New virtually scaling free adaptive CORDIC rotator

In this article we propose a novel CORDIC rotator algorithm that eliminates the problems of scale factor compensation and limited range of convergence associated with the classical CORDIC algorithm. In our scheme, depending on the target angle or the initial coordinate of the vector, a scaling by 1 or 1/?2 is needed that can be realised with minimal hardware. The proposed CORDIC rotator adaptively selects appropriate iteration steps and converges to the final result by executing 50% less number of iterations on an average compared to that required for the classical CORDIC. Unlike classical CORDIC, the final value of the scale factor is completely independent of number of executed iterations. Based on the proposed algorithm, a 16-bit pipelined CORDIC rotator implementation has been described. The silicon area of the fabricated pipelined CORDIC rotator core is 2.73 mm2. This is equivalent to 38 k inverter gates in IHP in-house 0.25 ?m BiCMOS technology. The average dynamic power consumption of the fabricated CORDIC rotator is 17 mW @ 2.5 V supply and 20Msps throughput. Currently, this CORDIC rotator is used as a part of the baseband processor for a project that aims to design a single-chip wireless modem compliant with IEEE 802.11a and Hiperlan/2

An approach to the application of shift-and-add algorithms on engineering and industrial processes

Different kinds of algorithms can be chosen so as to compute elementary functions. Among all of them, it is worthwhile mentioning the shift-and-add algorithms due to the fact that they have been specifically designed to be very simple and to save computer resources. In fact, almost the only operations usually involved with these methods are additions and shifts, which can be easily and efficiently performed by a digital processor. Shift-and-add algorithms allow fairly good precision with low cost iterations. The most famous algorithm belonging to this type is CORDIC. CORDIC has the capability of approximating a wide variety of functions with only the help of a slight change in their iterations. In this paper, we will analyze the requirements of some engineering and industrial problems in terms of type of operands and functions to approximate. Then, we will propose the application of shift-and-add algorithms based on CORDIC to these problems. We will make a comparison between the different methods applied in terms of the precision of the results and the number of iterations required.This research was supported by the Conselleria de Educacion of the Valencia Region Government under grant number GV/2011/043

Hough Transform recursive evaluation using Distributed Arithmetic

Paper submitted to the IFIP International Conference on Very Large Scale Integration (VLSI-SOC), Darmstadt, Germany, 2003.The Hough Transform (HT) is a useful technique in image segmentation, concretely for geometrical primitive detection. A Convolution-Based Recursive Method (CBRM) is presented for generic function evaluation. In this approach, calculations are carried out by a unique parametric formula which provides all function points by successive iteration. The case of combined trigonometric functions involved in the calculation of the HT is analyzed under this scope. An architecture for reconfigurable FPGA-based hardware, using Distributed Arithmetic (DA) implements the design. It provides memory and hardware resource saving as well as speed improvements according to the experiments carried out with the HT

Reconfigurable Architecture of UFMC Transmitter for 5G and Its FPGA Prototype

[EN] A universal-filtered multicarrier (UFMC) system that is a generalization of filtered orthogonal frequency-division multiplexing (OFDM) and filter-bank-based multicarrier is being considered as a potential candidate for fifth-generation due to its robustness against intercarrier interference as in cyclic-prefix-based OFDM systems. However, real-time hardware realization of multicarrier systems is limited by a large number of arithmetic units for inverse fast Fourier transform and pulse-shaping filters. In this paper, we aim to propose a low-complexity and reconfigurable architecture for a baseband UFMC transmitter. To the best of our knowledge, the proposed architecture is the first reconfigurable architecture that has the flexibility to choose the number of subcarriers in a subband without any change in hardware resources. In addition, the proposed architecture selects the filter from a group of filters with a single selection line. Moreover, we use a commercially available field-programmable gate array device for real-time testing and analyzing the baseband UFMC signal. From the extensive experiments, we study the occupied bandwidth, main-lobe power, and sidelobe power of the baseband signal with different filters in real-time scenarios. Finally, we measure the quantization error in baseband signal generation for the proposed UFMC transmitter architecture and find comparable with the error bound.Kumar, V.; Mukherjee, M.; Lloret, J. (2020). Reconfigurable Architecture of UFMC Transmitter for 5G and Its FPGA Prototype. IEEE Systems Journal. 14(1):28-38. https://doi.org/10.1109/JSYST.2019.2923549S283814

CORDIC algorithm and its applications

openThe CORDIC (Coordinate Rotation Digital Computer) algorithm is used for solving vast sets of functions such as trigonometric functions, hyperbolic functions and natural logarithms. This thesis is going to discuss how the algorithm works and its architecture implementation. It is also going to explore potential applications of the algorithm in digital communication systems, specifically for the realization of the DDS (Direct Digital Synthesis) and digital modulation.The CORDIC (Coordinate Rotation Digital Computer) algorithm is used for solving vast sets of functions such as trigonometric functions, hyperbolic functions and natural logarithms. This thesis is going to discuss how the algorithm works and its architecture implementation. It is also going to explore potential applications of the algorithm in digital communication systems, specifically for the realization of the DDS (Direct Digital Synthesis) and digital modulation

