The central objective of this work is to present an analysis of the asymptotic conformal Killing vectors in asymptotically-flat space-times of general relativity. This problem has been examined by two different methods; in Chapter 5 the asymptotic expansion technique originated by Newman and Unti [31] leads to a solution for asymptotically-flat spacetimes which admit an asymptotically shear-free congruence of null geodesics, and in Chapter 6 the conformal rescaling technique of Penrose [54] is used both to support the findings of the previous chapter and to set out a procedure for solution in the general case. It is pointed out that Penrose's conformal technique is preferable to the use of asymptotic expansion methods, since it can be established in a rigorous manner without leading to the possible convergence difficulties associated with asymptotic expansions. Since the asymptotic conformal symmetry groups of asymptotically flat space-times Are generalisations of the conformal group of Minkowski space-time we devote Chapters 3 and 4 to a study of the flat space case so that the results of later chapters may receive an interpretation in terms of familiar concepts. These chapters fulfil a second, equally important, role in establishing local isomorphisms between the Minkowski-space conformal group, 90(2,4) and SU(2,2). The SO(2,4) representation has been used by Kastrup [61] to give a physical interpretation using space-time gauge transformations. This appears as part of the survey of interpretative work in Chapter 7. The SU(2,2) representation of the conformal group has assumed a theoretical prominence in recent years. through the work of Penrose [9-11] on twistors. In Chapter 4 we establish contact with twistor ideas by showing that points in Minkowski space-time correspond to certain complex skew-symmetric rank two tensors on the SU(2,2) carrier space. These objects are, in Penrose's terminology [91, simple skew-symmetric twistors of valence [J. A particularly interesting aspect of conformal objects in space-time is explored in Chapter 8, where we extend the work of Geroch [16] on multipole moments of the Laplace equation in 3-space to the consideration. of Q tý =0 in Minkowski space-time. This development hinges upon the fact that multipole moment fields are also conformal Killing tensors. In the final chapter some elementary applications of the results of Chapters 3 and 5 are made to cosmological models which have conformal flatness or asymptotic conformal flatness. In the first class here we have 'models of the Robertson-Walker type and in the second class we have the asymptotically-Friedmann universes considered by Hawking [73]. / University of Bradford Research Studenship

<p> A multiple-input multiple-output (MIMO) communication system has the potential to provide reliable transmissions at high data rates. However, the computational cost of achieving this promising performance can be quite substantial. With an emphasis on practical implementations, the MIMO systems employing the low cost linear receivers are studied in this thesis. The optimum space-time block codes (STBC) that enable a linear receiver to achieve its best possible performance are proposed for various MIMO systems. These codes satisfy an intra and inter orthogonality property, and are called unitary trace-orthogonal codes. In addition, several novel transmission schemes are specially designed for linear receivers with the use of the proposed code structure. The applications of the unitary trace-orthogonal code are not restricted to systems employing linear receivers. The proposed code structure can be also applied to the systems employing other types of receivers where several originally intractable code design problems are successfully solved.</p> <p>The communication schemes presented in this thesis are outlined as follows: •For a MIMO system with N ≥ M, where M and N are the number of transmitter and receiver antennas, respectively, the optimal full rate linear STBC for linear receivers is proposed and named unitary trace-orthogonal code. The proposed code structure is proved to be necessary and sufficient to achieve the minimum detection error probability for the system. • When applied to a multiple input single output (MISO) communication system, a special linear unitary trace-orthogonal code, named the Toeplitz STBC, is proposed. The code enables a linear receiver to provide full diversity and to achieve the optimal tradeoff between the detection error and the data transmission rate. This is, thus far, the first code that possesses such properties for an arbitrary MISO system that employs a linear receiver. • In MIMO systems in which N ≥ M and the signals are transmitted at full symbol rate, the highest diversity gain achievable by linear receivers is analyzed and shown to be N - M + 1. To improve the performance of a linear receiver, a multi-block transmission scheme is proposed, in which signals are coded so that they span multiple independent channel realizations. An optimal full rate linear STBC for this system that minimizes the detection error probability is presented. The code is named multi-block unitary trace-orthogonal code. The resulting system has an improved diversity gain. Furthermore, by relaxing the code from the full symbol rate constraint, a special multi-block transmission scheme is proposed. This scheme achieves a much improved diversity gain than those with full symbol rate. • The unitary trace-orthogonal code can also be applied to a system that employs a maximum-likelihood (ML) receiver rather than the simple linear receiver. For such a system, a systematic design of full diversity unitary trace-orthogonal code is presented for an arbitrary data transmission rate. </p> <p>In summary, when a simple linear receiver is employed, unitary trace-orthogonal codes and their optimality properties are exploited for various multiple antenna communication systems. Some members from this code family can also enable an optimal performance of ML detection. </P> / Thesis / Doctor of Philosophy (PhD)

