Signal Constellations of Quasi-Orthogonal Space–Time Codes for MIMO Systems

Orthogonal space–time codes (OSTCs) have recently captivated considerable attention due to their properties of full diversity and low implementation complexity. Quasi-orthogonal space–time codes (QOSTCs) provide full diversity and rate one, which enables simple pair wise decoding to be performed as well as better results to be obtained. In this paper, we derive effective OSTCs and QOSTCs for multi-input multi-output systems, which enable us to calculate coding gain of the OSTC. In addition, the fast maximum-likelihood (ML) decoding at the receiver can be performed separately. Since the QOSTC has a fast ML decoding, the symbol pairs can be decoded independently. With the constellation rotation of the symbol, rotated version of QOSTC is generated. OSTCs are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm. This goal is achieved by properly choosing the signal constellations and comparing bit-error-rate (BER) to signal-to-noise ratio (SNR) for different quadrature pulse shift keying and quadrature-amplitude modulation techniques. The simulation results show that the QOSTC outperforms the OSTC at low SNR whereas it has higher complexity than the OSTC. From simulation result, we also compare the STC and space frequency code at BER versus SNR.