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SNR:
Short for signal-to-noise ratio, the ratio of the amplitude of a desired analog or digital data signal to the amplitude of noise in a transmission channel at a specific point in time. SNR is typically expressed logarithmically in decibels (dB).
SNR measures the quality of a transmission channel or an audio signal over a network channel. The greater the ratio, the easier it is to identify and subsequently isolate and eliminate the source of noise. A SNR of zero indicates that the desired signal is virtually indistinguishable from the unwanted noise.
BER:
Short for bit error rate. In a digital transmission, BER is the percentage of bits with errors divided by the total number of bits that have been transmitted, received or processed over a given time period. The rate is typically expressed as 10 to the negative power. For example, four erroneous bits out of 100,000 bits transmitted would be expressed as 4 x 10-5, or the expression 3 x 10-6 would indicate that three bits were in error out of 1,000,000 transmitted. BER is the digital equivalent to signal-to-noise ratio in an analog system.
They are also use as a standard in communication protocols. For example, if you have bluetooth, you need to have a minimum amount of SNR and achieve the BER in your equipment for it to be certified.
They are related but not necessarily the same. SNR is the physical limitation that you have between the signal power and the noise power. Different topologies will have different BER in the same situation. For example, normally you get higher performance (lower BER) using lower transfer rate like BPSK compare to 64QAM in the same SNR environment.
It depends on specific modulation and on channel condition. Generally, we will have BER proportional to alpha*SNR^{beta} where alpha is the multiplier and beta is the power of SNR. Usually beta is donated as diversity gain and is the slope of BER~SNR curve on loglog scale. alpha depends on how crowed the constellation is. The more crowed, the biger alpha.
Hi, friends.
Here is a pdf document which written by the Intersil specialist. It can answer your question about the relationship of BER and SNR.
Good Luck!
Chiyg
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