The last three decades have seen significant advances in the wireless communication field. As the data rates of wireless systems are increasing, the demand for mobile services also is increasing rapidly. Like other natural resources, radio spectrum suitable for mobile wireless communications is also limited. In order to keep up with this ever increasing demand, there is a requirement of new signal processing algorithms.

Diversity is a technique used in wireless systems to combat the effects of fading and thereby improve reliability of data transfer. There are many ways in which algorithms can exploit diversity in wireless channels. Hybrid-automatic repeat request (H-ARQ) schemes and relaying mechanisms are two such diversity extracting techniques. Even though these diversity achieving techniques have been well understood in theory, there are many ways in which one can optimize these techniques for specific application scenarios.In this thesis, we focus on improving the performance of retransmission schemes and relaying systems.

In the first part of the thesis, we improve the performance of H-ARQ schemes in the 3GPP- long term evolution (LTE) system by improving the performance of feedback signaling. We employ complex-field coding to extract the inherent frequency diversity available in the resources. Next, we provide a sub-optimal solution to the outage-optimal power allocation problem in incremental redundancy based H-ARQ system, whose performance is practically the same as that of the optimal solution.

In the later part of the thesis, we propose a retransmission scheme based on superposition coding (SPC) for the symmetric relaying scenario. We provide packet error probability (PEP) expressions and solutions for the optimal fraction of power allocated for the partners' data. Finally, we study the optimal bits-to-symbol mappings for SPC and its effect on an H-ARQ scheme and the symmetric relaying scenario using SPC.