Ferkans — Interactive Telecom Tutor

Why 3GPP Channel Models?

The one-ring and Kronecker models are analytically tractable but simplified. Real deployments involve multiple scattering clusters, dual polarization, height-dependent elevation angles, spatial consistency across frequency, and frequency-selective propagation. 3GPP's TR 38.901 defines the standardized channel model used for 5G NR system design and performance evaluation — it is the common language between network operators, equipment vendors, and standardization bodies.

Understanding TR 38.901 is not just academic: it determines whether a beamforming algorithm passes or fails the standardized performance test that gates 5G equipment certification.

Historical Note: From COST 207 to 3GPP TR 38.901

1989–2023

Standardized channel models have evolved over four decades:

COST 207 (1989): First standardized multipath channel models for GSM. Defined Typical Urban (TU), Bad Urban (BU), Rural Area (RA), and Hilly Terrain (HT) profiles with specified power-delay profiles.
3GPP SCM (2003): The first MIMO-aware standardized model (TR 25.996). Introduced spatial channel models with 6 cluster paths and azimuth angle spreads for 3G MIMO.
WINNER/WINNER+ (2005–2010): Extended SCM with more scenarios, wider bandwidth (100 MHz), and frequency range up to 6 GHz.
3GPP 3D channel model (2014, TR 36.873): Added elevation dimension for FD-MIMO (3D beamforming). Required for 4G LTE Advanced Pro.
3GPP TR 38.901 (2017–2023): Current definitive model. Covers 0.5–100 GHz, includes mmWave with blockage model, spatial consistency, O2I/O2O/I2I scenarios, CDL (Clustered Delay Line) and TDL (Tapped Delay Line) models.

Definition:
Geometry-Based Stochastic Channel Model (GBSM)

A geometry-based stochastic channel model generates channel realizations by randomly placing scattering clusters in a 3D geometric layout and computing the contribution of each cluster to the channel impulse response. The complex channel between transmit antenna $s$ and receive antenna $u$ at delay $\tau$ is:

$h_{u,s}(\tau) = \sum_{n=1}^{N_{\text{cl}}} \sum_{m=1}^{M_{\text{ray}}} \alpha_{n,m} \, e^{j\Phi_{n,m}} \, F_r(\phi_n^r) \, e^{j\mathbf{k}(\phi_n^r)^T \mathbf{d}_r^u} \, F_t(\phi_n^t) \, e^{j\mathbf{k}(\phi_n^t)^T \mathbf{d}_t^s} \, \delta(\tau - \tau_n),$

where:

$N_{\text{cl}}$ : number of clusters; $M_{\text{ray}}$ : rays per cluster
$\alpha_{n,m}$ : path amplitude; $\Phi_{n,m}$ : random phase
$F_r(\phi), F_t(\phi)$ : receive/transmit antenna element patterns
$\mathbf{k}(\phi)$ : wave vector; $\mathbf{d}_{r}^u, \mathbf{d}_{t}^s$ : antenna positions
$\tau_n$ : cluster excess delay

The GBSM framework decouples large-scale parameters (cluster delays, angular spreads) from small-scale parameters (ray phases, ray offsets). This enables efficient Monte Carlo simulation and systematic variation of environmental scenarios.

Definition:
Large-Scale Parameters in 3GPP TR 38.901

The 3GPP TR 38.901 model characterizes each link by seven large-scale parameters (LSPs) that remain constant within a coherence area (typically tens of meters):

Parameter	Symbol	Typical range (UMa NLoS)
Delay spread	$\text{DS}$	$\sigma_\tau \approx 10$ –100 ns
AoD azimuth spread	$\text{ASA}$	$10°$ – $60°$
AoA azimuth spread	$\text{ASD}$	$5°$ – $30°$
AoD elevation spread	$\text{ESA}$	$3°$ – $15°$
AoA elevation spread	$\text{ESD}$	$3°$ – $10°$
Ricean $K$ -factor	$K$	N/A (NLoS) or $0$ –10 dB (LoS)
Shadow fading	$\text{SF}$	$\sigma_{\text{SF}} \approx 4$ –8 dB

LSPs are modeled as correlated log-normal random variables with scenario-specific means, standard deviations, and cross-correlation coefficients tabulated in TR 38.901.

