Efficient FPGA implementation of high-throughput mixed radix multipath delay commutator FFT processor for MIMO-OFDM

This article presents and evaluates pipelined architecture designs for an improved high-frequency Fast Fourier Transform (FFT) processor implemented on Field Programmable Gate Arrays (FPGA) for Multiple Input Multiple Output Orthogonal Frequency Division Multiplexing (MIMO-OFDM). The architecture presented is a Mixed-Radix Multipath Delay Commutator. The presented parallel architecture utilizes fewer hardware resources compared to Radix-2 architecture, while maintaining simple control and butterfly structures inherent to Radix-2 implementations. The high-frequency design presented allows enhancing system throughput without requiring additional parallel data paths common in other current approaches, the presented design can process two and four independent data streams in parallel and is suitable for scaling to any power of two FFT size N. FPGA implementation of the architecture demonstrated significant resource efficiency and high-throughput in comparison to relevant current approaches within literature. The proposed architecture designs were realized with Xilinx System Generator (XSG) and evaluated on both Virtex-5 and Virtex-7 FPGA devices. Post place and route results demonstrated maximum frequency values over 400 MHz and 470 MHz for Virtex-5 and Virtex-7 FPGA devices respectively

Multipliers for Floating-Point Double Precision and Beyond on FPGAs

International audienceThe implementation of high-precision floating-point applications on reconfigurable hardware requires a variety of large multipliers: Standard multipliers are the core of floating-point multipliers; Truncated multipliers, trading resources for a well-controlled accuracy degradation, are useful building blocks in situations where a full multiplier is not needed. This work studies the automated generation of such multipliers using the embedded multipliers and adders present in DSP blocks of current FPGAs. The optimization of such multipliers is expressed as a tiling problem where a tile represents a hardware multiplier and super-tiles are the wiring of several hardware multipliers making efficient use of the DSP internal resources. This tiling technique is shown to adapt to full or truncated multipliers. It addresses arbitrary precisions including single, double but also in the quadruple precision introduced by the IEEE-754-2008 standard and currently unsupported by processor hardware. An open-source implementation is provided in the FloPoCo project

Customisable arithmetic hardware designs

Imperial Users onl

Arithmetic core generation using bit heaps

International audienceA bit heap is a data structure that holds the unevaluated sum of an arbitrary number of bits, each weighted by some power of two. Most advanced arithmetic cores can be viewed as involving one or several bit heaps. We claim here that this point of view leads to better global optimization at the algebraic level, at the circuit level, and in terms of software engineering. To demonstrate it, a generic software framework is introduced for the definition and optimization of bit heaps. This framework, targeting DSP-enabled FPGAs, is developed within the open-source FloPoCo arithmetic core generator. Its versatility is demonstrated on several examples: multipliers, complex multipliers, polynomials, and discrete cosine transform

Design of approximate overclocked datapath

Embedded applications can often demand stringent latency requirements. While high degrees of parallelism within custom FPGA-based accelerators may help to some extent, it may also be necessary to limit the precision used in the datapath to boost the operating frequency of the implementation. However, by reducing the precision, the engineer introduces quantisation error into the design. In this thesis, we describe an alternative circuit design methodology when considering trade-offs between accuracy, performance and silicon area. We compare two different approaches that could trade accuracy for performance. One is the traditional approach where the precision used in the datapath is limited to meet a target latency. The other is a proposed new approach which simply allows the datapath to operate without timing closure. We demonstrate analytically and experimentally that for many applications it would be preferable to simply overclock the design and accept that timing violations may arise. Since the errors introduced by timing violations occur rarely, they will cause less noise than quantisation errors. Furthermore, we show that conventional forms of computer arithmetic do not fail gracefully when pushed beyond the deterministic clocking region. In this thesis we take a fresh look at Online Arithmetic, originally proposed for digit serial operation, and synthesize unrolled digit parallel online arithmetic operators to allow for graceful degradation. We quantify the impact of timing violations on key arithmetic primitives, and show that substantial performance benefits can be obtained in comparison to binary arithmetic. Since timing errors are caused by long carry chains, these result in errors in least significant digits with online arithmetic, causing less impact than conventional implementations.Open Acces

