Low Complexity MIMO Precoding Codebooks from Orthoplex Packings

A construction of Grassmannian packings related to representation theory is applied to build implementation-friendly MIMO precoding codebooks when the number of transmit antennas is a power of a prime. Using the chordal distance as a metric, some of the corresponding packings appear to be optimal by meeting the othoplex bound. Also, by using only some of the codewords, smaller packings satisfying the equal power per antenna constraint may be found. Optimality with reference to this constraint may be shown by using a modification of the Conway-Hardin-Sloane´s spherical embedding of the Grassmann manifold for equal per-antenna codebooks.