Chapter Summary

Chapter Summary

Key Points

• 1.

  The steering vector is the foundation. $\mathbf{a}(\theta) = [1, e^{j\phi}, \dots, e^{j(N-1)\phi}]$ where $\phi = 2\pi d\sin\theta/\lambda$. With $d = \lambda/2$, no grating lobes, beamwidth $\approx 102°/N$, array gain $= N$.

• 2.

  Bartlett scans, Capon adapts, MUSIC super-resolves. Bartlett is simple but resolution-limited. Capon inverts $\mathbf{R}_{xx}$ for adaptive nulling. MUSIC exploits the noise subspace eigenstructure for super-resolution DOA estimation.

• 3.

  Hybrid beamforming makes mmWave practical. Split into analog (phase shifters, constant modulus) and digital (baseband) stages with $N_{\text{RF}} \ll N_t$ RF chains. DFT codebooks provide systematic beam design.

• 4.

  Always validate with sufficient snapshots. Capon and MUSIC need $L \gg N$ snapshots for accurate covariance estimation. Diagonal loading improves robustness of Capon in low-snapshot regimes.