Using Bayesian Inference in Design Applications

This dissertation presents a new approach for solving engineering design problems such as the design of antenna arrays and finite impulse response (FIR) filters. In this approach, a design problem is cast as an inverse problem. The tools and methods previously developed for Bayesian inference are adapted and utilized to solve design problems. Given a desired design output, Bayesian parameter estimation and model comparison are employed to produce designs that meet the prescribed design specifications and requirements. In the Bayesian inference framework, the solution to a design problem is the posterior distribution, which is proportional to the product of the likelihood and priors. The likelihood is obtained via the assignment of a distribution to the error between the desired and achieved design output. The priors are assigned distributions which express constraints on the design parameters. Other design requirements are implemented by modifying the likelihood. The posterior --- which cannot be determined analytically --- is approximated by a Markov chain Monte Carlo method by drawing a reasonable number of samples from it. Each posterior sample represents a design candidate and a designer needs to select a single candidate as the final design based on additional design criteria. The Bayesian inference framework has been applied to design antenna arrays and FIR filters. The antenna array examples presented here use different types of array such as planar array, symmetric, asymmetric and reconfigurable linear arrays to realize various desired radiation patterns which include broadside, end-fire, shaped beam, and three-dimensional patterns. Various practical design requirements such as a minimum spacing between two adjacent elements, limitations in the dynamic range and accuracy of the current amplitudes and phases, the ability to maintain antenna performance over a frequency band, and the ability to sustain the loss of an arbitrary element, have been incorporated. For the filter design application, all presented examples employ a linear phase FIR filter to produce various desired frequency responses. In practice, the filter coefficients are limited in dynamic range and accuracy. This requirement has been incorporated into two examples where the filter coefficients are represented by a sum of signed power-of-two terms

IIR modeling of interpositional transfer functions with a genetic algorithm aided by an adaptive filter for the purpose of altering free-field sound localization

The psychoacoustic process of sound localization is a system of complex analysis. Scientists have found evidence that both binaural and monaural cues are responsible for determining the angles of elevation and azimuth which represent a sound source. Engineers have successfully used these cues to build mathematical localization systems. Research has indicated that spectral cues play an important role in 3-d localization. Therefore, it seems conceivable to design a filtering system which can alter the localization of a sound source, either for correctional purposes or listener preference. Such filters, known as Interpositional Transfer Functions, can be formed from division in the z-domain of Head-related Transfer Functions. HRTF’s represent the free-field response of the human body to sound processed by the ears. In filtering applications, the use of IIR filters is often favored over that of FIR filters due to their preservation of resolution while minimizing the number of required coefficients. Several methods exist for creating IIR filters from their representative FIR counterparts. For complicated filters, genetic algorithms (GAs) have proven effective. The research summarized in this thesis combines the past efforts of researchers in the fields of sound localization, genetic algorithms, and adaptive filtering. It represents the initial stage in the development of a practical system for future hardware implementation which uses a genetic algorithm as a driving engine. Under ideal conditions, an IIR filter design system has been demonstrated to successfully model several IPTF pairs which alter sound localization when applied to non-minimum phase HRTF’s obtained from free-field measurement

Minimax passband group delay nonlinear phase peak constrained FIR filter design without imposing desired phase response

In this paper, a nonlinear phase finite impulse response (FIR) filter is designed without imposing a desired phase response. The maximum passband group delay of the filter is minimized subject to a positivity constraint on the passband group delay response of the filter as well as a specification on the maximum absolute difference between the desired magnitude square response and the designed magnitude square response over both the passband and the stopband. This filter design problem is a quadratic NP hard functional inequality constrained optimization problem. To tackle this problem, first, the one norm functional inequality constraint of the optimization problem is approximated by a smooth function so that the quadratic NP hard functional inequality constrained optimization problem is converted to a nonconvex functional inequality constrained optimization problem. Then, a modified filled function method is applied for finding the global minimum of the nonconvex optimization problem. By using a local minimum of the corresponding unconstrained optimization problem as the initial condition of our proposed global optimization algorithm, computer numerical simulation results show that our proposed approach could efficiently and effectively design a minimax passband group delay nonlinear phase peak constrained FIR filter without imposing a desired phase response

MIMO Radar Waveform Optimization With Prior Information of the Extended Target and Clutter

The concept of multiple-input multiple-output (MIMO) radar allows each transmitting antenna element to transmit an arbitrary waveform. This provides extra degrees of freedom compared to the traditional transmit beamforming approach. It has been shown in the recent literature that MIMO radar systems have many advantages. In this paper, we consider the joint optimization of waveforms and receiving filters in the MIMO radar for the case of extended target in clutter. A novel iterative algorithm is proposed to optimize the waveforms and receiving filters such that the detection performance can be maximized. The corresponding iterative algorithms are also developed for the case where only the statistics or the uncertainty set of the target impulse response is available. These algorithms guarantee that the SINR performance improves in each iteration step. Numerical results show that the proposed methods have better SINR performance than existing design methods

