Systems and methods are provided for decoding a signal vector in a transmission scheme that uses transmit diversity as well as HARQ, repetition coding, or any other protocol that allows a receiver to obtain multiple reception of common transmit information. An optical reflected image from an observed surface of an object to be measured and an optical reflected image from a reference surface are interfered with each other to generate interference light. A user-interface is provided to facilitate athlete selection under constraints that limit the overall pool of athlete candidates to just those participating in the corresponding real-world event, and that limit teams to a smaller subset of the athletes participating in the real-world event. Various other devices include support structure and one or more posts connected to opposite sides of the support structure and extending from one side of the valve annulus to another to modify the shape of the annulus.