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The adoption of orthogonal frequency-division multiplexing by wireless local area networks and audio/video broadcasting standards testifies to the importance of recovering block precoded transmissions propagating through frequency-selective finite-impulse response (FIR) channels. Existing block transmission standards invoke bandwidth-consuming error control codes to mitigate channel fades, and training sequences to identify the FIR channels. To enable block-by-block receiver processing, we design redundant precoders with cyclic prefix and superimposed training sequences for optimal channel estimation and guaranteed symbol detectability, regardless of the underlying frequency-selective FIR channels. Numerical results are presented to access the performance of the designed training and precoding schemes.

We study bounded and compact weighted composition operators, induced by a fixed analytic function and an analytic self-map of the open unit disk, between H ∞ and the Bloch space. z∈D (1 − |z| 2 )|f (z)| < ∞.