  In millimeter wave communications, hybrid analog-digital arrays consisting of
only a few radiofrequency (RF) chains offer an attractive alternative to costly
digital arrays. A limitation to hybrid arrays is that the number of streams
that can be transmitted simultaneously cannot exceed the number of RF chains.
We demonstrate that if the states of the analog components and the symbols
passed to the RF chains are jointly optimized on a symbol-by-symbol (SbS)
basis, it is possible to achieve the same degrees of freedom as a digital array
with linear precoding, thus effectively enabling the transmission of a large
number of streams. To this end, an algorithm for SbS hybrid precoding is
proposed based on a variation of orthogonal matching pursuit, particularly
suited to the structure of our problem, which makes it fast and precise.