Digital Filter Design Using Improved Artificial Bee Colony Algorithms

Digital filters are often used in digital signal processing applications. The design objective of a digital filter is to find the optimal set of filter coefficients, which satisfies the desired specifications of magnitude and group delay responses. Evolutionary algorithms are population-based meta-heuristic algorithms inspired by the biological behaviors of species. Compared to gradient-based optimization algorithms such as steepest descent and Newton’s like methods, these bio-inspired algorithms have the advantages of not getting stuck at local optima and being independent of the starting point in the solution space. The limitations of evolutionary algorithms include the presence of control parameters, problem specific tuning procedure, premature convergence and slower convergence rate. The artificial bee colony (ABC) algorithm is a swarm-based search meta-heuristic algorithm inspired by the foraging behaviors of honey bee colonies, with the benefit of a relatively fewer control parameters. In its original form, the ABC algorithm has certain limitations such as low convergence rate, and insufficient balance between exploration and exploitation in the search equations. In this dissertation, an ABC-AMR algorithm is proposed by incorporating an adaptive modification rate (AMR) into the original ABC algorithm to increase convergence rate by adjusting the balance between exploration and exploitation in the search equations through an adaptive determination of the number of parameters to be updated in every iteration. A constrained ABC-AMR algorithm is also developed for solving constrained optimization problems.There are many real-world problems requiring simultaneous optimizations of more than one conflicting objectives. Multiobjective (MO) optimization produces a set of feasible solutions called the Pareto front instead of a single optimum solution. For multiobjective optimization, if a decision maker’s preferences can be incorporated during the optimization process, the search process can be confined to the region of interest instead of searching the entire region. In this dissertation, two algorithms are developed for such incorporation. The first one is a reference-point-based MOABC algorithm in which a decision maker’s preferences are included in the optimization process as the reference point. The second one is a physical-programming-based MOABC algorithm in which physical programming is used for setting the region of interest of a decision maker. In this dissertation, the four developed algorithms are applied to solve digital filter design problems. The ABC-AMR algorithm is used to design Types 3 and 4 linear phase FIR differentiators, and the results are compared to those obtained by the original ABC algorithm, three improved ABC algorithms, and the Parks-McClellan algorithm. The constrained ABC-AMR algorithm is applied to the design of sparse Type 1 linear phase FIR filters of filter orders 60, 70 and 80, and the results are compared to three state-of-the-art design methods. The reference-point-based multiobjective ABC algorithm is used to design of asymmetric lowpass, highpass, bandpass and bandstop FIR filters, and the results are compared to those obtained by the preference-based multiobjective differential evolution algorithm. The physical-programming-based multiobjective ABC algorithm is used to design IIR lowpass, highpass and bandpass filters, and the results are compared to three state-of-the-art design methods. Based on the obtained design results, the four design algorithms are shown to be competitive as compared to the state-of-the-art design methods

NATURAL ALGORITHMS IN DIGITAL FILTER DESIGN

Digital filters are an important part of Digital Signal Processing (DSP), which plays vital roles within the modern world, but their design is a complex task requiring a great deal of specialised knowledge. An analysis of this design process is presented, which identifies opportunities for the application of optimisation. The Genetic Algorithm (GA) and Simulated Annealing are problem-independent and increasingly popular optimisation techniques. They do not require detailed prior knowledge of the nature of a problem, and are unaffected by a discontinuous search space, unlike traditional methods such as calculus and hill-climbing. Potential applications of these techniques to the filter design process are discussed, and presented with practical results. Investigations into the design of Frequency Sampling (FS) Finite Impulse Response (FIR) filters using a hybrid GA/hill-climber proved especially successful, improving on published results. An analysis of the search space for FS filters provided useful information on the performance of the optimisation technique. The ability of the GA to trade off a filter's performance with respect to several design criteria simultaneously, without intervention by the designer, is also investigated. Methods of simplifying the design process by using this technique are presented, together with an analysis of the difficulty of the non-linear FIR filter design problem from a GA perspective. This gave an insight into the fundamental nature of the optimisation problem, and also suggested future improvements. The results gained from these investigations allowed the framework for a potential 'intelligent' filter design system to be proposed, in which embedded expert knowledge, Artificial Intelligence techniques and traditional design methods work together. This could deliver a single tool capable of designing a wide range of filters with minimal human intervention, and of proposing solutions to incomplete problems. It could also provide the basis for the development of tools for other areas of DSP system design

Filter-Based Fading Channel Modeling

A channel simulator is an essential component in the development and accurate performance evaluation of wireless systems. A key technique for producing statistically accurate fading variates is to shape the flat spectrum of Gaussian variates using digital filters. This paper addresses various challenges when designing real and complex spectrum shaping filters with quantized coefficients for efficient realization of both isotropic and nonisotropic fading channels. An iterative algorithm for designing stable complex infinite impulse response (IIR) filters with fixed-point coefficients is presented. The performance of the proposed filter design algorithm is verified with 16-bit fixed-point simulations of two example fading filters

Communication Subsystems for Emerging Wireless Technologies

The paper describes a multi-disciplinary design of modern communication systems. The design starts with the analysis of a system in order to define requirements on its individual components. The design exploits proper models of communication channels to adapt the systems to expected transmission conditions. Input filtering of signals both in the frequency domain and in the spatial domain is ensured by a properly designed antenna. Further signal processing (amplification and further filtering) is done by electronics circuits. Finally, signal processing techniques are applied to yield information about current properties of frequency spectrum and to distribute the transmission over free subcarrier channels