Application-Specific Number Representation

Reconfigurable devices, such as Field Programmable Gate Arrays (FPGAs), enable application- specific number representations. Well-known number formats include fixed-point, floating- point, logarithmic number system (LNS), and residue number system (RNS). Such different number representations lead to different arithmetic designs and error behaviours, thus produc- ing implementations with different performance, accuracy, and cost. To investigate the design options in number representations, the first part of this thesis presents a platform that enables automated exploration of the number representation design space. The second part of the thesis shows case studies that optimise the designs for area, latency or throughput from the perspective of number representations. Automated design space exploration in the first part addresses the following two major issues: ² Automation requires arithmetic unit generation. This thesis provides optimised arithmetic library generators for logarithmic and residue arithmetic units, which support a wide range of bit widths and achieve significant improvement over previous designs. ² Generation of arithmetic units requires specifying the bit widths for each variable. This thesis describes an automatic bit-width optimisation tool called R-Tool, which combines dynamic and static analysis methods, and supports different number systems (fixed-point, floating-point, and LNS numbers). Putting it all together, the second part explores the effects of application-specific number representation on practical benchmarks, such as radiative Monte Carlo simulation, and seismic imaging computations. Experimental results show that customising the number representations brings benefits to hardware implementations: by selecting a more appropriate number format, we can reduce the area cost by up to 73.5% and improve the throughput by 14.2% to 34.1%; by performing the bit-width optimisation, we can further reduce the area cost by 9.7% to 17.3%. On the performance side, hardware implementations with customised number formats achieve 5 to potentially over 40 times speedup over software implementations

Efficient design and implementation of image processing algorithms on reconfigurable hardware using Handel-C

Computer manipulation of images is generally defined as Digital Image Processing (DIP). DIP is used in variety of applications, including video surveillance, target recognition, and image enhancement. These applications are usually implemented in software but may use special purpose hardware for speed. With advances in the VLSI technology hardware implementation has become an attractive alternative. Assigning complex computation tasks to hardware and exploiting the parallelism and pipelining in algorithms yield significant speedup in running times. In this thesis the image processing algorithms like median filter, basic morphological operators, convolution and edge detection algorithms are implemented on FPGA. A pipelined architecture of these algorithms is presented. The proposed architectures are capable of producing one output on every clock cycle. The hardware modeling was accomplished using Handel-C (DK2 environment). The algorithm was tested on standard image processing benchmarks and the results are compared with that obtained on software

Comparison of logarithmic and floating-point number systems implemented on Xilinx Virtex-II field-programmable gate arrays

The aim of this thesis is to compare the implementation of parameterisable LNS (logarithmic number system) and floating-point high dynamic range number systems on FPGA. The Virtex/Virtex-II range of FPGAs from Xilinx, which are the most popular FPGA technology, are used to implement the designs. The study focuses on using the low level primitives of the technology in an efficient way and so initially the design issues in implementing fixed-point operators are considered. The four basic operations of addition, multiplication, division and square root are considered. Carry- free adders, ripple-carry adders, parallel multipliers and digit recurrence division and square root are discussed. The floating-point operators use the word format and exceptions as described by the IEEE std-754. A dual-path adder implementation is described in detail, as are floating-point multiplier, divider and square root components. Results and comparisons with other works are given. The efficient implementation of function evaluation methods is considered next. An overview of current FPGA methods is given and a new piecewise polynomial implementation using the Taylor series is presented and compared with other designs in the literature. In the next section the LNS word format, accuracy and exceptions are described and two new LNS addition/subtraction function approximations are described. The algorithms for performing multiplication, division and powering in the LNS domain are also described and are compared with other designs in the open literature. Parameterisable conversion algorithms to convert to/from the fixed-point domain from/to the LNS and floating-point domain are described and implementation results given. In the next chapter MATLAB bit-true software models are given that have the exact functionality as the hardware models. The interfaces of the models are given and a serial communication system to perform low speed system tests is described. A comparison of the LNS and floating-point number systems in terms of area and delay is given. Different functions implemented in LNS and floating-point arithmetic are also compared and conclusions are drawn. The results show that when the LNS is implemented with a 6-bit or less characteristic it is superior to floating-point. However, for larger characteristic lengths the floating-point system is more efficient due to the delay and exponential area increase of the LNS addition operator. The LNS is beneficial for larger characteristics than 6-bits only for specialist applications that require a high portion of division, multiplication, square root, powering operations and few additions