Fast fixed-point optimization of DSP algorithms

In this chapter, the fast fixed-point optimization of Digital Signal Processing (DSP) algorithms is addressed. A fast quantization noise estimator is presented. The estimator enables a significant reduction in the computation time required to perform complex fixed-point optimizations, while providing a high accuracy. Also, a methodology to perform fixed-point optimization is developed. Affine Arithmetic (AA) is used to provide a fast Signal-to-Quantization Noise-Ratio (SQNR) estimation that can be used during the fixed-point optimization stage. The fast estimator covers differentiable non-linear algorithms with and without feedbacks. The estimation is based on the parameterization of the statistical properties of the noise at the output of fixed-point algorithms. This parameterization allows relating the fixedpoint formats of the signals to the output noise distribution by means of fast matrix operations. Thus, a fast estimation is achieved and the computation time of the fixed-point optimization process is significantly reduced. The proposed estimator and the fixed-point optimization methodology are tested using a subset of non-linear algorithms, such as vector operations, IIR filter for mean power computation, adaptive filters – for both linear and non-linear system identification – and a channel equalizer. The computation time of fixed-point optimization is boosted by three orders of magnitude while keeping the average estimation error down to 6% in most cases.

[1]  De Figueiredo,et al.  Self-validated numerical methods and applications , 1997 .

[2]  Wayne Luk,et al.  Ieee Transactions on Computer-aided Design of Integrated Circuits and Systems Accuracy Guaranteed Bit-width Optimization Abstract— We Present Minibit, an Automated Static Approach for Optimizing Bit-widths of Fixed-point Feedforward Designs with Guaranteed Accuracy. Methods to Minimize Both the In- , 2022 .

[3]  Gerhard J. Woeginger,et al.  The complexity of multiple wordlength assignment , 2002, Appl. Math. Lett..

[4]  George A. Constantinides.  Perturbation analysis for word-length optimization , 2003, 11th Annual IEEE Symposium on Field-Programmable Custom Computing Machines, 2003. FCCM 2003..

[5]  Gabriel Caffarena,et al.  Architectural synthesis of DSP circuits under simultaneous error and time constraints , 2010, 2010 18th IEEE/IFIP International Conference on VLSI and System-on-Chip.

[6]  Wayne Luk,et al.  Wordlength optimization for linear digital signal processing , 2003, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[7]  L. Jackson.  Roundoff-noise analysis for fixed-point digital filters realized in cascade or parallel form , 1970 .

[8]  Yvon Savaria,et al.  An automatic word length determination method , 2001, ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196).

[9]  Gabriel Caffarena,et al.  Design and Implementation of a Hardware Module for Equalisation in A 4G MIMO Receiver , 2006, 2006 International Conference on Field Programmable Logic and Applications.

[10]  W. P. Burleson,et al.  Search-based wordlength optimization for VLSI/DSP synthesis , 1994, Proceedings of 1994 IEEE Workshop on VLSI Signal Processing.

[11]  Wonyong Sung,et al.  Simulation-based word-length optimization method for fixed-point digital signal processing systems , 1995, IEEE Trans. Signal Process..

[12]  Octavio Nieto-Taladriz,et al.  Fast and accurate computation of the roundoff noise of linear time-invariant systems , 2008, IET Circuits Devices Syst..

[13]  Romuald Rocher,et al.  Automatic SQNR determination in non-linear and non-recursive fixed-point systems , 2004, 2004 12th European Signal Processing Conference.

[14]  B.L. Evans,et al.  Data wordlength reduction for low-power signal processing software , 2004, IEEE Workshop onSignal Processing Systems, 2004. SIPS 2004..

[15]  W. Luk,et al.  Truncation noise in fixed-point SFGs , 1999 .

[16]  Octavio Nieto-Taladriz,et al.  Improved Interval-Based Characterization of Fixed-Point LTI Systems With Feedback Loops , 2007, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[17]  Juan Antonio,et al.  Evaluación de los efectos de cuantificación en las estructuras de filtros digitales mediante técnicas de simulación basadas en extensiones de intervalos. , 2011 .

[18]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[19]  Gabriel Caffarena Fernández.  Combined Word-Length Allocation and High-Level Synthesis of Digital Signal Processing Circuits , 2008 .

[20]  B. Hayes,et al.  A Lucid Interval , 2003, American Scientist.

[21]  Peter Y. K. Cheung,et al.  Optimal combined word-length allocation and architectural synthesis of digital signal processing circuits , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[22]  Romuald Rocher,et al.  Analytical accuracy evaluation of fixed-point systems , 2007, 2007 15th European Signal Processing Conference.

[23]  Rob A. Rutenbar,et al.  Fast, Accurate Static Analysis for Fixed-Point Finite-Precision Effects in DSP Designs , 2003, ICCAD 2003.

[24]  Joos Vandewalle,et al.  Simulated‐annealing‐based optimization of coefficient and data word‐lengths in digital filters , 1988 .

[25]  Wayne Luk,et al.  Reconfigurable computing: architectures and design methods , 2005 .

[26]  Olivier Sentieys,et al.  A methodology for evaluating the precision of fixed-point systems , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[27]  Octavio Nieto-Taladriz,et al.  Analysis of limit cycles by means of affine arithmetic computer-aided tests , 2004, 2004 12th European Signal Processing Conference.

[28]  Robert W. Brodersen,et al.  A perturbation theory on statistical quantization effects in fixed-point DSP with non-stationary inputs , 2004, 2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512).

[29]  Brian L. Evans,et al.  Optimum Wordlength Search Using Sensitivity Information , 2006, EURASIP J. Adv. Signal Process..

[30]  Rob A. Rutenbar,et al.  Floating-point error analysis based on affine arithmetic , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[31]  Tokunbo Ogunfunmi,et al.  Adaptive Nonlinear System Identification: The Volterra and Wiener Model Approaches , 2007 .