Pairwise error probability
Pairwise error probability is the error probability that for a transmitted signal () its corresponding but distorted version () will be received. This type of probability is called ″pair-wise error probability″ because the probability exists with a pair of signal vectors in a signal constellation. It's mainly used in communication systems.
Expansion of the definition
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 is defined as the probability that, when is transmitted, is received.
- can be expressed as the probability that at least one is closer than to .
Using the upper bound to the probability of a union of events, it can be written:
Closed form computation
For the simple case of the additive white Gaussian noise (AWGN) channel:
The PEP can be computed in closed form as follows:
For a zero mean, variance Gaussian random variable:
- Prasad, 5th IEEE International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC '94) The Hague, the Netherlands, September 18–22, 1994 ; ICCC Regional Meeting on Wireless Computer Networks (WCN), the Hague, the Netherlands, September 21–23, 1994 ; edited by Jos H. Weber, Jens C. Arnbak, and Ramjee (1994). Wireless networks : catching the mobile future : proceedings. Amsterdam: IOS Press. pp. 564–575. ISBN 9051991932.
- Simon, Marvin K.; Alouini, Mohamed-Slim (2005). Digital Communication over Fading Channels (2. ed.). Hoboken: John Wiley & Sons. ISBN 0471715239.