Pairwise error probability is the error probability that for a transmitted signal (
) its corresponding but distorted version (
This type of probability is called ″pair-wise error probability″ because the probability exists with a pair of signal vectors in a signal constellation.
[1] In general, the received signal is a distorted version of the transmitted signal.
Thus, we introduce the symbol error probability, which is the probability
that the demodulator will make a wrong estimation
of the transmitted symbol
based on the received symbol, which is defined as follows: where M is the size of signal constellation.
The pairwise error probability
Using the upper bound to the probability of a union of events, it can be written: Finally: For the simple case of the additive white Gaussian noise (AWGN) channel: The PEP can be computed in closed form as follows:
is a Gaussian random variable with mean 0 and variance
Gaussian random variable: Hence,