Spectral Estimation of Weak Signals with Strong Interference via Modulo Sampling

This paper introduces a framework for spectral analysis of weak signals in the presence of strong interference that can potentially exceed the dynamic range of the analog-to-digital converter (ADC) employed for data acquisition. The framework combines modulo sampling to avoid ADC saturation with interference cancellation (IC) and adaptive spectral estimators such as amplitude and phase estimation of a sinusoid (APES) and Capon for high-resolution spectral analysis. Numerical simulations validate the proposed approach's ability to accurately recover weak signals' spectrum with significantly lower mean-squared error (MSE) in amplitude estimation compared to conventional methods in the considered scenarios. Notably, it is shown that APES and Capon are able to effectively reject the out-of-range interference and reveal weak spectral content, without requiring the interference cancellation step.