Editing Additive white Gaussian noise (section)

==Effects in phasor domain==
[[File:Noisy Phasor.jpg|thumb|300px|AWGN contributions in the phasor domain]]

In modern communication systems, bandlimited AWGN cannot be ignored. When modeling bandlimited AWGN in the [[phasor]] domain, statistical analysis reveals that the amplitudes of the real and imaginary contributions are independent variables which follow the [[Gaussian distribution]] model. When combined, the resultant phasor's magnitude is a [[Rayleigh distribution|Rayleigh-distributed]] random variable, while the phase is uniformly distributed from 0 to&nbsp;2{{pi}}.

The graph to the right shows an example of how bandlimited AWGN can affect a coherent carrier signal. The instantaneous response of the noise vector cannot be precisely predicted, however, its time-averaged response can be statistically predicted. As shown in the graph, we confidently predict that the noise phasor will reside about 38% of the time inside the 1''σ'' circle, about 86% of the time inside the 2''σ'' circle, and about 98% of the time inside the 3''σ'' circle.<ref name="rrd">{{citation
| title = Radio Receiver Design
| first = Kevin 
| last = McClaning
| publisher = Noble Publishing Corporation }}
</ref>