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In epidemiology it is often useful to monitor disease occurrences prospectively to determine the location and time when clusters of disease are forming. This aids in the prevention of illness and injury of the public and is the reason spatio-temporal disease surveillance methods are implemented. Care must be taken in the design and implementation of these types of surveillance methods so that the methods provide accurate information on the development of clusters. Here two spatio-temporal methods for prospective disease surveillance are considered. These include the local Knox monitoring method and a new wavelet-based prospective monitoring method. The local Knox surveillance method uses a cumulative sum (CUSUM) control chart for monitoring the local Knox statistic, which tests for space-time clustering each time there is an incoming observation. The detection of clusters of events occurring close together both temporally and spatially is important in finding outbreaks of disease within a specified geographic region. The local Knox surveillance method is based on the Knox statistic, which is often used in epidemiology to test for space-time clustering retrospectively. In this method, a local Knox statistic is developed for use with the CUSUM chart for prospective monitoring so that epidemics can be detected more quickly. The design of the CUSUM chart used in this method is considered by determining the in-control average run length (ARL) performance for different space and time closeness thresholds as well as for different control limit values. The effect of nonuniform population density and region shape on the in-control ARL is explained and some issues that should be considered when implementing this method are also discussed. In the wavelet-based prospective monitoring method, a surface of incidence counts is modeled over time in the geographical region of interest. This surface is modeled using Poisson regression where the regressors are wavelet functions from the Haar wavelet basis. The surface is estimated each time new incidence data is obtained using both past and current observations, weighing current observations more heavily. The flexibility of this method allows for the detection of changes in the incidence surface, increases in the overall mean incidence count, and clusters of disease occurrences within individual areas of the region, through the use of control charts. This method is also able to incorporate information on population size and other covariates as they change in the geographical region over time. The control charts developed for use in this method are evaluated based on their in-control and out-of-control ARL performance and recommendations on the most appropriate control chart to use for different monitoring scenarios is provided. / Ph. D.

Recently multiple antenna systems have received significant attention from researchers as a means to improve the energy and spectral efficiency of wireless systems. Among many classes of schemes, Space-Time Block codes (STBC) and Space-Time Trellis codes (STTC) have been the subject of many investigations. Both techniques provide a means for combatting the effects of multipath fading without adding much complexity to the receiver. This is especially useful in the downlink of wireless systems. In this thesis we investigate the impact of channel estimation error on the performance of both STBC and STTC. Channel estimation is especially important to consider in multiple antenna systems since (A) for coherent systems there are more channels to estimate due to multiple antennas and (B) the decoupling of data streams relies on correct channel estimation. The latter effect is due to the intentional cross-talk introduced into STBC. / Master of Science

Simultaneous two-point three-component four-sensor hot-wire velocity measurements taken in three flows of aeroacoustic interest are here analyzed. The analyses provide information on the turbulence structure of the flows as it would be encountered by hypothetical noise producing blades passing through the flows. Two-point measurements taken in the first flow, a lifting wake from a rectangular NACA 0012 half wing, are used to calculate space-time correlation functions and 'pointwise' wave number frequency spectra. Two upwash spectra, calculated for locations in the region of the wake that is roughly homogenous in the spanwise direction, are direct estimates of the full wave number frequency spectra at their locations. As such, they are used to perform aeroacoustic calculations, and the results are compared to results achieved using the von Kármán isotropic spectrum. Amiet's approximation, where the wave number frequency spectra can be represented by the correlation length scales is found to hold reasonably well for the measured spectra. The two-point measurements in the second flow, a vortex/blade-tip interaction, are analyzed to provide information useful to researchers of blade-wake interaction noise produced by helicopter rotors. Space-time correlation functions and wave number frequency spectra are calculated for five cuts through the region of interaction. The correlation functions provide information concerning the turbulence length scales found in the interaction region. The spectra are compared to the von Kármán isotropic spectrum and found to be greatly different. However, the spectra do bear some resemblance to spectra calculated in the spanwise homogenous region of the lifting wake. The two-point measurements taken in the third flow, the wake from a fan cascade, are analyzed to provide information of use to modelers of broadband noise produced through rotor wake/stator interactions. In particular, space-time correlation functions are calculated for a grid of two-point measurements, which allows the estimation of the turbulence structure as seen by a passing stator blade. Space-time correlation functions and wave number frequency spectra are calculated for various stator configurations. The implications of engine operating speed and stator configuration for broadband noise production are discussed. <i> [Vita removed March 2, 2012. GMc]</i> / Master of Science

