We refer to channels of communication that link the user to information systems as cognitive communication channels. One especially interesting research topic related to cognitive communication channels deals with a special application called sensory substitution, when information is conveyed through a channel other than the one that is normally used for the given application. Our goal is to develop engineering systems for the remote teleoperation of robots using sensory substitution to convey feedback information in meaningful ways. Such applications could help reduce the cognitive load for the user on the one hand, and help alleviate the effect of control instabilities and hidden parameters on the other. In this paper, we present a tensor algebraic approach for the compact representation of complete sensory substitution channels. Using HOSVD, we transform our representations into canonical, orthogonal forms. Through a combination of rank-reduction and error compensation techniques, we propose an iterative and hierarchical parameter space exploration method which may help users tune the generated sensory substituted signals in a more intuitive fashion. As an application example, we present a mapping between tactile percepts and auditory parameters in order to convey the tactile experience of a robot to a remote user through sound. In order to be able to apply a wide a wide range of mathematical analysis tools - such as principal component analysis and user performance-oriented adaptivity - we demonstrate that it is possible to convert our models into HOSVD-based canonical forms. The verification of the enhanced parameter space exploration method using rank reduction and error compensation in this application remains part of our future work.