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Abstract: The theory of orthogonal designs dates back over a century. Since Radon’s classical result implying the set of dimensions for which real square orthogonal designs exist, several generalizations of real square orthogonal designs have followed, including generalized real orthogonal designs and complex orthogonal designs, generalized complex orthogonal designs, and generalized complex linear processing orthogonal designs. Tarokh, Jafarkhani and Calderbank pioneered using generalized complex orthogonal designs to construct space-time Block codes (STBCs), which are used to transmit data over wireless channels using multiple transmit antennas. Their work extends Alamouti’s scheme for wireless communications with two transmit antennas. In this work a construction technique for generalized Complex linear processing orthogonal designs, is introduced which are p × n matrices X Satisfying XHX = fI, where f is a complex quadratic form, I is the identity matrix, and X has complex entries. These matrices generalize the familiar notations of orthogonal designs and generalized complex orthogonal designs. We explain the application of these matrices to space-time block coding for multipleantenna wireless communications. In particular, the Practical strengths of the space-time block codes constructed using the proposed technique (i.e. Quasi Orthogonal Space time block codes) are discussed and Interference can also be eliminated. Keywords: Antenna Diversity, Rayleigh Fading, Space–time Coding, Transmit Diversity, Interference.