Summary

Chapter 27 Summary: Millimeter-Wave and Sub-THz Communications

Key Points

• 1.

  mmWave Propagation and the CI Path Loss Model. The close-in (CI) model $PL^{CI}(f,d) = \text{FSPL}(f,1\,\text{m}) + 10n\log_{10}(d) + X_\sigma$ provides a physically grounded, single-parameter characterisation of mmWave path loss. The PLE is remarkably stable across frequencies when the FSPL anchor is used: $n \approx 2.0$ (LOS) and $n \approx 3.0$--$3.5$ (NLOS) for urban micro-cell environments at 28--73 GHz. Blockage by human bodies (20--40 dB), vehicles, and buildings is the dominant impairment, modelled by the exponential LOS probability $p_\text{LOS}(d) = e^{-\beta d}$.

• 2.

  Hybrid Beamforming Architectures. Full digital beamforming is impractical at mmWave due to the power consumption and cost of wideband RF chains. Hybrid analog-digital architectures split precoding into a phase-shifter-based analog stage $\mathbf{F}_\text{RF}$ (unit-modulus constrained) and a low-dimensional digital stage $\mathbf{F}_\text{BB}$, using $N_\text{RF} \ll N_t$ RF chains. The OMP-based algorithm exploits mmWave channel sparsity to select analog beamforming vectors from a dictionary, achieving within 1--3 dB of the fully digital baseline when $N_\text{RF} \geq 2N_s$.

• 3.

  Beam Management in 5G NR. High-gain directional beams are essential at mmWave but must be accurately pointed. 5G NR defines a hierarchical beam management framework: SSB beam sweeping (P1) for initial acquisition, CSI-RS refinement (P2/P3) for narrowing, and periodic tracking for mobility. Hierarchical codebooks reduce the beam search overhead from $N$ to $2\log_2 N$ measurements. Beam failure recovery handles blockage-induced outages through candidate beam identification and rapid re-establishment, with typical interruption times of 30--80 ms.

• 4.

  FR3 Upper Mid-Band Spectrum (7--24 GHz). The upper mid-band, designated FR3 by 3GPP, offers a sweet spot between the coverage of sub-6 GHz and the capacity of mmWave. Frequencies at 7--24 GHz provide 500 MHz--2 GHz of bandwidth, meaningful diffraction around obstacles, and tolerable outdoor-to-indoor penetration (5--10 dB through standard glass). WRC-23 identified several FR3 bands for IMT, but coexistence with incumbent radar, satellite, and fixed wireless services requires protection distances and transmit power limits.

• 5.

  Sub-THz Communications (100--300 GHz). Sub-THz frequencies promise 10--50 GHz of bandwidth per carrier but face atmospheric absorption peaks (O$_2$ at 60 GHz, H$_2$O at 183 GHz), extreme path loss, and severe hardware limitations (PA efficiency below 5--8%, high phase noise). Transmission windows at 75--110 GHz (W-band) and 130--175 GHz (D-band) offer manageable atmospheric loss for short-range links.

• 6.

  Near-Field MIMO and Beam Focusing. At sub-THz frequencies, the Fraunhofer distance $d_F = 2D^2/\lambda$ can reach tens of metres for large arrays, placing most links in the radiative near field. The spherical-wave channel model replaces the far-field plane-wave assumption, enabling beam focusing (energy concentrated at a specific 3D point) and spatial multiplexing in pure LOS. The number of near-field spatial degrees of freedom scales as $D^2/(4\lambda d_0)$, potentially reaching hundreds for large arrays at short range — a qualitative departure from far-field MIMO.