Design and analysis of short word length DSP systems for mobile communication

Recently, many general purpose DSP applications such as Least Mean Squares-Like single-bit adaptive filter algorithms have been developed using the Short Word Length (SWL) technique and have been shown to achieve similar performance as multi-bit systems. A key function in SWL systems is sigma delta modulation (ΣΔM) that operates at an over sampling ratio (OSR), in contrast to the Nyquist rate sampling typically used in conventional multi-bit systems. To date, the analysis of SWL (or single-bit) DSP systems has tended to be performed using high-level tools such as MATLAB, with little work reported relating to their hardware implementation, particularly in Field Programmable Gate Arrays (FPGAs). This thesis explores the hardware implementation of single-bit systems in FPGA using the design and implementation in VHDL of a single-bit ternary FIR-like filter as an illustrative example. The impact of varying OSR and bit-width of the SWL filter has been determined, and a comparison undertaken between the area-performance-power characteristics of the SWL FIR filter compared to its equivalent multi-bit filter. In these experiments, it was found that single-bit FIR-like filter consistently outperforms the multi-bit technique in terms of its area, performance and power except at the highest filter orders analysed in this work. At higher orders, the ΣΔ approach retains its power and performance advantages but exhibits slightly higher chip area. In the second stage of thesis, three encoding techniques called canonical signed digit (CSD), 2’s complement, and Redundant Binary Signed Digit (RBSD) were designed and investigated on the basis of area-performance in FPGA at varying OSR. Simulation results show that CSD encoding technique does not offer any significant improvement as compared to 2’s complement as in multi-bit domain. Whereas, RBSD occupies double the chip area than other two techniques and has poor performance. The stability of the single-bit FIR-like filter mainly depends upon IIR remodulator due to its recursive nature. Thus, we have investigated the stability IIR remodulator and propose a new model using linear analysis and root locus approach that takes into account the widely accepted second order sigma-delta modulator state variable upper bounds. Using proposed model we have found new feedback parameters limits that is a key parameter in single-bit IIR remodulator stability analysis. Further, an analysis of single-bit adaptive channel equalization in MATLAB has been performed, which is intended to support the design and development of efficient algorithm for single-bit channel equalization. A new mathematical model has been derived with all inputs, coefficients and outputs in single-bit domain. The model was simulated using narrowband signals in MATLAB and investigated on the basis of symbol error rate (SER), signal-to-noise ratio (SNR) and minimum mean squared error (MMSE). The results indicate that single-bit adaptive channel equalization is achievable with narrowband signals but that the harsh quantization noise has great impact in the convergence

Image Processing Using FPGAs

This book presents a selection of papers representing current research on using field programmable gate arrays (FPGAs) for realising image processing algorithms. These papers are reprints of papers selected for a Special Issue of the Journal of Imaging on image processing using FPGAs. A diverse range of topics is covered, including parallel soft processors, memory management, image filters, segmentation, clustering, image analysis, and image compression. Applications include traffic sign recognition for autonomous driving, cell detection for histopathology, and video compression. Collectively, they represent the current state-of-the-art on image processing using FPGAs

Efficient FPGA implementation and power modelling of image and signal processing IP cores

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Field Programmable Gate Arrays (FPGAs) are the technology of choice in a number ofimage and signal processing application areas such as consumer electronics, instrumentation, medical data processing and avionics due to their reasonable energy consumption, high performance, security, low design-turnaround time and reconfigurability. Low power FPGA devices are also emerging as competitive solutions for mobile and thermally constrained platforms. Most computationally intensive image and signal processing algorithms also consume a lot of power leading to a number of issues including reduced mobility, reliability concerns and increased design cost among others. Power dissipation has become one of the most important challenges, particularly for FPGAs. Addressing this problem requires optimisation and awareness at all levels in the design flow. The key achievements of the work presented in this thesis are summarised here. Behavioural level optimisation strategies have been used for implementing matrix product and inner product through the use of mathematical techniques such as Distributed Arithmetic (DA) and its variations including offset binary coding, sparse factorisation and novel vector level transformations. Applications to test the impact of these algorithmic and arithmetic transformations include the fast Hadamard/Walsh transforms and Gaussian mixture models. Complete design space exploration has been performed on these cores, and where appropriate, they have been shown to clearly outperform comparable existing implementations. At the architectural level, strategies such as parallelism, pipelining and systolisation have been successfully applied for the design and optimisation of a number of cores including colour space conversion, finite Radon transform, finite ridgelet transform and circular convolution. A pioneering study into the influence of supply voltage scaling for FPGA based designs, used in conjunction with performance enhancing strategies such as parallelism and pipelining has been performed. Initial results are very promising and indicated significant potential for future research in this area. A key contribution of this work includes the development of a novel high level power macromodelling technique for design space exploration and characterisation of custom IP cores for FPGAs, called Functional Level Power Analysis and Modelling (FLPAM). FLPAM is scalable, platform independent and compares favourably with existing approaches. A hybrid, top-down design flow paradigm integrating FLPAM with commercially available design tools for systematic optimisation of IP cores has also been developed

