Design and FPGA Implementation of CORDIC-based 8-point 1D DCT Processor

CORDIC or CO-ordinate Rotation DIgital Computer is a fast, simple, efficient and powerful algorithm used for diverse Digital Signal Processing applications. Primarily developed for real-time airborne computations, it uses a unique computing technique which is especially suitable for solving the trigonometric relationships involved in plane co-ordinate rotation and conversion from rectangular to polar form. It comprises a special serial arithmetic unit having three shift registers, three adders/subtractors, Look-Up table and special interconnections. Using a prescribed sequence of conditional additions or subtractions the CORDIC arithmetic unit can be controlled to solve either of the following equations: Y’=K (Ycos λ+ Xsin λ) X’=K (Xcos λ - Ysin λ); where K is a constant In this project: • A CORDIC-based processor for sine/cosine calculation was designed using VHDL programming in Xilinx ISE 10.1. The CORDIC module was tested for its functionality and correctness by test-bench analysis. Subsequently, FPGA implementation of the CORDIC core followed by ChipScopePro analysis of the output logic waveforms was performed. • Using this CORDIC core a DCT processor was designed to calculate the 8-point 1D DCT. The functionality and operational correctness of this processor was tested, first on the test-bench and then via ChipScopePro analysis, post FPGA implementation. The output obtained in both the cases was compared with the actual values to test for consistency and the percentage of accuracy was established. Power consumption and FPGA resource utilization were observed. The results obtained were discussed

FPGA-BASED IMPLEMENTATION OF DUAL-FREQUENCY PATTERN SCHEME FOR 3-D SHAPE MEASUREMENT

Structured Light Illumination (SLI) is the process where spatially varied patterns are projected onto a 3-D surface and based on the distortion by the surface topology, phase information can be calculated and a 3D model constructed. Phase Measuring Profilometry (PMP) is a particular type of SLI that requires three or more patterns temporarily multiplexed. High speed PMP attempts to scan moving objects whose motion is small so as to have little impact on the 3-D model. Given that practically all machine vision cameras and high speed cameras employ a Field Programmable Gate Array (FPGA) interface directly to the image sensors, the opportunity exists to do the processing on camera. This thesis focuses on the design, implementation, testing, and evaluation of a camera-projector system to implement a PMP dual-frequency scheme for 3-D shape measurement on a single FPGA chip. The processor architecture is implemented and tested using the Xilinx Spartan 3 FPGA chip on an Opal Kelly development board. The hardware is described using VHDL and Verilog Hardware Description Languages (HDLs)

HIGH PERFORMANCE, LOW COST SUBSPACE DECOMPOSITION AND POLYNOMIAL ROOTING FOR REAL TIME DIRECTION OF ARRIVAL ESTIMATION: ANALYSIS AND IMPLEMENTATION

This thesis develops high performance real-time signal processing modules for direction of arrival (DOA) estimation for localization systems. It proposes highly parallel algorithms for performing subspace decomposition and polynomial rooting, which are otherwise traditionally implemented using sequential algorithms. The proposed algorithms address the emerging need for real-time localization for a wide range of applications. As the antenna array size increases, the complexity of signal processing algorithms increases, making it increasingly difficult to satisfy the real-time constraints. This thesis addresses real-time implementation by proposing parallel algorithms, that maintain considerable improvement over traditional algorithms, especially for systems with larger number of antenna array elements. Singular value decomposition (SVD) and polynomial rooting are two computationally complex steps and act as the bottleneck to achieving real-time performance. The proposed algorithms are suitable for implementation on field programmable gated arrays (FPGAs), single instruction multiple data (SIMD) hardware or application specific integrated chips (ASICs), which offer large number of processing elements that can be exploited for parallel processing. The designs proposed in this thesis are modular, easily expandable and easy to implement. Firstly, this thesis proposes a fast converging SVD algorithm. The proposed method reduces the number of iterations it takes to converge to correct singular values, thus achieving closer to real-time performance. A general algorithm and a modular system design are provided making it easy for designers to replicate and extend the design to larger matrix sizes. Moreover, the method is highly parallel, which can be exploited in various hardware platforms mentioned earlier. A fixed point implementation of proposed SVD algorithm is presented. The FPGA design is pipelined to the maximum extent to increase the maximum achievable frequency of operation. The system was developed with the objective of achieving high throughput. Various modern cores available in FPGAs were used to maximize the performance and details of these modules are presented in detail. Finally, a parallel polynomial rooting technique based on Newton’s method applicable exclusively to root-MUSIC polynomials is proposed. Unique characteristics of root-MUSIC polynomial’s complex dynamics were exploited to derive this polynomial rooting method. The technique exhibits parallelism and converges to the desired root within fixed number of iterations, making this suitable for polynomial rooting of large degree polynomials. We believe this is the first time that complex dynamics of root-MUSIC polynomial were analyzed to propose an algorithm. In all, the thesis addresses two major bottlenecks in a direction of arrival estimation system, by providing simple, high throughput, parallel algorithms

Optimization of DSSS Receivers Using Hardware-in-the-Loop Simulations

Over the years, there has been significant interest in defining a hardware abstraction layer to facilitate code reuse in software defined radio (SDR) applications. Designers are looking for a way to enable application software to specify a waveform, configure the platform, and control digital signal processing (DSP) functions in a hardware platform in a way that insulates it from the details of realization. This thesis presents a tool-based methodolgy for developing and optimizing a Direct Sequence Spread Spectrum (DSSS) transceiver deployed in custom hardware like Field Programmble Gate Arrays (FPGAs). The system model consists of a tranmitter which employs a quadrature phase shift keying (QPSK) modulation scheme, an additive white Gaussian noise (AWGN) channel, and a receiver whose main parts consist of an analog-to-digital converter (ADC), digital down converter (DDC), image rejection low-pass filter (LPF), carrier phase locked loop (PLL), tracking locked loop, down-sampler, spread spectrum correlators, and rectangular-to-polar converter. The design methodology is based on a new programming model for FPGAs developed in the industry by Xilinx Inc. The Xilinx System Generator for DSP software tool provides design portability and streamlines system development by enabling engineers to create and validate a system model in Xilinx FPGAs. By providing hierarchical modeling and automatic HDL code generation for programmable devices, designs can be easily verified through hardware-in-the-loop (HIL) simulations. HIL provides a significant increase in simulation speed which allows optimization of the receiver design with respect to the datapath size for different functional parts of the receiver. The parameterized datapath points used in the simulation are ADC resolution, DDC datapath size, LPF datapath size, correlator height, correlator datapath size, and rectangular-to-polar datapath size. These parameters are changed in the software enviornment and tested for bit error rate (BER) performance through real-time hardware simualtions. The final result presents a system design with minimum harware area occupancy relative to an acceptable BER degradation