Definition:
Clustered Delay Line (CDL) and Tapped Delay Line (TDL) Models

For calibration and conformance testing, 3GPP TR 38.901 defines simplified deterministic channel models:

CDL (Clustered Delay Line): A fixed set of $N_{\text{cl}}$ clusters with specified delays, power fractions, azimuth/elevation angles, and per-cluster angle spreads. Five CDL profiles: CDL-A (NLoS, dense multipath), CDL-B (NLoS, medium spread), CDL-C (NLoS, large spread), CDL-D (LoS, low spread), CDL-E (LoS, very low spread). The CDL-D model corresponds roughly to the one-ring model with $K \approx 7$ dB.

TDL (Tapped Delay Line): Collapses the spatial structure, giving only power-delay profiles for single-antenna or MIMO-agnostic simulations. Five profiles: TDL-A through TDL-E.

$h_{u,s}^{\text{CDL}}(t, \tau) = \sum_{n=1}^{N_{\text{cl}}} P_n^{1/2} \left(\sum_{m=1}^{20} e^{j\Phi_{n,m}} e^{j\mathbf{k}(\phi_{n,m}^r) \cdot \mathbf{d}_r^u} e^{j\mathbf{k}(\phi_{n,m}^t) \cdot \mathbf{d}_t^s}\right) \delta(\tau - \tau_n)$

CDL models are used for link-level simulations (e.g., comparing MMSE vs. ZF receivers). TDL models are used for waveform-level tests (OFDM synchronization, PAPR reduction). For massive MIMO system-level design, the full stochastic GBSM is preferred.

3GPP TR 38.901: Channel Realization Generation (Simplified)

Complexity:

O(N_{ ext{cl}} \cdot M_{ ext{ray}} \cdot N_t \cdot N_r \cdot N_{ ext{sub}})

Input: Scenario (UMa/UMi/RMa/Indoor), frequency

f_0

, BS/UE positions, array geometries

Output: Channel matrix sequence

\{\mathbf{H}(t)\}

1. General parameters: Determine path loss, shadow fading from scenario tables

2. Large-scale parameters (LSP): Generate correlated (DS, ASA, ASD, ESA, ESD, K, SF)

using scenario correlation matrix (Table 7.5-6)

3. Small-scale parameters:

a. Generate

N_{\text{cl}}

cluster delays

\{\tau_n\}

from exponential distribution with mean DS

b. Generate cluster powers

\{P_n\}

from exponential decay model

c. Generate cluster angles (azimuth + elevation for AoD and AoA) from wrapped Gaussian

d. Generate

M_{\text{ray}} = 20

sub-path offsets per cluster from fixed offset table

4. Cross-polarization: Apply XPR (cross-polarization ratio) to each sub-path

5. Channel coefficient generation: For each (TX ant, RX ant, subcarrier) triple,

sum contributions from all

N_{\text{cl}} \times M_{\text{ray}}

sub-paths

6. Apply spatial consistency (optional): Correlate LSPs across nearby UE positions

7. Mobility: Apply Doppler shift

f_{D,n} = \frac{f_0}{c} v \cos(\phi_n^r - \phi_v)

per sub-path

Step 5 dominates the compute cost. For $N_{\text{cl}} = 20$ , $M_{\text{ray}} = 20$ , $N_t = 64$ , $N_r = 2$ , $N_{\text{sub}} = 1024$ : approximately $20 \times 20 \times 64 \times 2 \times 1024 \approx 52M$ complex multiplications per channel sample.

Definition:
QuaDRiGa: Quasi-Deterministic Radio Channel Generator

QuaDRiGa (Quasi-Deterministic Radio Channel Generator) is an open-source MATLAB/Octave channel simulator developed at Fraunhofer HHI that implements 3GPP TR 38.901, WINNER+, and custom channel models with additional features:

Spatial consistency: LSPs and cluster positions evolve continuously as a UE moves, avoiding unrealistic discontinuities at coherence area boundaries.
Dual-mobility: Handles both BS and UE motion simultaneously.
Multi-frequency: Generates frequency-correlated channels for carrier aggregation.
Arrays: Handles arbitrary 2D/3D array configurations (ULA, UPA, conformal arrays).
3D-MIMO: Full 3D elevation + azimuth support.

