Ferkans — Interactive Telecom Tutor

Why Millimeter Waves?

The sub-6 GHz spectrum that powered four generations of cellular systems is nearly exhausted. Millimeter-wave (mmWave) bands — loosely defined as 24–100 GHz — offer an order of magnitude more bandwidth. A single mmWave carrier at 28 GHz can deliver 400–800 MHz of contiguous spectrum, compared to 20 MHz typical at 2 GHz. This abundance of bandwidth is the primary driver for mmWave adoption in 5G NR (FR2), fixed wireless access, and backhaul.

The price paid for this bandwidth is severe: free-space path loss scales as $f^2$ , diffraction is negligible, and most building materials become nearly opaque. Understanding these propagation challenges is essential before designing link budgets, beamforming, and beam management procedures.

Definition:
Close-In (CI) Free-Space Reference Distance Path Loss Model

The close-in (CI) path loss model uses a 1-metre free-space reference distance and a single-parameter fit for the path-loss exponent (PLE):

$PL^{CI}(f,d)\;[\text{dB}] = \underbrace{32.4 + 20\log_{10}(f_{\text{GHz}})}_{\text{FSPL}(f,1\,\text{m})} + 10\,n\,\log_{10}(d) + X_\sigma$

where:

$f_{\text{GHz}}$ is the carrier frequency in GHz,
$d$ is the 3D Tx–Rx separation in metres ( $d \geq 1$ m),
$n$ is the path-loss exponent (PLE), fit by minimum mean-square error (MMSE) regression to measurement data,
$X_\sigma \sim \mathcal{N}(0, \sigma^2)$ is the shadow fading (dB) with standard deviation $\sigma$ .

The CI model is physically anchored: at $d = 1$ m it reduces to the theoretical free-space path loss, and the single parameter $n$ captures all environment-dependent propagation effects. This makes the model robust, parsimonious, and frequency-stable across the entire mmWave range.

The competing ABG (alpha-beta-gamma) model used by 3GPP has three floating parameters and can exhibit unphysical behaviour at short distances. The CI model with its single-parameter PLE is preferred for its physical grounding and stability across frequencies (Rappaport et al., 2015).

,

Measured Path-Loss Exponents Across Frequencies and Environments

Extensive measurement campaigns at NYU Wireless, Nokia Bell Labs, and other groups have established the following representative PLE and shadow fading values for the CI model:

Environment	Condition	$n$	$\sigma$ (dB)	Frequencies
UMi street canyon	LOS	1.98–2.1	3.1–4.2	28, 39, 73 GHz
UMi street canyon	NLOS	3.2–3.5	8.0–9.7	28, 39, 73 GHz
UMa	LOS	2.0	4.0	28, 73 GHz
UMa	NLOS	2.9–3.4	7.8–9.6	28, 73 GHz
InH office	LOS	1.6–1.8	1.2–3.6	28, 73, 140 GHz
InH office	NLOS	2.7–3.2	8.7–11.3	28, 73, 140 GHz
InH shopping mall	LOS	1.7–1.9	2.0–3.0	28, 39 GHz

Two key observations: (1) the PLE is remarkably stable across frequency when the CI model is used — most of the frequency dependence is captured by the FSPL $(f,1\,\text{m})$ anchor; (2) NLOS PLEs are significantly higher ( $n \approx 3$ – $3.5$ ) than LOS ( $n \approx 2$ ), reflecting the absence of diffraction at mmWave.

CI Model Path Loss Across Frequencies

Compare close-in path loss predictions for different carrier frequencies and environments. Adjust the frequency to see the FSPL anchor shift, and the environment to change the path-loss exponent and shadow fading standard deviation. Environment 1 = UMi-LOS ( $n=2.0$ , $\sigma=3.6$ dB), 2 = UMi-NLOS ( $n=3.4$ , $\sigma=9.0$ dB), 3 = InH-LOS ( $n=1.7$ , $\sigma=2.5$ dB).

Parameters

f

(GHz)28

Environment1

d_\text{max}

(m)200

Blockage — The Dominant Impairment at mmWave

At sub-6 GHz frequencies, signals diffract around obstacles and penetrate building walls with modest loss. At mmWave frequencies, the wavelength ( $\lambda \approx 5$ – $11$ mm at 28–60 GHz) is far smaller than most obstacles, so diffraction provides negligible relief. Blockage by human bodies, vehicles, and buildings causes abrupt shadowing events of 15–40 dB lasting hundreds of milliseconds. This makes blockage the single most important channel impairment at mmWave and sub-THz frequencies.

