Space Time Coding with Multiple Antenna Systems

Recently there has been considerable interest in wireless communication systems using multiple antennas. Theoretical analysis shows that such systems can provide spacial and temporal diversity gain if appropriate signal sets are employed. This dissertation analyzes and designs suitable signal constellations for such systems. Diversity product and diversity sum will be derived as two important parameters to design constellations. A basic question is what the maximal diversity product or diversity sum could be. In this dissertation we derive general upper bounds on the diversity sum and the diversity product for unitary constellations of any dimension and any size using packing techniques on a compact Lie group. We generalize one complex dimensional phase shift keying (PSK) signal and introduce space time constellations from generalized phase shift keying (GPSK) signals based on the complex and real orthogonal designs. The resulting space time constellations reallocate the energy among transmit antennas and feature good diversity, consequently their performances are better than some of the existing compatible codes. Moreover, since the decoding of our proposed codes can be decomposed into one dimensional PSK signal demodulation, maximum likelihood (ML) decoding of our codes can be implemented in a very efficient way. Group structure and other algebraic approaches have been considered to construct fully diverse unitary constellations in the literature. Our observation, however, indicates that full diversity can be easily obtained with h.d. random constellations. In this dissertation we also propose constellations with suitable structure which allow one to construct codes of any dimension and any size with excellent diversity using geometrical symmetry and numerical methods. We demonstrate how these structured constellations out-perform currently existing constellations and explain why the proposed constellation structure admit simple decoding algorithms such as sphere decoding. The presented design methods apply to any dimensional constellation of any size. Moreover, codes based on the proposed structure are very flexible and can be optimized for any signal to noise ratio.