Pairwise error probability

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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.[1] It's mainly used in communication systems.[1]

Expansion of the definition[edit]

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[edit]

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 .

For a zero mean, variance Gaussian random variable:


See also[edit]


  1. ^ a b Stüber, Gordon L. Principles of mobile communication (3rd ed.). New York: Springer. p. 281. ISBN 1461403642. 

Further reading[edit]

  • 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.