Systematic synthesis of parallel architectures for the computation of higher order cumulants
Fine granularity parallel architectures for the efficient estimation of higher order statistics (HOS) are systematically derived in this paper. A unified methodology for constructing locally recursive algorithms and space–time linear mapping operators that lead to highly pipelined architectures cons...
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| Vydáno v: | Parallel computing Ročník 26; číslo 5; s. 655 - 676 |
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| Jazyk: | angličtina |
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Elsevier B.V
2000
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| ISSN: | 0167-8191, 1872-7336 |
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| Abstract | Fine granularity parallel architectures for the efficient estimation of higher order statistics (HOS) are systematically derived in this paper. A unified methodology for constructing locally recursive algorithms and space–time linear mapping operators that lead to highly pipelined architectures consisting of multiple, tightly coupled array stages is discussed first. Then a
farm of processors is synthesized that consumes second and fourth order moment estimates to produce the
fourth order cumulants. The unified array synthesis methodology allows for the characterization of all valid solutions and the derivation of closed-form expressions for the permissible linear scheduling functions thus facilitating the search for a design instance meeting the architect's specified objectives. Achieving minimum latency and an optimal space–time matching between the farm and the moments generator architecture (derived in [E.S. Manolakos, H.M. Stellakis, Systematic synthesis of parallel architectures for the real-time estimation of higher order statistical moments, Parallel Algorithms and Applications (to appear)]) were the two main specifications driving the synthesis. A linear array solution, that is simpler to interface with the moments generator at the expense of adding some control complexity is also derived. As a result, a two-stage integrated VLSI architecture, that may accept data samples from the host and compute in real-time
all non-redundant moment and cumulant terms,
up to the fourth order is now possible. |
|---|---|
| AbstractList | Fine granularity parallel architectures for the efficient estimation of higher order statistics (HOS) are systematically derived in this paper. A unified methodology for constructing locally recursive algorithms and space-time linear mapping operators that lead to highly pipelined architectures consisting of multiple, tightly coupled array stages is discussed first. Then a farm of processors is synthesized that consumes second and fourth order moment estimates to produce the fourth order cumulants. The unified array synthesis methodology allows for the characterization of all valid solutions and the derivation of closed-form expressions for the permissible linear scheduling functions thus facilitating the search for a design instance meeting the architect's specified objectives. Achieving minimum latency and an optimal space-time matching between the farm and the moments generator architecture were the two main specifications driving the synthesis. A linear array solution, that is simpler to interface with the moments generator at the expense of adding some control complexity is also derived. As a result, a two-stage integrated VLSI architecture, that may accept data samples from the host and compute in real-time all non-redundant moment and cumulant terms, up to the fourth order is now possible. Fine granularity parallel architectures for the efficient estimation of higher order statistics (HOS) are systematically derived in this paper. A unified methodology for constructing locally recursive algorithms and space–time linear mapping operators that lead to highly pipelined architectures consisting of multiple, tightly coupled array stages is discussed first. Then a farm of processors is synthesized that consumes second and fourth order moment estimates to produce the fourth order cumulants. The unified array synthesis methodology allows for the characterization of all valid solutions and the derivation of closed-form expressions for the permissible linear scheduling functions thus facilitating the search for a design instance meeting the architect's specified objectives. Achieving minimum latency and an optimal space–time matching between the farm and the moments generator architecture (derived in [E.S. Manolakos, H.M. Stellakis, Systematic synthesis of parallel architectures for the real-time estimation of higher order statistical moments, Parallel Algorithms and Applications (to appear)]) were the two main specifications driving the synthesis. A linear array solution, that is simpler to interface with the moments generator at the expense of adding some control complexity is also derived. As a result, a two-stage integrated VLSI architecture, that may accept data samples from the host and compute in real-time all non-redundant moment and cumulant terms, up to the fourth order is now possible. |
