OFDM Feature Vector

Statistical measures that capture the shape of a signal's probability distribution beyond second-order statistics (variance). For OFDM signals, the large number of independent subcarriers causes the central limit theorem to produce a near-Gaussian amplitude distribution.

• Fourth-order cumulant (C42): Approaches zero for Gaussian-like OFDM signals, providing strong discrimination against single-carrier modulations like QPSK or 16QAM.
• Robustness: Cumulants are theoretically immune to Gaussian noise, making them effective at low signal-to-noise ratios.
• Practical use: Often combined with sixth and eighth-order cumulants to form a feature vector that distinguishes between CP-OFDM, DFT-s-OFDM, and single-carrier schemes.

Features derived from the periodic statistical properties of OFDM signals. The cyclic prefix and embedded pilot subcarriers introduce spectral correlation that single-carrier signals lack.

• Spectral Correlation Density (SCD): A two-dimensional function measuring correlation between spectral components at different frequencies. OFDM produces distinct peaks at cycle frequencies corresponding to the symbol rate and subcarrier spacing.
• Cyclic Autocorrelation Function (CAF): Reveals periodicity in the signal's autocorrelation. The cyclic prefix creates a peak at a lag equal to the useful symbol duration.
• Feature extraction: The alpha profile (cycle frequency domain) and the magnitude of SCD peaks at specific frequency separations are flattened into vector elements for classification.

Direct measurements from the power spectral density (PSD) and time-frequency representations that characterize the OFDM signal's bandwidth occupancy and subcarrier structure.

• Occupied bandwidth: The frequency range containing a specified percentage of total signal power, used to estimate the number of active subcarriers.
• Subcarrier spacing estimate: Derived from the periodicity in the frequency domain or from spectrogram ridge detection that identifies individual subcarrier energy peaks.
• Spectrogram variance: The statistical variance of energy across time-frequency bins captures the structured resource block allocation patterns in LTE and 5G NR signals.
• Out-of-band roll-off: The sharpness of spectral decay at band edges differs between OFDM variants and single-carrier modulations.

The Peak-to-Average Power Ratio (PAPR) distribution of an OFDM signal is a direct consequence of multi-carrier summation. The complementary cumulative distribution function (CCDF) of PAPR provides discriminative features.

• Mean PAPR: CP-OFDM typically exhibits a mean PAPR 2-3 dB higher than DFT-s-OFDM due to the DFT precoding that mimics single-carrier transmission.
• CCDF percentiles: The PAPR value at specific probability points (e.g., 10⁻³, 10⁻⁴) forms a feature set that distinguishes OFDM from constant-envelope modulations.
• Kurtosis of amplitude: The fourth standardized moment of the instantaneous amplitude captures the heavy-tailed distribution characteristic of OFDM's high-PAPR events.

Features extracted from the autocorrelation function of the received IQ samples that exploit the redundant structure introduced by the cyclic prefix.

• CP-induced correlation peak: The autocorrelation magnitude at a lag equal to the useful OFDM symbol duration (Tu) produces a distinct plateau or peak. The width of this correlation plateau estimates the CP length.
• Correlation coefficient: The normalized autocorrelation value at the CP lag serves as a detection statistic and a feature indicating OFDM presence.
• Multiple lag analysis: Computing autocorrelation across a range of candidate symbol durations enables blind estimation of the FFT size and CP ratio without prior synchronization.

Features that capture hardware-induced imperfections in the transmitter's quadrature modulator, which can serve as both nuisance parameters and discriminative fingerprints.

• IQ gain imbalance: The ratio of I-branch to Q-branch amplitude, estimated from the image rejection ratio in the frequency domain.
• Quadrature skew: The deviation from 90-degree phase offset between I and Q channels, detectable via the correlation between the real and imaginary components of the baseband signal.
• DC offset: The residual carrier feedthrough measured as a spectral spike at the center frequency, often present in direct-conversion transmitters.
• These features are included in the vector to either compensate for their effects or to perform RF fingerprinting for transmitter identification.

Statistical measures of a signal's distribution beyond second-order statistics, used to discriminate between modulation types and waveform structures. For OFDM signals, fourth-order cumulants are particularly effective because the central limit theorem drives the time-domain samples toward a Gaussian distribution.

• C40 and C42 are the most common cumulant features for OFDM vs. single-carrier discrimination
• OFDM signals exhibit near-zero fourth-order cumulant values due to their Gaussian-like time-domain characteristics
• Robust to carrier phase and frequency offsets, making them ideal for blind classification
• Computed from baseband IQ samples after coarse power normalization

Periodic patterns in the statistical moments of OFDM signals generated by the cyclic prefix, pilot subcarriers, and frame structure. The Spectral Correlation Density (SCD) function reveals these hidden periodicities as distinct peaks in the cyclic frequency domain.

• Cyclic prefix induces correlation at lags equal to the useful symbol duration
• Pilot subcarriers create cyclostationary features at multiples of the subcarrier spacing
• Enables blind estimation of symbol rate, CP length, and FFT size
• Highly robust to stationary noise and interference due to noise's lack of cyclostationarity

A frequency-domain feature that measures the peakedness of the signal's power spectral density. OFDM signals exhibit a characteristic flat-topped spectrum with sharp roll-off at band edges, producing distinct spectral kurtosis signatures.

• High kurtosis at band edges indicates sharp spectral transitions typical of OFDM
• Low kurtosis in the passband reflects the flat, noise-like in-band spectrum
• Computed by applying kurtosis calculation to successive FFT output bins
• Effective for distinguishing OFDM from spread-spectrum and single-carrier waveforms

Features derived from the lagged autocorrelation function of the received signal, exploiting the redundancy introduced by the cyclic prefix. The autocorrelation magnitude peaks at the useful symbol duration lag.

• Peak-to-average ratio of the autocorrelation function indicates CP presence
• Correlation lag profile reveals CP length and useful symbol duration
• Phase of the autocorrelation peak provides coarse carrier frequency offset estimate
• Computationally efficient and suitable for real-time feature extraction on FPGAs

Features that capture the gain and phase mismatch between the in-phase and quadrature branches of a transmitter or receiver. These hardware imperfections create mirror-frequency interference that manifests as distinct patterns in the signal constellation.

• Image Rejection Ratio (IRR) quantifies the severity of IQ imbalance
• OFDM signals with high PAPR are particularly susceptible to IQ modulator nonlinearities
• Can serve as RF fingerprinting features for transmitter identification
• Estimated via circularity measures of the complex baseband signal

The Peak-to-Average Power Ratio distribution of OFDM signals follows a characteristic pattern due to the summation of many independent subcarriers. Statistical moments of the PAPR Complementary Cumulative Distribution Function (CCDF) serve as discriminative features.

• Mean, variance, skewness, and kurtosis of instantaneous power samples
• OFDM exhibits higher 99.9th percentile PAPR compared to single-carrier waveforms
• DFT-s-OFDM shows lower PAPR than CP-OFDM, enabling waveform type discrimination
• Features are sensitive to transmitter power amplifier nonlinearities, adding device-specific signatures