Design of broadband beamformers with low complexity

2011-2012 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

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

A study of optimization and optimal control computation : exact penalty function approach

In this thesis, We propose new computational algorithms and methods for solving four classes of constrained optimization and optimal control problems. In Chapter 1, we present a brief review on optimization and optimal control. In Chapter 2, we consider a class of continuous inequality constrained optimization problems. The continuous inequality constraints are first approximated by smooth function in integral form. Then, we construct a new exact penalty function, where the summation of all these approximate smooth functions in integral form, called the constraint violation, is appended to the objective function. In this way, we obtain a sequence of approximate unconstrained optimization problems. It is shown that if the value of the penalty parameter is sufficiently large, then any local minimizer of the corresponding unconstrained optimization problem is a local minimizer of the original problem. For illustration, three examples are solved using the proposed method.From the solutions obtained, we observe that the values of their objective functions are amongst the smallest when compared with those obtained by other existing methods available in the literature. More importantly, our method finds solutions which satisfy the continuous inequality constraints.In Chapter 3, we consider a general class of nonlinear mixed discrete programming problems. By introducing continuous variables to replace the discrete variables, the problem is first transformed into an equivalent nonlinear continuous optimization problem subject to original constraints and additional linear and quadratic constraints. However, the existing gradient-based optimization techniques have difficulty to solve this equivalent nonlinear optimization problem effectively due to the new quadratic inequality constraint. Thus, an exact penalty function is employed to construct a sequence of unconstrained optimization problems, each of which can be solved effectively by unconstrained optimization techniques, such as conjugate gradient or quasi-Newton types of methods.It is shown that any local optimal solution of the unconstrained optimization problem is a local optimal solution of the transformed nonlinear constrained continuous optimization problem when the penalty parameter is sufficiently large. Numerical experiments are carried out to test the efficiency of the proposed method.In Chapter 4, we investigate the optimal design of allpass variable fractional delay (VFD) filters with coefficients expressed as sums of signed powers-of-two terms, where the weighted integral squared error is minimized. A new optimization procedure is proposed to generate a reduced discrete search region. Then, a new exact penalty function method is developed to solve the optimal design of allpass variable fractional delay filter with signed powers-of-two coefficients. Design examples show that the proposed method is highly effective. Compared with the conventional quantization method, the solutions obtained by our method are of much higher accuracy. Furthermore, the computational complexity is low.In Chapter 5, we consider an optimal control problem in which the control takes values from a discrete set and the state and control are subject to continuous inequality constraints. By introducing auxiliary controls and applying a time-scaling transformation, we transform this optimal control problem into an equivalent optimal control problem subject to original constraints and additional linear and quadratic constraints, where the decision variables are taking values from a feasible region, which is the union of some continuous sets. However, due to the new quadratic constraints, standard optimization techniques do not perform well when they are applied to solve the transformed problem directly.We introduce a novel exact penalty function to penalize constraint violations, and then append this penalty function to the objective function, forming a penalized objective function. This leads to a sequence of approximate optimal control problems, each of which can be solved by using optimal control techniques, and consequently, many optimal control software packages, such as MISER 3.4, can be used. Convergence results how that when the penalty parameter is sufficiently large, any local solution of the approximate problem is also a local solution of the original problem. We conclude this chapter with some numerical results for two train control problems.In Chapter 6, some concluding remarks and suggestions for future research directions are made

Digital pre-distortion of radio frequency digital to analog converters in a DOCSIS application

The use of Community Antenna Television Network (CATV) cable systems are a very common way that subscribers use to access the internet and download data. The transmitters that send the signals to subscribers must conform to a very stringent specification known as DOCSIS. Using traditional high frequency design techniques to meet this specification often lead to a lengthy and difficult production process where several calibrations have to be made. In order to send a digitally modulated signal that conforms to the DOCSIS specification some sort of conversion between the discrete digital domain and the analog domain must occur. To accomplish this a Digital to Analog converter is used. In recent years, the clocking or sampling frequency that can be used for Digital to Analog converters (DACs) has been rapidly increasing. The clocking frequency is directly proportional to the bandwidth that can be transmitted. DAC's that have exceptionally high clocking frequencies can be referred to as Radio Frequency DAC's. The clocking frequency of these devices has now progressed to the point where direct digital synthesis can be used for a DOCSIS transmitter without any analog frequency conversion stages. Since Radio Frequency DAC's are real devices the output is not a perfect representation of the discrete signal that is sent to it. Unwanted distortion is added that can be measured at the analog output. Removal of this distortion or at least significantly reducing it could be the difference meeting or or not meeting the DOCSIS specification. This thesis will explore the usage of these devices in this application. The basic structure of DAC's as well as the distortion signals themselves will be investigated in order to develop a method where the distortion can be removed. Ideally this can be done in a way that is suitable to be integrated into a transmitter architecture and meet the specification. The frequency response of the major distortion products across the DOCSIS band is measured. Once this is done a way to match these frequency responses is needed so a cancellation signal can be created that removes the distortion. A method is developed that uses an iterative algorithm to find filter coefficients whose frequency response matches that of the distortion signals as closely as possible. Since these cancellation signals are added to the discrete signal to be transmitted before the interface with the Radio Frequency DAC the process is known as pre-distortion. The generated coefficients are used in digital filters as part of a pre-distortion design. Tests are performed with discrete signals that are close approximates to a DOCSIS signal that would be sent to a subscriber. Measured results show a decrease in the power of targeted distortion signals. The reduction of the distortion level is enough that the DOCSIS specification is met for all test signals

