FPGA Based Parallel Architecture for the Computation of Third-Order Cross Moments
Higher-order Statistics (HOS), also known as
cumulants, cross moments and their frequency domain counterparts,
known as poly spectra have emerged as a powerful signal processing
tool for the synthesis and analysis of signals and systems. Algorithms
used for the computation of cross moments are computationally
intensive and require high computational speed for real-time
applications. For efficiency and high speed, it is often advantageous
to realize computation intensive algorithms in hardware. A promising
solution that combines high flexibility together with the speed of a
traditional hardware is Field Programmable Gate Array (FPGA). In
this paper, we present FPGA-based parallel architecture for the
computation of third-order cross moments. The proposed design is
coded in Very High Speed Integrated Circuit (VHSIC) Hardware
Description Language (VHDL) and functionally verified by
implementing it on Xilinx Spartan-3 XC3S2000FG900-4 FPGA.
Implementation results are presented and it shows that the proposed
design can operate at a maximum frequency of 86.618 MHz.
[1] C. L. Nikias and A. P. Petropulu, Higher-Order Spectra Analysis: A
Nonlinear Signal Processing Framework. Englewood Cliffs, New
Jersey: Prentice Hall, 1993.
[2] S. A. Alshebeili, "Estimation of higher-order moments via discrete
orthogonal laguerre functions," in Proc. of 3rd IEEE Int. Conf. on Signal
Processing, vol. 1, Oct. 1996, pp. 11-14.
[3] P. Paajarvi and J. P. Leblanc, "Online adaptive blind deconvolution
based on third-order moments," IEEE Signal Processing Letters, vol. 12,
No.12, Dec. 2005, pp. 863 ¶Çâ¡ 866.
[4] L. Wenkai, "Blind channel estimation using zero-lag slice of third-order
moment," IEEE Signal Processing Letters, vol.12, No.10, Oct. 2005, pp.
725 ¶Çâ¡ 727.
[5] R. E. Ahmed, M. A. Al-Turaigi, and S. A. Alshebeili, "VLSI
Architecture for computing third-order cumulants," International
Journal of Electronics, vol. 77, No. 1, 1994, pp. 95-104.
[6] M. A. Al-Turaigi and S. A. Alshebeili, "A high-speed systolic array for
computing third-order cumulants," Canadian Journal of Electrical and
Computer Engineering, vol. 22, no. 1, 1997, pp.19-23.
[7] S. A. Alshebeili, "Computation of higher-order cross moments based on
matrix multiplication," Journal of the Franklin Institute, 338, 2001, pp.
811-816.
[8] M. A. Al-Turaigi, R. E. Ahmed, and S. A. Alshebeili, "A concurrent
system for the computation of higher-order moments," Journal of
Circuits, Systems and Signal Processing, vol. 18, no. 2, 1999, pp. 111 ¶Çâ¡
130.
[9] M. A. Aloqeely, M. A. Al-Turaigi, and S. A. Alshebeili, "A new
approach for the design of linear systolic arrays for computing thirdorder
cumulants," Integration: the VLSI Journal, vol. 24, 1997, pp.
1¶Çâ¡17.
[10] H. M. Stellakis and E.S. Manolakos, "Adaptive computation of higher
order moments and its systolic realization," International Journal of
Adaptive Control and Signal Processing, vol. 10, 1996, pp. 283-302.
[11] T. Tuan, S. Kao, A.Rahman, S. Das, and S.Trimberger, " A 90 nm lowpower
FPGA for battery-powered applications," in Proc. of 14th
ACM/SIGDA Int. Symp. on FPGAs, Feb. 2006, pp. 3-11.
[12] S. M. Qasim and S. A. Abbasi, "A Novel FPGA-based approach for
digital waveform generation using orthogonal functions," Journal of
Circuits, Systems and Computers, vol.16, no. 6, 2007, pp. 895-909.
[1] C. L. Nikias and A. P. Petropulu, Higher-Order Spectra Analysis: A
Nonlinear Signal Processing Framework. Englewood Cliffs, New
Jersey: Prentice Hall, 1993.
