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We consider the problem of optimal precoder design for a multi-input single-output wideband wireless system to maximize two different figures of merit: the total communication capacity and the total received power, subject to individual power constraints on each transmit element. We show that the two optimal precoders satisfy a separation principle that reveals a simple structure for these precoders. We use this separation principle extensively to derive several interesting properties of these two optimal precoders. Some key analytical results are as follows. We show that the power-maximizing precoders must concentrate all their energy in a small number of active channels that cannot exceed the number of input terminals. The capacity-maximizing precoder turns out to be very different from the classical water filling solutions and also very different from the power-maximizing precoders except at asymptotically low …