Prerequisites & Notation

Prerequisites

This chapter synthesises the entire book, connecting RF imaging to channel estimation, networked sensing, and communication system optimisation. The reader should be comfortable with the imaging forward model, sparse recovery algorithms, and deep unfolding.

  • MIMO radar and virtual aperture (Chapter 11)(Review ch11)

    Self-check: Can you write the MIMO radar sensing matrix and explain virtual aperture extension?

  • Sparse reconstruction: LASSO, ADMM, group sparsity (Chapter 14)(Review ch14)

    Self-check: Can you formulate and solve the LASSO problem for imaging?

  • Learned OAMP and deep unfolding (Chapter 18)(Review ch18)

    Self-check: Can you explain how unrolled OAMP learns denoisers and step sizes?

  • ISAC fundamentals: CRB-rate tradeoff, waveform design (Chapter 29)(Review ch29)

    Self-check: Can you state the CRB-rate Pareto frontier for ISAC waveform design?

Chapter Notation

Notation specific to Chapter 30. Standard symbols (A\mathbf{A}, c\mathbf{c}, w\mathbf{w}) retain their meaning from earlier chapters.

SymbolMeaningIntroduced
had\mathbf{h}_{\mathrm{ad}}Sparse angular-delay channel vector
Φ\boldsymbol{\Phi}Pilot sensing matrix for channel estimation
Ag\mathbf{A}_{g}Local sensing matrix at node gg
σ\boldsymbol{\sigma}Scene reflectivity vector (distributed imaging)
G=(V,E)\mathcal{G} = (\mathcal{V}, \mathcal{E})Communication graph connecting sensing nodes
γ\gammaGraph spectral gap (consensus convergence rate)
ρ\rhoADMM penalty parameter
H^DT\hat{\mathbf{H}}_{\mathrm{DT}}Digital twin predicted channel
ηpilot\eta_{\mathrm{pilot}}Pilot overhead fraction
Jimg\mathcal{J}_{\mathrm{img}}Imaging quality objective (e.g., NMSE, SSIM)
← Ch 29Channel Estimation as Imaging