Architectural implementation of cordic unit and its applications

The ubiquity of DSP has made increasing demand to develop area efficient and accurate architectures in carrying out many nonlinear arithmetic operations. One such architecture is CORDIC unit which has many applications in the field of DSP including implementing transforms based on Fourier basis. This report presents architecture of CORDIC, embedded with a scaling unit that has only minimal number of adders and shifters. It can be implemented in rotation mode as well as vectoring mode. The purpose of the design is to get a scaling free CORDIC unit preserving the design of original algorithm. The proposed design has a considerable reduction in hardware when compared with other scaling free architectures. The analysis of error for different word lengths and different input ranges for fixed word length gives a better choice to choose the parameters. The error in rotation mode for 16 bit data path, obtained for Y equivalent input is 0.073% and for X equivalent input is 0.067%. We also report architecture of a DFT core that is implemented using low latency CORDIC. A scaling unit has been included to get scaled outputs. The reported DFT core architecture has 22 adders in total, in addition to 2 CORDIC units. DDS or NCO are nowadays prominently used in the applications of RF signal processing, satellite communications, etc. This report also brings out the FPGA implementation of one such DDS which has quadrature outputs. The proposed DDS design, which is based on pipelined CORDIC, has considerable improvement in terms of SFDR compared to other existing designs at reduced hardware. This report also proposes multiplier-less architecture for the implementation of radix-2^2 folded pipelined complex FFT core based on CORDIC technique. The number of points considered in the work is sixteen and the folding is done by a factor of four

The implementation and applications of multiple-valued logic

Multiple-Valued Logic (MVL) takes two major forms. Multiple-valued circuits can implement the logic directly by using multiple-valued signals, or the logic can be implemented indirectly with binary circuits, by using more than one binary signal to represent a single multiple-valued signal. Techniques such as carry-save addition can be viewed as indirectly implemented MVL. Both direct and indirect techniques have been shown in the past to provide advantages over conventional arithmetic and logic techniques in algorithms required widely in computing for applications such as image and signal processing. It is possible to implement basic MVL building blocks at the transistor level. However, these circuits are difficult to design due to their non binary nature. In the design stage they are more like analogue circuits than binary circuits. Current integrated circuit technologies are biased towards binary circuitry. However, in spite of this, there is potential for power and area savings from MVL circuits, especially in technologies such as BiCMOS. This thesis shows that the use of voltage mode MVL will, in general not provide bandwidth increases on circuit buses because the buses become slower as the number of signal levels increases. Current mode MVL circuits however do have potential to reduce power and area requirements of arithmetic circuitry. The design of transistor level circuits is investigated in terms of a modern production technology. A novel methodology for the design of current mode MVL circuits is developed. The methodology is based upon the novel concept of the use of non-linear current encoding of signals, providing the opportunity for the efficient design of many previously unimplemented circuits in current mode MVL. This methodology is used to design a useful set of basic MVL building blocks, and fabrication results are reported. The creation of libraries of MVL circuits is also discussed. The CORDIC algorithm for two dimensional vector rotation is examined in detail as an example for indirect MVL implementation. The algorithm is extended to a set of three dimensional vector rotators using conventional arithmetic, redundant radix four arithmetic, and Taylor's series expansions. These algorithms can be used for two dimensional vector rotations in which no scale factor corrections are needed. The new algorithms are compared in terms of basic VLSI criteria against previously reported algorithms. A pipelined version of the redundant arithmetic algorithm is floorplanned and partially laid out to give indications of wiring overheads, and layout densities. An indirectly implemented MVL algorithm such as the CORDIC algorithm described in this thesis would clearly benefit from direct implementation in MVL