[2] S. A. Alshebeili, "Estimation of higher-order moments via discrete
orthogonal laguerre functions," in Proc. of 3rd IEEE Int. Conf. on Signal
Processing, vol. 1, Oct. 1996, pp. 11-14.
[3] P. Paajarvi and J. P. Leblanc, "Online adaptive blind deconvolution
based on third-order moments," IEEE Signal Processing Letters, vol. 12,
No.12, Dec. 2005, pp. 863 ¶Çâ¡ 866.
[4] L. Wenkai, "Blind channel estimation using zero-lag slice of third-order
moment," IEEE Signal Processing Letters, vol.12, No.10, Oct. 2005, pp.
725 ¶Çâ¡ 727.
[5] R. E. Ahmed, M. A. Al-Turaigi, and S. A. Alshebeili, "VLSI
Architecture for computing third-order cumulants," International
Journal of Electronics, vol. 77, No. 1, 1994, pp. 95-104.
[6] M. A. Al-Turaigi and S. A. Alshebeili, "A high-speed systolic array for
computing third-order cumulants," Canadian Journal of Electrical and
Computer Engineering, vol. 22, no. 1, 1997, pp.19-23.
[7] S. A. Alshebeili, "Computation of higher-order cross moments based on
matrix multiplication," Journal of the Franklin Institute, 338, 2001, pp.
811-816.
[8] M. A. Al-Turaigi, R. E. Ahmed, and S. A. Alshebeili, "A concurrent
system for the computation of higher-order moments," Journal of
Circuits, Systems and Signal Processing, vol. 18, no. 2, 1999, pp. 111 ¶Çâ¡
130.
[9] M. A. Aloqeely, M. A. Al-Turaigi, and S. A. Alshebeili, "A new
approach for the design of linear systolic arrays for computing thirdorder
cumulants," Integration: the VLSI Journal, vol. 24, 1997, pp.
1¶Çâ¡17.
[10] H. M. Stellakis and E.S. Manolakos, "Adaptive computation of higher
order moments and its systolic realization," International Journal of
Adaptive Control and Signal Processing, vol. 10, 1996, pp. 283-302.
[11] T. Tuan, S. Kao, A.Rahman, S. Das, and S.Trimberger, " A 90 nm lowpower
FPGA for battery-powered applications," in Proc. of 14th
ACM/SIGDA Int. Symp. on FPGAs, Feb. 2006, pp. 3-11.
[12] S. M. Qasim and S. A. Abbasi, "A Novel FPGA-based approach for
digital waveform generation using orthogonal functions," Journal of
Circuits, Systems and Computers, vol.16, no. 6, 2007, pp. 895-909.
@article{"International Journal of Electrical, Electronic and Communication Sciences:56569", author = "Syed Manzoor Qasim and Shuja Abbasi and Saleh Alshebeili and Bandar Almashary and Ateeq Ahmad Khan", title = "FPGA Based Parallel Architecture for the Computation of Third-Order Cross Moments", abstract = "Higher-order Statistics (HOS), also known as
cumulants, cross moments and their frequency domain counterparts,
known as poly spectra have emerged as a powerful signal processing
tool for the synthesis and analysis of signals and systems. Algorithms
used for the computation of cross moments are computationally
intensive and require high computational speed for real-time
applications. For efficiency and high speed, it is often advantageous
to realize computation intensive algorithms in hardware. A promising
solution that combines high flexibility together with the speed of a
traditional hardware is Field Programmable Gate Array (FPGA). In
this paper, we present FPGA-based parallel architecture for the
computation of third-order cross moments. The proposed design is
coded in Very High Speed Integrated Circuit (VHSIC) Hardware
Description Language (VHDL) and functionally verified by
implementing it on Xilinx Spartan-3 XC3S2000FG900-4 FPGA.
Implementation results are presented and it shows that the proposed
design can operate at a maximum frequency of 86.618 MHz.", keywords = "Cross moments, Cumulants, FPGA, Hardware Implementation.", volume = "2", number = "2", pages = "254-5", }