Direct Inversion of the Sample Covariance Matrix

Direct Inversion of the Sample Covariance Matrix

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The usefulness of an adaptive array often depends on its convergence rate. For example, when adaptive radars simultaneously reject jamming and clutter while providing automatic platform motion compensation, then rapid convergence to steady-state solutions is essential. Convergence of adaptive sensor arrays using the popular maximum signal-to-noise ratio (SNR) or least mean squares (LMS) algorithms depend on the eigenvalues of the noise covariance matrix. When the covariance matrix eigenvalues differ by orders of magnitude, then convergence is exceedingly long and highly example dependent. One way to speed convergence and circumvent the convergence rate dependence on eigenvalue distribution is to directly compute the adaptive weights using the sample covariance matrix of the signal environment.

Chapter Contents:

  • 5.1 The Direct Matrix Inversion (DMI) Approach
  • 5.2 Diagonal Loading of the Sample Covariance Matrix
  • 5.3 Factorization Methods
  • 5.4 Transient Response Comparisons
  • 5.5 Sensitivity to Eigenvalue Spread
  • 5.6 Summary and Conclusions
  • 5.7 Problems
  • 5.8 References

Inspec keywords: matrix inversion; least mean squares methods; covariance matrices; array signal processing; jamming; adaptive antenna arrays; radar clutter; motion compensation

Other keywords: adaptive array; convergence rate; direct inversion; adaptive sensor arrays; radar jamming; eigenvalue distribution; adaptive radars; sample covariance matrix; radar clutter; signal-tonoise ratio; noise covariance matrix; least mean squares algorithms; motion compensation

Subjects: Linear algebra (numerical analysis); Antenna arrays; Signal processing and detection; Interpolation and function approximation (numerical analysis)

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