Equivariant adaptive selective transmission

In this paper, we consider the problem of selective transmission-the dual of the blind source separation task-in which a set of independent source signals are adaptively premixed prior to a nondispersive physical mixing process so that each source can be independently monitored in the far field. Following similar procedures for information-theoretic blind source separation, we derive a stochastic gradient algorithm for iteratively estimating the premixing matrix in the selective transmission problem, and through a simple modification, we obtain a second algorithm whose performance is equivariant with respect to the channel´s mixing characteristics. The local stability conditions for the algorithms about any selective transmission solution are shown to be the same as those for similar source separation algorithms. Practical implementation issues are discussed, including the estimation of the combined system matrix and the reordering and scaling of the received signals within the algorithm. Mean square error-based selective transmission algorithms are also derived for performance comparison purposes. Simulations indicate the useful behavior of the premixing algorithms for selective transmission