Channel Simulation

The foundational thermal noise model. AWGN adds a random signal with a flat power spectral density and Gaussian amplitude distribution to the IQ stream.

• Models: Johnson-Nyquist noise in receiver front-ends.
• Parameter: Noise power relative to signal power, quantified as Signal-to-Noise Ratio (SNR) in dB.
• Impact: Fills the constellation diagram with a noise cloud, increasing symbol error probability.
• Usage: The baseline impairment against which all classifier robustness is measured.

Models the effect of a signal arriving at the receiver via multiple reflected, diffracted, and scattered paths with no dominant Line-of-Sight (LOS) component.

• Mechanism: Constructive and destructive interference between delayed copies causes deep frequency-selective fades.
• Parameter: Delay spread and Doppler spread define the channel's coherence bandwidth and time.
• Impact: Causes Inter-Symbol Interference (ISI) and rapid amplitude/phase fluctuations, severely distorting the constellation.
• Model: A tapped-delay line filter with time-varying complex coefficients drawn from a Rayleigh distribution.

A fading model for environments where a dominant Line-of-Sight (LOS) path exists alongside weaker scattered multipath components.

• Parameter: The K-factor, defined as the power ratio between the dominant LOS path and the scattered paths.
• Behavior: As K → ∞, the channel approaches a pure AWGN channel (no fading). As K → 0, it degenerates to Rayleigh fading.
• Impact: Causes a non-zero mean phase shift and a less severe amplitude fade compared to Rayleigh, resulting in a tighter constellation cluster.

The residual frequency difference between the transmitter and receiver local oscillators (LOs) due to hardware imperfections and Doppler shift.

• Manifestation: A continuous, constant-rate phase rotation of the entire received IQ constellation.
• Impact: Without correction, the constellation spins, making modulation classification impossible as symbols drift across decision boundaries.
• Simulation: Multiplied onto the complex baseband signal as a complex exponential, exp(j·2π·Δf·t).
• Mitigation: CFO estimation and compensation is a critical preprocessing step before classification.

Short-term, random phase fluctuations in the local oscillator, modeled as a Wiener process or a power-law spectral density.

• Source: Imperfections in oscillator phase-locked loops (PLLs).
• Impact: Causes a random rotational jitter around each constellation point, distinct from the constant rotation of CFO.
• Effect: Smears constellation points into arcs, increasing the error vector magnitude (EVM) and degrading high-order QAM classification.
• Model: A random walk in phase applied sample-by-sample to the IQ stream.

A hardware impairment in direct-conversion (zero-IF) receivers where the I and Q branches have mismatched gain (amplitude imbalance) or are not perfectly orthogonal (phase imbalance).

• Gain Imbalance: The I component is amplified differently than Q, stretching the constellation along one axis.
• Phase Imbalance: The I and Q mixers are not exactly 90° apart, skewing the constellation into a parallelogram.
• Impact: Creates a mirror-image interference from the negative frequency spectrum onto the desired signal, destroying the integrity of the modulation format.

The fundamental thermal noise model injected into synthetic IQ streams. AWGN adds a random signal with a flat power spectral density and Gaussian amplitude distribution to the complex baseband samples. It is the simplest and most universal impairment, parameterized solely by the desired Signal-to-Noise Ratio (SNR).

• Models thermal agitation in receiver front-end electronics
• Applied independently to both I and Q components
• Foundation for benchmarking classifier robustness across SNR levels

Statistical models that simulate multipath propagation by applying time-varying amplitude and phase distortions to the IQ stream. Rayleigh fading models non-line-of-sight (NLOS) scenarios with no dominant path, while Rician fading includes a strong line-of-sight (LOS) component parameterized by the K-factor.

• Implemented via sum-of-sinusoids or filtered Gaussian noise methods
• Critical for simulating mobile environments and Doppler spread
• Teaches classifiers to handle deep fades and rapid phase rotations

A deliberate residual frequency shift applied between the transmitter and receiver local oscillators. CFO causes the entire IQ constellation to rotate continuously at a constant angular velocity proportional to the offset in Hertz. This impairment is essential for training classifiers to be invariant to phase rotation.

• Modeled as a complex exponential multiplication: e^(j2πΔf·t)
• Often combined with phase noise for realistic oscillator simulation
• Tests a model's ability to learn rotational invariance without explicit preprocessing

A hardware impairment model that introduces gain mismatch (ε) and phase error (φ) between the In-Phase and Quadrature branches of a direct-conversion receiver. The result is a distorted, non-orthogonal constellation that appears skewed or elliptical.

• Gain imbalance: I branch scaled by (1+ε), Q branch by (1-ε)
• Phase imbalance: Q branch shifted by φ degrees from perfect 90° orthogonality
• Essential for training robust classifiers that generalize across receiver hardware variations

A channel model that simulates time-dispersive propagation where multiple delayed copies of the signal arrive at the receiver. Implemented as a tapped delay line (TDL) filter, each tap represents a distinct propagation path with its own delay, amplitude, and phase.

• Power Delay Profile (PDP) defines tap weights and delays
• Causes inter-symbol interference (ISI) in the IQ stream
• Standardized profiles include EPA, EVA, and ETU for LTE/5G testing

A stochastic impairment that models the short-term frequency instability of local oscillators. Phase noise adds a random, time-varying phase error to the IQ samples, causing constellation points to smear tangentially. It is characterized by a power spectral density mask (dBc/Hz at offset frequencies).

• Modeled as a Wiener process or filtered Gaussian noise on the phase component
• Degrades classification of high-order QAM schemes with dense constellations
• Critical for simulating realistic mmWave and low-cost SDR front-ends