Prerequisites & Notation

Before You Begin

This chapter develops the MIMO radar concept and shows how waveform diversity creates a virtual aperture that dramatically enlarges the sensing matrix A\mathbf{A}. We build from single-antenna radar (Chapter 7) and the sensing operator framework (Chapter 8) to the multi-transmit, multi-receive, multi-frequency case that underpins our research problem.

Prerequisites:

  • Radar equation and matched filtering(Review ch07)

    Self-check: Can you write the radar range equation and explain why matched filtering maximises SNR?

  • Array steering vectors and beamforming(Review ch08)

    Self-check: Can you write the steering vector a(θ)\mathbf{a}(\theta) for a ULA and derive the beamwidth?

  • The sensing operator and Kronecker structure(Review ch08)

    Self-check: Can you explain why A\mathbf{A} has Kronecker structure when spatial and frequency responses separate?

Notation for This Chapter

Symbols introduced or specialised in this chapter. See also the global notation table in the front matter.

SymbolMeaningIntroduced
NtN_tNumber of transmit antennass01
NrN_rNumber of receive antennass01
NvN_vNumber of virtual array elements (=NtNr= N_t N_r)s01
a(θ)\mathbf{a}(\theta)Transmit steering vectors01
a^(θ)\hat{\mathbf{a}}(\theta)Receive steering vectors01
aV(θ)\mathbf{a}_V(\theta)Virtual array steering vector (=a(θ)⊗a^(θ)= \mathbf{a}(\theta) \otimes \hat{\mathbf{a}}(\theta))s01
si\mathbf{s}_{i}Position of transmitter iis01
rj\mathbf{r}_{j}Position of receiver jjs01
p\mathbf{p}Target / voxel positions03
κ\kappaWavenumber 2π/λ2\pi / \lambdas03
κs,r\kappa_{\mathbf{s},\mathbf{r}}Combined Tx-Rx wavenumber vectors03
A\mathbf{A}MIMO sensing matrixs04
c\mathbf{c}Discretised reflectivity vectors04
w\mathbf{w}Noise vectors04
f0f_0Carrier frequencys03
WWSignal bandwidths03
← Ch 10MIMO Radar Concept