<p>Particle filters are being used in a number of state estimation applications because of their capability to effectively solve nonlinear andnon-Gaussian problems. However, they have high computational requirements and this becomes even more so in the case of multitarget tracking, where data association is the bottleneck. In order to perform data association and estimation jointly, typically an augmented state vector, whose dimensions depend on the number of targets, is used in particle filters. As the number of targets increases, the corresponding computational load in creases exponentially. In this case, parallelization is a possibility for achieving real-time feasibility in large-scale multitarget tracking applications. In this paper, we present an optimization-based scheduling algorithm that minimizes the total computation time for the bus-connected heterogeneous primary-secondary architecture. This scheduler is capable of selecting the optimal number of processors from a large pool of secondary processors and mapping the particles among the selected ones. A new distributed resampling algorithm suitable for parallel computing is also proposed. Furthermore, a less communication intensive parallel implementation of the particle filter without sacrificing tracking accuracy using an efficient load balancing technique, in which optimal particle migration among secondary processors is ensured, is presented. Simulation results demonstrate the tracking effectiveness of the new parallel particle filter and the speedup achieved using parallelization.</p> / Master of Applied Science (MASc)

<p>In this thesis, a new paradigm is proposed for designing the transmitter and receiver for quadrature-amplitude-modulated signalling over a mobile radio channel. The new paradigm is based on a discrete-multipath linear time-variant model of the mobile radio channel, and hence the title of the thesis. The time-variant input-output relationship of the discrete multipath channel (DMC) is governed by a set of parameters which can be obtained in finite time by probing, that is, by transmitting a pre-assigned signal and then performing computations on the received signal. Therefore, once the parameters of the DMC's input-output relationship have been obtained in this manner, the receiver can, in principle, determine the subsequently transmitted data-carrying signal, or, the data itself, by performing computations on the received signal, which operation is referred to as signalling.</p> <p>Thus, the thesis proposes a philosophy of design based on alternate probing and signalling, and shows that when the transmitted signal is generated by quadrature amplitude modulation (QAM) the composition of QAM and DMC lends itself to this philosophy of design, even in the presence of intersymbol interference (lSI) and additive white Gaussian noise (AWGN).</p> <p>As regards probing, it is shown that by transmitting a suitable quadrature-amplitude. modulated signal all parameters of the DMC, or, rather, of the composition of QAM and DMC, can be estimated in the presence of AWGN. In particular, the maximum-likelihood method of estimation is shown to have the statistical properties needed to justify the philosophy of design.</p> <p>As regards signalling, based on the assumption that the parameters of the DMC, or, rather, of the composition of QAM and DMC, are known by the receiver, it is shown how the receiver may decide which data sequence was likely transmitted, taking into account lSI and AWGN according to some optimal rule. Motivated by the classical receiver design principals used for quadrature-amplitude-modulated signalling over a linear time-invariant channel in the presence of lSI and AWGN, namely.</p> <p>1. linear zero-forcing equalizer,</p> <p>2. decision-feedback zero-forcing equalizer,</p> <p>3. linear mean-square-error equalizer,</p> <p>4. decision-feedback mean-square-error equalizer,</p> <p>5. maximum-likelihood sequence estimator of the Forney-type,</p> <p>6. maximum·likelihood sequence estimator of the Ungerboeck type,</p> <p>the thesis shows how these principles can be generalized for quadrature-amplitude-modulated signalling over a DMC in the presence of lSI and AWGN. Despite the DMC's being time-variant, these generalized receivers can be implemented with a bank of continuous-time time-invariant filters at the front.</p> <p>The thesis, although mainly theoretical, illustrates some of the above methods through computer simulations. More specifically, numerical results are given for probing by maximum-likelihood method and signalling by a linear zero-forcing equalizer, under various system specifications and scenarios involving the geometry of propagation and speeds of movement.</p> / Doctor of Philosophy (PhD)