Embedded electronic systems driven by run-time reconfigurable hardware

Abstract This doctoral thesis addresses the design of embedded electronic systems based on run-time reconfigurable hardware technology –available through SRAM-based FPGA/SoC devices– aimed at contributing to enhance the life quality of the human beings. This work does research on the conception of the system architecture and the reconfiguration engine that provides to the FPGA the capability of dynamic partial reconfiguration in order to synthesize, by means of hardware/software co-design, a given application partitioned in processing tasks which are multiplexed in time and space, optimizing thus its physical implementation –silicon area, processing time, complexity, flexibility, functional density, cost and power consumption– in comparison with other alternatives based on static hardware (MCU, DSP, GPU, ASSP, ASIC, etc.). The design flow of such technology is evaluated through the prototyping of several engineering applications (control systems, mathematical coprocessors, complex image processors, etc.), showing a high enough level of maturity for its exploitation in the industry.Resumen Esta tesis doctoral abarca el diseño de sistemas electrónicos embebidos basados en tecnología hardware dinámicamente reconfigurable –disponible a través de dispositivos lógicos programables SRAM FPGA/SoC– que contribuyan a la mejora de la calidad de vida de la sociedad. Se investiga la arquitectura del sistema y del motor de reconfiguración que proporcione a la FPGA la capacidad de reconfiguración dinámica parcial de sus recursos programables, con objeto de sintetizar, mediante codiseño hardware/software, una determinada aplicación particionada en tareas multiplexadas en tiempo y en espacio, optimizando así su implementación física –área de silicio, tiempo de procesado, complejidad, flexibilidad, densidad funcional, coste y potencia disipada– comparada con otras alternativas basadas en hardware estático (MCU, DSP, GPU, ASSP, ASIC, etc.). Se evalúa el flujo de diseño de dicha tecnología a través del prototipado de varias aplicaciones de ingeniería (sistemas de control, coprocesadores aritméticos, procesadores de imagen, etc.), evidenciando un nivel de madurez viable ya para su explotación en la industria.Resum Aquesta tesi doctoral està orientada al disseny de sistemes electrònics empotrats basats en tecnologia hardware dinàmicament reconfigurable –disponible mitjançant dispositius lògics programables SRAM FPGA/SoC– que contribueixin a la millora de la qualitat de vida de la societat. S’investiga l’arquitectura del sistema i del motor de reconfiguració que proporcioni a la FPGA la capacitat de reconfiguració dinàmica parcial dels seus recursos programables, amb l’objectiu de sintetitzar, mitjançant codisseny hardware/software, una determinada aplicació particionada en tasques multiplexades en temps i en espai, optimizant així la seva implementació física –àrea de silici, temps de processat, complexitat, flexibilitat, densitat funcional, cost i potència dissipada– comparada amb altres alternatives basades en hardware estàtic (MCU, DSP, GPU, ASSP, ASIC, etc.). S’evalúa el fluxe de disseny d’aquesta tecnologia a través del prototipat de varies aplicacions d’enginyeria (sistemes de control, coprocessadors aritmètics, processadors d’imatge, etc.), demostrant un nivell de maduresa viable ja per a la seva explotació a la indústria

Numerical solutions of differential equations on FPGA-enhanced computers

Conventionally, to speed up scientific or engineering (S&E) computation programs on general-purpose computers, one may elect to use faster CPUs, more memory, systems with more efficient (though complicated) architecture, better software compilers, or even coding with assembly languages. With the emergence of Field Programmable Gate Array (FPGA) based Reconfigurable Computing (RC) technology, numerical scientists and engineers now have another option using FPGA devices as core components to address their computational problems. The hardware-programmable, low-cost, but powerful “FPGA-enhanced computer” has now become an attractive approach for many S&E applications. A new computer architecture model for FPGA-enhanced computer systems and its detailed hardware implementation are proposed for accelerating the solutions of computationally demanding and data intensive numerical PDE problems. New FPGAoptimized algorithms/methods for rapid executions of representative numerical methods such as Finite Difference Methods (FDM) and Finite Element Methods (FEM) are designed, analyzed, and implemented on it. Linear wave equations based on seismic data processing applications are adopted as the targeting PDE problems to demonstrate the effectiveness of this new computer model. Their sustained computational performances are compared with pure software programs operating on commodity CPUbased general-purpose computers. Quantitative analysis is performed from a hierarchical set of aspects as customized/extraordinary computer arithmetic or function units, compact but flexible system architecture and memory hierarchy, and hardwareoptimized numerical algorithms or methods that may be inappropriate for conventional general-purpose computers. The preferable property of in-system hardware reconfigurability of the new system is emphasized aiming at effectively accelerating the execution of complex multi-stage numerical applications. Methodologies for accelerating the targeting PDE problems as well as other numerical PDE problems, such as heat equations and Laplace equations utilizing programmable hardware resources are concluded, which imply the broad usage of the proposed FPGA-enhanced computers

