AWGN (Additive White Gaussian Noise)

Additive White Gaussian Noise (AWGN) is a fundamental statistical noise model used in communication systems to simulate the impact of random noise on signals. It represents random, uncorrelated noise with constant spectral density and normally distributed amplitude, providing a reference model for theoretical analysis and system simulations.

Definition and Characteristics

AWGN combines three core properties:

• Additive: The noise is independent of the transmitted signal and adds linearly to it.

• White: Power is uniformly distributed across all frequencies, resulting in a flat spectral density.

• Gaussian: The amplitude follows a normal distribution centered around zero.

This model provides a simplified but effective way to study how systems behave under noise-limited conditions.

Probability Distribution of AWGN

The amplitude of AWGN follows a Gaussian (normal) distribution with zero mean. The probability density function is:

p(x) = (1/√(2πσ²)) × e^(-(x–μ)² / (2σ²))

Where:

• μ is the mean (typically 0)

• σ² is the variance (noise power)

Most noise values cluster near zero, with extreme values occurring less frequently.

Mathematical Representation

In a typical communication system, AWGN is modeled as:

r(t) = s(t) + n(t)

Where:

• r(t) is the received signal

• s(t) is the transmitted signal

• n(t) is the Gaussian noise component

This model allows system performance analysis using signal-to-noise ratios (SNR) and bit error rates (BER).

Example: Signal Degradation by SNR

Consider a voice signal transmitted over an AWGN channel:

• At 20 dB SNR, the noise power is 100 times weaker than the signal → clear audio quality.

• At 10 dB SNR, the noise is only 10 times weaker → audible distortion and static.

• Lower SNR values result in degraded intelligibility and higher error rates.

This illustrates how noise impacts signal clarity depending on power ratios.

Role in Communication System Design

AWGN serves as the baseline model in:

• Modulation and coding performance analysis

• Capacity estimation of ideal channels (Shannon limit)

• BER simulations for modulation schemes (e.g., QPSK, OFDM)

• Reference benchmarking in communication link design

Although real-world channels often include fading, interference, and non-Gaussian noise, AWGN remains the standard for first-order performance predictions and system optimization.