<p>The problem of radar modeling is of critical importance to Electronic Warfare applications such as radar recognition and threat analysis. As modern radar signals become steadily more complex, so do the issues associated with radar modeling and signal processing. Traditional, data-centric approaches to radar signal processing can no longer cope with the increasing complexity of radar signals. The main contribution of this thesis is the novel, model-centric approach to radar signal processing that utilizes methods from the theory of formal languages and syntactic pattern recognition.</p> <p>In this thesis, we focus our attention on modeling of Multi-Function Radars (MFRs)---the class of radars that currently presents the greatest challenges to the radar signal processing community. The characteristic feature of MFRs is the complex hierarchical signal structure often utilized by these radars. This complexity in MFR signals makes the classic radar signal processing techniques inadequate.</p> <p>We consider MFRs as stochastic discrete event systems that are "communicating" information using some stochastic formal languages. We then show how these languages can be modeled by grammars that can be derived using a priori information available in the databases of electronic intelligence. We also demonstrate how these grammars can capture the complex MFR signal structures and exploit the relationships between the internal processes within MFRs and signals emitted by these radars. We refer to this MFR modeling approach as "syntactic modeling".</p> <p>We also take advantage of the hierarchical nature of the MFR signals and develop a layered radar model where processing of related features of radar signals is confined to a certain modeling layer, and only the information relevant to the next layer of radar signal processing in propagated forward. This hierarchical radar modeling approach enables to keep the complexity of MFR models manageable.</p> <p>We demonstrate the applicability of the developed approach using computer simulations of synthetic MFR signals and provide two complete case studies demonstrating how the principles developed in this thesis can be applied to modeling of real-life MFRs.</p> / Doctor of Philosophy (PhD)

<p>Array processing has been successfully applied in many areas such as radar, sonar and wireless communications. Most conventional array processing techniques are based on idealistic assumptions that are not valid in many practical situations. This thesis contributes to the development of novel array processing techniques for direction finding and parameter estimation in the presence of complicated spatio-temporal sources.</p> <p>We address the problem of estimating the Directions-Of-Arrival (DOAs) of weak desired sources observed in the background of strong interference. We develop a new approach to beamspace preprocessing with improved robustness against out-of-sector interfering sources. Our techniques design the beamspace matrix filter based on proper tradeoffs between the in-sector (passband) source distortion and out-of-sector (stopband) source attenuation. We also introduce the novel concept of adaptive beamspace preprocessing that offers a significant improvement in the DOA estimation performance. Computationally efficient convex formulations for these beamspace matrix filter design problems are derived using second-order cone (SOC) programming.</p> <p>We also develop a generalized Capon spatial spectrum estimator for localizing multiple incoherently distributed sources in sensor arrays. The proposed generalized Capon technique estimates the source central angles and angular spreads by means of a two-dimensional spectral search. The proposed method has a substantially improved performance compared to several popular spread source localization techniques.</p> <p>A new search-free ESPRIT-type algorithm for estimating the DOAs of multiple chirp signals using Spatial Time-Frequency Distributions (STFDs) is developed. An averaged STFD matrix (or multiple averaged STFD matrices) is used instead of the covariance matrix to estimate the signal and noise subspaces. The proposed algorithm is shown to provide significant performance improvement over the traditional ESPRIT algorithm for FM sources, specifically in situations with closely-spaced sources and low Signal-to-Noise Ratios (SNRs).</p> <p>We also develop a new algorithm for estimating the parameters of multiple wideband polynomial-phase signals (PPSs) using sensor arrays. Our approach is based on extending the high-order instantaneous moment (HIM) concept by, introducing a new nonlinear transformation called the spatial high-order instantaneous moment (SHIM). We apply this transformation to multiple wideband PPSs and employ the resulting SHIM to provide recursive estimates of the PPSs parameters. The data received at each sensor yields a different estimate of each frequency coefficient. Employing the multiple estimates simultaneously, the proposed algorithm removes the outliers and obtains a better final estimate. STFD-based methods are used in conjunction with the SHIM to estimate the DOAs of the observed signals. The proposed algorithm is shown to have an improved performance compared to the well-known chirp beam-former approach [31]. Furthermore, our algorithm is computationally more attractive as it requires multiple one-dimensional searches instead of a multi-dimensional search.</p> / Doctor of Philosophy (PhD)

