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Extending the concept of IIR filtering to array processing using approximate spatial IIR structure

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Abstract

Various array processing techniques applied to uniform linear arrays are involuntarily realized using structures that are analogous to finite impulse response filters. This observation leads to the following question: “can we extend infinite impulse response (IIR) filtering to array processing?”. In this paper, we introduce the concept of IIR array in spatial domain. Note that IIR array here does not mean time-domain IIR filtering for array beamforming which is commonly understood. This paper is dedicated to the study of an alternate approach for array signal processing which defines IIR structure in spatial domain. To illustrate the applicability of the concept of IIR array, we propose a new direction-of-arrival estimation technique as well as a beamformer with the spatial domain IIR array implementation. The performance of the proposed methods are comparable to the existing techniques. These illustrations are intended to introduce a new approach which potentially can offer more degrees of freedom to control the performance of the array and reduce the complexity of the system for a desired performance.

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References

  • Capon J. (1969) High-resolution frequency-wavenumber spectrum analysis. Proceedings of the IEEE 57(8): 1408–1418

    Article  Google Scholar 

  • Godara L. C. (1997) Application of antenna arrays to mobile communications. ii. beam-forming and direction-of-arrival considerations. Proceedings of the IEEE 85(8): 1195–1245

    Article  Google Scholar 

  • Ko C., Li C. (1994) An adaptive IIR structure for the separation, enhancement, and tracking of multiple sinusoids. IEEE Transactions on Signal Processing 42(10): 2832–2834

    Article  Google Scholar 

  • Krim H., Viberg M. (1996) Two decades of array signal processing research: The parametric approach. IEEE Signal Processing Magazine 13(4): 67–94

    Article  Google Scholar 

  • Liu, Y., & Lin, Z. (2004). Active array beamforming using the frequency-response masking technique. In Proceedings of the International Symposium on Circuits System ISCAS, (pp. 197–200).

  • Liu Y., Lin Z. (2006) On the applications of the frequency-response masking technique in array beamforming. Circuits, Systems and Signal Processing 25(2): 201–224

    Article  MathSciNet  MATH  Google Scholar 

  • Nehorai A. (1985) A minimal parameter adaptive notch filter with constrained poles and zeros. IEEE Transactions on Acoustics Speech and Signal Processing 33(4): 983–996

    Article  Google Scholar 

  • Pei S., Tseng C. (1994) Complex adaptive IIR notch filter algorithm and its applications. IEEE Transactions on Circuits and Systems Part II: Analog and Digital Signal Processing 41(2): 158–163

    Google Scholar 

  • Roy R., Kailath T. (1989) Esprit-estimation of signal parameters via rotational invariance techniques. IEEE Transactions on Acoustics Speech and Signal Processing 37(7): 984–995

    Article  Google Scholar 

  • Schmidt R. (1986) Multiple emitter location and signal parameter estimation. IEEE Transactions on Antennas and Propagation 34(3): 276–280

    Article  Google Scholar 

  • Shynk J. (1986) A complex adaptive algorithm for IIR filtering. IEEE Transactions on Acoustics Speech and Signal Processing 34(5): 1342–1344

    Article  Google Scholar 

  • Stoica P., Nehorai A. (1988) Performance analysis of an adaptive notch filter with constrained poles and zeros. IEEE Transactions on Acoustics Speech and Signal Processing 36(6): 911–919

    Article  MathSciNet  MATH  Google Scholar 

  • Therrien C. (1992) Discrete random signals and statistical signal processing. Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

  • Trees H. L. V. (2002) Detection, estimation, and modulation theory, part IV, optimum array processing. Wiley, New York

    Google Scholar 

  • Tseng C., Pei S. (2001) Stable IIR notch filter design with optimal pole placement. IEEE Transactions on Signal Processing 49(11): 2673–2681

    Article  MathSciNet  Google Scholar 

  • Vaidyanathan, P. P., & Weng C. (2010) Active beamforming with interpolated FIR filtering. In Proceedings of International Symposium on Circuits System ISCAS, (pp. 173–176).

  • Van Veen B. D., Buckley K. M. (1988) Beamforming: A versatile approach to spatial filtering. IEEE ASSP Magazine 5(2): 4–24

    Article  Google Scholar 

  • Xiao Y., Takeshita Y., Shida K. (2001) Steady-state analysis of a plain gradient algorithm for a second-order adaptive IIR notch filter with constrained poles and zeros. IEEE Transactions on Circuits and Systems Part II: Analog and Digital Signal Processing 48(7): 733–740

    MATH  Google Scholar 

  • Xiao, Y., Ma, L., & Khorasani, K. (2004). A novel wideband doa estimation technique based on harmonic source model for a uniform linear array. In Proceedings of International Symposium on Circuits and Systems ISCAS ’04, (Vol. 3).

  • Xiao Y., Ma L., Khorasani K., Ikuta A. (2005) Statistical performance of the memoryless nonlinear gradient algorithm for the constrained adaptive IIR notch filter. IEEE Transactions on Circuits and Systems I: Regular Papers 52(8): 1691–1702

    Article  Google Scholar 

  • Zhou J., Li G. (2004) Plain gradient based direct frequency estimation using second-order constrained adaptive IIR notch filter. Electronics Letters 40(5): 351–352

    Article  Google Scholar 

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Correspondence to Fuxi Wen.

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Wen, F., Ng, B.P. & Reddy, V.V. Extending the concept of IIR filtering to array processing using approximate spatial IIR structure. Multidim Syst Sign Process 24, 157–179 (2013). https://doi.org/10.1007/s11045-011-0163-2

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  • DOI: https://doi.org/10.1007/s11045-011-0163-2

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