Change Point Detection

The fundamental architectural divide in change point detection determines whether analysis occurs in real-time on streaming data or retrospectively on a complete dataset.

• Online (Sequential) Detection: Processes each new spectrum observation as it arrives, minimizing detection delay. Algorithms like CUSUM and Page-Hinkley maintain a running statistic and trigger an alarm when it exceeds a threshold.
• Offline (Retrospective) Detection: Analyzes a fixed historical time series to identify all change points simultaneously. Methods like Binary Segmentation and PELT optimize a global cost function.
• Trade-off: Online methods prioritize low latency for proactive handoff, while offline methods offer higher statistical accuracy for post-hoc traffic pattern analysis.

Bayesian approaches quantify uncertainty in change point estimation by computing a full posterior distribution over possible change locations rather than a single point estimate.

• Inference Mechanism: The model computes the probability that a change occurred at each time step given all observed data, using Bayes' theorem to update beliefs recursively.
• Run-Length Distribution: A core concept where the algorithm tracks the time elapsed since the last change point, resetting to zero when a new regime is detected.
• Advantage in Spectrum: Provides a prediction confidence interval around the detected change, allowing the cognitive radio to make risk-aware handoff decisions rather than binary triggers.

Parametric change point detectors rely on likelihood ratios to compare the probability of observing data under a null hypothesis of no change versus an alternative hypothesis of a distributional shift.

• Generalized Likelihood Ratio (GLR): Computes the ratio of maximum likelihoods under pre-change and post-change parameter estimates, detecting shifts in mean, variance, or spectral density.
• Sequential Probability Ratio Test (SPRT): An optimal online method that continues sampling until the cumulative likelihood ratio crosses a decision boundary, minimizing expected detection delay for a given false alarm rate.
• Application: Detecting a shift in the ON/OFF traffic model parameters of a primary user, such as a sudden increase in channel holding time.

When the underlying distribution of spectrum occupancy is unknown or non-stationary, non-parametric methods detect changes without assuming a specific statistical model.

• Kernel Change Point Detection: Uses maximum mean discrepancy to compare distributions in a reproducing kernel Hilbert space, detecting changes in higher-order moments.
• Rank-Based Statistics: The Mann-Whitney U statistic and Kolmogorov-Smirnov test detect shifts by comparing the empirical cumulative distribution functions of two windows.
• Robustness: These methods are essential in contested electromagnetic environments where adversarial interference or jamming creates non-standard noise distributions that violate Gaussian assumptions.

Deep learning architectures learn to detect regime shifts directly from raw spectrum data, capturing complex, non-linear patterns invisible to classical statistical tests.

• Siamese Networks: Compare feature embeddings of two sliding windows; a large distance between embeddings signals a change point.
• Temporal Convolutional Networks (TCNs): Process long sequences of spectrum occupancy data with dilated convolutions, learning hierarchical representations of traffic pattern transitions.
• Autoencoder Reconstruction Error: An autoencoder trained on normal spectrum behavior produces a spike in reconstruction error when a primary user's traffic pattern abruptly changes, functioning as an unsupervised change point detector.
• Integration: These models feed directly into LSTM Spectrum Predictors by triggering model retraining when a concept drift is detected.

Understanding the distinction between gradual concept drift and abrupt change points is critical for designing adaptive spectrum mobility systems.

• Change Point: An instantaneous, structural break in the data-generating process. Example: A primary user switches from a Poisson arrival pattern to a periodic transmission schedule.
• Concept Drift: A slow, incremental evolution of the statistical properties over time. Example: A cellular base station's load gradually increases over hours as users wake up.
• Detection Strategy: Change point detectors use threshold-based alarms for sudden shifts, while drift detectors like ADWIN or DDM monitor the error rate of a predictive model for gradual degradation.
• Operational Impact: A change point triggers an immediate model reset, while concept drift initiates a continuous model adaptation or fine-tuning cycle.

A stochastic framework used to mathematically represent the temporal behavior of licensed spectrum users. The most common formulation is the ON/OFF traffic model, where a channel alternates between busy (ON) and idle (OFF) periods.

• Exponential ON/OFF: Memoryless, analytically tractable
• Markovian arrival process: Captures bursty, correlated traffic
• Phase-type distributions: Models complex holding time patterns
• Accurate activity models are the foundation for change point detection and proactive handoff

A statistical model that infers unobservable channel occupancy states from observable signal measurements. HMMs are foundational for Bayesian change point detection in spectrum sensing.

• Hidden states: True channel status (idle/busy)
• Observations: RSSI, energy detector output, cyclostationary features
• Transition matrix: Encodes the probability of state changes
• The Viterbi algorithm decodes the most likely sequence of hidden states, revealing abrupt occupancy shifts

A particle filter method for non-linear, non-Gaussian state estimation in spectrum mobility. SMC uses a set of weighted samples (particles) to approximate the posterior belief state of channel occupancy.

• Handles multi-modal distributions common in spectrum data
• Each particle represents a hypothesis about the current channel state
• Particles are resampled based on how well they predict new observations
• Enables online change point detection without Gaussian assumptions

A non-parametric Bayesian method that provides a predictive distribution over future channel idle times, including a prediction confidence interval to quantify uncertainty.

• Defined by a kernel function (RBF, Matérn) capturing temporal correlations
• Naturally identifies change points where the predictive variance spikes
• Does not require specifying a fixed functional form for the data
• The uncertainty envelope is critical for risk-aware spectrum handoff decisions

A statistical hypothesis test determining whether past observations of one frequency channel's occupancy improve the prediction of another channel's state. This reveals causal influence between spectrum bands.

• Tests if lagged values of Channel A provide statistically significant information about Channel B
• A sudden change in Granger-causal relationships can signal a network-wide anomaly
• Used to build causal graphs of spectrum interdependence
• Requires stationarity; change point detection is often applied as a preprocessing step