Communication over a wireless channel is a challenging task because of the inherent fading effects. Any wireless communication system employs some form of diversity improving techniques in order to improve the reliability of the channel. This thesis deals with efficient code design for two different spatial diversity techniques, viz, diversity by employing multiple antennas at the transmitter and/or the receiver, and diversity through cooperative commu- nication between users. In other words, this thesis deals with efficient code design for (1) multiple-input multiple-output (MIMO) channels, and (2) wireless relay channels. Codes for the MIMO channel are termed space-time (ST) codes and those for the relay channels are called distributed ST codes. The first part of the thesis focuses on ST code construction for MIMO fading channel with perfect channel state information (CSI) at the receiver, and no CSI at the transmitter. As a measure of performance we use the rate-diversity tradeoff and the Diversity-Multiplexing Gain (D-MG) Tradeoff, which are two different tradeoffs characterizing the tradeoff between the rate and the reliability achievable by any ST code. We provide two types of code constructions that are optimal with respect to the rate-diversity tradeoff; one is based on the rank-distance codes which are traditionally applied as codes for storage devices, and the second construction is based on a matrix representation of a cayley algebra. The second contribution in ST code constructions is related to codes with a certain nonvanishing determinant (NVD) property. Motivation for these constructions is a recent result on the necessary and sufficient conditions for an ST code to achieve the D-MG tradeoff. Explicit code constructions satisfying these conditions are provided for certain number of transmit antennas. The second part of the thesis focuses on distributed ST code construction for wireless relay channel. The transmission protocol follows a two-hop model wherein the source broadcasts a vector in the first hop and in the second hop the relays transmit a vector that is a transformation of the received vector by a relay-specific unitary transformation. While the source and relays do not have CSI, at the destination we assume two different scenarios (a) destina- tion with complete CSI (b) destination with only the relay-destination CSI. For both these scenarios, we derive a Chernoff bound on the pair-wise error probability and propose code design criteria. For the first case, we provide explicit construction of distributed ST codes with lower decoding complexity compared to codes based on some earlier system models. For the latter case, we propose a novel differential encoding and differential decoding technique and also provide explicit code constructions. At the heart of all these constructions is the cyclic division algebra (CDA) and its matrix representations. We translate the problem of code construction in each of the above scenarios to the problem of constructing CDAs satisfying certain properties. Explicit examples are provided to illustrate each of these constructions.

