Low PAPR square STBCs from complex partial-orthogonal designs (CPODs)

Abstract

Space-time codes from complex orthogonal designs (CODs) with no zero entries offer low Peak to Average Power Ratio (PAPR) and avoid the problem of switching off antennas. But square CODs for 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sup> antennas with a+1 complex variables, with no zero entries were discovered only for a ⩽ 3 and if a+1 = 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sup> , for k ⩾ 4. In this paper, a method of obtaining no zero entry (NZE) square designs, called Complex Partial-Orthogonal Designs (CPODs), for 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a+1</sup> antennas whenever a certain type of NZE code exists for 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sup> antennas is presented. Then, starting from a so constructed NZE CPOD for n = 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a+1</sup> antennas, a construction procedure is given to obtain NZE CPODs for 2n antennas, successively. Compared to the CODs, CPODs have slightly more ML decoding complexity for rectangular QAM constellations and the same ML decoding complexity for other complex constellations. Using the recently constructed NZE CODs for 8 antennas our method leads to NZE CPODs for 16 antennas. The class of CPODs do not offer full-diversity for all complex constellations. For the NZE CPODs presented in the paper, conditions on the signal sets which will guarantee fulldiversity are identified. Simulation results show that bit error performance of our codes is same as that of the CODs under average power constraint and superior to CODs under peak power constraint.