Performance guarantees of spectral methods for passive sensing of multiple channels

We study passive sensing of time invariant systems, which is cast as a multichannel blind deconvolution problem. In a particular scenario where the unknown channel impulse responses are time limited, spectral methods based on the commutativity of convolution have been proposed in 1990s, but these classical methods suffer from noise sensitivity. Inspired from the observation that certain applications allow extra priors on the coefficients of the impulse responses, the authors proposed a modified spectral method from the classical methods for improved noise tolerance and provided non-asymptotic error analysis. In this paper, we provide a sharpened error bound by using recently developed analysis tools. A Monte Carlo simulation confirms that the empirical performance of the spectral method is aligned with the new error bound.