TABLE OF CONTENTS In this section, we generalize orthogonal designs to non-square real matrices. We start the discussion by the definition of a generalized orthogonal design from [136].
A generalized real orthogonal design is a T N matrix 
with real entries x 1, ? x 1, x 2, ? x 2, , x K, ? x K such that
| (4.55) |  |
where I N is the N N identity matrix and ? is a constant.
A real space-time block code is defined by using as a transmission matrix. Let us assume a constellation with 2 b symbols. For each block of Kb bits, the encoder first picks K symbols ( s 1, s 2, , s K) from the constellation. Then, x k is replaced by s k in to arrive at C = ( s 1, s 2, , s K). At time t = 1, 2, , T, the ( t, n)th element of C, C t , n, is transmitted from antenna n for n = 1, 2, , N. There are three parameters in Definition 4.5.1 that define different properties of the corresponding codes. The number of transmit antennas is N. For each block, K symbols are transmitted over T time slots.