QuaDRiGa is widely used for 5G and 6G research, with published results confirming its close match to COST 2100 and 3GPP TR 38.901 measurement-based validation.

The QuaDRiGa source code and documentation are freely available at https://quadriga-channel-model.de. For massive MIMO simulation at $N_t = 64$ , expect 1–5 seconds per channel realization on a standard workstation.

⚠️Engineering Note

Choosing the Right 3GPP Scenario

TR 38.901 defines four primary deployment scenarios, each with different channel statistics and propagation characteristics:

UMa (Urban Macro): BS at 25 m, ISD 200–500 m. Dominant use case for sub-6 GHz massive MIMO. DS $\approx$ 60 ns, ASD $\approx$ 5–8°, ASA $\approx$ 17°.
UMi (Urban Micro, Street Canyon): BS at 10 m, ISD 100–200 m. High blockage probability. Suitable for small cells and distributed massive MIMO.
RMa (Rural Macro): Large ISD (up to 5 km), low angular spread (ASD $\approx$ 2°). Most favorable for beamforming gain; LOS probability > 50% at < 500 m.
InH (Indoor Hotspot): Factory, office. High DS (100–200 ns), high ASA (24–30°). Channel nearly isotropic — i.i.d. model reasonable.

Choosing the wrong scenario leads to optimistic (or pessimistic) beamforming gain estimates. For example, using UMa parameters for an indoor deployment overestimates spatial selectivity and underestimates interference.

Practical Constraints

•
UMa NLoS: ASD $\approx 5°$ (transmit side) → high spatial correlation → JSDM-friendly
•
InH: ASA $\approx 30°$ → near-isotropic → i.i.d. model reasonable
•
RMa: ASD $\approx 2°$ → very high correlation → rank-1 approximation often valid
•
All scenarios: frequency-dependent parameters (3.5 GHz vs 28 GHz differ significantly)

📋 Ref: 3GPP TR 38.901, Table 7.5-6

Channel Matrix Realizations: i.i.d. vs Correlated

Side-by-side heatmaps of $|\mathbf{H}|$ for (left) i.i.d. Rayleigh and (right) spatially correlated channels with one-ring covariance. The correlated channel shows structured patterns — rows and columns are no longer independent. Adjust the angular spread to interpolate between the two extremes.

Parameters

N_t

16

N_r

8

Angular spread

\Delta\theta

(degrees)10

Common Mistake: CDL Models Are Not Substitute for Stochastic Models

Mistake:

Using CDL-A/B/C/D/E fixed profiles to evaluate a "realistic" channel without generating multiple independent channel realizations from the stochastic GBSM.

Correction:

CDL models fix all cluster parameters (delays, angles, powers) and only randomize the small-scale phases. This means all generated realizations share the same macroscopic structure. For evaluating algorithms that exploit spatial correlation statistics (covariance-based precoding, JSDM, pilot decontamination), you need variation in LSPs across realizations — which only the full stochastic GBSM provides.

CDL models are appropriate for: waveform-level tests, OFDM synchronization, PHY layer comparison where the propagation environment is fixed. They are NOT appropriate for: evaluating the impact of angular spread variation, testing spatial correlation exploitation, or estimating outage probabilities.

Example: Reading a CDL-D Channel Profile

The 3GPP CDL-D profile specifies 13 clusters with delays and powers including a strong LoS component (cluster 1: $\tau_1 = 0$ ns, $P_1 = 0$ dBm relative). If the carrier frequency is $f_0 = 3.5$ GHz, the UE moves at $v = 30$ km/h in the horizontal plane, and AoA of the LoS path is $\phi_1^r = 0°$ : what is the Doppler shift on the LoS path?

Solution

Doppler shift formula

The Doppler shift for a path at angle of arrival $\phi^r$ relative to the UE velocity direction $\phi_v$ is: $f_{D} = \frac{v f_0}{c} \cos(\phi^r - \phi_v).$ With $v = 30/3.6 = 8.33$ m/s, $f_0 = 3.5 \times 10^9$ Hz, $c = 3 \times 10^8$ m/s: $f_{D,\max} = \frac{8.33 \times 3.5 \times 10^9}{3 \times 10^8} \approx 97.2 \text{ Hz}.$

LoS path Doppler

For the LoS path at $\phi_1^r = 0°$ with the UE moving toward the BS ( $\phi_v = 0°$ ): $f_{D,1} = 97.2 \cos(0° - 0°) = 97.2 \text{ Hz}.$ The coherence time is $T_c \approx 1/(2 f_{D,\max}) \approx 5.1$ ms. At 5G NR subframe duration of 1 ms (15 kHz SCS), approximately 5 subframes fit within one coherence interval — consistent with standard TDD channel estimation.