| Author | Stellakis, Haris M. Manolakos, Elias S. |
| Author_xml | – sequence: 1 givenname: Elias S. surname: Manolakos fullname: Manolakos, Elias S. email: elias@ece.neu.edu organization: Electrical and Computer Engineering Deptartment, 442 Dana Research Bld., Northern University, Boston, MA 02115, USA – sequence: 2 givenname: Haris M. surname: Stellakis fullname: Stellakis, Haris M. organization: Radio Systems Department, Wireless and Secure Systems Laboratory, GTE Laboratories Inc., Waltham MA 02254, USA |
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| References_xml | – volume: 10 start-page: 10 year: 1993 end-page: 37 ident: BIB9 article-title: Signal processing with higher-order spectra publication-title: IEEE Signal Processing – year: 1989 ident: BIB20 publication-title: VLSI Array Processors – volume: 60 start-page: 65 year: 1997 end-page: 126 ident: BIB10 article-title: Bibliography on higher order statistics publication-title: Signal Processing – volume: 36 start-page: 341 year: 1994 end-page: 354 ident: BIB16 article-title: An array of processors for the real-time estimation of the fourth and lower order moments publication-title: Signal Processing – volume: 42 start-page: 1746 year: 1994 end-page: 1765 ident: BIB3 article-title: Application of higher order spectral analysis to cubically non-linear system identification publication-title: IEEE Transactions on Signal Processing – reference: Y.-T. Hwang, Y.H. Hu, On systolic mapping of multi-stage algorithms, in: Proceedings of International Conference on Application Specific Array Processors, 1992, pp. 47–61 – volume: 33 start-page: 393 year: 1987 end-page: 407 ident: BIB2 article-title: Identification of linear stochastic systems via second- and fourth-order cumulant matching publication-title: IEEE Transactions on Information Theory – reference: J.F. Cardoso, Super-symmetric decomposition of the fourth-order cumulant tensor, blind identification of more sources than sensors, in: Proceedings of ICASSP, 1991, pp. 3109–3112 – volume: 140 start-page: 371 year: 1993 end-page: 379 ident: BIB12 article-title: Analysis of floating point roundoff errors in estimation of higher order statistics publication-title: IEEE Proceedings-F Radar and Signal Processing – reference: DG2VHDL: a tool to facilitate the synthesis of parallel VLSI architectures, http://www.cdsp.neu.edu/info/faculty/manolakos/dg2vhdl_root.html – year: 1996 ident: BIB6 publication-title: Mathematical Statistics for Economics and Business – reference: M. Binder, H. Pesaran, Stochastic growth models and their econometric implications. Journal of Economic Growth 4 (1999) 139–183 – reference: M.J. Hinich, D.M. Patterson, Evidence of nonlinearity in the trade-by-trade stock market return generating process, in: J. Geweke, W.A. Barnett, K. Shell (Eds.), Chaos, Sunspots, Bubbles, and Nonlinearity, Cambridge University Press, New York, 1989, pp. 383–409 – reference: D. Sornette, P. Simonetti, J.V. Andersen, Nonlinear covariance matrix and portofolio theory for non-gaussian multivariate distributions, Research Papers in Economics (RePEc), 1999 – reference: A. Stone, E.S. Manolakos, DG2VHDL: a tool to facilitate the high level synthesis of parallel processing array architectures, Journal of VLSI Signal Processing Systems 24 (1) (Feb. 2000) – volume: 22 start-page: 19 year: 1997 end-page: 23 ident: BIB15 article-title: A high speed systolic array for computing third-order cumulants publication-title: Integration – The VLSI Journal – reference: E.S. Manolakos, H.M. 