Outage Probability under Path Loss and Shadowing
The combined effects of path loss and shadowing have important implications for wireless system design. In wireless systems there is typically a target minimum received power level Pmin below which performance becomes unacceptable
- With shadowing the received power at any given distance from the transmitter is log-normally distributed with some probability of falling below Pmin.
- Outage probability pout(Pmin, d) under path loss and shadowing to be the probability that the received power at a given distance d, Pr(d), falls below Pmin: pout(Pmin, d) = p(Pr(d) <Pmin).
- For the combined path loss and shadowing model
- where the Q function is defined as the probability that a Gaussian random variable x with mean zero and variance one is bigger than z:
- The conversion between the Q function and complementary error function is