Additive White Gaussian Noise (AWGN)

The noise signal n(t) is linearly summed with the original transmitted signal s(t) at the receiver front-end.

• The received signal is mathematically expressed as r(t) = s(t) + n(t)
• This linear superposition simplifies analysis and simulation
• Unlike multiplicative fading, the noise power is independent of the signal amplitude
• In IQ sample processing, this means the noise adds a random complex vector to each constellation point

The noise exhibits a flat power spectral density across all frequencies of interest, analogous to white light containing all visible wavelengths equally.

• The power spectral density is constant: N₀/2 watts per hertz
• This implies the noise samples are uncorrelated in time
• In discrete IQ streams, this translates to independent noise contributions on each sample
• Real-world thermal noise approximates this flatness up to extremely high frequencies (~THz)

The instantaneous amplitude of the noise follows a normal (Gaussian) probability density function with zero mean.

• The probability density function is: p(n) = (1/√(2πσ²)) · exp(-n²/(2σ²))
• The zero-mean property ensures no DC bias is introduced
• The variance σ² equals the total noise power
• Both the In-Phase (I) and Quadrature (Q) noise components are independent and identically distributed Gaussians

The SNR quantifies the relative power of the clean signal to the AWGN, typically expressed in decibels (dB).

• Defined as SNR = 10 · log₁₀(P_signal / P_noise)
• In IQ terms, SNR = E[|s|²] / (2σ²) for complex baseband
• Low SNR regimes (e.g., < 0 dB) cause severe constellation smearing
• Modulation classifiers are benchmarked across a range of SNRs to assess robustness
• A classifier's performance curve vs. SNR is a primary design metric

Each noise sample is statistically independent from all others, a direct consequence of the white spectral property.

• The autocorrelation function is a delta function: R_nn(τ) = (N₀/2) · δ(τ)
• This means knowing the noise value at one instant provides zero information about the noise at any other instant
• For neural network training, this justifies treating each IQ segment as an independent draw from the noise distribution
• Real-world impulse noise or burst interference violates this assumption

AWGN is the primary source of aleatoric uncertainty that modulation classifiers must overcome.

• It sets the theoretical lower bound on classification error via the Shannon limit
• Training with synthetic AWGN at varied SNRs is essential for robust deployment
• Classifiers learn to identify modulation-specific structure amidst the Gaussian cloud
• Higher-order modulations (e.g., 256-QAM) are more susceptible to AWGN due to denser constellations
• I/Q normalization and denoising preprocessing steps aim to mitigate AWGN effects before inference

The probability density function governing AWGN amplitude samples. The Central Limit Theorem justifies its use, as thermal noise results from the sum of many independent electron movements. Key properties:

• Zero mean (μ = 0)
• Variance σ² equals the noise power
• 68.3% of samples fall within ±σ of the mean
• The Q-function computes tail probabilities for error rate analysis

The power per unit bandwidth of the noise, measured in watts per hertz (W/Hz). For AWGN, this is flat across all frequencies—hence 'white.' The total noise power is N₀ × B, where B is the receiver bandwidth. In digital communications, the critical parameter is E_b/N₀ (energy per bit to noise density ratio), which determines the theoretical bit error rate.

The ratio of signal power to noise power, typically expressed in decibels (dB). For IQ sample processing:

• SNR = P_signal / P_noise
• SNR_dB = 10 × log₁₀(SNR)
• Low SNR (< 0 dB): noise power exceeds signal power
• High SNR (> 20 dB): signal dominates, classification is easier
• Modulation classifiers are benchmarked across an SNR range, often from -20 dB to +30 dB

AWGN models the Johnson-Nyquist noise generated by the random thermal agitation of electrons in resistive components of the receiver front-end. The noise power is:

• P_noise = k × T × B
• k = Boltzmann's constant (1.38 × 10⁻²³ J/K)
• T = absolute temperature in Kelvin
• B = bandwidth in Hz At room temperature (290K), this yields a noise floor of approximately -174 dBm/Hz.

In complex baseband representation, AWGN is modeled as:

• n(t) = n_I(t) + j × n_Q(t)
• Both n_I and n_Q are independent, real-valued Gaussian processes
• Each has half the total noise power (σ²/2 per component)
• The noise envelope follows a Rayleigh distribution
• The noise phase is uniformly distributed over [0, 2π] This preserves the circular symmetry of thermal noise in the complex plane.

AWGN is the primary impairment used in synthetic I/Q dataset generation for training modulation classifiers:

• Clean modulated signals are generated programmatically
• AWGN is added at multiple SNR levels to create diverse training examples
• This teaches the network to extract features robust to noise
• I/Q augmentation often includes AWGN injection to improve generalization
• Classifiers trained on AWGN-only may fail under real-world fading, requiring additional channel impairments in training