Example: Generating Large-Scale Parameters for a UMa Link

Describe the procedure to draw one realization of the delay spread (DS) for a UMa NLoS link at 3.5 GHz, distance $d = 200$ m, BS height 25 m, UE height 1.5 m. Use the TR 38.901 parameters: $\mu_{\text{DS}} = -7.03$ , $\sigma_{\text{DS}} = 0.66$ (in log-seconds).

Solution

Sample the log-normal LSP

The delay spread is modeled as log-normal: $\log_{10}(\text{DS}) \sim \mathcal{N}(\mu_{\text{DS}}, \sigma_{\text{DS}}^2)$ . Draw $z \sim \mathcal{N}(0,1)$ and compute: $\text{DS} = 10^{\mu_{\text{DS}} + \sigma_{\text{DS}} z} = 10^{-7.03 + 0.66 z}$ seconds.

Example realization

For $z = 0.5$ (one standard deviation above mean): $\text{DS} = 10^{-7.03 + 0.33} = 10^{-6.70} \approx 2.0 \times 10^{-7} = 200$ ns. This gives coherence bandwidth $B_c \approx 1/(5 \times 200 \text{ ns}) = 1$ MHz. At 15 kHz subcarrier spacing: approximately 67 subcarriers per coherence bandwidth. In 5G NR, Type II CSI feedback uses 4–8 sub-bands of width $\sim 1$ MHz — well-matched to this coherence bandwidth.

Geometry-Based Stochastic Channel Model (GBSM)

A class of channel models where scattering clusters are placed stochastically in 3D space, and the channel impulse response is computed from the geometry of all cluster positions, path delays, and antenna array responses. The 3GPP TR 38.901 model is the standard GBSM for 5G. GBSMs bridge physical geometry (angles, delays) and stochastic statistics (cluster distributions, large-scale parameters).

Clustered Delay Line (CDL)

A deterministic channel model defined by a fixed set of clusters with specified power, delay, azimuth/elevation angles, and per-cluster angle spreads. Used in 3GPP standardized link-level testing. Five CDL profiles (A–E) cover NLoS and LoS scenarios. CDL models randomize only the small-scale phase offsets per realization.

Angular Spread

A measure of the angular dispersion of arriving (or departing) signal energy. Defined as the RMS spread of the power angular spectrum. In 3GPP TR 38.901, the azimuth angle spread of departure (ASD) and arrival (ASA) are tabulated per scenario. Narrow angular spread implies high spatial correlation; wide spread implies near-isotropic scattering.

Theorem: Covariance Subspace and Favorable Propagation

Let $\mathbf{h}_k \sim \mathcal{CN}(\mathbf{0}, \mathbf{R}_k)$ and $\mathbf{h}_j \sim \mathcal{CN}(\mathbf{0}, \mathbf{R}_j)$ be independent channel vectors for users $k$ and $j$ . If the covariance matrices are orthogonal in the sense that $\mathbf{R}_k \mathbf{R}_j = \mathbf{0}$ (their column spaces are orthogonal), then $\mathbb{E}[|\mathbf{h}_k^H \mathbf{h}_j|^2] = 0$ and favorable propagation holds exactly (not just asymptotically): $\mathbf{h}_k^H \mathbf{h}_j = 0$ almost surely.

Orthogonal covariance subspaces mean the two users' channels live in perpendicular subspaces of $\mathbb{C}^{N_t}$ — their inner product vanishes exactly. This is the idealized version of the one-ring angular separation condition: if two users' angular supports do not overlap, their covariance matrices have orthogonal column spaces.

Show Hint

Write $\\mathbf{h}_k = \\mathbf{R}_k^{1/2} \\tilde{\\mathbf{h}}_k$ and $\\mathbf{h}_j = \\mathbf{R}_j^{1/2} \\tilde{\\mathbf{h}}_j$ with $\\tilde{\\mathbf{h}}_k, \\tilde{\\mathbf{h}}_j$ i.i.d. $\\mathcal{CN}(0, \\mathbf{I})$ .

