Does having encryption on a wireless network improve signal strength and therefore reduce the number of connection...
To my knowledge, enabling encryption has no impact whatsoever on signal strength. Signal strength is an attribute of the physical medium (RF), while encryption simply alters the length and payload encoding of the data link frames sent over that medium. If your client's received signal strength (RSSI) is N for a given AP without encryption, it should still be N with encryption.
Lisa Phifer responds to a common complaint: I'm constantly losing my wireless network connection. What can I do?
That said, what you might be getting at is the "stickiness" of clients after they connect to an AP. Clients scan all channels in their spare time, looking for other APs that might offer better service than the one they are using. A client that is willing to connect to any open AP is far more likely to accidentally connect (or at least try to connect) to other nearby APs, dropping their existing connection to do so. On the other hand, a client that is configured to connect only to a single known SSID will be less easily distracted by neighbor APs. Furthermore, if the AP requires encryption for that SSID, the odds of a "rogue AP" luring clients away are diminished. So, I can see how one might argue that encryption reduces the accidental connection losses otherwise caused by client-initiated roaming.
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