<p>The linear array is one of the most important types of multi-element sensor arrays, being extensively used in radar, sonar, telecommunications, radio astronomy and medical imaging systems. Traditionally, the array assumes uniform geometry with an inter-sensor spacing of λ/2, which limits resolvability because of the fixed aperture. Since the 1950's, much work has been done on designing nonuniform arrays with focus on conventional beamforming techniques. One of the typical results is the Minimum Redundancy (MR) arrays which provide improved performance over the uniform array.</p> <p>In this thesis, this issue is re-investigated from the viewpoint of high resolution array processing. A new criterion (called DOBC), based on D-Optimality, is developed, which yields a new array geometry by minimizing a measure of joint estimation error with respect to the array geometry parameters. The sensor gain and phase calibration errors and their effects on high resolution array signal processing are also examined, and formulae are developed to evaluate such effects.</p> <p>In addition, the Modified Forward-Backward Linear Prediction (MFBLP) method is modified to substantially improve the low SNR performance without increase in computational load. A form of Cramer-Rao lower bound (CRLB) is derived for a reduced model which facilitates performance comparisons in directions of arrival (DOA) estimation.</p> <p>Computer experiments are conducted to verify our analysis. We conclude that (1) the DOBC design outperforms the conventional uniform array and the MR array; (2) the formulae developed predict very well the behaviour of high resolution algorithms in the presence or absence of calibration errors. The design criterion and formulae can be used by the system designer to design a new array geometry given the performance requirement and hardware specifications, to evaluate the expected performance of an array, given information about hardware specifications, or to develop hardware specifications given the performance requirement.</p> / Doctor of Philosophy (PhD)

<p>This thesis addresses itself to computer-aided yield-driver design of microwave circuits using implementable, efficient approximation and optimization techniques. Basic concepts of yield-driven design are identified. A number of approaches to statistical design are reviewed. Their features and limitations are discussed. The recent generalized ℓp centering approach and one-sided ℓ₁ optimization algorithm are addressed. A highly efficient quadratic approximation, specially applicable to statistical design, is presented. A set of very simple and easy-to-implement formulas is derived. This approximation technique is also applied to gradient functions of circuit responses to provide higher accuracy. A combined approach to attack large scale problem is presented, which explores the most powerful capabilities of hardware and software available to us, namely, the supercomputer, efficient quadratic modeling, fast and dedicated simulation, and state-of-the-art optimization. Yield-driven design techniques are extended to deal with tunable circuits by considering tuning tolerances. A 5-channel waveguide multiplexer is considered as an example both for the combined approach and for the treatment of tunable circuits. Yield-driven design of nonlinear microwave circuits with statistically characterized devices is considered. Relevant concepts are introduced. The efficient Integrated Gradient Approximation Technique (IGAT) is presented in the statistical design environment, which avoids the prohibitive computational burden resulting from the traditional perturbation scheme. A novel approach, called Feasible Adjoint Sensitivity Technique (FAST), is derived to calculate sensitivities of nonlinear circuits that are simulated in the harmonic balance environment. By taking advantage of the computational efficiency of adjoint analysis and the implementational simplicity of the perturbation technique, FAST is responsible for great savings of computational effort required for yield-driven design of nonlinear circuits.</p> / Doctor of Philosophy (PhD)

