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Space-Time Block Codes from square complex orthogonal designs (SCOD) havebeen extensively studied and most of the existing SCODs contain large number ofzero. The zeros in the designs result in high peak-to-average power ratio(PAPR) and also impose a severe constraint on hardware implementation of thecode when turning off some of the transmitting antennas whenever a zero istransmitted. Recently, rate 1/2 SCODs with no zero entry have been reported for8 transmit antennas. In this paper, SCODs with no zero entry for $2^a$ transmitantennas whenever $a+1$ is a power of 2, are constructed which includes the 8transmit antennas case as a special case. More generally, for arbitrary valuesof $a$, explicit construction of $2^a\times 2^a$ rate $\frac{a+1}{2^a}$ SCODswith the ratio of number of zero entries to the total number of entries equalto $1-\frac{a+1}{2^a}2^{\lfloor log_2(\frac{2^a}{a+1}) \rfloor}$ is reported,whereas for standard known constructions, the ratio is $1-\frac{a+1}{2^a}$. Thecodes presented do not result in increased signaling complexity. Simulationresults show that the codes constructed in this paper outperform the codesusing the standard construction under peak power constraint while performingthe same under average power constraint.

Square Complex Orthogonal Designs with Low PAPR and Signaling Complexity