A wide range of modern large-scale systems relies on recovering a signal from noisy linear measurements. In many applications, the useful signal has inherent properties, such as sparsity, low-rankness, or boundedness, and making use of these properties and structures allow a more efficient recovery. Hence, a significant amount of work has been dedicated to developing and analyzing algorithms that can take advantage of the signal structure. Especially, since the advent of Compressed Sensing (CS) there has been significant progress towards this direction. Generally speaking, the signal structure can be harnessed by solving an appropriate regularized or constrained M-estimator. In modern Multi-input Multi-output (MIMO) communication systems, all transmitted signals are drawn from finite constellations and are thus bounded. Besides, most recent modulation schemes such as Generalized Space Shift Keying (GSSK) or Generalized Spatial Modulation (GSM) yield signals that are inherently sparse. In the recovery procedure, boundedness and sparsity can be promoted by using the ℓ1 norm regularization and by imposing an ℓ∞ norm constraint respectively. In this thesis, we propose novel optimization algorithms to recover certain classes of structured signals with emphasis on MIMO communication systems. The exact analysis permits a clear characterization of how well these systems perform. Also, it allows an automatic tuning of the parameters. In each context, we define the appropriate performance metrics and we analyze them exactly in the High Dimentional Regime (HDR). The framework we use for the analysis is based on Gaussian process inequalities; in particular, on a new strong and tight version of a classical comparison inequality (due to Gordon, 1988) in the presence of additional convexity assumptions. The new framework that emerged from this inequality is coined as Convex Gaussian Min-max Theorem (CGMT).

Adaptive filters have found applications in many signal processing problems. In some situations, linear constraints are imposed on the filter weights such that the filter is forced to exhibit a certain desired response. Several algorithms for linearly constrained least-squares adaptive filtering have been developed in the literature. When implemented with finite precision arithmetic, these algorithms are inevitably subjected to rounding errors. It is essential to understand how these algorithms react to rounding errors.In this thesis, the numerical properties of three linearly constrained least-squares adaptive filtering algorithms, namely, the linearly constrained fast least algorithm, the linear systolic array for MVDR beamforming and the linearly constrained QRD-RLS algorithm, are studied. It is shown that all these algorithms can be separated into a constrained part and an unconstrained part. The numerical properties of unconstrained least-squares algorithms (i.e., the unconstrained part of the linearly constrained algorithms under study) are reviewed from the perspectives of error propagation, error accumulation and numerical persistency. It is shown that persistent excitation and sufficient numerical resolution are needed to ensure the stability of the CRLS algorithm, while the QRD-RLS algorithm is unconditionally stable. The numerical properties of the constrained algorithms are then examined. Based on the technique of how the constraints are applied, these algorithms can be grouped into two categories. The first two algorithms admit a similar structure in that the unconstrained parts preceed the constrained parts. Error propagation analysis shows that this structure gives rise to unstable error propagation in the constrained part. In contrast, the constrained part of the third algorithm preceeds the unconstrained part. It is shown that this algorithm gives an ++ / exact solution to a linearly constrained least-squares adaptive filtering problem with perturbed constraints and perturbed input data. A minor modification to the constrained part of the linearly constrained QRD-RLS algorithm is proposed to avoid a potential numerical difficulty due to the Gaussian elimination operation employed in the algorithm.

In this thesis, the multi-carrier (MC) code division multiple access (CDMA) system in Rayleigh fading channel is considered. The system performance will be degraded due to multiple access interference (MAI) or background noise. It is know that linearly constrained inverse QR-decomposition (LC-IQRD) recursive least-square algorithm can overcome the problems. The main concern of this thesis is to implement the circuit of LC-IQRD algorithm. FPGA components and sets up a high efficient programmable hardware module. In this thesis, we implemented the circuit of LC-IQRD algorithm via a chip of Field Programmable Gate Array (FPGA) with Verilog HDL. The conventional IQRD circuit design employs systolic array architecture. The advantages of systolic array architecture include modularity and hardware simplicity. These properties are extremely desirable for VLSI implementation. In fact, we expect to reduce the execution time of the conventional IQRD algorithm circuit design. Therefore, in this thesis a modified IQRD circuit design is proposed to improve the effect of circuit implementation. It also has advantage of modularity and reduces the execution time. In order to degrade complexity of LC-IQRD algorithm circuit design, the area and speed of circuit are the consideration in this thesis. The data source is produced by Matlab software. We verify the performance of the system in terms of BER (bit error rate) and SINR (signal to interference and noise ratio).Finally, LC-IQRD algorithm circuit is realized in the Altera EP20k1500EFC-33 chip and on the Quartus II of Altera. The algorithm circuit uses 51536 logic elements (LE) for 30 bits fixed point design.

