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I've been trying to model some radio signal properties of wireless networks wrt its usefulness. For example, most WiFi network adapters would decrease their transmission rate if the overall quality of the signal is bad so as to avoid re-transmission, errors, etc.

What is the relationship of the received signal strength (measured in dBm) and the signal-to-noise ratio (SNR) wrt the overall signal quality? Ideally, I am looking for an equation or paper reference.

Thanks!

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Signal strength is only important in determining signal quality insofar as it affects the signal-to-noise ratio (SNR). As the name implies, SNR is determined by dividing the signal power by the noise power in the same bandwidth ($\frac SN$).

Claude Shannon, the pioneer of information theory, came up with a formula that gives an upper limit to how much information (you can think of this as bits) can be transmitted for a given SNR and bandwidth $B$ (I will note, though, that Wikipedia calls it the Shannon-Hartley theorem). The formula is as follows-

$$ C = B\log_2\left(1 + \frac{S}{N}\right) $$ where $C$ is the channel capacity in bits/s, $B$ is the bandwidth, and $\frac{S}{N}$ is the SNR. Modern transmitters/receivers try to get as close to this limit as they can through a number of means. One way is to increase the bits per symbol as the SNR improves (e.g. going from QPSK to 16-QAM). Another is to reduce the error correction coding as the SNR improves, and increase it when it worsens.

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  • $\begingroup$ Excellent answer. Thank you very much! This is exactly what I was looking for. $\endgroup$ – vmivanov Jul 24 '13 at 18:28

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