<p>In this thesis, a MISO wireless communication system having even transmitter antennas and a single receiver antenna is considered, where neither the transmitter nor the receiver knows channel state information. Particularly when the number of transmitter antennas is two, a novel concept called a uniquely factorable constellation pair (UFCP) is first proposed for the systematic design of a noncoherent full diversity collaborative unitary space-time block code by normalizing two Alamouti codes. It is proved that such a unitary UFCP code assures the unique identification of both channel coefficients and transmitted signals in a noise-free case as well as full diversity for the noncoherent maximum likelihood (ML) receiver in a noise case. To further improve error performance, an optimal unitary UFCP code is designed by appropriately and uniquely factorizing a pair of energy-efficient cross quadrature amplitude modulation (QAM) constellations to maximize the coding gain subject to a transmission bit rate constraint. After a deep investigation of the fractional coding gain function, a technical approach developed in this thesis to maximizing the coding gain is to carefully design an energy scale to compress the first three largest energy points in the corner of the QAM constellations in the denominator of the objective as well as carefully design a constellation triple forming two UFCPs, with one collaborating with the other two so as to make the accumulated minimum Euclidean distance along the two transmitter antennas in the numerator of the objective as large as possible and at the same time, to avoid as many corner points of the QAM constellations with the largest energy as possible to achieve the minimum of the numerator. In other words, the optimal coding gain is attained by intelligent constellations collaboration and efficient energy compression. Another contribution of this thesis is to generalize the design for the two transmitter antennas into that of the noncoherent system with any even number of transmitter antennas. Using the Alamouti coding scheme and the Toeplitz matrix structure, a novel noncoherent nonunitary space-time block code, which is called an Alamoutibased Toeplitz space-time block code, is proposed. By the fundamentals of Galois theory and algebraic number theory, two important properties on the two Alamouti codes generated from a pair of coprime phase shift keying (PSK) constellations, i.e., the uniqueness of factorization itself and the shift-invariant uniqueness of factorization, are first revealed and rigorously proved. Then, it is further shown that it is these two kinds of the unique factorizations that enable the unique blind identification of both the channel coefficients and the transmitted signals by only processing two block received signals as well as noncoherent full diversity with a generalized likelihood ratio test (GLRT) receiver. In addition, a full diversity unitary code design is also proposed by simply applying the QR decomposition to the full diversity nonunitary Alamoutibased Toeplitz space-time block code. Computer simulations demonstrate that error performance of both optimal unitary UFCP code and Alamouti-based Toeplitz code presented in this thesis outperform those of the differential code and the SNR-efficient training code, which is the best code in current literatures for the system.</p> / Master of Applied Science (MASc)

Direct-Sequence Code Division Multiple Access (DS-CDMA), over the last few years, has become a popular technique and finds a place in many modern communication systems. The performance of this technique is closely linked to the signature (or spreading) sequences employed in the system. In the past, there have been many successful attempts by research groups to construct families of signature sequences that offer the potential gains promised by theoretical bounds. In this thesis, we present constructions of families of signature sequences over the AM-PSK and QAM alphabet with low correlation. In this thesis, we construct a family of sequences over the 8-ary AM-PSK constella- tion, Family AOpt(16) that is asymptotically optimal with respect to the Welch bound on maximum magnitude of correlation for complex sequences. The maximum magnitude of correlation for this family, θmax, is upper bounded by √N , where N is the period of the sequences. The 8-ary AM-PSK constellation is a subset of the 16-QAM constellation. We also construct two families of sequences over 16-QAM, Family A16A, and Family A16,B , with the maximum magnitude of correlation upper bounded by √2√N . We construct a family, A(M 2), of sequences over the 2m+1-ary AM-PSK constellation of period N = 2r- 1 and family size (N + 1)/2m-1 . The 2m+1-ary AM-PSK constellation is a subset of the M 2-QAM constellation with M =2m . The maximum nontrivial normalized correlation parameter is bounded above by θmax < a √N where a ranges from 1.34 in the case of M 2 = 16 to √5 for large m. Apart from low correlation values, the family possesses several interesting and useful features. In Family A(M 2), users have the ability to transmit 2m bits of data per period of the spreading sequence. The sequences in Family A(M 2) are balanced; all points from the 2m+1-ary AM-PSK constellation occur approximately equally often in sequences of long period. The Euclidean distance between the signals assigned to a particular user in A(M 2), corresponding to different data symbols, is larger than the corresponding value for the case when 2m+1-PSK modulation and spreading is used. Perhaps most interestingly, Family A(M 2) permits users on the reverse link of a CDMA system to communicate asynchronously at varying data rates by switching between different QAM constellations. Family A(M 2) is compatible with QPSK sequence families S(p) in the sense that the maximum correlation magnitude is increased only slightly if one adds sequences from (p) S(p)\ S(0) to Family A(M 2). We also construct families of sequences over AM-PSK that tradeoff data rate per sequence period and θmax for a given family size. We have extended the construction of sequences over AM-PSK constellation to construct sequences over the M 2-QAM constellation for M =2m . The QAM sequence families, Families (AM 2), have size, data rate and minimum squared Euclidean distance same as the corresponding AM-PSK construction but have higher values of θmax. Also included in the thesis are constructions for large families of sequences over the M 2-QAM alphabet.