This thesis focuses on the concept of uniquely factorable constellations (UFCs) in the design of space-time block codes (STBCs) for wireless communication systems using three different approaches. Based on intelligent constellation collaboration, UFCs can provide the systematic design of a full diversity code with improved coding gain. Firstly, motivated by the energy-efficient hexagonal lattice carved from the Eisenstein integer domain, hexagonal UFCs and hexagonal uniquely factorable constellation pairs (UFCPs), of various sizes, are constructed for a noncoherent single-input multiple-output (SIMO) system. It is proved that these designs assure the blind unique identification of channel coefficients and transmitted signals in a noise-free case and full diversity for the noncoherent maximum likelihood (ML) receiver in a noisy case. In addition, an optimal energy scale is found to maximize the coding gain. Secondly, using a matrix similar to the Alamouti matrix and the UFCP concept based on the quadrature amplitude modulation (QAM) constellation, a novel energy-efficient unitary STBC is designed for a noncoherent multiple-input single-output (MISO) system with two transmitter antennas and one receiver antenna by using the QR decomposition. It is shown that the proposed UFCP-STBC design also allows for the blind unique identification of both the transmitted signals and channel coefficients as well as full diversity. In addition, an optimal unitary UFCP-STBC is devised to maximize the coding gain subject to a transmission bit rate constraint. The last approach is to demonstrate how the UFCP concept is applied to the systematic design of a coherent relay network coding system. A class of uniquely factorable Alamouti matrix pairs is proposed for the design of a novel amplify-forward relay network coding scheme, which allows the relay node to transmit its own information. By carefully making use of the Alamouti coding structure and strategically encoding the signals from the two antennas at the relay node, the resulting coding scheme enables the optimal full diversity gain and better coding gain for the ML detector. Comprehensive computer simulations show that the three uniquely factorable designs presented in this thesis have the best error performance compared to the current designs in literature. / Thesis / Candidate in Philosophy

This thesis considers the modulation division based on the concept of uniquely factorable constellation pair (UFCP) and uniquely decodable constellation group (UDCG) in multiuser wireless communication networks. We first consider a two-hop relay network consisting of two single-antenna users and a two-antenna relay node, for which a novel distributed concatenated Alamouti code is devised. This new design allows the source and relay nodes to transmit their own information to the destination node concurrently at the symbol level with the aid of the UFCP generated from both PSK and square QAM constellations as well as by jointly processing the noisy signals received at the relay node. Moreover, an asymptotic symbol error probability (SEP) formula is derived for the ML receiver, showing that the maximum diversity gain function is achieved, which is proportional to $\ln \mathtt{SNR}/\mathtt{SNR}^2$. Then, we concentrate on the point-to-point correlated multiple-input and multiple-output (MIMO) communication systems where full knowledge of channel state information (CSI) is available at the receiver and only the first- and second-order statistics of the channels are available at the transmitter. When the number of antenna elements of both ends goes to infinity while keeping their ratio constant, the asymptotic SEP analysis is carried out for either optimally precoded or uniformly precoded correlated large MIMO fading channels using the zero-forcing (ZF) detector with equally likely PAM, PSK or square QAM constellations. For such systems, we reveal some very nice structures which inspire us to explore two very useful mathematical tools (i.e., the Szego's theorem on large Hermitian Toeplitz matrices and the well-known limit: $\lim_{x\to\infty}(1+1/x)^x=e$), for the systematic study of asymptotic behaviors on their error performance. This new approach enables us to attain a very simple expression for the SEP limit as the number of the available antenna elements goes to infinity. In what follows, the problem of precoder design using a zero-forcing decision-feedback (ZF-DF) detector is also addressed. For such a MIMO system, our principal goal is to efficiently design an optimal precoder that minimizes the asymptotic SEP of the ZF-DF detector under a perfect decision feedback. By fully taking advantage of the product majorization relationship among eigenvalues, singular-values and Cholesky values of the precoded channel matrix parameters, a necessary condition for the optimal solution to satisfy is first developed and then the structure of the optimal solution is characterized. With these results, the original non-convex problem is reformulated into a convex one that can be efficiently solved by using an interior-point method. In addition, by scaling up the antenna array size of both terminals without bound for such a network, we propose a novel method as we did for the ZF receiver scenario to analyze the asymptotic SEP performance of an equal-diagonal QRS precoded large MIMO system when employing an abstract Toeplitz correlation model for the transmitter antenna array. This new approach has a simple expression with a fast convergence rate and thus, is efficient and effective for error performance evaluation. For multiuser communication networks, we first consider a discrete-time multiple-input single-output (MISO) Gaussian broadcast channel (BC) where perfect CSI is available at both the transmitter and all the receivers. We propose a flexible and explicit design of a uniquely decomposable constellation group (UDCG) based on PAM and rectangular QAM constellations. With this new concept, a modulation division (MD) transmission scheme is developed for the considered MISO BC. The proposed MD scheme enables each receiver to uniquely and efficiently recover their desired signals from the superposition of mutually interfering cochannel signals in the absence of noise. Using max-min fairness as a design criterion, the optimal transmitter beamforming problem is solved in a closed-form for two-user MISO BC. Then, for a general case with more than two receivers, a user-grouping based beamforming scheme is developed, where the grouping method, beamforming vector design and power allocation problems are addressed by employing weighted max-min fairness. Then, we consider an uplink massive single-input and multiple-output (SIMO) network consisting of a base station (BS) and several single-antenna users. To recover the transmitted signal matrix of all the users when the antenna array size is large, a novel multi-user space-time modulation (MUSTM) scheme is proposed for the considered network based on the explicit construction of QAM uniquely-decomposable constellation groups (QAM-UDCGs). In addition, we also develop a sub-constellation allocation method at the transmitter side to ensure the signal matrix is always invertible. In the meanwhile, an efficient training correlation receiver (TCR) is proposed which calculates the correlation between the received sum training signal vector and the sum information carrying vector. Moreover, the optimal power allocation problems are addressed by maximizing the coding gain or minimizing the average SEP of the received sum signal under both average and peak power constraints on each user. The proposed transmission scheme not only allows the transmitted signals with strong mutual interference to be decoded by a simple TCR but it also enables the CSI of all the users to be estimated within a minimum number of time slots equal to that of the users. Comprehensive computer simulations are carried out to verify the effectiveness of the proposed uniquely decomposable space-time modulation method in various network topologies and configurations. Our modulation division method will be one of the promising technologies for the fifth generation (5G) communication systems. / Dissertation / Doctor of Philosophy (PhD)