Prerequisites & Notation

Prerequisites for This Chapter

  • Electromagnetic scattering and the Born approximation(Review ch06)

    Self-check: Can you write the Born-approximation integral relating the reflectivity function to the scattered field?

  • The sensing matrix A\mathbf{A} and the forward model y=Ac+w\mathbf{y} = \mathbf{A}\mathbf{c} + \mathbf{w}(Review ch07)

    Self-check: Can you construct A\mathbf{A} for a monostatic radar with NtN_t antennas and NfN_f frequencies?

  • Wireless channel models (path loss, fading, multipath)(Review ch06)

    Self-check: Can you describe the Rayleigh and Rician fading models and their physical origin?

•

Born approximation, Green's function, scattering integral.

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Sensing operator construction, Kronecker structure, spatial sampling.

Notation and Conventions

The following notation is used throughout this chapter. All symbols follow the conventions established in Chapters 6-7, with extensions for scene representation and channel model variations.

SymbolMeaningIntroduced
c(p)c(\mathbf{p})Complex reflectivity function at position p\mathbf{p}
c\mathbf{c}Discretized reflectivity vector [c(p1),…,c(pQ)]T[c(\mathbf{p}_{1}), \ldots, c(\mathbf{p}_{Q})]^T
ci,j,qc_{i,j,q}Scattering coefficient for Tx ii, Rx jj, voxel qq
γi,j,q\gamma_{i,j,q}Scattering power (variance of ci,j,qc_{i,j,q})
A\mathbf{A}Sensing matrix
y\mathbf{y}Observation vector: y=Ac+w\mathbf{y} = \mathbf{A}\mathbf{c} + \mathbf{w}
κ\kappaWavenumber: κ=2π/λ\kappa = 2\pi/\lambda
Ω\OmegaTarget region in space
αk\alpha_kComplex reflectivity of kk-th point scatterer
χ(p)\chi(\mathbf{p})Contrast function: εr(p)−1\varepsilon_r(\mathbf{p}) - 1
Γ\GammaReflection coefficient (wall, surface)
σRCS\sigma_{\text{RCS}}Radar cross-section
← Ch 7Scene Representations