Three categories of blockage must be modelled:

Self-blockage: The user's own body blocks certain angular sectors (typically 120° azimuth behind the hand-held device).
Dynamic blockage: Pedestrians, vehicles, and other moving objects intermittently obstruct the link.
Static blockage: Buildings and permanent structures create NLOS conditions.

Theorem: Exponential Blockage Model

Consider a random field of blockers modelled as a Boolean line process with spatial density $\lambda_B$ (blockers/m²), each of width $w$ and height drawn from a distribution. For a link of length $d$ at height $h_{\text{link}}$ , the probability that the LOS path is not blocked (i.e., the LOS probability) is approximately:

$p_{\text{LOS}}(d) = e^{-\beta\, d}$

where the blockage parameter $\beta$ depends on the blocker density, width, and height distribution:

$\beta = \lambda_B\, w\, \mathbb{E}\!\left[\max\!\left(0,\; h_B - h_{\text{link}} \cdot \frac{r}{d}\right)\right]$

Here $h_B$ is the blocker height and $r$ is the distance from Tx to the blocker. For a simplified model with uniform blocker heights exceeding the link height:

$\beta \approx \lambda_B\, w$

The blockage probability (NLOS probability) is therefore:

$p_{\text{NLOS}}(d) = 1 - e^{-\beta\, d}$

As the link distance $d$ increases, the signal must pass through a longer corridor of potential blockers. Each additional metre of path independently risks encountering a blocker (a Poisson-like argument), leading to the exponential decay of the LOS probability. Dense environments ( $\lambda_B \uparrow$ ) and wide blockers ( $w \uparrow$ ) both increase $\beta$ and make NLOS conditions more likely.

Proof

Poisson Boolean Model Derivation

Model the positions of blocker centres as a 2D homogeneous Poisson point process (PPP) with intensity $\lambda_B$ . A blocker at position $(x, y)$ obstructs the direct path from Tx to Rx if it intersects the line segment connecting them.

For a blocker of width $w$ oriented uniformly at random, the probability that it intersects a line of length $d$ passing within distance $w/2$ of its centre is proportional to $w\,d$ in the thinning of the PPP.

The number of blockers intersecting the LOS path follows a Poisson distribution with mean $\mu = \lambda_B \cdot w \cdot d$ . The probability of zero intersecting blockers is:

$p_{\text{LOS}}(d) = \Pr(N_{\text{block}} = 0) = e^{-\mu} = e^{-\lambda_B w d} = e^{-\beta d}.$

$\blacksquare$

Human-Body Shadowing Loss

Measurements at 28 GHz show that a single human body crossing the direct path causes 20–35 dB of attenuation. At 73 GHz the loss is 25–40 dB due to the smaller Fresnel zone. The shadowing event lasts $\sim$ 200–500 ms for a pedestrian walking at 1 m/s across a beam of 10° half-power beamwidth at 10 m range.

These deep, abrupt fades are fundamentally different from Rayleigh fading (which averages over many scatterers) and require dedicated countermeasures: beam tracking to find alternative paths, multi-panel diversity, or multi-connectivity to fall back to a sub-6 GHz anchor carrier.

Outdoor-to-indoor penetration is similarly severe at mmWave: modern low-emissivity (Low-E) glass attenuates 28 GHz signals by 30–40 dB, and concrete walls add 20–50 dB. This effectively eliminates outdoor-to-indoor coverage at mmWave, requiring dedicated indoor small cells.

Material	28 GHz loss (dB)	73 GHz loss (dB)
Clear glass	3–5	5–8
Low-E glass (IRR)	30–40	35–45
Drywall	5–7	6–9
Concrete (15 cm)	20–35	30–50
Brick	15–28	25–40
Human body	20–35	25–40

LOS Probability Decay Animation

Watch how the LOS probability

p_\text{LOS}(d) = e^{-\beta d}

decays with distance for different blocker densities. Higher blocker density causes faster decay, pushing the LOS/NLOS transition closer to the transmitter.

LOS probability versus distance for three blocker densities

\beta = 0.005

,

0.01

, and

0.02

m

^{-1}

, showing the exponential decay that dominates mmWave link reliability.

Blockage Outage Probability

Visualise the LOS probability $p_\text{LOS}(d) = e^{-\lambda_B w d}$ as a function of link distance for different blocker densities and widths. The plot also shows the resulting effective path loss (weighted average of LOS and NLOS CI models) to illustrate how blockage degrades the average link budget.

