Square Complex Orthogonal Designs with Low PAPR

Space-Time Block Codes from square complex orthogonal designs (SCOD) have been extensively studied and most of the existing SCODs contain large number of zero resulting in high peak to average of power ratio (PAPR) and also impose a severe constraint on hardware implementation of the code when turning off some of the transmitting antennas whenever a zero is transmitted. Recently, maximal-rate SCODs with no zero entry have been reported for 8 transmit antennas, constructed using Amicable Orthogonal Designs. In this paper, maximal-rate SCODs with no zero entry for 2^a transmit antennas whenever a+1 is a power of 2 are constructed which includes the 8 transmit antennas case as a special case. More generally, for arbitrary values of a, explicit construction of 2^a times 2^a maximal-rate SCODs with the fraction of number of zero entries to the total number of entries equal to [1-(a-1)/(2^a)] 2^[log2^{(2 a /a+1)]} is reported. Moreover, it is shown that these codes are obtainable by premultiplying the well known SCODs with appropriate scaled unitary matrices consisting of nonzero entries that are plusmn1 only. A procedure to compute these scaled unitary matrices is also presented.