AbstractsMathematics

Cooperative relaying is a promising technique to enhance the reliability and data-rate of wireless networks. Among different cooperative relaying schemes, the half-duplex non-orthogonal amplify-and-forward (NAF) protocol is popular due to its low implementation complexity and performance advantages. This thesis investigates precoder design for a cooperative half-duplex single-relay NAF system from an information theoretic point of view using a novel mutual information-based design criterion.The first part of the thesis considers the design of a 2x2 precoder for the NAF half duplex single relay network in the presence of the direct link using mutual information (MI) as the main performance metric. Different from precoder design methods using pairwise error probability (PEP) analysis, which are valid only at high signal-to-noise ratios (SNR), the proposed precoder design can apply to any SNR region, which is of more interest from both information-theoretic and practical points of view. A MI-based criterion is developed for a cooperative frame length of 2, which corresponds to the case of using a 2x2 precoder. The design criterion is established in a closed-form, which can be helpful in finding an optimal precoder. Then it is analytically shown that a good precoder should have all entries that are equal in magnitude, which is different from the optimal precoders obtained thus far using the conventional PEP criterion. Simulation results indicate that the proposed class of precoders outperform the existing precoders in terms of the mutual information performance.The second part of the thesis extends the precoder design to an arbitrary block length of 2T. In general, for this case, a precoder of size 2Tx2T needs to be considered to optimize the MI performance. Similar to the 2 × 2 precoder design, a MI-based design criterion is first established. While the criterion can be expressed in closed form, the design of optimal precoders in this case is not possible, due to the complexity of the optimization problem. As an alternative, a novel grouping technique, which is referred to as symbol grouping, in which a group of only P = 2 information symbols are pre-coded to improve the MI, is proposed. It is then demonstrated that the grouping technique yields a much simpler design criterion and an optimal 2x2 precoder can be developed. Numerical results show that the proposed precoding technique outperforms existing precoder designs while keeping the receiver complexity at a minimum.