Set-partition methods and orthogonal designs

Space-time block codes based on orthogonal designs are useful from practical point of view as these codes admit symbol-by-symbol maximum-likelihood decoding and also achieve full diversity. Though the square orthogonal designs have been studied quite extensively, there is very little progress in the area of non-square orthogonal designs. Some of the results pertaining to rectangular orthogonal designs have been obtained through various combinatorial methods which are quite involved and complicated. In this paper, we study non-square orthogonal designs using set partition methods. Using this method, some of the problems in complex orthogonal designs have been addressed. Moreover, the proposed method provides a simple and an elegant approach for the study of rectangular designs.