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IV, 1993, pp. 2310–2313 – volume: 24 start-page: 33 year: 1991 end-page: 43 ident: BIB13 article-title: Parallel processing for biomedical signal processing: higher order spectral analysis – an application publication-title: IEEE Computer – volume: 24 start-page: 1 year: 1997 end-page: 17 ident: BIB14 article-title: A new approach for the design of linear systolic arrays for computing third order cumulants publication-title: Integration – The VLSI Journal – volume: 10 start-page: 283 year: 1996 end-page: 302 ident: BIB17 article-title: Adaptive computation of higher order moments and its systolic realization publication-title: International Journal of Adaptive Control and Signal Processing – reference: E.S. Manolakos, H.M. Stellakis, Systematic synthesis of parallel architectues for the real-time estimation of higher order statitical moments, Parallel Algorithms and Applications (to appear) – reference: H. Nelis, E.F. Deprettere, A Systematic method for mapping algorithms of arbitrarily large dimensions onto fixed size systolic arrays, in: Proceedings of IEEE International Symposium on Circuits and Systems, 1987, pp. 559–563 – reference: J. Bu, E.F. Deprettere, L. Thiele, Systolic array implemenation of nested loop programs, in: Proceedings of IEEE International Conference on ASAP, 1990, pp. 31–42 – reference: A. Stone, E.S. Manolakos, Using DG2VHDL to synthesize an FPGA implementation of the 1-D discrete wavelet transform, in: Proceedings of IEEE Signal Processing Systems (SiPS), 1998, pp. 489–498 – volume: 33 start-page: 393 issue: 3 year: 1987 ident: 10.1016/S0167-8191(99)00125-8_BIB2 article-title: Identification of linear stochastic systems via second- and fourth-order cumulant matching publication-title: IEEE Transactions on Information Theory doi: 10.1109/TIT.1987.1057308 – volume: 42 start-page: 1746 issue: 7 year: 1994 ident: 10.1016/S0167-8191(99)00125-8_BIB3 article-title: Application of higher order spectral analysis to cubically non-linear system identification publication-title: IEEE Transactions on Signal Processing doi: 10.1109/78.298282 – volume: 140 start-page: 371 year: 1993 ident: 10.1016/S0167-8191(99)00125-8_BIB12 article-title: Analysis of floating point roundoff errors in estimation of higher order statistics publication-title: IEEE Proceedings-F Radar and Signal Processing doi: 10.1049/ip-f-2.1993.0055 – ident: 10.1016/S0167-8191(99)00125-8_BIB26 doi: 10.1109/SIPS.1998.715811 – ident: 10.1016/S0167-8191(99)00125-8_BIB1 – ident: 10.1016/S0167-8191(99)00125-8_BIB23 doi: 10.1109/ASAP.1992.218582 – volume: 24 start-page: 1 issue: 1 year: 1997 ident: 10.1016/S0167-8191(99)00125-8_BIB14 article-title: A new approach for the design of linear systolic arrays for computing third order cumulants publication-title: Integration – The VLSI Journal doi: 10.1016/S0167-9260(97)80001-6 – year: 1996 ident: 10.1016/S0167-8191(99)00125-8_BIB6 – volume: 22 start-page: 19 issue: 1 year: 1997 ident: 10.1016/S0167-8191(99)00125-8_BIB15 article-title: A high speed systolic array for computing third-order cumulants publication-title: Integration – The VLSI Journal – ident: 10.1016/S0167-8191(99)00125-8_BIB7 – volume: 10 start-page: 10 issue: 3 year: 1993 ident: 10.1016/S0167-8191(99)00125-8_BIB9 article-title: Signal processing with higher-order spectra publication-title: IEEE Signal Processing doi: 10.1109/79.221324 – ident: 10.1016/S0167-8191(99)00125-8_BIB25 – ident: 10.1016/S0167-8191(99)00125-8_BIB4 doi: 10.1109/ICASSP.1991.150113 – volume: 333B start-page: 349 year: 1996 ident: 10.1016/S0167-8191(99)00125-8_BIB11 article-title: Implementation aspects of various higher-order statistics estimators publication-title: Journal of the Franklin Institure – Engineering and Applied Mathematics doi: 10.1016/0016-0032(96)00022-1 – ident: 10.1016/S0167-8191(99)00125-8_BIB19 – ident: 10.1016/S0167-8191(99)00125-8_BIB21 – ident: 10.1016/S0167-8191(99)00125-8_BIB18 doi: 10.1109/ICASSP.1993.319634 – volume: 36 start-page: 341 issue: 3 year: 1994 ident: 10.1016/S0167-8191(99)00125-8_BIB16 article-title: An array of processors for the real-time estimation of the fourth and lower order moments publication-title: Signal Processing doi: 10.1016/0165-1684(94)90032-9 – volume: 60 start-page: 65 year: 1997 ident: 10.1016/S0167-8191(99)00125-8_BIB10 article-title: Bibliography on higher order statistics publication-title: Signal Processing doi: 10.1016/S0165-1684(97)00065-0 – year: 1989 ident: 10.1016/S0167-8191(99)00125-8_BIB20 – volume: 24 start-page: 33 issue: 3 year: 1991 ident: 10.1016/S0167-8191(99)00125-8_BIB13 article-title: Parallel processing for biomedical signal processing: higher order spectral analysis – an application publication-title: IEEE Computer doi: 10.1109/2.73511 – ident: 10.1016/S0167-8191(99)00125-8_BIB22 doi: 10.1109/ASAP.1990.145440 – ident: 10.1016/S0167-8191(99)00125-8_BIB8 – volume: 10 start-page: 283 issue: 2/3 year: 1996 ident: 10.1016/S0167-8191(99)00125-8_BIB17 article-title: Adaptive computation of higher order moments and its systolic realization publication-title: International Journal of Adaptive Control and Signal Processing doi: 10.1002/(SICI)1099-1115(199603)10:2/3<283::AID-ACS351>3.0.CO;2-B – ident: 10.1016/S0167-8191(99)00125-8_BIB5 doi: 10.1023/A:1009802421114 – ident: 10.1016/S0167-8191(99)00125-8_BIB24 |
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