This thesis has two main contributions:​ the designs of differential/non-differential unitary space-time codes for m uitiple-antenna systems and the analysis of the diversity gain when using space-time coding among nodes in wireless networks.

Capacity has long been a bottleneck in wireless communications. Recently, muitipleantenna techniques have been used in wireless communications to combat the fading effect, which improves both the channel capacity and performance greatly. A recently proposed m ethod for communicating with multiple antennas over block-fading channels is unitary space-time modulation, which can achieve the channel capacity at high SNR. However, it is not clear how to generate well performing unitary spacetime codes that lend themselves to efficient encoding and decoding. In this thesis, the design of unitary space-time codes using Cayley transform is proposed. The codes are designed based on an information-theoretic criterion and have a polynomial-time near-maximum-likelihood decoding algorithm. Simulations suggest that the resulting codes allow for effective high-rate data transmissions in muitiple-antenna communication systems without knowing the channel. Another well-known transmission scheme for muitiple-antenna systems with unknown channel information at both the transm itter and the receiver is differential unitary space-time modulation. It can be regarded as a generalization of DPSK and is suitable for continuous fading. In differential unitary space-time modulation, fully diverse constellations, i.e., sets of unitary matrices whose pairwise differences are non-singular, are wanted for their good pairwise error properties. In this thesis, Lie groups and their representations are used in solving the design problem. Fully diverse differential unitary space-time codes for systems with four and three transmit antennas are constructed based on the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Lie groups Sp(2) and SU(3). The designed codes have high diversity products, lend themselves to a fast maximumdikelihood decoding algorithm, and simulation results show th at they outperform other existing codes, especially at high SNR.

Then the idea of space-time coding devised for multiple-antenna systems is applied to communications over wireless networks. In wireless relay networks, the relay nodes encode the signals they receive from the transm it node into a distributed space-time code and transm it the encoded signals to the receive node. It is shown in this thesis th at at very high SNR, the diversity gain achieved by this scheme is almost the same as th at of a muitiple-antenna system whose number of transm it antennas is the same as the number of relay nodes in the network, which means th at the relay nodes work as if they can cooperate fully and have full knowledge of the message. However, at m oderate SNR, the diversity gain of the wireless network is inferior to that of the muitiple-antenna system. It is further shown th at for a fixed total power consumed in the network, the optimal power allocation is th at the transm itter uses half the power and the relays share the other half fairly. This result addresses the question of what performance a relay network can achieve. Both it and its extensions have many applications to wireless ad hoc and sensory network communications.