<p>This thesis presents an in-depth investigation of microwave FET device modeling and unified DC, small-signal and large-signal computer-aided design of microwave circuits. Advances in microwave FET device modeling are reviewed. The physical, analytical and nonlinear empirical models and their relationship are discussed. A new integrated DC and small-signal FET model parameter extraction approach is presented which simultaneously fits the FET model responses to the DC and small-signal measurements. Detailed formulas are derived to explore the relationship between the nonlinear DC equivalent circuit and the small-signal equivalent circuit linearized at given bias points. A large-signal FET model parameter extraction approach is introduced. The power spectrum responses of the model are calculated employing the newly exploited harmonic balance (HB) technique for efficient nonlinear frequency-domain circuit simulation. State-of-the-art optimization tools are used to fit model responses to corresponding measurements. Special considerations are given to weighting factor assignment which takes into account the wide spread magnitude of the error functions in the optimization. The HB technique for nonlinear frequency domain simulation of microwave circuits is discussed. The formulations of the HB equation, its Jacobian matrix and the related discrete Fourier transformation are described. A new approach for constructing the multiport matrix especially suitable for HB based circuit optimization is presented. The theoretical background of the unified DC, small-signal and large-signal circuit simulation is investigated. Derivations of the inherent consistency between DC/small-signal simulation and general nonlinear HB simulation are presented. A novel circuit design concept is introduced which explores the seamless integration of DC/small-signal and large-signal circuit design with multi-dimensional specifications. Examples of simultaneous DC/small-signal/large-signal FET model parameter extraction and a small-signal broad-band amplifier design are given to demonstrate the concept.</p> / Doctor of Philosophy (PhD)

<p>This thesis addresses the detection problem in array signal processing in two aspects: (a) detection problems in white noise environments; (b) detection problems in unknown coloured (spatially correlated) noise environments. New criteria for determining the number of signals in both these kinds of noise environments are developed. The performance of the new methods is analyzed theoretically and is confirmed by computer simulations using Monte Carlo method. The status of the existing methods for detection in array processing are reviewed. For the white noise environment, some unfavourable characteristics of existing methods are discussed, for example, the subjective threshold setting required by the traditional threshold methods, and the rigid performance of the information theoretic criteria. A new method, namely Eigen-Threshold (ET) method is proposed and analyzed theoretically and checked by computer simulations. The new method demonstrates superiority over the existing methods by: (a) not requiring a subjective threshold setting as required by the traditional threshold methods; (b) possessing a flexible performance which can be easily controlled by a single parameter, in contrast to the rigid performance given by the information theoretic criteria. By properly choosing the control parameter, the new method gives better performance than both AIC and MDL. Because of these advantages, the new ET method is more applicable in practice than other existing methods. Besides enjoying the same merit of not requiring a subjective threshold setting, the ET method gives a quantitative controllable performance which is useful in practice, because although the asymptotic consistency argument used in information theoretic criteria and some other methods has important theoretical significants but: (a) in any practical application the sample size can only be a limited number; (b) when the sample size N is given, and a quantitative performance is desired, the asymptotic consistency argument may not make too much sense since such arguments could not give even an approximate error level except predicting whether the error rate will go to zero when N goes to infinity. For the more difficult detection problem in the case of spatially correlated noise, there has not been any satisfactory method developed so far. By assuming a banded structure for the noise covariance matrix, which is true for many engineering applications, and applying a bi-array structure combined with canonical correlation analysis, a new elegant method is developed in this thesis. The new method, called Canonical Correlation Test (CCT) method, gives a reliable, simple, theoretically sound solution to the detection problem in unknown coloured noise environments. Massive simulations have shown that the new method is extremely robust to changes in the noise spectrum. Again, the new method is characterized by a quantitatively controllable performance. To compare the new methods with the existing methods, the widely accepted AIC and MDL criteria are used for comparison purpose through out this thesis.</p> / Doctor of Philosophy (PhD)