Parameters

\lambda_B

(blockers/m²)0.01

Blocker width (m)0.5

f

(GHz)28

Example: 28 GHz Outdoor Small-Cell Link Budget

A 5G NR small cell operating at $f = 28$ GHz has the following parameters:

Transmit power: $P_t = 30$ dBm (1 W)
Bandwidth: $B = 400$ MHz
Tx antenna: $N_t = 256$ -element UPA, gain $G_t = 24$ dBi
Rx antenna: $N_r = 16$ -element UPA, gain $G_r = 12$ dBi
Noise figure: $NF = 7$ dB
Target distance: $d = 150$ m, UMi-LOS ( $n = 2.0$ , $\sigma = 3.6$ dB)

(a) Compute the path loss using the CI model.

(b) Compute the received SNR.

(c) Estimate the achievable throughput assuming 256-QAM with rate-3/4 coding (spectral efficiency $\eta = 6$ bps/Hz) and a 10 dB SNR margin for blockage and fading.

Solution

FSPL anchor at 1 m

$\text{FSPL}(28\,\text{GHz}, 1\,\text{m}) = 32.4 + 20\log_{10}(28) = 32.4 + 28.9 = 61.3\;\text{dB}$ $

CI path loss (mean)

$PL^{CI} = 61.3 + 10 \times 2.0 \times \log_{10}(150) = 61.3 + 20 \times 2.176 = 61.3 + 43.5 = 104.8\;\text{dB}$ $

Thermal noise power

$N_0 = -174 + 10\log_{10}(400 \times 10^6) + NF = -174 + 86.0 + 7 = -81.0\;\text{dBm}$ $

Received SNR

$\text{SNR} = P_t + G_t + G_r - PL - N_0KATEXPLACEHOLDER0END= 30 + 24 + 12 - 104.8 - (-81.0) = 42.2\;\text{dB}$ $After subtracting a 10 dB margin for blockage/fading:$ \text{SNR}_{\text{eff}} = 32.2$ dB.

Achievable throughput

With 256-QAM rate-3/4 ( $\eta = 6$ bps/Hz) and 400 MHz bandwidth:

$R = \eta \times B = 6 \times 400 \times 10^6 = 2.4\;\text{Gbps}$

Even with the Shannon bound $R = B\log_2(1 + \text{SNR}_{\text{lin}}) = 400 \times \log_2(1 + 10^{3.22}) \approx 400 \times 10.7 = 4.28$ Gbps, indicating substantial margin. $\blacksquare$

Quick Check

In the CI path loss model, what is the physical significance of the FSPL $(f, 1\,\text{m})$ anchor term?

It accounts for atmospheric absorption at the carrier frequency

It provides a physically grounded reference point equal to the theoretical free-space loss at 1 metre, ensuring the model is tied to fundamental physics rather than being a pure curve fit

It represents the minimum detectable path loss of the measurement equipment

It models the near-field to far-field transition distance

Correction:

It provides a physically grounded reference point equal to the theoretical free-space loss at 1 metre, ensuring the model is tied to fundamental physics rather than being a pure curve fit

Correct. The CI model anchors path loss to the Friis equation at $d = 1$ m, so that $PL^{CI}(f, 1\,\text{m}) = \text{FSPL}(f, 1\,\text{m})$ exactly. This physical grounding makes the single-parameter PLE stable across frequencies and prevents unphysical extrapolation, unlike multi-parameter models (e.g., ABG) that may produce negative path loss at short distances.

Common Mistake: Confusing Frequency-Dependent Path Loss with Antenna Gain

Mistake:

Claiming that "mmWave frequencies experience more path loss because higher frequencies attenuate more in free space," as if the medium itself absorbs more energy at higher frequencies.

Correction:

Free-space path loss is not a property of the medium — it is a consequence of the effective aperture of an isotropic antenna shrinking as $A_e = \lambda^{2}/(4\pi)$ . A fixed-area receive antenna captures the same power density at 28 GHz and 2 GHz. The $f^2$ factor in the Friis equation arises from comparing isotropic antennas, whose effective area decreases with wavelength. At mmWave, this "loss" is compensated by deploying arrays with many elements in the same physical aperture, restoring or even exceeding the link budget.

Common Mistake: Assuming NLOS mmWave Links Are Always Unusable

Mistake:

Concluding that mmWave NLOS links are infeasible because the path loss exponent is $n \approx 3.0$ – $3.5$ and diffraction is negligible.

Correction:

While diffraction is indeed weak at mmWave, strong specular reflections from smooth surfaces (glass facades, metal structures) and scattering from rough surfaces create viable NLOS paths. Measurements at 28 GHz show that reflected paths are only 5–15 dB weaker than LOS. Beam tracking to find and exploit these reflected paths — rather than relying on the direct path alone — is the standard approach in 5G NR FR2 deployments.

