Prerequisites & Notation

Before You Begin

This chapter requires linear algebra (Chapter 6), signal processing (Chapter 7), and MIMO channel concepts (Chapter 21).

  • Eigendecomposition and matrix inversion (Chapter 6)(Review ch06)

    Self-check: Can you compute eigenvalues with np.linalg.eigh?

  • FFT and spectral analysis (Chapter 7)(Review ch07)

    Self-check: Can you compute and interpret a power spectrum?

  • MIMO channels and array geometry (Chapter 21)(Review ch21)

    Self-check: Do you know the relationship between antenna spacing and spatial correlation?

Notation for This Chapter

Array processing notation.

SymbolMeaningIntroduced
mathbfa(theta)\\mathbf{a}(\\theta)Array steering vector for direction θ\thetas01
NNNumber of array elementss01
ddInter-element spacings01
lambda\\lambdaWavelengths01
mathbfRxx\\mathbf{R}_{xx}Array covariance matrixs02
mathbfw\\mathbf{w}Beamforming weight vectors02
P(theta)P(\\theta)Spatial power spectrums02
← Ch 23Array Response and Steering Vectors