Tharindu Udupitiya | Searcharxiv

arXiv2026

Standard Condition Number-Based Robust Signal Detection with Whitening under Uncertainty

Robust signal detection in colored noise with unknown covariance is essential in radar, cognitive radio, integrated sensing and communication (ISAC), and quantum sensing applications. This paper develops a unified analytical framework for the Standard Condition Number (SCN) detector, which employs the ratio of the largest to smallest eigenvalues of the whitened sample covariance matrix. The framework jointly covers both ideal conditions in which the training and sensing noise statistics are identical and disturbed conditions in which interference or jamming alters the sensing covariance. Despite the SCN's practical relevance, its finite-sample false-alarm and detection behavior has not been analytically characterized. Using random matrix theory (RMT), we derive general expressions for these probabilities, provide closed-form results for special cases, and show that the SCN preserves the Constant False Alarm Rate (CFAR) property under covariance mismatch. Analytical and simulation results confirm that the proposed unified framework delivers consistent detection performance and greater robustness than conventional eigenvalue- and LRT-based detectors.

eess.SP↗

arXiv2026

Standard Condition Number-Based Detection for MIMO ISAC Systems under Noise Uncertainty

This paper presents a unified analytical and optimization framework for Standard Condition Number (SCN)-based detection in MIMO Integrated Sensing and Communication (ISAC) systems operating under noise uncertainty. Conventional detectors such as the Likelihood Ratio Test (LRT) and Energy Detector (ED) suffer from false-alarm inflation when interference or jamming alters the noise covariance. To overcome this limitation, the SCN detector, defined as the ratio of the largest to smallest eigenvalues of the sample covariance matrix is analytically characterized for the first time in an ISAC setting. Closed-form expressions for the false-alarm and detection probabilities are derived using random matrix theory for a two-antenna sensing receiver and generalized to arbitrary MIMO dimensions. The analysis proves that the SCN maintains a constant false alarm rate (CFAR) property and remains resilient to covariance mismatch, providing theoretical justification for its robustness in dynamic environments. Leveraging these results, a tractable ISAC power-allocation problem is formulated to minimize total detection error subject to communication rate and power constraints, yielding an interpretable sequential solution. Numerical evaluations verify the theory and demonstrate that the proposed SCN detector consistently outperforms LRT and eigenvalue-based benchmarks, particularly under strong interference and jamming typical of modern multiuser networks.

eess.SP↗