Effects in 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 distributed random variable while the phase is uniformly distributed from 0 to 2π.
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 inside the 1σ circle about 38% of the time; the noise phasor will reside inside the 2σ circle about 86% of the time; and the noise phasor will reside inside the 3σ circle about 98% of the time.
Read more about this topic: Additive White Gaussian Noise
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