The Group Research department in Tait Electronics has a reconfigurable platform for MIMO research. In particular, the platform has an adaptive multivariate DFE with the LMS algorithm currently implemented. The LMS algorithm has been simulated and optimised for implementation on the FPGA. The main objective of the research is to investigate an alternative, the RLS algorithm by comparing its performance to the LMS algorithm. The RLS algorithm is known to be more complex than the LMS algorithm but offers the potential for improved performance due to its fast-converging nature. This thesis provides a performance investigation of these adaptive filter algorithms on the MIMO system for the purpose of real-time implementation on the Tait platform. In addition to performance investigation, stability analysis and a feasibility study is shown for the RLS algorithm on the FPGA. The research is industry based and is supported by FRST.

New adaptive-filtering algorithms, also known as adaptation algorithms, are proposed. The new algorithms can be broadly classified into two categories, namely, steepest-descent and Newton-type adaptation algorithms. Several new methods have been used to bring about improvements regarding the speed of convergence, steady-state misalignment, robustness with respect to impulsive noise, re-adaptation capability, and computational load of the proposed algorithms. In chapters 2, 3, and 8, several adaptation algorithms are developed that belong to the steepest-descent family. The algorithms of chapters 2 and 3 use two error bounds with the aim of reducing the computational load, achieving robust performance with respect to impulsive noise, good tracking capability and significantly reduced steady-state misalignment. The error bounds can be either prespecified or estimated using an update formula that incorporates a modified variance estimator. Analyses pertaining to the steady-state mean-square error (MSE) of some of these algorithms are also presented. The algorithms in chapter 8 use a so-called \textit{iterative/shrinkage method} to obtain a variable step size by which improved convergence characteristics can be achieved compared to those in other state-of-the-art competing algorithms. Several adaptation algorithms that belong to the Newton family are developed in chapters 4-6 with the aim of achieving robust performance with respect to impulsive noise, reduced steady-state misalignment, and good tracking capability without compromising the initial speed of convergence. The algorithm in chapter 4 imposes a bound on the $L_1$ norm of the gain vector in the crosscorrelation update formula to achieve robust performance with respect to impulsive noise in stationary environments. In addition to that, a variable forgetting factor is also used to achieve good tracking performance for applications in nonstationary environments. The algorithm in chapter 5 is developed to achieve a reduced steady-state misalignment and improved convergence speed and a reduced computational load. The algorithm in chapter 6 is essentially an extension of the algorithm in chapter 5 designed to achieve robust performance with respect to impulsive noise and reduced computational load. Analyses concerning the asymptotic stability and steady-state MSE of these algorithms are also presented. An algorithm that minimizes Reny's entropy of the error signal is developed in chapter 7 with the aim of achieving faster convergence and reduced steady-state misalignment compared to those in other algorithms of this family. Simulation results are presented that demonstrate the superior convergence characteristics of the proposed algorithms with respect to state-of-the-art competing algorithms of the same family in network-echo cancelation, acoustic-echo cancelation, system-identification, interference-cancelation, time-series prediction, and time-series filtering applications. In addition, simulation results concerning system-identification applications are also used to verify the accuracy of the MSE analyses presented. / Graduate

An accurate estimate of the mass of a passenger vehicle is important for several safety systems and environmental aspects. In this thesis, an algorithm for estimating the mass of a passenger vehicle using the recursive least squares methodis presented. The algorithm is based on a physical model of the vehicle and is designed to be able to run in real-time onboard a vehicle and uses the wheel torque signal calculated in the electrical control unit in the engine. Therefore no estimation of the powertrain is needed. This is one contribution that distinguishes this thesis from previous work on the same topic, which has used the engine torque. The benefit of this is that no estimation of the dynamics in the powertrain is needed. The drawback of using this method is that the algorithm is dependenton the accuracy of the estimation done in the engine electrical control unit. Two different versions of the recursive least squares method (RLS) have been developed - one with a single forgetting factor and one with two forgetting factors. The estimation performance of the two versions are compared on several different real-world driving scenarios, which include driving on country roads, highways, and city roads, and different loads in the vehicle. The algorithm with a single forgetting factor estimates the mass with an average error for all tests of 4.42% and the algorithm with multiple forgetting factors estimates the mass with an average error of 4.15 %, which is in line with state-of-the-art algorithms that are presented in other studies. In a sensitivity analysis, it is shown that the algorithms are robust to changes in the drag coefficient. The single forgetting factor algorithm is robust to changes in the rolling resistance coefficient whereas the multiple forgetting factor algorithm needs the rolling resistance coefficient to be estimated with fairly good accuracy. Both versions of the algorithm need to know the wheel radius with an accuracy of 90 %. The results show that the algorithms estimate the mass accurately for all three different driving scenarios and estimate highway roads best with an average error of 2.83 % and 2.69 % for the single forgetting factor algorithm and the multiple forgetting factor algorithm, respectively. The results indicate it is possible to use either algorithm in a real-world scenario, where the choice of which algorithm depends on sought-after robustness.

