有限群表現理論在複數時空編碼上之設計及應用

Abstract

The designing potential of using quaternionic numbers to identify a 4 × 4 real orthogonal space-time block code has been exploited in various communication articles. Although it has been shown that orthogonal codes in full rate exist only for 2 Tx-antennas in complex constellations, a series of complex quasi-orthogonal codes for 4 Tx-antennas is still proposed to have good performance recently. This quasi-orthogonal scheme enables the codes reach the optimal non-orthogonality, which can be measured by taking the expectation over all transmitted signals of the ratios between the powers of the off-diagonal and diagonal components. In Chapter 1 of this thesis, we extend the quaternionic identification to the above encoding methods. Based upon tensor product for giving the quaternionic space a linear extension, a complete necessary and sufficient condition of identifying any given complex quasi-orthogonal code with the extended space is generalized by considering every possible 2-dimensional R-algebra. In Chapter 2, a new set of quasi-orthogonal space-time block codes for 4 Txantennas derived by a group-theoretic methodology on the generalized quaternion group of order 16 is presented. We show that these new codes achieve full diversity whenever a square lattice constellation is adopted. From the simulation results, the new designs perform very closely to quasi-orthogonal codes with constellation rotations and admit high coding gains (in fact we prove their coding gains are optimal among those codes whose diagonal entries are all within z1, z1†, or multiples of them by a uni-power coefficient). Without a search of the optimal rotation angle and any constellation expansion, our new codes yield an advantageous transmission scheme for QPSK and 16-QAM modulations.