<p>In this thesis, blind multiuser detection of Direct Sequence Code Division Multiple Access (DS-CDMA) signals over time-varying time-dispersive channels is considered. A number of methods for multiuser detection over time-dispersive channels have been proposed previously. Blind multiuser detection requires that the signature waveform of the desired user be reconstructed (blindly) at the receiver. In time-dispersive channels the knowledge of the channel order (length) is needed in order to reconstruct the signature waveform exactly. Previous works in this regard assumed the knowledge of the channel length or they considered an over estimated channel length. However, when the channel length assumed at the receiver differs from the actual one, the performance of the system can degrade significantly. Hence we propose a new multiple model approach that considers many channel-conditioned multiuser detectors in parallel in order to obtain a better estimate via soft decision, instead of making a hard decision about the channel length. We use the Interacting Multiple Model (IMM) estimator, which consists of multiple Kalman filters, to find a better overall estimate from the channel-conditioned filters. Further, in a time-varying environment, where the channel length varies with time, the proposed scheme tracks the channel order very well (without assuming known channel length), and hence performs better than previous methods. Simulation results show that the proposed method outperforms the existing ones in terms of signal to interference plus noise ratio and bit error rate in a time-varying channel.</p> / Master of Applied Science (MASc)

<p>In this thesis the linear precoder which minimizes the bit error rate (BER) is derived for block transmission systems in which zero forcing (ZF) equalization and threshold detection are applied. Because the bit error rate for block transmission is a highly non-linear function of the precoder parameters, its minimization has been regarded as being difficult to implement. Therefore designers have attempted to find low BER precoders indirectly by optimizing alternative objectives, such as minimizing the Mean Square Error (MMSE), or maximizing the received signal-to-noise ratio (SNR). However, these precoders do not minimize the BER directly, and it is this problem which is the subject of the thesis.</p> <p>The block transmission systems considered in this thesis employ block by block processing at the receiver, and therefore elimination of inter-block interference (IEI) is desirable. We will design Minimum BER (MBER) precoders for two schemes which eliminate IEI, namely zero padding (ZP) and cyclic prefix (CP). Based on the bit error rate formula derived in the thesis, an analytic solution for the MBER precoder at moderate-to-high SNRs is derived via a two-stage optimization process using Jensen's inequality. At moderate-to-high SNRs, the bit error rate is a convex function of the autocorrelation matrix which is, itself, a function of the precoder matrix because of the use of a zero-forcing equalizer. Simulations and analyses are given to the two sets of precoders based on ZP and CP respectively to verify the optimal precoders derived. The BER improvement of the ZP-MBER/CP-MBER precoders over other ZP/CP precoders is substantial, and the ZP-MBER precoder is superior to the CPMBER precoder in performance. The latter also outperforms the scheme of discrete multitone (DMT) with water filling power loading, and cyclic prefix orthogonal frequency division multiplexing (CP-OFDM). The CP-MBER precoder is shown to be a two-stage modification IV of the transmitting scheme for tandard DMT. Firstly the water filling algorithm is replaced by the MMSE power loading algorithm suggested in the thesis, and secondly, the power loading is augmented by multiplication with a DFT matrix. It is shown that the CP-MBER precoder does not require more power to transmit a cyclic prefix than the CP-OFDM or water-filling DMT precoder.</p> <p>A simple test which determines whether the SNR is high enough for our MBER precoder design to be optimal is provided. Furthermore, methods to guarantee sufficient SNR are suggested. One can either increase the transmitting power, or drop sub-channels and hence avoid transmission on the sub-channels which correspond to the small eigen-values of the channel. The MBER precoder design after dropping sub-channels is also discussed.</p> <p>For the precoders which are characterized by an arbitrary unitary matrix in their solutions, the optimal unitary matrix which minimizes the BER is designed. Therefore, minimization of BER is achieved within the optimal solution set of the precoders. Applications of the design are discussed. Simulations and analytic evaluations are presented to show the BER improvement provided by the optimal unitary matrix</p> / Master of Engineering (ME)