Historical Note: The Road to mmWave Cellular

2012–2018

Until 2012, the wireless community widely believed that mmWave frequencies above 10 GHz were unsuitable for mobile communications due to severe propagation challenges. This changed dramatically when Ted Rappaport and colleagues at NYU Wireless conducted extensive outdoor propagation measurements at 28 and 73 GHz in New York City. Their 2013 IEEE Access paper demonstrated that with directional antennas providing 24.5 dBi gain, reliable outdoor links up to 200 m were achievable in both LOS and NLOS conditions. Samsung independently demonstrated a 28 GHz prototype achieving over 1 Gbps in outdoor conditions. These results catalysed the inclusion of mmWave bands in 5G NR (FR2), standardised by 3GPP in Release 15 (2018). The first commercial 5G mmWave deployments by Verizon began in late 2018 in selected US cities.

⚠️Engineering Note

mmWave Link Budget Margin Requirements

mmWave link budgets must include substantially larger margins than sub-6 GHz systems due to dynamic impairments:

Blockage margin: 15–25 dB. Human-body blockage causes 20–35 dB attenuation at 28 GHz, but this can be partially mitigated by beam switching to reflected paths (recovering 10–15 dB). A typical design margin of 15 dB accounts for residual blockage with beam recovery.
Rain attenuation: At 28 GHz, heavy rain (50 mm/hr) adds $\sim$ 7 dB/km. For a 200 m small-cell link, this is only 1.4 dB — usually negligible. At 73 GHz, heavy rain adds $\sim$ 20 dB/km (4 dB at 200 m).
Beam misalignment: With a 7° beamwidth (256 elements), a 3° pointing error reduces gain by $\sim$ 3 dB. Beam tracking errors should be budgeted at 2–4 dB.
Implementation loss: Phase quantisation (0.5–1 dB for 4–6 bit phase shifters), feed network loss (3–6 dB at mmWave), and amplifier backoff (3–5 dB for OFDM PAPR) collectively add 7–12 dB.

A typical 28 GHz small-cell link budget allocates 20–25 dB total margin, leaving an operating range of 100–200 m.

Practical Constraints

•
Blockage margin: 15-25 dB depending on environment density
•
Implementation loss: 7-12 dB (phase shifters + feed + PA backoff)
•
Rain attenuation at 28 GHz: ~7 dB/km (negligible for small cells)

Key Takeaway

At mmWave frequencies, the link budget is dominated by three factors: free-space path loss (compensated by high-gain arrays), blockage (mitigated by beam tracking and multi-connectivity), and atmospheric absorption (negligible below 100 GHz for links under 200 m). The CI model provides a reliable, single-parameter characterisation that separates the frequency-dependent FSPL anchor from the environment-dependent PLE.

Millimeter Wave (mmWave)

Radio frequencies in the range 24–100 GHz, corresponding to wavelengths of 3–12.5 mm. In 5G NR, mmWave is designated as FR2 (24.25–52.6 GHz) and FR2-2 (52.6–71 GHz).

Close-In (CI) Path Loss Model

A single-parameter path-loss model anchored to the theoretical free-space loss at 1 m: $PL^{CI} = \text{FSPL}(f,1\text{m}) + 10n\log_{10}(d) + X_\sigma$ . Preferred for its physical grounding and frequency stability.

Path-Loss Exponent (PLE)

The exponent $n$ in the CI model governing the rate of power decay with distance. $n = 2$ corresponds to free space; typical mmWave values range from 1.7 (InH-LOS) to 3.5 (UMi-NLOS).

Propagation at mmWave and Sub-THz Frequencies

Why Millimeter Waves?

Definition: Close-In (CI) Free-Space Reference Distance Path Loss Model

Measured Path-Loss Exponents Across Frequencies and Environments

CI Model Path Loss Across Frequencies

Parameters

Blockage — The Dominant Impairment at mmWave

Theorem: Exponential Blockage Model

Poisson Boolean Model Derivation

Human-Body Shadowing Loss

LOS Probability Decay Animation

Blockage Outage Probability

Parameters

Example: 28 GHz Outdoor Small-Cell Link Budget

FSPL anchor at 1 m

CI path loss (mean)

Thermal noise power

Received SNR

Achievable throughput

Quick Check

Common Mistake: Confusing Frequency-Dependent Path Loss with Antenna Gain

Common Mistake: Assuming NLOS mmWave Links Are Always Unusable

Historical Note: The Road to mmWave Cellular

mmWave Link Budget Margin Requirements

Key Takeaway

Millimeter Wave (mmWave)

Close-In (CI) Path Loss Model

Path-Loss Exponent (PLE)

Definition:
Close-In (CI) Free-Space Reference Distance Path Loss Model