Online signature verification systems on a low-cost FPGA

This paper describes three different approaches for the implementation of an online signature verification system on a low-cost FPGA. The system is based on an algorithm, which operates on real numbers using the double-precision floating-point IEEE 754 format. The doubleprecision computations are replaced by simpler formats, without affecting the biometrics performance, in order to permit efficient implementations on low-cost FPGA families. The first approach is an embedded system based on MicroBlaze, a 32-bit soft-core microprocessor designed for Xilinx FPGAs, which can be configured by including a single-precision floating-point unit (FPU). The second implementation attaches a hardware accelerator to the embedded system to reduce the execution time on floating-point vectors. The last approach is a custom computing system, which is built from a large set of arithmetic circuits that replace the floating-point data with a more efficient representation based on fixed-point format. The latter system provides a very high runtime acceleration factor at the expense of using a large number of FPGA resources, a complex development cycle and no flexibility since it cannot be adapted to other biometric algorithms. By contrast, the first system provides just the opposite features, while the second approach is a mixed solution between both of them. The experimental results show that both the hardware accelerator and the custom computing system reduce the execution time by a factor ×7.6 and ×201 but increase the logic FPGA resources by a factor ×2.3 and ×5.2, respectively, in comparison with the MicroBlaze embedded system.This research was funded by Spanish MCIN/AEI/10.13039/501100011033, grant number PID2019-107274RB-I00.Peer ReviewedPostprint (published version

High sample-rate Givens rotations for recursive least squares

The design of an application-specific integrated circuit of a parallel array processor is considered for recursive least squares by QR decomposition using Givens rotations, applicable in adaptive filtering and beamforming applications. Emphasis is on high sample-rate operation, which, for this recursive algorithm, means that the time to perform arithmetic operations is critical. The algorithm, architecture and arithmetic are considered in a single integrated design procedure to achieve optimum results. A realisation approach using standard arithmetic operators, add, multiply and divide is adopted. The design of high-throughput operators with low delay is addressed for fixed- and floating-point number formats, and the application of redundant arithmetic considered. New redundant multiplier architectures are presented enabling reductions in area of up to 25%, whilst maintaining low delay. A technique is presented enabling the use of a conventional tree multiplier in recursive applications, allowing savings in area and delay. Two new divider architectures are presented showing benefits compared with the radix-2 modified SRT algorithm. Givens rotation algorithms are examined to determine their suitability for VLSI implementation. A novel algorithm, based on the Squared Givens Rotation (SGR) algorithm, is developed enabling the sample-rate to be increased by a factor of approximately 6 and offering area reductions up to a factor of 2 over previous approaches. An estimated sample-rate of 136 MHz could be achieved using a standard cell approach and O.35pm CMOS technology. The enhanced SGR algorithm has been compared with a CORDIC approach and shown to benefit by a factor of 3 in area and over 11 in sample-rate. When compared with a recent implementation on a parallel array of general purpose (GP) DSP chips, it is estimated that a single application specific chip could offer up to 1,500 times the computation obtained from a single OP DSP chip

