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We provide a novel framework to study subspace codes for non-coherentcommunications in wireless networks. To this end, an analog operator channel isdefined with inputs and outputs being subspaces of $\mathbb{C}^n$. Then acertain distance is defined to capture the performance of subspace codes interms of their capability to recover from interference and rank-deficiency ofthe network. We also study the robustness of the proposed model with respect toan additive noise. Furthermore, we propose a new approach to construct subspacecodes in the analog domain, also regarded as Grassmann codes, by leveragingpolynomial evaluations over finite fields together with characters associatedto finite fields that map their elements to the unit circle in the complexplane. The constructed codes, referred to as character-polynomial (CP) codes,are shown to perform better comparing to other existing constructions ofGrassmann codes in terms of the trade-off between the rate and the normalizedminimum distance, for a wide range of values for $n$.

Analog Subspace Coding: A New Approach to Coding for Non-Coherent Wireless Networks