Compute $\\mathbf{h}_k^H \\mathbf{h}_j = \\tilde{\\mathbf{h}}_k^H \\mathbf{R}_k^{H/2} \\mathbf{R}_j^{1/2} \\tilde{\\mathbf{h}}_j$ . Use $\\mathbf{R}_k \\mathbf{R}_j = \\mathbf{0}$ to show the middle matrix is zero.

If $\\mathbf{R}_k \\mathbf{R}_j = \\mathbf{0}$ , then $\\mathbf{R}_k^{1/2} \\mathbf{R}_j^{1/2} = ?$ (use that the square root of a PSD matrix inherits the orthogonality).

Proof

Express via square roots

Write $\mathbf{h}_k = \mathbf{R}_k^{1/2} \tilde{\mathbf{h}}_k$ and $\mathbf{h}_j = \mathbf{R}_j^{1/2} \tilde{\mathbf{h}}_j$ where $\tilde{\mathbf{h}}_k, \tilde{\mathbf{h}}_j \sim \mathcal{CN}(\mathbf{0}, \mathbf{I})$ are independent. Then: $\mathbf{h}_k^H \mathbf{h}_j = \tilde{\mathbf{h}}_k^H \mathbf{R}_k^{1/2} \mathbf{R}_j^{1/2} \tilde{\mathbf{h}}_j$ .

Use covariance orthogonality

Let $\mathbf{R}_k = \mathbf{U}_k \boldsymbol{\Lambda}_k \mathbf{U}_k^H$ and $\mathbf{R}_j = \mathbf{U}_j \boldsymbol{\Lambda}_j \mathbf{U}_j^H$ be eigendecompositions. $\mathbf{R}_k \mathbf{R}_j = \mathbf{0}$ implies $\mathbf{U}_k^H \mathbf{U}_j = \mathbf{0}$ on the support subspaces (columns of $\mathbf{U}_k$ and $\mathbf{U}_j$ are orthogonal). Therefore $\mathbf{R}_k^{1/2} \mathbf{R}_j^{1/2} = \mathbf{U}_k \boldsymbol{\Lambda}_k^{1/2} \mathbf{U}_k^H \mathbf{U}_j \boldsymbol{\Lambda}_j^{1/2} \mathbf{U}_j^H = \mathbf{0}$ .

Conclusion

Since $\mathbf{R}_k^{1/2} \mathbf{R}_j^{1/2} = \mathbf{0}$ , we have $\mathbf{h}_k^H \mathbf{h}_j = \tilde{\mathbf{h}}_k^H \cdot \mathbf{0} \cdot \tilde{\mathbf{h}}_j = 0$ almost surely. The inner product is exactly zero for every realization — not just in expectation or asymptotically. $\blacksquare$

One-Ring Model Geometry — Geometry of the one-ring model. The user equipment (UE) is surrounded by local scatterers uniformly distributed on a ring of radius $r$ . The elevated base station (BS) with $N_t$ antenna elements observes signals arriving from the angular window $[\theta_0 - \Delta\theta, \theta_0 + \Delta\theta]$ (mean angle $\theta_0$ , angular spread $\Delta\theta$ ). As the UE moves or the scattering environment changes, the statistical model is parameterized only by $\theta_0$ and $\Delta\theta$ .

Key Takeaway

3GPP TR 38.901 is the lingua franca of 5G channel modeling. It bridges the mathematical models of this chapter (one-ring, Kronecker) to the standardized evaluation framework used by industry. The CDL profiles offer tractable fixed-structure channels; the full GBSM provides statistically varied realizations needed for system-level design. QuaDRiGa implements TR 38.901 with spatial consistency and is the tool of choice for research-grade 5G/6G channel simulation.

Quick Check

A massive MIMO base station in an urban macro deployment (3GPP UMa scenario) observes an ASD (azimuth angle spread of departure) of about 5°. For a 64-antenna ULA, what is the approximate effective rank of the transmit covariance matrix $\mathbf{R}_t$ ?

64 (full rank)

Approximately 2–5

Approximately 32

1 (rank-1)