Efficient reconfigurable architectures for 3D medical image compression

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Recently, the more widespread use of three-dimensional (3-D) imaging modalities, such as magnetic resonance imaging (MRI), computed tomography (CT), positron emission tomography (PET), and ultrasound (US) have generated a massive amount of volumetric data. These have provided an impetus to the development of other applications, in particular telemedicine and teleradiology. In these fields, medical image compression is important since both efficient storage and transmission of data through high-bandwidth digital communication lines are of crucial importance. Despite their advantages, most 3-D medical imaging algorithms are computationally intensive with matrix transformation as the most fundamental operation involved in the transform-based methods. Therefore, there is a real need for high-performance systems, whilst keeping architectures exible to allow for quick upgradeability with real-time applications. Moreover, in order to obtain efficient solutions for large medical volumes data, an efficient implementation of these operations is of significant importance. Reconfigurable hardware, in the form of field programmable gate arrays (FPGAs) has been proposed as viable system building block in the construction of high-performance systems at an economical price. Consequently, FPGAs seem an ideal candidate to harness and exploit their inherent advantages such as massive parallelism capabilities, multimillion gate counts, and special low-power packages. The key achievements of the work presented in this thesis are summarised as follows. Two architectures for 3-D Haar wavelet transform (HWT) have been proposed based on transpose-based computation and partial reconfiguration suitable for 3-D medical imaging applications. These applications require continuous hardware servicing, and as a result dynamic partial reconfiguration (DPR) has been introduced. Comparative study for both non-partial and partial reconfiguration implementation has shown that DPR offers many advantages and leads to a compelling solution for implementing computationally intensive applications such as 3-D medical image compression. Using DPR, several large systems are mapped to small hardware resources, and the area, power consumption as well as maximum frequency are optimised and improved. Moreover, an FPGA-based architecture of the finite Radon transform (FRAT)with three design strategies has been proposed: direct implementation of pseudo-code with a sequential or pipelined description, and block random access memory (BRAM)- based method. An analysis with various medical imaging modalities has been carried out. Results obtained for image de-noising implementation using FRAT exhibits promising results in reducing Gaussian white noise in medical images. In terms of hardware implementation, promising trade-offs on maximum frequency, throughput and area are also achieved. Furthermore, a novel hardware implementation of 3-D medical image compression system with context-based adaptive variable length coding (CAVLC) has been proposed. An evaluation of the 3-D integer transform (IT) and the discrete wavelet transform (DWT) with lifting scheme (LS) for transform blocks reveal that 3-D IT demonstrates better computational complexity than the 3-D DWT, whilst the 3-D DWT with LS exhibits a lossless compression that is significantly useful for medical image compression. Additionally, an architecture of CAVLC that is capable of compressing high-definition (HD) images in real-time without any buffer between the quantiser and the entropy coder is proposed. Through a judicious parallelisation, promising results have been obtained with limited resources. In summary, this research is tackling the issues of massive 3-D medical volumes data that requires compression as well as hardware implementation to accelerate the slowest operations in the system. Results obtained also reveal a significant achievement in terms of the architecture efficiency and applications performance.Ministry of Higher Education Malaysia (MOHE), Universiti Tun Hussein Onn Malaysia (UTHM) and the British Counci

Time domain based image generation for synthetic aperture radar on field programmable gate arrays

Aerial images are important in different scenarios including surface cartography, surveillance, disaster control, height map generation, etc. Synthetic Aperture Radar (SAR) is one way to generate these images even through clouds and in the absence of daylight. For a wide and easy usage of this technology, SAR systems should be small, mounted to Unmanned Aerial Vehicles (UAVs) and process images in real-time. Since UAVs are small and lightweight, more robust (but also more complex) time-domain algorithms are required for good image quality in case of heavy turbulence. Typically the SAR data set size does not allow for ground transmission and processing, while the UAV size does not allow for huge systems and high power consumption to process the data. A small and energy-efficient signal processing system is therefore required. To fill the gap between existing systems that are capable of either high-speed processing or low power consumption, the focus of this thesis is the analysis, design, and implementation of such a system. A survey shows that most architectures either have to high power budgets or too few processing capabilities to match real-time requirements for time-domain-based processing. Therefore, a Field Programmable Gate Array (FPGA) based system is designed, as it allows for high performance and low-power consumption. The Global Backprojection (GBP) is implemented, as it is the standard time-domain-based algorithm which allows for highest image quality at arbitrary trajectories at the complexity of O(N3). To satisfy real-time requirements under all circumstances, the accelerated Fast Factorized Backprojection (FFBP) algorithm with a complexity of O(N2logN) is implemented as well, to allow for a trade-off between image quality and processing time. Additionally, algorithm and design are enhanced to correct the failing assumptions for Frequency Modulated Continuous Wave (FMCW) Radio Detection And Ranging (Radar) data at high velocities. Such sensors offer high-resolution data at considerably low transmit power which is especially interesting for UAVs. A full analysis of all algorithms is carried out, to design a highly utilized architecture for maximum throughput. The process covers the analysis of mathematical steps and approximations for hardware speedup, the analysis of code dependencies for instruction parallelism and the analysis of streaming capabilities, including memory access and caching strategies, as well as parallelization considerations and pipeline analysis. Each architecture is described in all details with its surrounding control structure. As proof of concepts, the architectures are mapped on a Virtex 6 FPGA and results on resource utilization, runtime and image quality are presented and discussed. A special framework allows to scale and port the design to other FPGAs easily and to enable for maximum resource utilization and speedup. The result is streaming architectures that are capable of massive parallelization with a minimum in system stalls. It is shown that real-time processing on FPGAs with strict power budgets in time-domain is possible with the GBP (mid-sized images) and the FFBP (any image size with a trade-off in quality), allowing for a UAV scenario