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.

Eigenvalue-Based Detection in MIMO Systems for Integrated Sensing and Communication

This paper considers a MIMO Integrated Sensing and Communication (ISAC) system, where a base station simultaneously serves a MIMO communication user and a remote MIMO sensing receiver, without channel state information (CSI) at the transmitter. Existing MIMO ISAC literature often prioritizes communication rate or detection probability, typically under constant false-alarm rate (CFAR) assumptions, without jointly analyzing detection reliability and communication constraints. To address this gap, we adopt an eigenvalue-based detector for robust sensing and use a performance metric, the total detection error, that jointly captures false-alarm and missed-detection probabilities. We derive novel closed-form expressions for both probabilities under the eigenvalue detector, enabling rigorous sensing analysis. Using these expressions, we formulate and solve a joint power allocation and threshold optimization problem that minimizes total detection error while meeting a minimum communication rate requirement. Simulation results demonstrate that the proposed joint design substantially outperforms conventional CFAR-based schemes, highlighting the benefits of power- and threshold-aware optimization in MIMO ISAC systems.