TABLE OF CONTENTS An orthogonal design is defined for any arbitrary indeterminate variables x 1, x 2, , x N. The theory of orthogonal designs and its generalization provide designs that are orthogonal for any real or complex values of x 1, x 2, , x N. However, in practice, in a communication system, variables x 1, x 2, , x N are members of a constellation that has a finite number of signals instead of the real or complex numbers with infinite number of possibilities. Therefore, it is useful to study a class of STBCs that provide all nice properties of orthogonal STBCs only for a finite set of constellation symbols. In fact, while a complex orthogonal design does not exist for more than two transmit antennas, if we restrict the symbols to real numbers IR ? CI, real orthogonal designs exist for four and eight transmit antennas. These real orthogonal designs are provided in (4.38) and (4.40). We study the possibility of such designs by defining pseudo-orthogonal designs over a finite subset of numbers. The definition of a pseudo-orthogonal design is identical to that of an orthogonal design with the addition of the condition that the indeterminate variables x 1, x 2, , x N are from finite sets of numbers. These finite sets can be any practical constellation, for example PSK or QAM. Note that while the definition...