<p>In the railway industry, slip control has always been essential due to the low friction between the wheels and the rail. In this master’s thesis we have gathered several slip control methods and evaluated them. These evaluations were performed in Matlab-Simulink on a slip process model of a railway vehicle. The objective with these evaluations were to show advantages and disadvantages with the different slip control methods. </p><p>The results clearly show the advantage of using a slip optimizing control method, i.e. a method that finds the optimal slip and thereby maximizes the use of adhesion. We have developed two control strategies that we have found superior in this matter. These methods have a lot in common. For instance they both use an adhesion observer and non-linear gain, which enables fast optimization. The difference lies in how this non-linear gain is formed. One strategy uses an adaptive algorithm to estimate it and the other uses fuzzy logic. </p><p>A problem to overcome in order to have well functioning slip controllers is the formation of vehicle velocity. This is a consequence of the fact that most slip controllers use the velocity as a control signal.</p>

The code division multiple access (CDMA) system implemented by the direct-sequence (DS) spread spectrum (SS) technique is one of the most promising multiplexing technologies for the wireless communications services. The SS communication adopts a technique of using much wider bandwidth necessary to transmit the information over the channel, and has been proposed for third generation broadband wireless access. The capacity and performance of the DS-CDMA system are mainly limited by the multiple access interference (MAI) and the inter-symbol-interference (ISI) caused by the multipath-fading channel. To circumvent the above-mentioned problems many adaptive multiuser detectors, for instance the minimum mean square error (MMSE) and the minimum output energy (MOE) criteria, subject to certain constraints, have been proposed. Since the LCMV criterion is the linearly constrained (LC) version of MOE, it is high sensitivity to the channel mismatch caused by the unreliable estimation. In order to deal with this problem, the LC constant modulus (LCCM) criterion was considered to avoid capturing the interfering user instead of the desired user when the power of interfering user is much higher than the desired user. In this thesis, based on the Min/Max criterion we propose a novel blind LCCM recursive least-square (RLS) algorithm, with the generalized side-lobe canceller (GSC) structure, named as the CM GSC-RLS algorithm, to effectively alleviate the effect of MAI and ISI for DS-CDMA receiver, for time-varying channel. Due to the variation of channel at the receiver, the desired user amplitude or power is not available and has to be estimated. To solve this problem, we propose a simple scheme to estimate the parameter of constant modulus, adaptively, associated with the CM GSC-RLS algorithm. With the new proposed algorithm, the amplitude variation of desired user, due to changing characteristics of channel, can be tracked, effectively. Thus, better performance achievement, in terms of output signal-to-interference-plus-noise ratio (SINR) and bit error rate (BER), over the conventional GSC-RLS algorithms can be expected.

In the railway industry, slip control has always been essential due to the low friction between the wheels and the rail. In this master’s thesis we have gathered several slip control methods and evaluated them. These evaluations were performed in Matlab-Simulink on a slip process model of a railway vehicle. The objective with these evaluations were to show advantages and disadvantages with the different slip control methods. The results clearly show the advantage of using a slip optimizing control method, i.e. a method that finds the optimal slip and thereby maximizes the use of adhesion. We have developed two control strategies that we have found superior in this matter. These methods have a lot in common. For instance they both use an adhesion observer and non-linear gain, which enables fast optimization. The difference lies in how this non-linear gain is formed. One strategy uses an adaptive algorithm to estimate it and the other uses fuzzy logic. A problem to overcome in order to have well functioning slip controllers is the formation of vehicle velocity. This is a consequence of the fact that most slip controllers use the velocity as a control signal.

There are many novel techniques have been invented to provide high-data rate with high quality communication services for future wireless communications systems. Recently, a novel digital modulation technology for multiple accesses, referred to as the Multi-Carrier Code Division Multiple Access (MC-CDMA), has been proposed to support high data rate transmission; it is based on the combination of CDMA and orthogonal frequency division multiplexing (OFDM). The MC-CDMA has been shown to be an effective technique for combating multipath fading. With MC-CDMA system, a user¡¦s spreading code can be modulated on separate subcarriers, undergo frequency-flat fading channel and offers frequency diversity advantage. But in a multi-user environment, othogonality among spreading codes is severely distorted due to multipath delay spread, such that the system capacity will be limited by the multiple access interferences (MAI). Similar situations exist due to possible narrowband interference (NBI) from other systems. Effective interference reduction will render system capacity to increase, which means interference suppression techniques are vital in improving overall system performance. In this thesis, we propose a new linearly constrained recursive least square algorithm, with diagonal loading approach, referred to as the DL-LC RLS algorithms, to further improve the system performance. The proposed diagonal loading RLS algorithm is different from conventional diagonal loading RLS algorithm, in which the diagonal loading was used to improve the robustness to pointing errors in beamforming problem. However, in this thesis, the diagonal loading approach could be used to alleviate the effect due to multiple access interference (MAI), such that under certain circumstances, better performance could be achieved. Basically, in the proposed algorithm, the power of interference plus noise of received signal will be estimated and subtracted from the diagonal terms of the autocorrelation matrix of received signal. After that instead of using the original autocorrelation matrix, the new correlation matrix, with subtracting power related to the interference plus noise, will be involved during the adaptation processes for updating the weights of the multi-user detector. Finally, computer simulation results, in terms of bit error rate, are used to demonstrate the merits of the proposed scheme compared with the conventional RLS algorithm approach without using the diagonal approaches.