Prerequisites & Notation

Before You Begin

Integrated sensing and communications (ISAC) is a 6G cornerstone: one waveform, one hardware, two services. Adding RIS to ISAC expands both the sensing and the communication footprint. This chapter assumes fluency with the joint optimization framework (Ch. 5-7) and basic radar concepts (matched filter, CFAR). It develops the ISAC-specific optimization with a RIS in the loop and culminates in the CommIT RIS-ISAC beamforming framework.

  • Joint active-passive beamforming (Ch. 5-7)(Review ch05)

    Self-check: Recall the AO framework and its outer-inner structure for MU-RIS.

  • Radar fundamentals: matched filter, CFAR, ambiguity function(Review ch29)

    Self-check: Derive the matched-filter output SNR for a target with radar cross-section (RCS).

  • ISAC waveform design(Review ch29)

    Self-check: State the key tradeoff between radar-ambiguity-function sidelobes and communication-spectral-efficiency.

  • Cramér-Rao bound (CRB) for parameter estimation(Review ch11)

    Self-check: For Gaussian observation y=hθ+w\mathbf{y} = \mathbf{h}\theta + \mathbf{w}, what is the CRB on θ\theta?

  • Semidefinite relaxation and manifold optimization(Review ch06)

    Self-check: Recall the SDR lift for unit-modulus QCQP.

Notation for This Chapter

ISAC-specific notation on top of the single-RIS conventions. Sensing-side metrics (beampattern, CRB) coexist with communication-side metrics (SINR, rate).

SymbolMeaningIntroduced
t\mathbf{t}Radar target position (Cartesian coords)s01
σt\sigma_tRadar cross-section (RCS) of the targets02
PrsensP_r^{\text{sens}}Received sensing power (radar return)s02
SNRsens\text{SNR}_{\text{sens}}Sensing SNR: Prsens/σ2P_r^{\text{sens}} / \sigma^2s02
SNRcomm\text{SNR}_{\text{comm}}Per-user communication SINRs02
Pdes(θ)P_{\text{des}}(\boldsymbol{\theta})Desired radar beampattern (power as function of angle)s03
γcomm\gamma_{\text{comm}}Communication QoS threshold (minimum SINR)s03
γsens\gamma_{\text{sens}}Sensing beampattern MSE thresholds03
a(θ)\mathbf{a}(\boldsymbol{\theta})Steering vector at radar angle θ\boldsymbol{\theta}s02