Rate bounds for relay channels using MIMO methods

The capacity of the symbol-asynchronous single-relay channel with multipath is investigated. Due to the slow propagation speed of sound in water and surface/floor reflections, such channels are highly relevant to underwater acoustic communication systems. The symbol-asynchronous single-relay channel can be modeled as a MIMO relay channel with memory; thus MIMO capacity results can be invoked to determine rate bounds. Lower and upper bounds on the capacity are derived under the assumptions of both known and unknown time delays. Conditions for characterizing capacity (when the upper and lower bounds match) are also derived and the optimality of OFDM type of signaling can be readily inferred from the analysis. Numerical examples are provided to illustrate the results.