A Novel Approach to General Linearly Constrained Adaptive Arrays

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  • ABSTRACT

    A novel approach to general linearly constrained adaptive arrays is presented to improve the nulling performance in coherent and noncoherent environments. The narrowband and broadband linearly constrained adaptive arrays are implemented to examine the array performance. It is shown that the proposed approach performs better than the conventional adaptive arrays and the nulling performance depends on the gain factor for the desired response.


  • KEYWORD

    Adaptive array , Sensor , Linear constraint , Narrowband , Broadband , Coherent/noncoherent , Nulling performance

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  • [Fig. 1.] General linearly constrained narrowband adaptive array. LMS: least mean square.
    General linearly constrained narrowband adaptive array. LMS: least mean square.
  • [Fig. 2.] General linearly constrained broadband adaptive array. LMS: least mean square.
    General linearly constrained broadband adaptive array. LMS: least mean square.
  • [Fig. 3.] Variation in the power of the error signal in terms of the gain factor for one coherent signal interference case.
    Variation in the power of the error signal in terms of the gain factor for one coherent signal interference case.
  • [Fig. 4.] Comparison of the array output and desired signal for one coherent signal interference case for 1 ≤ k ≤ 1,000.
    Comparison of the array output and desired signal for one coherent signal interference case for 1 ≤ k ≤ 1,000.
  • [Fig. 5.] Comparison of the array output and desired signal for one coherent signal interference case for 29,001 ≤ k ≤ 30,000.
    Comparison of the array output and desired signal for one coherent signal interference case for 29,001 ≤ k ≤ 30,000.
  • [Fig. 6.] Comparison of the beam patterns for one coherent signal interference case.
    Comparison of the beam patterns for one coherent signal interference case.
  • [Fig. 7.] Variation in the power of the error signal in terms of the gain factor for two coherent signal interference case.
    Variation in the power of the error signal in terms of the gain factor for two coherent signal interference case.
  • [Fig. 8.] Comparison of the array output and desired signal for two coherent signal interference case for 1 ≤ k ≤ 1,000.
    Comparison of the array output and desired signal for two coherent signal interference case for 1 ≤ k ≤ 1,000.
  • [Fig. 9.] Comparison of the array output and desired signal for two coherent signal interference case for 29,001 ≤ k ≤ 30,000.
    Comparison of the array output and desired signal for two coherent signal interference case for 29,001 ≤ k ≤ 30,000.
  • [Fig. 10.] Comparison of the beam patterns for the two-coherent interference case.
    Comparison of the beam patterns for the two-coherent interference case.
  • [Fig. 11.] Variation in the power of the error signal in terms of the gain factor for the one noncoherent interference case.
    Variation in the power of the error signal in terms of the gain factor for the one noncoherent interference case.
  • [Fig. 12.] Comparison of the array output and desired signal for the one noncoherent interference case for 1 ≤ k ≤ 1,000.
    Comparison of the array output and desired signal for the one noncoherent interference case for 1 ≤ k ≤ 1,000.
  • [Fig. 13.] Comparison of the array output and desired signal for the one noncoherent interference case for 29,001 ≤ k ≤ 30,000.
    Comparison of the array output and desired signal for the one noncoherent interference case for 29,001 ≤ k ≤ 30,000.
  • [Fig. 14.] Comparison of the beam patterns for the one noncoherent signal interference case.
    Comparison of the beam patterns for the one noncoherent signal interference case.
  • [Fig. 15.] Variation of the power of the error signal in terms of gain factor for one coherent interference case.
    Variation of the power of the error signal in terms of gain factor for one coherent interference case.
  • [Fig. 16.] Comparison of the array output (solid line) and desired signal (dotted line) for one coherent interference case; (a) g = 0.33, (b) Frost, (c) g = 2, for 1 ≤ k ≤ 1,000.
    Comparison of the array output (solid line) and desired signal (dotted line) for one coherent interference case; (a) g = 0.33, (b) Frost, (c) g = 2, for 1 ≤ k ≤ 1,000.
  • [Fig. 17.] Comparison of the array output (solid line) and desired signal (dotted line) for one coherent interference case; (a) g = 0.33, (b) Frost, (c) g = 2, for 29,001 ≤ k ≤ 30,000.
    Comparison of the array output (solid line) and desired signal (dotted line) for one coherent interference case; (a) g = 0.33, (b) Frost, (c) g = 2, for 29,001 ≤ k ≤ 30,000.
  • [Fig. 18.] Comparison of beam patterns for one coherent interference case at 30° .
    Comparison of beam patterns for one coherent interference case at 30° .
  • [Fig. 19.] Variation in the power of the error signal in terms of the gain factor for the two coherent signal interference case.
    Variation in the power of the error signal in terms of the gain factor for the two coherent signal interference case.
  • [Fig. 20.] Comparison of the array output (solid line) and desired signal (dotted line) for two coherent signal interference case; (a) g = 0.29, (b )Frost, (c) g = 2.0, for 1 ≤ k ≤ 1,000.
    Comparison of the array output (solid line) and desired signal (dotted line) for two coherent signal interference case; (a) g = 0.29, (b )Frost, (c) g = 2.0, for 1 ≤ k ≤ 1,000.
  • [Fig. 21.] Comparison of the array output (solid line) and desired signal (dotted line) for the two coherent signal interference case; (a) g = 0.29, (b) Frost, (c) g = 2.0, for 29,001 ≤ k ≤ 30,000.
    Comparison of the array output (solid line) and desired signal (dotted line) for the two coherent signal interference case; (a) g = 0.29, (b) Frost, (c) g = 2.0, for 29,001 ≤ k ≤ 30,000.
  • [Fig. 22.] Comparison of the beam patterns for the two coherent signal interference case at -54.3° , 57.5° .
    Comparison of the beam patterns for the two coherent signal interference case at -54.3° , 57.5° .
  • [Fig. 23.] Variation in the power of the error signal in terms of the gain factor for one noncoherent interference case.
    Variation in the power of the error signal in terms of the gain factor for one noncoherent interference case.
  • [Fig. 24.] Comparison of array output (solid line) and desired signal (dotted line) for one noncoherent interference case; (a) g = 0.09, (b) Frost, (c) g = 2.0, for 1 ≤ k ≤ 1,000.
    Comparison of array output (solid line) and desired signal (dotted line) for one noncoherent interference case; (a) g = 0.09, (b) Frost, (c) g = 2.0, for 1 ≤ k ≤ 1,000.
  • [Fig. 25.] Comparison of array output (solid line) and desired signal (dotted line) for one noncoherent interference case; (a) g = 0.09, (b) Frost, (c) g = 2.0, for 29,001 ≤ k ≤ 30,000.
    Comparison of array output (solid line) and desired signal (dotted line) for one noncoherent interference case; (a) g = 0.09, (b) Frost, (c) g = 2.0, for 29,001 ≤ k ≤ 30,000.
  • [Fig. 26.] Comparison of the beam patterns for the one noncoherent interference case at -48.5° .
    Comparison of the beam patterns for the one noncoherent interference case at -48.5° .