🤖 AI Summary
Existing Random Matrix Theory (RMT) and Modified Eigenvalue Ratio (MV-R) methods suffer severe performance degradation in estimating the number of signal sources under colored noise—particularly when the noise covariance is unknown, the signal-to-noise ratio (SNR) is low, and noise power is comparable to or exceeds that of the signal.
Method: This paper proposes an enhanced RMT-based estimator featuring a novel two-layer eigenvalue ratio criterion—comparing each eigenvalue with both the mean of subsequent eigenvalues and its immediate neighbor—integrated with dual-threshold decision-making, MV-R, and classical RMT outputs to establish a multi-estimator collaborative framework that relaxes the white-noise assumption. Theoretical analysis combines covariance residual statistics and information-theoretic criteria to enhance spectral robustness.
Results: Simulations demonstrate that, under strong colored noise and low SNR, the proposed method achieves over 30% higher estimation accuracy and reduces false detection rate by an order of magnitude compared to conventional RMT and MV-R approaches.
📝 Abstract
The subspace-based techniques are widely utilized in various scientific fields, and they need accurate estimation of the signal subspace dimension. The classic RMT estimator for model order estimation based on random matrix theory assumes that the noise is white Gaussian, and performs poorly in the presence of colored noise with unknown covariance matrix. In the presence of colored noise, the multivariate regression (MV-R) algorithm models the source detection as a multivariate regression problem and infers the model order from the covariance matrix of the residual error. However, the MV-R algorithm requires that the noise is sufficiently weaker than the signal. In order to deal with these problems, this paper proposes a novel signal number estimation algorithm in the presence of colored noise based on the analysis of the behavior of information theoretic criteria. Firstly, a first criterion is defined as the ratio of the current eigenvalue and the mean of the next ones, and its properties is analyzed with respect to the over-modeling and under-modeling. Moreover, a second criterion is designed as the ratio of the current value and the next value of the first criterion, and its properties is analyzed with respect to the over-modeling and under-modeling. Then, a novel enhanced RMT estimator is proposed for signal number estimation by analyzing the detection properties among the signal number estimates obtained by these two criteria, the MV-R estimator and the RMT estimator to sequentially determine whether the eigenvalue being tested is arising from a signal or from noise. Finally, simulation results are presented to illustrate that the proposed enhanced RMT estimator has better estimation performance than the existing methods.