Some Optimizations of Hardware Multiplication by Constant Matrices

International audienceThis paper presents some improvements on the optimization of hardware multiplication by constant matrices. We focus on the automatic generation of circuits that involve constant matrix multiplication, i.e. multiplication of a vector by a constant matrix. The proposed method, based on number recoding and dedicated common sub-expression factorization algorithms was implemented in a VHDL generator. Our algorithms and generator have been extended to the case of some digital filters based on multiplication by a constant matrix and delay operations. The obtained results on several applications have been implemented on FPGAs and compared to previous solutions. Up to 40% area and speed savings are achieved

Multiplierless CSD techniques for high performance FPGA implementation of digital filters.

I leverage FastCSD to develop a new, high performance iterative multiplierless structure based on a novel real-time CSD recoding, so that more zero partial products are introduced. Up to 66.7% zero partial products occur compared to 50% in the traditional modified Booth's recoding. Also, this structure reduces the non-zero partial products to a minimum. As a result, the number of arithmetic operations in the carry-save structure is reduced. Thus, an overall speed-up, as well as low-power consumption can be achieved. Furthermore, because the proposed structure involves real time CSD recoding and does not require a fixed value for the multiplier input to be known a priori, the proposed multiplier can be applied to implement digital filters with non-fixed filter coefficients, such as adaptive filters.My work is based on a dramatic new technique for converting between 2's complement and CSD number systems, and results in high-performance structures that are particularly effective for implementing adaptive systems in reconfigurable logic.My research focus is on two key ideas for improving DSP performance: (1) Develop new high performance, efficient shift-add techniques ("multiplierless") to implement the multiply-add operations without the need for a traditional multiplier structure. (2) There is a growing trend toward design prototyping and even production in FPGAs as opposed to dedicated DSP processors or ASICs; leverage this trend synergistically with the new multiplierless structures to improve performance.Implementation of digital signal processing (DSP) algorithms in hardware, such as field programmable gate arrays (FPGAs), requires a large number of multipliers. Fast, low area multiply-adds have become critical in modern commercial and military DSP applications. In many contemporary real-time DSP and multimedia applications, system performance is severely impacted by the limitations of currently available speed, energy efficiency, and area requirement of an onboard silicon multiplier.I also introduce a new multi-input Canonical Signed Digit (CSD) multiplier unit, which requires fewer shift/add/subtract operations and reduced CSD number conversion overhead compared to existing techniques. This results in reduced power consumption and area requirements in the hardware implementation of DSP algorithms. Furthermore, because all the products are produced simultaneously, the multiplication speed and thus the throughput are improved. The multi-input multiplier unit is applied to implement digital filters with non-fixed filter coefficients, such as adaptive filters. The implementation cost of these digital filters can be further reduced by limiting the wordlength of the input signal with little or no sacrifice to the filter performance, which is confirmed by my simulation results. The proposed multiplier unit can also be applied to other DSP algorithms, such as digital filter banks or matrix and vector multiplications.Finally, the tradeoff between filter order and coefficient length in the design and implementation of high-performance filters in Field Programmable Gate Arrays (FPGAs) is discussed. Non-minimum order FIR filters are designed for implementation using Canonical Signed Digit (CSD) multiplierless implementation techniques. By increasing the filter order, the length of the coefficients can be decreased without reducing the filter performance. Thus, an overall hardware savings can be achieved.Adaptive system implementations require real-time conversion of coefficients to Canonical Signed Digit (CSD) or similar representations to benefit from multiplierless techniques for implementing filters. Multiplierless approaches are used to reduce the hardware and increase the throughput. This dissertation introduces the first non-iterative hardware algorithm to convert 2's complement numbers to their CSD representations (FastCSD) using a fixed number of shift and logic operations. As a result, the power consumption and area requirements required for hardware implementation of DSP algorithms in which the coefficients are not known a priori can be greatly reduced. Because all CSD digits are produced simultaneously, the conversion speed and thus the throughput are improved when compared to overlap-and-scan techniques such as Booth's recoding