Abstract

The multiple antennas communication system have been well studied in wireless communication during recent years to increase the rate or performance of a wireless communication system. By exploiting the independent multipath propagations during different transmitter-receiver pair, a MIMO system can either increase the data throughput or operation range at the same bandwidth and same overall transmit power. In order to exploit the potential high rate or high performance, space-time coding plays a prominent rule in MIMO research.

In this dissertation, we focus on the lattice based STBC design. The main advantages of this design method are: the linear structure present us a systematic construction method for variable data rate at the same time permit simple decoding method like sphere decoding at the same time. In Chapter 2, a new systematic cyclotomic lattice design scheme is proposed firstly by using algebraic number theory. As an application, it is used for diagonal STBC (cyclotomic STBC) and linear pre-code for Rayleigh fast fading channel. Furthermore, optimal cyclotomic STBC/lattices from the design for different numbers of transmit antennas are obtained based on the normalized diversity products criterion.

In Chapter 3, we present two tight upper bounds for the normalized diversity products of 2 x 2 diagonal STBCs from quadratic extensions on [special characters omitted](i) and [special characters omitted](j). Two such codes are shown to reach the tight upper bounds and therefore have the maximal normalized diversity products. We then present an n x n diagonal STBC design method directly from 2n real integers based on extended complex lattices (of generating matrix size n x 2n) that are shown to have better normalized diversity products than the optimal diagonal cyclotomic codes do.

In Chapter 4, we consider the case where the normalized diversity product is redefined based on the finite lattice. For full rate STBCs, we present a transformation technique such that the normalized diversity product of the transformed code with the multi-layer structure is better than the one of the transformed code with the cyclic division algebra structure.

In Chapter 5, we show that the diversity products of the full transmit diversity space time block code(STBC) proposed recently by Lu-Kumar (we call them Lu-Kumar's codes) with QAM constellations are lower bounded by 4.