It is well known that communication using multiple antennas provides high data rate and reliability. Coding across space and time is necessary to fully exploit the gains offered by multiple input multiple output (MIMO) systems. One such popular method of coding for MIMO systems is space-time block coding. In applications where the terminals do not have enough physical space to mount multiple antennas, relaying or cooperation between multiple single antenna terminals can help achieve spatial diversity in such scenarios as well. Relaying techniques can also help improve the range and reliability of communication. Recently it has been shown that certain space-time block codes (STBCs) can be employed in a distributed fashion in single antenna relay networks to extract the same benefits as in point to point MIMO systems. Such STBCs are called distributed STBCs. However an important practical issue with STBCs and DSTBCs is its associated high maximum likelihood (ML) decoding complexity. The central theme of this thesis is to systematically construct STBCs and DSTBCs applicable for various scenarios such that are amenable for low decoding complexity. The first part of this thesis provides constructions of high rate STBCs from crossed product algebras that are minimum mean squared error (MMSE) optimal, i.e., achieves the least symbol error rate under MMSE reception. Moreover several previous constructions of MMSE optimal STBCs are found to be special cases of the constructions in this thesis. It is well known that STBCs from orthogonal designs offer single symbol ML decoding along with full diversity but the rate of orthogonal designs fall exponentially with the number of transmit antennas. Thus it is evident that there exists a tradeoff between rate and ML decoding complexity of full diversity STBCs. In the second part of the thesis, a definition of rate of a STBC is proposed and the problem of optimal tradeoff between rate and ML decoding complexity is posed. An algebraic framework based on extended Clifford algebras is introduced to study the optimal tradeoff for a class of multi-symbol ML decodable STBCs called ‘Clifford unitary weight (CUW) STBCs’ which include orthogonal designs as a special case. Code constructions optimally meeting this tradeoff are also obtained using extended Clifford algebras. All CUW-STBCs achieve full diversity as well. The third part of this thesis focusses on constructing DSTBCs with low ML decoding complexity for two hop, amplify and forward based relay networks under various scenarios. The symbol synchronous, coherent case is first considered and conditions for a DSTBC to be multi-group ML decodable are first obtained. Then three new classes of four-group ML decodable full diversity DSTBCs are systematically constructed for arbitrary number of relays. Next the symbol synchronous non-coherent case is considered and full diversity, four group decodable distributed differential STBCs (DDSTBCs) are constructed for power of two number of relays. These DDSTBCs have the best error performance compared to all previous works along with low ML decoding complexity. For the symbol asynchronous, coherent case, a transmission scheme based on orthogonal frequency division multiplexing (OFDM) is proposed to mitigate the effects of timing errors at the relay nodes and sufficient conditions for a DSTBC to be applicable in this new transmission scheme are given. Many of the existing DSTBCs including the ones in this thesis are found to satisfy these sufficient conditions. As a further extension, differential encoding is combined with the proposed transmission scheme to arrive at a new transmission scheme that can achieve full diversity in symbol asynchronous, non-coherent relay networks with no knowledge of the timing errors at the relay nodes. The DDSTBCs in this thesis are proposed for application in the proposed transmission scheme for symbol asynchronous, non-coherent relay networks. As a parallel to the non-coherent schemes based on differential encoding, we also propose non-coherent schemes for symbol synchronous and symbol asynchronous relay networks that are based on training. This training based transmission scheme leverages existing coherent DSTBCs for non-coherent communication in relay networks. Simulations show that this training scheme when used along with the coherent DSTBCs in this thesis outperform the best known DDSTBCs in the literature. Finally, in the last part of the thesis, connections between multi-group ML decodable unitary weight (UW) STBCs and groups with real elements are established for the first time. Using this connection, we translate the necessary and sufficient conditions for multi-group ML decoding of UW-STBCs entirely in group theoretic terms. We discuss various examples of multi-group decodable UW-STBCs together with their associated groups and list the real elements involved. These examples include orthogonal designs, quasi-orthogonal designs among many others.

This thesis addresses the design of low-complexity coding schemes for wireless relay networks and multiple access channels. The first part of the thesis is on wireless relay networks and the second part is on multiple access channels. Distributed space-time coding is a well known technique to achieve spatial diversity in wireless networks wherein, several geographically separated nodes assist a source node to distributively transmit a space-time block code (STBC) to the destination. Such STBCs are referred to as Distributed STBCs (DSTBCs). In the first part of the thesis, we focus on designing full diversity DSTBCs with some nice properties which make them amenable for implementation in practice. Towards that end, a class of full diversity DST-BCs referred to as Co-ordinate Interleaved DSTBCs (CIDSTBCs) are proposed for relay networks with two-antenna relays. To construct CIDSTBCs, a technique called co-ordinate vector interleaving is introduced wherein, the received signals at different antennas of the relay are processed in a combined fashion. Compared to the schemes where the received signals at different antennas of the relay are processed independently, we show that CIDSTBCs provide coding gain which comes in with negligible increase in the processing complexity at the relays. Subsequently, we design single-symbol ML decodable (SSD) DSTBCs for relay networks with single-antenna nodes. In particular, two classes of SSD DSTBCs referred to as (i) Semi-orthogonal SSD Precoded DSTBCs and (ii) Training-Symbol Embedded (TSE) SSD DSTBCs are proposed. A detailed analysis on the maximal rate of such DSTBCs is presented and explicit DSTBCs achieving the maximal rate are proposed. It is shown that the proposed codes have higher rates than the existing SSD DSTBCs. In the second part, we study two-user Gaussian Multiple Access Channels (GMAC). Capacity regions of two-user GMAC are well known. Though, capacity regions of such channels provide insights into the achievable rate pairs in an information theoretic sense, they fail to provide information on the achievable rate pairs when we consider finitary restrictions on the input alphabets and analyze some real world practical signal constellations like QAM and PSK signal sets. Hence, we study the capacity aspects of two-user GMAC with finite input alphabets. In particular, Constellation Constrained (CC) capacity regions of two-user SISO-GMAC are computed for several orthogonal and non-orthogonal multiple access schemes (abbreviated as O-MA and NO-MA schemes respectively). It is first shown that NO-MA schemes strictly offer larger capacity regions than the O-MA schemes for finite input alphabets. Subsequently, for NO-MA schemes, code pairs based on Trellis Coded Modulation (TCM) are proposed such that any rate pair on the CC capacity region can be approached. Finally, we consider a two-user Multiple-Input Multiple-Output (MIMO) fading MAC and design STBC pairs such that ML decoding complexity is reduced.

