Singular Detection in Noncoherent Communications

This paper proposes a general analysis of codeword detection in noncoherent communications. Motivated by the existence of error floors in various regimes, fundamental characteristics of signal design are investigated. In particular, the necessary and sufficient conditions for asymptotically singular detection (i.e. error-free in the limit) are derived from classical results in detection theory. By leveraging tools from linear algebra and the theory of Hilbert spaces, we are able to characterize asymptotic singularity in two main scenarios: the large array and high SNR regimes. The results generalize previous works and extend the notion of unique identification, as well as re-contextualize the geometry of Grassmannian constellations from an alternative perspective.