Year

2007

Degree Name

Doctor of Philosophy

Department

School of Computing Science and Software Engineering

Abstract

Problems concerned with the algebraic structure and existence of orthogonal designs and complementary sequences with zero aperiodic autocorrelation have long been of interest in combinatorics, coding theory and applied statistics. Over the last few decades, due to an increased demand for wireless services, new technologies have had to be considered since traditional methods are reaching their technical or financial limits. This has motivated the study of new applications of algebraic structures for wireless communications to improve system performance. For example, space-time block codes (STB Cs) from orthogonal designs for multiple-input multiple-output (M IM O) wireless systems have received a lot of attention due to their inherent orthogonality, which guarantees a full transmit diversity and a simple linear decoding. The objective of this research is to investigate the construction of orthogonal designs and complementary sequences in terms of wireless communication applications. One thread of this thesis is the introduction of amicable orthogonal designs over the real and quaternion domain in the context of STB Cs from orthogonal designs. Another part is the study of Golay complementary sequences and their applications as orthogonal spreading sequences for direct sequence code division multiple access (D S-CD M A) systems. We address the following problems in this thesis: ² The current complex orthogonal STB Cs for more than two antennas are not delay optimal or full rate, and even contain many z eros, which will impede their practical implementation. We first introduce some new complex orthogonal codes of order eight with fewer wasted time slots compared to conventional codes. Furthermore, for those complex STB Cs constructed from amicable orthogonal designs containing z eros and irrational numbers in their coefficient matrices, we use the representation theory of Cliord algebras to improve the form of complex orthogonal STB Cs. B y applying this proposed method, we can construct square, maximum rate complex codes with less z eros and no irrational numbers, e.g. transmitted symbols are equally dispersed through transmit antennas. ² However, given any arbitrary order and type, many amicable orthogonal designs are left undecided, since they cannot be constructed using current techniques. We thus introduce the concept of orthogonal designs equivalence. By searching all the equivalence classes of orthogonal designs we find new amicable orthogonal designs of order eight. In addition, some undecided cases can be concluded with non-existence after searching all the equivalence classes of an orthogonal design with the same order and type. We then summarize all the existence and non-existence results of amicable orthogonal designs with order eight. ² Motivated by the success of space-time block codes from orthogonal designs, we also discuss the construction of amicable orthogonal designs over the quaternion domain (AOD Q ) for their possible applications as space-time-polarization block codes, since the additional polarization diversity can be modelled by means of quaternions. We construct some new AOD Q s using the Kronecker product with real amicable orthogonal designs or real weighing matrices from an amicable family. ² Complementary pairs and orthogonal spreading sequences constructed on the basis of complementary sequences have long been studied for channel separation in D S-CD M A systems. H owever, it is hard to generate sequences with both good autocorrelation and cross-correlation properties so as to achieve a good interference performance. We derive a new class of quadri-phase orthogonal spreading sequences from small mutually orthogonal (M O) complementary sets. We then apply a sequence modification method based on choosing a diag- onal H -equivalent matrix to optimize the correlation properties of sequences. The modifed sequences exhibit a reasonable compromise between autocorrela- tion and cross-correlation characteristics, and, as shown through simulations, lead to good performance when used in an asynchronous multi-user CD M A system.

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