AWGn

AWGN stands for additive white Gaussian noise, a widely used statistical model for random disturbances in communication systems. In this model, the channel output equals the sum of the transmitted signal and an independent noise term that is Gaussian distributed and has a flat (white) power spectral density across frequencies. The Gaussian assumption reflects the central limit theorem, while the white property implies no correlation between samples at different times.

Mathematically, in continuous time the received signal is y(t) = x(t) + n(t), where n(t) is a zero-mean Gaussian process with two-sided power spectral density S_n(f) = N0/2 for all f. The average noise power in a bandwidth B is N0 B. In discrete time, the model is y[k] = x[k] + w[k], with w[k] ~ N(0, sigma^2) independent and identically distributed.

Key properties include its memoryless nature with respect to noise and its tractability for analysis. The white Gaussian model provides a convenient upper bound on performance and is used to benchmark coding, modulation, and receiver design. Real channels may deviate from the ideal assumptions, but AWGN remains a foundational reference.

Applications and capacity: AWGN is used to model many physical channels and to derive fundamental limits. The Shannon capacity of a real-valued AWGN channel with bandwidth B and average signal power P is C = B log2(1 + P/(N0 B)) bits per second. The model also underpins error-rate predictions and practical system design, while acknowledging its limitations in the presence of fading, interference, or non-Gaussian noise.