This thesis describes the use of a multi-amplitude minimum shift keying (MAMSK) signal in various types of wireless communication system. A MAMSK signal is a bandwidth efficient modulation scheme obtained by superimposing ℳ minimum shift keying (MSK) signals with unequal amplitudes. The overall phase of a MAMSK signal is controlled by the phase of the largest component MSK signal which allows the use of a low-complexity differential detector. A closed form expression for the average bit error rate (BER) for coherent detection of an MAMSK in AWGN is derived and is shown to achieve the same BER as that of square constellation quadrature amplitude modulation (QAM) with the same average transmit power. We describe the design and implementation of a STBC-based MIMO radio system in conjunction with MAMSK modulation. The proposed system provides high capacity data transmission by carrying information not only in the phases but also in the amplitude. Despite using a simple MAMSK differential receiver the system achieves performance within 1 dB of coherent detection. The existing MSK modems in conjunction with STBC could easily be modified to construct the proposed system. The MAMSK modulation scheme is extended to a multiuser relaying network where two nodes cooperate in a half-duplex environment to achieve diversity gain. The cooperative scheme is based on superposition modulation using a decode-and-forward (DF) strategy. In the proposed scheme, each node simultaneously transmits its own and the relayed signals by superimposing one on the other. A MAMSK signal is an excellent choice for this type of cooperative communication due its being obtained by a superposition technique. The proposed system exploits the overall phase of a MAMSK signal which allows differential detection and as a result it provides the lowest decoding complexity and memory requirements among the existing superposition based cooperation schemes. The performance of the system is evaluated by simulation, where it is shown that the MAMSK cooperative system outperforms a conventional DF scheme in terms of both power and bandwidth efficiency.

Spatial diversity is an effective technique to combat the effects of severe fading in wireless environments. Recently, cooperative communications has emerged as an attractive communications paradigm that can introduce a new form of spatial diversity which is known as cooperative diversity, that can enhance system reliability without sacrificing the scarce bandwidth resource or consuming more transmit power. It enables single-antenna terminals in a wireless relay network to share their antennas to form a virtual antenna array on the basis of their distributed locations. As such, the same diversity gains as in multi-input multi-output systems can be achieved without requiring multiple-antenna terminals. In this thesis, a new approach to cooperative communications via distributed extended orthogonal space-time block coding (D-EO-STBC) based on limited partial feedback is proposed for cooperative relay networks with three and four relay nodes and then generalized for an arbitrary number of relay nodes. This scheme can achieve full cooperative diversity and full transmission rate in addition to array gain, and it has certain properties that make it alluring for practical systems such as orthogonality, flexibility, low computational complexity and decoding delay, and high robustness to node failure. Versions of the closed-loop D-EO-STBC scheme based on cooperative orthogonal frequency division multiplexing type transmission are also proposed for both flat and frequency-selective fading channels which can overcome imperfect synchronization in the network. As such, this proposed technique can effectively cope with the effects of fading and timing errors. Moreover, to increase the end-to-end data rate, this scheme is extended for two-way relay networks through a three-time slot framework. On the other hand, to substantially reduce the feedback channel overhead, limited feedback approaches based on parameter quantization are proposed. In particular, an optimal one-bit partial feedback approach is proposed for the generalized D-O-STBC scheme to maximize the array gain. To further enhance the end-to-end bit error rate performance of the cooperative relay system, a relay selection scheme based on D-EO-STBC is then proposed. Finally, to highlight the utility of the proposed D-EO-STBC scheme, an application to cognitive radio is studied.