Eigenvalue-Based Detection

The foundation of the method lies in computing the sample covariance matrix from multiple receiver observations. For a received signal vector x(n), the matrix is formed by averaging outer products over N samples. Under noise-only conditions, this matrix approximates a scaled identity matrix σ²I, while the presence of a spread spectrum signal introduces off-diagonal correlation structure that alters the eigenvalue distribution.

The MME detector computes the ratio of the maximum eigenvalue (λ_max) to the minimum eigenvalue (λ_min) of the sample covariance matrix. Under pure noise, this ratio approaches 1 as sample size increases. When a signal is present, λ_max increases proportionally to signal power while λ_min remains near the noise floor, causing the ratio to exceed a decision threshold derived from random matrix theory.

The EME method normalizes total received energy by the minimum eigenvalue rather than relying on a fixed noise estimate. The test statistic is the ratio of average power (trace of covariance matrix) to λ_min. This approach combines the simplicity of energy detection with the noise-floor independence of eigenvalue methods, providing robust performance when noise power fluctuates.

Decision thresholds are analytically derived using Tracy-Widom distributions from random matrix theory. For an M-antenna receiver with N samples, the limiting distribution of the largest eigenvalue of a Wishart matrix provides exact false-alarm probabilities. This eliminates the need for empirical threshold calibration and enables operation at arbitrarily low signal-to-noise ratios.

Unlike energy detection, eigenvalue-based methods require no noise variance estimation. The noise floor is implicitly referenced through the minimum eigenvalue, which tracks ambient noise even as it varies with temperature, interference, or receiver gain changes. This makes the technique particularly valuable in dynamic electromagnetic environments where noise uncertainty degrades conventional detectors.

The framework naturally extends to multiple receive antennas or cooperative sensing networks. With M antennas, the covariance matrix dimension grows, and signal eigenvalues separate more distinctly from the noise floor. Cooperative schemes fuse eigenvalue statistics across geographically distributed nodes, dramatically improving detection of low-probability-of-intercept signals through spatial diversity.

The fundamental mathematical object from which eigenvalues are derived. It captures the statistical correlation between multiple receiver antennas or time-lagged versions of a single signal.

• Structure: An N x N matrix where N is the number of receivers or time lags.
• Diagonal elements: Represent the signal power at each receiver.
• Off-diagonal elements: Represent the cross-correlation between receivers.
• Computation: Estimated from a finite number of received IQ samples, making it a random matrix subject to fluctuations.

The branch of probability theory that provides the asymptotic limits for eigenvalue distributions, enabling the calculation of precise detection thresholds without empirical calibration.

• Marchenko-Pastur Law: Describes the limiting spectral distribution of a pure noise covariance matrix.
• Tracy-Widom Distribution: Models the fluctuations of the largest noise eigenvalue, critical for setting false alarm rates.
• Finite Sample Effects: RMT corrects for biases that occur when the number of samples is not significantly larger than the matrix dimension.

A specific blind detection test statistic that computes the ratio of the largest eigenvalue to the smallest eigenvalue of the sample covariance matrix.

• Noise-Only Case: The ratio approaches a theoretical limit predicted by the Tracy-Widom distribution.
• Signal Present: The largest eigenvalue inflates due to signal correlation, pushing the ratio above the threshold.
• Key Advantage: Completely blind to noise power; no noise floor estimation is required.
• Robustness: Highly resilient to noise uncertainty, a major flaw in simple energy detectors.

A direct comparison highlighting why eigenvalue methods are superior for spread spectrum and low-SNR regimes.

• Energy Detection: Compares raw received power to a noise floor estimate. Fails catastrophically under noise uncertainty (SNR wall).
• Eigenvalue Detection: Exploits signal correlation structure. Immune to noise uncertainty.
• Sensitivity: Eigenvalue methods can detect signals well below the noise floor where energy detectors are blind.
• Complexity Trade-off: Eigenvalue decomposition is computationally heavier than simple power integration but is manageable on modern FPGAs.

A class of high-resolution techniques that partition the eigenvector space into a signal subspace and a noise subspace for parameter estimation.

• MUSIC (Multiple Signal Classification): Uses the orthogonality between signal and noise subspaces to estimate carrier frequencies or directions of arrival.
• Minimum Description Length (MDL): An information-theoretic criterion used to estimate the number of signal sources by analyzing the decay of eigenvalues.
• Application: Once a signal is detected via eigenvalues, subspace methods can blindly estimate its chip rate or hopping pattern.

A computationally lighter alternative to the MME test that avoids explicit eigenvalue decomposition, suitable for resource-constrained edge devices.

• Statistic: Computes the ratio of the sum of absolute values of all matrix elements to the sum of absolute values of diagonal elements.
• Mechanism: Off-diagonal elements are non-zero only when correlated signals are present.
• Performance: Slightly lower sensitivity than MME but significantly lower computational complexity.
• Use Case: Ideal for real-time, low-power spectrum sensing in tactical man-portable SIGINT systems.