Summary

Chapter 7 Summary: Antennas and Array Fundamentals

Key Points

• 1.

  Antenna parameters quantify radiation performance: directivity $D$ measures focusing ability, gain $G = \eta D$ includes ohmic losses, and effective area $A_e = G\lambda^{2}/(4\pi)$ links the antenna to the Friis equation. Beamwidth, sidelobe level, and polarization complete the description.

• 2.

  Uniform linear arrays (ULAs) create electronically steerable beams via the array factor $\mathrm{AF}(\theta) = \sum_{n=0}^{N-1} w_n e^{j n k d \sin\theta}$. The steering vector $\mathbf{a}(\theta) \in \mathbb{C}^N$ encodes the spatial signature of direction $\theta$. Half-wavelength spacing avoids grating lobes.

• 3.

  Beamwidth scales as $\lambda/(Nd\cos\theta_0)$: more elements and wider aperture produce narrower beams. Sidelobes are $-13.3$ dB for uniform weights; amplitude tapering (Hanning, Taylor) trades beamwidth for lower sidelobes.

• 4.

  Planar and circular arrays extend beamforming to two dimensions. The UPA array factor separates into azimuth and elevation components. The 3GPP antenna model (TR 38.901) uses dual-polarized UPA panels for 5G NR base station simulations.

• 5.

  The spatial channel model expresses the MIMO channel matrix as $\mathbf{H} = \sum_l \alpha_l\, \mathbf{a}_r(\theta_l)\, \mathbf{a}_t^H(\phi_l)$, linking physical propagation (AoA, AoD, path gain) to the algebraic channel matrix. Angular spread determines the channel rank and spatial multiplexing potential.

• 6.

  Practical considerations include mutual coupling (degrades patterns when $d < \lambda/2$), element pattern versus array pattern, polarization diversity for decorrelation, and the architecture choice among analog, digital, and hybrid beamforming — balancing cost, power, and flexibility.