Spectrum Occupancy Matrix

The matrix is fundamentally a 3D or 4D data structure, organizing raw spectrum data into a grid for algorithmic consumption.

• Time Axis: Represents sequential sensing periods, capturing the temporal dynamics of channel usage.
• Frequency Axis: Represents discrete frequency bins, capturing the spectral dimension of occupancy.
• Space Axis: Represents geographic coordinates or sensor node IDs, capturing spatial correlation.
• Power Axis (4D): Often includes a fourth dimension for received signal strength indicator (RSSI) or power spectral density (PSD) values, moving beyond binary busy/idle states.

The matrix can encode occupancy in two primary formats, each with distinct information content.

• Binary Matrix: A sparse matrix where '1' indicates a busy channel and '0' indicates a spectrum hole, derived by applying an energy detection threshold to raw power measurements.
• Real-Valued Matrix: Stores continuous power measurements in dBm, preserving granular signal strength data. This format is essential for interference temperature management and soft decision fusion in cooperative sensing.

The matrix's structure explicitly captures the physical dependencies of radio propagation.

• Temporal Correlation: Adjacent time slices in the matrix reflect the channel's coherence time, showing how long a frequency remains occupied or idle.
• Spectral Correlation: Adjacent frequency bins capture the channel's coherence bandwidth, showing how occupancy spills over into neighboring channels.
• Spatial Correlation: Adjacent spatial cells capture the geographic correlation of shadowing and path loss, enabling models like Convolutional LSTM to learn how usage propagates through an environment.

The dimensions of the matrix represent a critical engineering trade-off between sensing fidelity and computational load.

• Time Resolution: A fine-grained time axis (e.g., 1 ms bins) captures fast-fading and bursty traffic but generates massive data volumes.
• Frequency Resolution: A narrow frequency bin (e.g., 1 kHz) allows precise identification of narrowband signals but increases the matrix's column count exponentially.
• Spatial Resolution: A dense grid of sensors improves localization accuracy but demands high-bandwidth backhaul for data aggregation.
• The Curse of Dimensionality: High-resolution matrices become sparse and computationally intractable, requiring dimensionality reduction techniques like Principal Component Analysis (PCA) before model training.

The matrix is the direct input tensor for deep learning models that forecast future spectrum states.

• Sequence-to-Sequence Input: A sliding window of historical matrices is fed into models like Transformers or LSTMs to predict the next matrix in the sequence.
• Channel Attention: The matrix format allows attention mechanisms to weigh the importance of specific frequency bands or spatial regions for a given prediction.
• Ground Truth Labeling: A future matrix serves as the ground truth for supervised learning, enabling the calculation of loss functions like Binary Cross-Entropy for occupancy prediction.

A raw spectrum occupancy matrix is inherently noisy due to imperfections in the sensing process.

• False Positives: Noise spikes can cause an energy detector to incorrectly mark an idle bin as busy, introducing errors into the matrix.
• False Negatives: Shadowing or deep fading can cause a primary user's signal to fall below the detection threshold, creating a hidden node problem in the matrix.
• Uncertainty Quantification: Advanced systems augment the matrix with a confidence score per cell, often derived from a Hidden Markov Model (HMM) that filters noisy observations into a probabilistic state estimation.

The matrix is a multi-dimensional array where axes typically represent time, frequency, and space. Each cell contains a power measurement or a binary occupancy decision. A fourth dimension, such as angle of arrival or user identity, can be added for advanced spatial filtering. This structure is the native input format for Convolutional Neural Networks (CNNs) and Spatiotemporal Graph Neural Networks.

A 2D slice of the matrix is a spectrogram, plotting frequency against time with amplitude represented by color. This is the most common visualization of the occupancy matrix. Key processing steps include:

• Fast Fourier Transform (FFT) to convert I/Q samples to frequency domain.
• Averaging over time bins to reduce noise variance.
• Thresholding to convert continuous power values into binary occupancy states.

To add the spatial dimension, data from multiple distributed sensors is fused. Techniques include Kriging for spatial interpolation and Radio Environment Maps (REMs). The resulting 3D matrix allows models to learn how spectrum usage propagates geographically. This is critical for cooperative spectrum sensing where a network of sensors builds a unified, geotagged view of the electromagnetic environment.

The matrix can store data in two primary formats:

• Binary Occupancy: A hard decision (0 or 1) based on an energy detection threshold. Simple but loses information below the noise floor.
• Continuous Power Values: Raw power spectral density (dBm/Hz). Preserves information for soft-decision fusion and enables more sophisticated models like Gaussian Processes to predict future power levels, not just idle/busy states.

Spectrum occupancy matrices are often highly sparse, especially in underutilized bands. Efficient storage and processing require compression techniques:

• Coordinate List (COO) format for storing only non-zero entries.
• Compressed Sparse Row (CSR) for fast matrix-vector multiplication.
• Dimensionality reduction via Principal Component Analysis (PCA) to extract dominant usage patterns before feeding into a prediction model.

The matrix is constructed using a sliding window over a raw signal stream. The window size and overlap define the time-frequency resolution trade-off. A long window provides fine frequency resolution but smears fast events in time. For bursty signals like radar, a short-time Fourier transform (STFT) with high overlap is essential to capture transient occupancy events without spectral leakage.