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Complex orthogonal designs (CODs) have been successfully implemented in wireless systems as complex orthogonal space-time block codes (COSTBCs). Certain properties of the underlying CODs affect the performance of the codes. In addition to the main properties of a COD's rate and decoding delay, a third consideration is whether the COD can achieve transceiver signal linearization, a property that facilitates practical implementation by, for example, significantly simplifying the receiver structure for iterative decoding. It has been shown that a COD can achieve this transceiver signal linearization if the nonzero entries in any given row of the matrix are either all conjugated or all nonconjugated. This paper determines the conditions under which maximum rate CODs can achieve this desirable property. For an odd number of transmit antennas, it is shown that maximum rate CODs that achieve the lower bound on decoding delay can also achieve transceiver signal linearization. In contrast, for an even number of transmit antennas, maximum rate CODs that achieve the lower bound on delay cannot achieve this linearization. In this latter case, linearization is possible only if the COD achieves at least twice the lower bound on delay. This work highlights the tradeoffs among these three important properties. [ABSTRACT FROM AUTHOR]

Complex orthogonal space-time block codes (COSTBCs) based on generalized complex orthogonal designs (CODs) have been successfully implemented in wireless systems with multiple transmit antennas and single or multiple receive antennas. It has been shown that for a maximum rate COD with 2m - 1 or 2m columns, a lower bound on decoding delay is (2m m-i) and this delay is achievable when the number of columns is congruent to 0, 1, or 3 modulo 4. In this paper, the final case is addressed, and it is shown that when the number of columns is congruent to 2 modulo 4, the lower bound on decoding delay cannot be achieved. In this case, the shortest decoding delay a maximum rate COD can achieve is twice the lower bound. New. techniques for analyzing CODs are introduced with connections to binary vector spaces. [ABSTRACT FROM AUTHOR]

Abstract: The success of applying generalized complex orthogonal designs as space–time block codes recently motivated the definition of quaternion orthogonal designs as potential building blocks for space–time-polarization block codes. This paper offers techniques for constructing quaternion orthogonal designs via combinations of specially chosen complex orthogonal designs. One technique is used to build quaternion orthogonal designs on complex variables for any even number of columns. A second related technique is applied to maximum rate complex orthogonal designs to generate an infinite family of quaternion orthogonal designs on complex variables such that the resulting designs have no zero entries. This second technique is also used to generate an infinite family of quaternion orthogonal designs defined over quaternion variables that display a regular redundancy. The proposed constructions are theoretically important because they provide the first known direct techniques for building infinite families of orthogonal designs over quaternion variables for any number of columns. [Copyright &y& Elsevier]