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

FPGA Implementation of the Front-End of a DOCSIS 3.0 Receiver

The introduction of cable television (CATV) in the 1940s and 1950s has significantly influenced communications technology. Originally supplying only one-way television programming, the CATV industry recognized the potential of two-way communications. Starting with the introduction of pay-per view services in the 1980s, two-way communications over CATV networks eventually expanded into supplying internet access services. The increased demand for CATV services, and thus the increased demand for CATV equipment, has led the CATV industry to develop interoperability standards. The primary standard now used by the CATV industry is the Data Over Cable Service Specification (DOCSIS). DOCSIS defines both the upstream (data towards the CATV provider) and downstream (data towards the CATV customer) transmission channels. This includes specifications for the modulators and demodulators used in these channels. The number of manufacturers of CATV modulators and demodulators has greatly increased over the last twenty years and continues to do so. As the number of competitive CATV equipment suppliers increases, these manufacturers must look to ways to remain competitive by reducing time-to-market and costs associated with equipment design, as well as allowing their designs to be flexible so that they may adapt to the improvements in DOCSIS. In the past, manufacturers have primarily used Application Specific Integrated Circuits (ASICs) to implement digital hardware designs for CATV equipment. ASICs have a very high initial setup cost and do not allow for system modifications without a complete redesign. Recently, Field Programmable Gate Array (FPGA) technology has been introduced that allows manufacturers to both modify their designed digital hardware structures without a complete physical hardware redesign, as well as providing a reduced initial setup cost. Although in the long term, ASICs provide a cheaper alternative to FPGAs when produced in quantity, FPGAs provide quicker time-to-market in new product development and allow changes to made after initial release. This ability to change designs after release and the quicker time-to-market has led manufacturers to adopt FPGAs in new products. A critical component in the upstream channel of a DOCSIS compliant system is the Quadrature Amplitude Modulated (QAM) receiver. The data received at the QAM receiver have undergone several impairments including additive noise, timing offset, and frequency and phase mismatches between the transmitted modulated signal and the signal received at the demodulator. It is the function of the front-end of the receiver to correct for these impairments. This thesis presents methods for, and an example of, the design and implementation of a DOCSIS compliant QAM receiver front-end that corrects for timing, phase and frequency impairments experienced in the upstream communication channel when additive noise is present. The circuits presented are designed and implemented to reduce hardware costs when using FPGA technology. In addition, the circuits designed do not use proprietary logic, which gives designers more flexibility when implementing their own demodulator front-end circuitry. The FPGA implementation presented in this thesis achieves an average MER of 54.3 dB in a no-noise channel and close to 31 dB MER in a 25 dBc AWGN channel. The overall design uses 65 dedicated 18-bit by 18-bit multipliers and 2,970 bytes of RAM to implement the digital front-end of the receiver

Design of discrete-time filters for efficient implementation

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 325-333).The cost of implementation of discrete-time filters is often strongly dependent on the number of non-zero filter coefficients or the precision with which the coefficients are represented. This thesis addresses the design of sparse and bit-efficient filters under different constraints on filter performance in the context of frequency response approximation, signal estimation, and signal detection. The results have applications in several areas, including the equalization of communication channels, frequency-selective and frequency-shaping filtering, and minimum-variance distortionless-response beamforming. The design problems considered admit efficient and exact solutions in special cases. For the more difficult general case, two approaches are pursued. The first develops low-complexity algorithms that are shown to yield optimal or near-optimal designs in many instances, but without guarantees. The second focuses on optimal algorithms based on the branch-and-bound procedure. The complexity of branch-and-bound is reduced through the use of bounds that are good approximations to the true optimal cost. Several bounding methods are developed, many involving relaxations of the original problem. The approximation quality of the bounds is characterized and efficient computational methods are discussed. Numerical experiments show that the bounds can result in substantial reductions in computational complexity.by Dennis Wei.Ph.D