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<p>In this thesis, we consider a coherent MIMO system, emphasizing on the simplicity of implementation at both the code generator and the receiver. Specifically, we consider the transmission of a space-time block code (STBC) that is a linear combination of coding matrices weighted by the information symbols through a receiver-correlated flat-fading channel and received by a linear ZF detector. Our target is the design of a code which, while maintaining full data-transmission rate, minimizes the asymptotic average (over all the random channel coefficients) bit error probability of an ZF detector. To this end, we first ensure that the full data rate of symbols is maintained, and then, based on the BER for 4-QAM signals, we derive the conditions for optimal codes and establish a code structure that minimizes the asymptotic average bit error probability. We also prove that the diversity gain of our M × N MIMO system is N − M + 1. The resulting optimum code structure requires the individual coding matrices to be mutually orthogonal when vectorized and is related to covariance matrix of correlated channel. The first optimum structural characteristics of the coding matrices is described as trace-orthogonal. A new approach to express expected value of random correlated channel has been proposed as well. From simulation results we can see that advantage of optimum code over uncoded system is more apparent as channel correlation is higher.</p> / Master of Applied Science (MASc)

<p> In this thesis, we present a novel signalling scheme for blind channel identification of Alamouti space-time coded (STBC) channel and a space-time coded multiple-input single-output (MISO) system under flat fading environment. By using p-ary and q-ary PSK signals (where p and q are co-prime integers), we prove that a) under a noise-free environment, only two distinct pairs of symbols are needed to uniquely decode the signal and identify the channel, and b) under complex Gaussian noise, if the pth and qth order statistics of the received signals are available, the channel coefficients can also be uniquely determined. In both cases, simple closed-form solutions are derived by exploiting specific properties of the Alamouti STBC code and linear Diophantine equation theory.</p> <p> When only a limited number of received data are available, under Gaussian noise environment, we suggest the use of the semi-definite relaxation method and/or the sphere decoding method to implement blind ML detection so that the joint estimation of the channel and the transmitted symbols can be efficiently facilitated. Simulation results show that blind ML detection methods with our signalling scheme provide superior normalized mean square error in channel estimation compared to the method using only one constellation and that the average symbol error rate is close to that of the coherent detector (which necessitates perfect channel knowledge at the receiver), particularly when the SNR is high.</p> / Thesis / Master of Applied Science (MASc)

Space-time codes (STC) are a class of signaling techniques, offering coding and diversity gains along with improved spectral efficiency. These codes exploit both the spatial and the temporal diversity of the wireless link by combining the design of the error correction code, modulation scheme and array processing. STC are well suited for improving the downlink performance, which is the bottleneck in asymmetric applications such as downstream Internet. Three original contributions to the area of STC are presented in this dissertation. First, the development of analytic tools that determine the fundamental limits on the performance of STC in a variety of channel conditions. For trellis-type STC, transfer function based techniques are applied to derive performance bounds over Rayleigh, Rician and correlated fading environments. For block-type STC, an analytic framework that supports various complex orthogonal designs with arbitrary signal cardinalities and array configurations is developed. In the second part of the dissertation, the Virginia Tech Space-Time Advanced Radio (VT-STAR) is designed, introducing a multi-antenna hardware laboratory test bed, which facilitates characterization of the multiple-input multiple-output (MIMO) channel and validation of various space-time approaches. In the third part of the dissertation, two novel space-time architectures paired with iterative processing principles are proposed. The first extends the suitability of STC to outdoor wireless communications by employing iterative equalization/decoding for time dispersive channels and the second employs iterative interference cancellation/decoding to solve the error propagation problem of Bell-Labs Layered Space-Time Architecture (BLAST). Results show that remarkable energy and spectral efficiencies are achievable by combining concepts drawn from space-time coding, multiuser detection, array processing and iterative decoding. / Ph. D.