VLSI Implementation of a Cost-Efficient Loeffler-DCT Algorithm with Recursive CORDIC for DCT-Based Encoder

This paper presents a low-cost and high-quality; hardware-oriented; two-dimensional discrete cosine transform (2-D DCT) signal analyzer for image and video encoders. In order to reduce memory requirement and improve image quality; a novel Loeffler DCT based on a coordinate rotation digital computer (CORDIC) technique is proposed. In addition; the proposed algorithm is realized by a recursive CORDIC architecture instead of an unfolded CORDIC architecture with approximated scale factors. In the proposed design; a fully pipelined architecture is developed to efficiently increase operating frequency and throughput; and scale factors are implemented by using four hardware-sharing machines for complexity reduction. Thus; the computational complexity can be decreased significantly with only 0.01 dB loss deviated from the optimal image quality of the Loeffler DCT. Experimental results show that the proposed 2-D DCT spectral analyzer not only achieved a superior average peak signal–noise ratio (PSNR) compared to the previous CORDIC-DCT algorithms but also designed cost-efficient architecture for very large scale integration (VLSI) implementation. The proposed design was realized using a UMC 0.18-μm CMOS process with a synthesized gate count of 8.04 k and core area of 75,100 μm2. Its operating frequency was 100 MHz and power consumption was 4.17 mW. Moreover; this work had at least a 64.1% gate count reduction and saved at least 22.5% in power consumption compared to previous designs

CORDICのハードウェア構成及び応用に関する研究

電気通信大学201

High-Throughput FPGA Implementation of QR Decomposition

Munoz, S.D.; Hormigo, J. "High-Throughput FPGA Implementation of QR Decomposition" IEEE Transactions on in Circuits and Systems II: Express Briefs,vol.62, no.9, pp.861-865, Sept. 2015 doi: 10.1109/TCSII.2015.2435753This brief presents a hardware design to achieve high-throughput QR decomposition, using Givens Rotation Method. It utilizes a new two-dimensional systolic array architecture with pipelined processing elements, which are based on the COordinate Rotation DIgital Computer (CORDIC) algorithm. CORDIC computes vector rotations through shifts and additions. This approach allows a continuous computation of QR factorizations with simple hardware. A fixed-point FPGA architecture for 4 x 4 matrices has been optimized by balancing the number of CORDIC iterations with the final error. As a result, compared to other previous proposals for FPGA, our design achieves at least 50% more throughput, and much less resource utilization.Ministry of Education and Science of Spain and Junta of Andalucia under contracts TIN2013-42253-P and P07-TIC-02630, respectively

A Joint Filter and Spectrum Shifting Architecture for Low Complexity Flexible UFMC in 5G

© 2021 IEEE. Personal use of this material is permitted. Permissíon from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertisíng or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.[EN] The hardware realization of Universal Filtered Multi Carrier (UFMC) architecture has attracted significant attention in fifth generation (5G) and beyond. In addition to the flexibility in fast Fourier transform (FFT)-length, a flexible prototype filter in combination with multiplicative complex spectrum shifting co-efficients is required for realizing flexible UFMC architecture. The existing architectures of UFMC transmitter commonly adopted fixed-size FFT-length, number of subbands, subband size, and filter-length. Moreover, the lack of flexible prototype filter and spectrum localization of filter co-efficients to individual subbands limits the flexible UFMC system design. In this paper, we propose VLSI architecture for a flexible length prototype filter that can generate spectrally shifted filter co-efficients to individual subbands in tune with the changing value of FFT-length, number of subbands, subband size, and filter-length. For 16-bit word size architecture, our proposed design produces filter co-efficients and spectrum shifting co-efficients upto length, 2(15). Thus, any desired combination of FFT-length, number of subbands, subband size and filter-length is selected to generate the filter co-efficients for the individual subbands. Moreover, complex multiplication and addition operations are reduced in proposed architecture, quantitatively, about 58.81% reduction in filtering unit is achieved over the state-of-the-art architecture. Finally, hardware implementation output and XILINX post route simulation result matches perfectly with MATLAB simulations.Kumar, V.; Mukherjee, M.; Lloret, J.; Ren, Z.; Kumari, M. (2021). A Joint Filter and Spectrum Shifting Architecture for Low Complexity Flexible UFMC in 5G. IEEE Transactions on Wireless Communications. 20(10):6706-6714. https://doi.org/10.1109/TWC.2021.3076039S67066714201