Spectrum Occupancy Multivariate Forecasting

The core mechanism that distinguishes multivariate from univariate models. By ingesting external regressors such as time-of-day, adjacent channel activity, and hardware sensor telemetry, the model learns cross-channel and environmental correlations.

• Adjacent Channel Power: Activity on neighboring frequencies often precedes changes on the target channel.
• Temporal Features: Hour-of-day, day-of-week, and holiday indicators capture human-driven usage cycles.
• Spectral Context: Wideband energy statistics provide a macro-view of band congestion.

Captures the statistical relationships between multiple frequency bands simultaneously. A transmission on one channel may indicate an imminent cascade of activity across a bonded or adjacent spectrum block.

• Correlation Matrices: Quantify how occupancy states co-vary across the frequency dimension.
• Granger Causality Tests: Statistically validate if one channel's history helps predict another's future state.
• Spatiotemporal Convolutions: CNNs applied across the frequency axis learn localized spectral patterns.

A foundational statistical model where each channel's occupancy is a linear function of its own past values and the past values of all other channels in the system.

• Endogenous System: Treats all channels as mutually dependent variables.
• Impulse Response Analysis: Traces how a shock on one frequency propagates through the spectrum over time.
• Stationarity Requirement: Requires differencing or transformation if spectrum data exhibits trends or seasonality.

Neural networks designed to ingest multi-dimensional input tensors of shape [time_steps, features, channels] for non-linear feature extraction.

• Multivariate LSTM: Each time step feeds a vector of features from all covariates into the recurrent cell.
• Temporal Fusion Transformer: Uses variable selection networks to weigh the importance of each covariate at each time step.
• Attention Mechanisms: Learn which historical time points and which input features are most relevant for the current forecast.

Techniques to interpret which covariates most influence the forecast, critical for model debugging and spectrum policy insight.

• SHAP Values: Game-theoretic approach to assign each feature a contribution score for a specific prediction.
• Permutation Importance: Measures the drop in forecast accuracy when a single covariate's values are randomly shuffled.
• Attention Weight Visualization: For transformer models, attention maps reveal which past time steps and features the model focuses on.

Real-world sensor networks are unreliable. Multivariate models must gracefully degrade when exogenous data streams fail.

• Data Imputation: Forward-fill, interpolation, or learned embeddings for missing sensor values.
• Masking Mechanisms: Training the model to ignore specific features by randomly dropping them during training.
• Fallback Hierarchies: Automatically reverting to a univariate model if all external covariates become unavailable.

The defining characteristic of multivariate forecasting is the use of external variables to improve prediction accuracy. In spectrum occupancy, these covariates provide context beyond the target channel's own history.

• Temporal covariates: Time of day, day of week, and holiday indicators to capture human activity cycles.
• Spectral covariates: Occupancy states of adjacent or harmonic channels to model device switching patterns.
• Spatial covariates: Data from neighboring sensors to account for transmitter mobility.

A model predicting a cellular uplink channel might use the downlink channel's activity as a leading indicator, as user equipment transmission often follows base station grants.

The specific duration into the future for which a forecast is generated, critically determining model architecture and application. Different horizons serve distinct operational needs in dynamic spectrum access.

• Short-term (milliseconds to seconds): Enables real-time collision avoidance and reactive frequency hopping. Requires low-latency online learning models.
• Medium-term (seconds to minutes): Supports proactive channel selection for session-based communications like Wi-Fi or LTE.
• Long-term (hours to days): Informs network planning, spectrum auctions, and energy-saving sleep mode scheduling.

Multivariate models excel at longer horizons by leveraging persistent exogenous patterns like diurnal cycles.