Spectrogram Ridge Detection

Ridge detection operates on the spectrogram—a 2D representation of signal power across time and frequency. Each OFDM subcarrier manifests as a persistent horizontal energy ridge at its center frequency. The algorithm traces these local maxima through time, distinguishing true subcarriers from transient noise spikes by enforcing continuity constraints. This transforms raw spectral data into a structured map of active transmission resources, revealing the signal's time-frequency occupancy pattern without prior knowledge of modulation parameters.

Once ridges are identified, the frequency separation between adjacent ridges directly yields the subcarrier spacing (Δf). Key aspects:

• Peak detection: Locate ridge centroids in the frequency dimension
• Histogram analysis: Build a distribution of inter-ridge distances to identify the dominant spacing
• Standard mapping: Match measured Δf against known numerologies (15 kHz for LTE, 15/30/60/120 kHz for 5G NR)
• Accuracy: Performance degrades at low SNR where ridges fragment, requiring robust tracking algorithms

Ridge temporal persistence reveals OFDM symbol boundaries. By analyzing the duration of continuous ridge segments before phase discontinuities or amplitude drops, the algorithm estimates:

• Useful symbol length (Tu): The FFT window duration, inversely related to subcarrier spacing (Tu = 1/Δf)
• Cyclic prefix duration (Tcp): Detected by observing ridge continuity through the guard interval
• Total symbol period (Ts = Tu + Tcp): Extracted from periodic ridge amplitude modulation patterns This enables blind reconstruction of the OFDM frame timing structure.

Several computational approaches exist for extracting ridges from spectrograms:

• Greedy peak tracking: Follows local maxima frame-by-frame with frequency jump penalties, simple but prone to drift
• Dynamic programming: Optimizes ridge paths globally using cost functions balancing energy maximization and smoothness constraints
• Kalman filtering: Models ridge frequency evolution as a state-space process, predicting position and correcting with measurements
• Hough transform: Detects linear ridge segments in the time-frequency image, robust to gaps but computationally intensive
• Deep learning: CNNs trained on labeled spectrograms can directly segment ridge regions end-to-end

Ridge detection enables completely blind OFDM signal characterization without demodulation:

1. Number of active subcarriers: Count of detected ridges
2. Occupied bandwidth: Frequency span from lowest to highest ridge
3. Subcarrier spacing: Mean inter-ridge frequency gap
4. Symbol timing: Ridge duration and periodicity analysis
5. Guard band detection: Gaps between ridge clusters and band edges This capability is critical for spectrum monitoring, cognitive radio, and electronic warfare applications where signal parameters are unknown a priori.

Ridge detection performance degrades under challenging conditions:

• Low SNR: Ridges fragment and disappear into the noise floor, requiring longer integration times
• Frequency-selective fading: Deep fades can erase individual ridges, causing missed detections
• Doppler spread: High mobility smears ridges in frequency, reducing spacing estimation accuracy
• Co-channel interference: Overlapping signals create false ridge connections
• Time-frequency resolution tradeoff: Spectrogram window size must balance frequency resolution (longer window) against temporal resolution (shorter window) Mitigation strategies include adaptive thresholding, multi-taper spectral estimation, and ridge connectivity heuristics.

A compact numerical representation of an OFDM signal's discriminative characteristics used as input to machine learning classifiers. Feature vectors derived from ridge detection include:

• Ridge count: Number of detected subcarrier energy ridges
• Ridge spacing statistics: Mean and variance of inter-ridge frequency gaps
• Ridge curvature metrics: Quantifying frequency drift over time
• Energy distribution: Power concentration across detected ridges These engineered features bridge classical signal processing and statistical machine learning, enabling lightweight classifiers for real-time spectrum monitoring applications.

The process of measuring the occupied bandwidth of an OFDM transmission by detecting the active subcarrier edges. Ridge detection directly supports this by:

• Edge detection: Identifying the first and last energy ridges in the frequency dimension
• Guard band analysis: Measuring the unused subcarriers at band edges
• Energy thresholding: Applying adaptive thresholds to distinguish active subcarriers from noise Combined with subcarrier spacing estimates, bandwidth estimation enables protocol fingerprinting by matching measured parameters against known standards (e.g., LTE 1.4 MHz vs. 20 MHz configurations).