers an $80 model (the HWREN1) that supports 2.4GHz 802.11n and is designed for indoor use; the Netgear WN2000RPT delivers similar functionality for $70.
Implement Streaming Media Solutions
If you can browse the Web and download e-mail on your Wi-Fi, but run into dropped signals or issues with streaming multimedia, you're probably having problems with signal interference, especially if you're using 2.4GHz 802.11n (or even worse, 802.11b/g) Wi-Fi. In densely populated areas, even if other devices aren't in use, many neighboring networks may be competing for bandwidth: If more than three devices are trying to use the 2.4GHz spectrum simultaneously, someone will get knocked off, at least briefly. This isn't usually a problem for nonmedia applications--you wouldn't notice a small delay in e-mail delivery, for example--but it becomes quickly apparent with streaming media, which can stutter or freeze.
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